*Multiple core/fibers:* Thirdly, using different optical fibers or different optical fiber cores is another approach to produce BFS with different thermal and strain coefficients for simultaneous measurement of temperature and strain. In [26], the optical fibers are deployed with the configuration that the first half of the sensing is tightly bonded to the structure to be monitored, which is sensitive to both strain and temperature, and the second half is loosely deployed and collocated to sense the temperature only. Optical fibers with dual core structure [36,43] have been reported for distributed Brillouin sensing applications. Through appropriate designing of the fiber core profile, the strain and temperature coefficients of the two sensing fiber cores are different, forming the sensing matrix equation (Equation (1)) and enable discriminative sensing of both parameters. By measuring the BGS in two cores (the central core and one of the outer cores) of a seven-core multicore fiber (MCF), the BFS in these two cores show different strain and temperature coefficients, suggesting the feasibility of using MCF based Brillouin sensing for discriminative distributed measurement of temperature and strain [37]. structure to be monitored, which is sensitive to both strain and temperature, and the second half is loosely deployed and collocated to sense the temperature only. Optical fibers with dual core structure [36,43] have been reported for distributed Brillouin sensing applications. Through appropriate designing of the fiber core profile, the strain and temperature coefficients of the two sensing fiber cores are different, forming the sensing matrix equation (Equation (1)) and enable discriminative sensing of both parameters. By measuring the BGS in two cores (the central core and one of the outer cores) of a seven-core multicore fiber (MCF), the BFS in these two cores show different strain and temperature coefficients, suggesting the feasibility of using MCF based Brillouin sensing for discriminative distributed measurement of temperature and strain [37].

*Multi-peak BGS due to multiple acoustic and optical modes:* More recently, an ellipticalcore FMF based Brillouin optical time domain reflectometry (BOTDR) was reported to achieve distributed temperature and strain measurement, levering the multiple Brillouin peaks from the interaction between both higher-order optical modes (LP01 and LP11 mode) and higher-order acoustic modes. Optimum sensing performance can be achieved by choosing proper optical-acoustic mode pairs [35]. This scheme of using selected higherorder optical and modes and higher-order acoustic modes in the elliptical-core FMF offers an alternative approach to achieve temperature and strain discrimination in BOTDA, re-

*Multiple core/fibers:* Thirdly, using different optical fibers or different optical fiber cores is another approach to produce BFS with different thermal and strain coefficients for simultaneous measurement of temperature and strain. In [26], the optical fibers are deployed with the configuration that the first half of the sensing is tightly bonded to the

*Photonics* **2021**, *8*, x FOR PEER REVIEW 7 of 15

quiring a configuration of the selective mode launcher.

Further improvement can be achieved by optimizing the material and the structure of the MCF to enlarge the difference from the cores [11,37]. MCF with heterogeneous cores as shown in Figure 4 is reported to show ~70 MHz BFS difference between the central core and the outer cores, which are made from different preforms. The experimental results showed the heterogeneous cores have enlarged difference in the temperature sensitivities and indistinguishable strain sensitivities, enabling a simultaneous and discriminative dual parameter measurement [38]. Distributed bending sensing application deduced from strain measurements of the MCF based Brillouin sensors are explored subsequently [44]. Further improvement can be achieved by optimizing the material and the structure of the MCF to enlarge the difference from the cores [11,37]. MCF with heterogeneous cores as shown in Figure 4 is reported to show ~70 MHz BFS difference between the central core and the outer cores, which are made from different preforms. The experimental results showed the heterogeneous cores have enlarged difference in the temperature sensitivities and indistinguishable strain sensitivities, enabling a simultaneous and discriminative dual parameter measurement [38]. Distributed bending sensing application deduced from strain measurements of the MCF based Brillouin sensors are explored subsequently [44].

**Figure 4.** (**a**) Cross-sectional view of the MCF used in the experiment. (**b**) Relative index profile of the MCF. (Reprinted/Adapted) with permission from [38] © The Optical Society. **Figure 4.** (**a**) Cross-sectional view of the MCF used in the experiment. (**b**) Relative index profile of the MCF. (Reprinted/Adapted) with permission from [38] © The Optical Society.

*BFS and birefringence/fluorescence:* The fourth approach is through simultaneous monitoring two independent physical parameters of BFS and the fiber birefringence or fluorescence. The birefringence is characterized through the measurement of the diffraction spectrum of the dynamic acoustic grating generated in SBS, or Brillouin dynamic grating (BDG). The combination of BFS and the birefringence was firstly explored using polarization-maintaining fiber (PMF), reporting a discrimination accuracy of 3 *με* and 0.08 °C [45]. Compared with the conventional PMF, polarization-maintaining photonic crystal fiber (PM-PCF) acquires fiber birefringence from the non-circular core in the all-silica holey cladding structure, thus inherently possessing much less temperature sensitivity. Discriminative measurement of strain and temperature using the configuration as depicted *BFS and birefringence/fluorescence:* The fourth approach is through simultaneous monitoring two independent physical parameters of BFS and the fiber birefringence or fluorescence. The birefringence is characterized through the measurement of the diffraction spectrum of the dynamic acoustic grating generated in SBS, or Brillouin dynamic grating (BDG). The combination of BFS and the birefringence was firstly explored using polarization-maintaining fiber (PMF), reporting a discrimination accuracy of 3 *µε* and 0.08 ◦C [45]. Compared with the conventional PMF, polarization-maintaining photonic crystal fiber (PM-PCF) acquires fiber birefringence from the non-circular core in the all-silica holey cladding structure, thus inherently possessing much less temperature sensitivity. Discriminative measurement of strain and temperature using the configuration as depicted in Figure 5, is achieved by monitoring the BFS and BDG of the PM-PCF for the temperature range of −40 ◦C to 80 ◦C and the strain range of 0–800 *µε.* In addition, leveraging the weak temperature sensitivity of the fiber birefringence in the temperature range from 5 ◦C to 80 ◦C, temperature-insensitive strain measurement is possible by using the BDG measurement alone [31]. Combination of BFS and fluorescence are used to demonstrate discriminative strain and temperature measurement in erbium-doped optical fiber [39].

*Athermal/atensic optical fibers:* If complete discrimination of temperature and strain measurement is not required, an optical fiber with immunity to one parameter is desirable for single sensing parameter measurement. It has been shown in Figure 6 that highly Ge doped fibers presented negligible temperature dependence, and the temperature coefficient even decreased to zero when removing the fiber coating, paving the way to develop athermal optical fibers for temperature-free Brillouin strain sensing [40]. Likewise, optical fibers that are insensitive to strain or atensic fibers can be designed and developed for strain-free Brillouin temperature sensing [11]. However, these approaches to develop athermal or atensic fibers through fiber material composition optimization suffer from a significant reduction of the sensitivity to strain or temperature and in the Brillouin gain [11]. °C to 80 °C, temperature-insensitive strain measurement is possible by using the BDG measurement alone [31]. Combination of BFS and fluorescence are used to demonstrate discriminative strain and temperature measurement in erbium-doped optical fiber [39].

in Figure 5, is achieved by monitoring the BFS and BDG of the PM-PCF for the temperature range of −40 °C to 80 °C and the strain range of 0–800 *με.* In addition, leveraging the weak temperature sensitivity of the fiber birefringence in the temperature range from 5

*Photonics* **2021**, *8*, x FOR PEER REVIEW 8 of 15

− *με*

**Figure 5.** Experimental setup of distributed temperature and strain sensing using BDG and BGS. Reproduced from [31]. Copyright (2017) The Japan Society of Applied Physics. **Figure 5.** Experimental setup of distributed temperature and strain sensing using BDG and BGS. Reproduced from [31]. Copyright (2017) The Japan Society of Applied Physics.

[11]. **Figure 6.** (**a**) Brillouin frequency shift versus the temperature increase in five different fibers; (**b**) SBS temperature coefficient versus GeO2-core doping levels. Reproduced with permission [40]. Licensed under a Creative Commons Attribution (CC BY) license.

#### *3.3. Multiplexed Distributed Sensing Systems of BOTDA and Other Distributed Fiber Sensor Technologies*

(a) (b) This section is focused on the reported work of specialty fibers in hybrid distributed sensing systems based on Brillouin scattering phenomena, e.g., BOTDA or BOTDR, and other DFS technologies based on Raman or Rayleigh scattering phenomena. For example, utilizing the space-division multiplexed (SDM) system configuration, MCF represent a desirable platform to develop a compact system to multiplex different distributed sensing techniques. A recent review paper introduced the research progress of MCF based hybrid distributed fiber sensor systems [46].

**Figure 6.** (**a**) Brillouin frequency shift versus the temperature increase in five different fibers; (**b**) SBS temperature coefficient versus GeO2-core doping levels. Reproduced with permission [40]. Licensed under a Creative Commons Attribution (CC BY) license. *3.3. Multiplexed Distributed Sensing Systems of BOTDA and Other Distributed Fiber Sensor Technologies Hybrid Brillouin-Rayleigh sensing:* Firstly, hybrid Brillouin-Rayleigh sensing systems have been reported to achieve simultaneous dual parameter measurements of temperature and strain, providing benefits of improved data processing and analytics for distance compensation and accuracy enhancement [47]. Standard optical fibers are used in the reported hybrid sensing system. The BFS and Rayleigh frequency shifts are measured to decouple the strain and temperature based on the following two equations, e.g., Equations (2) and (3):

This section is focused on the reported work of specialty fibers in hybrid distributed

$$
\Delta v\_B = \mathbb{C}\_{11}\Delta \varepsilon + \mathbb{C}\_{12}\Delta T \tag{2}
$$

$$
\Delta \upsilon\_R = \mathbf{C}\_{21} \Delta \varepsilon + \mathbf{C}\_{22} \Delta T \tag{3}
$$

desirable platform to develop a compact system to multiplex different distributed sensing ∆*vB* and ∆*vR* are the shift of the Brillouin and Raman gain spectrum, respectively. The strain and temperature coefficients are denoted by *C*11 and *C*12 in Brillouin sensing system; *C*21 and *C*22 in Rayleigh sensing system, respectively. Subsequently, a more compact system of the hybrid Brillouin-Rayleigh sensing system through SDM configuration based on the MCF is reported for distributed temperature sensing as shown in Figure 7. Two spatially

Δ = Δ + Δ*Τ* (3)

Δ and Δ are the shift of the Brillouin and Raman gain spectrum, respectively. The strain and temperature coefficients are denoted by and in Brillouin sensing system; and in Rayleigh sensing system, respectively. Subsequently, a more compact system of the hybrid Brillouin-Rayleigh sensing system through SDM configuration based on the MCF is reported for distributed temperature sensing as shown in Figure 7.

Δ = Δ + Δ (2)

techniques. A recent review paper introduced the research progress of MCF based hybrid

*Hybrid Brillouin-Rayleigh sensing:* Firstly, hybrid Brillouin-Rayleigh sensing systems have been reported to achieve simultaneous dual parameter measurements of temperature and strain, providing benefits of improved data processing and analytics for distance compensation and accuracy enhancement [47]. Standard optical fibers are used in the reported hybrid sensing system. The BFS and Rayleigh frequency shifts are measured to decouple the strain and temperature based on the following two equations, e.g., Equations

separated sensors of BOTDA and Φ-OTDR are realized in the central core and outer core, respectively. Distributed temperature sensing using the 1.565 km MCF was demonstrated to achieve 2.5 m spatial resolution, large measurement range (10 ◦C) by BOTDA, and 0.1 ◦C small temperature variation detection by Φ-OTDR with ~0.001 ◦C resolution [48]. Two spatially separated sensors of BOTDA and − OTDR are realized in the central core and outer core, respectively. Distributed temperature sensing using the 1.565 km MCF was demonstrated to achieve 2.5 m spatial resolution, large measurement range (10 °C) by BOTDA, and 0.1 °C small temperature variation detection by − OTDR with ~0.001 °C resolution [48].

*Photonics* **2021**, *8*, x FOR PEER REVIEW 9 of 15

distributed fiber sensor systems [46].

(2) and (3):

**Figure 7.** Experimental setup of the MCF based SDM hybrid BOTDA and Φ-OTDR system. (Reprinted/Adapted) with permission from [48] © The Optical Society. **Figure 7.** Experimental setup of the MCF based SDM hybrid BOTDA and Φ-OTDR system. (Reprinted/Adapted) with permission from [48] © The Optical Society.

*Hybrid Brillouin-Raman sensing:* Hybrid Raman/Brillouin optical time domain reflectometry/analysis (RODTR and BOTDR or BOTDA) configurations using standard optical fibers are reported to realize distributed sensing of temperature and strain. The temperature measurement is determined by Raman based sensor without other cross-sensitivity from strain. Based on the temperature measurement, the strain measurement is computed and discriminated from both a strain and temperature dependent Brillouin frequency shift in the BOTDR sensor [49]. Recent advances of the hybrid Raman and Brillouin sensing systems have been reviewed, presenting promising techniques based on pulse coding to address the challenges of the tradeoff between the sensing distance and spatial resolution in the hybrid sensing system [50]. To address the incompatibility of input power requirement for hybrid ROTDR and BOTDR in standard single mode fibers, an MCF based hybrid ROTDR and BOTDR is reported for discriminative and distributed sensing of temperature and strain using a single laser source, shared pump generation devices and separate interrogation fiber channels (Figure 8). The reported system achieved worst temperature and strain resolutions about 2.2 °C and 40 *με*, respectively, in a 6 km sensing range *Hybrid Brillouin-Raman sensing:* Hybrid Raman/Brillouin optical time domain reflectometry/analysis (RODTR and BOTDR or BOTDA) configurations using standard optical fibers are reported to realize distributed sensing of temperature and strain. The temperature measurement is determined by Raman based sensor without other cross-sensitivity from strain. Based on the temperature measurement, the strain measurement is computed and discriminated from both a strain and temperature dependent Brillouin frequency shift in the BOTDR sensor [49]. Recent advances of the hybrid Raman and Brillouin sensing systems have been reviewed, presenting promising techniques based on pulse coding to address the challenges of the tradeoff between the sensing distance and spatial resolution in the hybrid sensing system [50]. To address the incompatibility of input power requirement for hybrid ROTDR and BOTDR in standard single mode fibers, an MCF based hybrid ROTDR and BOTDR is reported for discriminative and distributed sensing of temperature and strain using a single laser source, shared pump generation devices and separate interrogation fiber channels (Figure 8). The reported system achieved worst temperature and strain resolutions about 2.2 ◦C and 40 *µε*, respectively, in a 6 km sensing range with a 3 m spatial resolution [51]. The research progress of MCF based hybrid distributed fiber sensor systems is reviewed in [46]. *Photonics* **2021**, *8*, x FOR PEER REVIEW 10 of 15 with a 3 m spatial resolution [51]. The research progress of MCF based hybrid distributed fiber sensor systems is reviewed in [46].

**Figure 8.** Experimental setup of the MCF based SDM hybrid ROTDR and BOTDR system. (Reprinted/Adapted) with permission from [51] © The Optical Society. **Figure 8.** Experimental setup of the MCF based SDM hybrid ROTDR and BOTDR system. (Reprinted/Adapted) with permission from [51] © The Optical Society.

#### *3.4. Distributed Sensing of Other Parameters 3.4. Distributed Sensing of Other Parameters*

*Curvature sensing:* The dependence of the BFS on longitudinal strain variations (compression/elongation) is exploited to develop distributed curvature sensing using an optical fiber. Since the first sensing demonstration with an SMF (BFS ~ 1.6 MHz for a 1.5 m of *Curvature sensing:* The dependence of the BFS on longitudinal strain variations (compression/elongation) is exploited to develop distributed curvature sensing using an optical fiber. Since the first sensing demonstration with an SMF (BFS ~ 1.6 MHz for a 1.5 m of

SMF winded around a rod of 25 mm diameter [52]), different optical fibers have been

dius curvature from 0.7 cm to 3.4 cm) [53]*.* MCF was successfully used for demonstrating curvature radius and orientation measurements (with a BFS sensitivity of 2.06 MHz/m−1) by correlating the difference of BFS between the central core and outer six cores, paving the way to full 3D shape determination using an optical fiber [44]. The interest of an RCF, with an inner and outer core diameter of 7.38 μm and 15.14 μm, respectively, and a Δncorecladding ~ 0.0131, was demonstrated for measuring distributed small curvature radius by exploiting its excellent bending loss resistance (α < 0.01 dB for a radius of 0.5 cm) in comparison to an SMF that suffers from macro-bending losses (α > 10 dB). In addition to a higher sensitivity than SMFs (with BFS ~ 32.9 MHz for a radius of 0.5 cm), the RCF enables distributed curvature sensing without temperature or axial strain sensitivity by measur-

*Pressure sensing:* PM-PCF composed of only silica and air, which exhibits a very low thermal sensitivity, was used for hydrostatic pressure sensing by measuring the birefringence changes through exciting and probing the BDG (with a differential pulse-width pair Brillouin optical time domain analysis, DPP-BOTDA) [55]. A linear dependence of the Birefringence BFS difference of about 199 MHz/MPa has been measured for hydrostatic

*Characterization of Fiber-Optic Parametric Amplifier (FOPA) and nonlinear optical fibers:* FOPA gain that relies on strict phase-matching conditions imposed by the four-wave mixing process was measured along the length of the highly non-linear fiber by using BOTDA in a novel scheme where the parametric amplification acts on the BOTDA pump [56]. The fluctuation measurements of the zero-dispersion wavelength (ZDW) along the highly nonlinear fiber of a FOPA was also demonstrated (with ZDW fluctuations as low as 0.02 nm along 200 m of the fiber and 2 m longitudinal resolution) [57,58]. These demonstrations offer new possibilities for precisely characterizing the chromatic dispersion along highly nonlinear fibers, i.e., including local fluctuation, which is a key parameter for nu-

ing its Brillouin gain variation [54], as shown in Figure 9.

merous nonlinear optic applications.

pressure from 0 to 1.1 PM with a measurement error of 0.025 MPa.

SMF winded around a rod of 25 mm diameter [52]), different optical fibers have been investigated. Among them, a few-mode fiber was used to improve the sensitivity (~5 time for a radius curvature of 0.8 cm) and to extend the range of curvature measurements (radius curvature from 0.7 cm to 3.4 cm) [53]. MCF was successfully used for demonstrating curvature radius and orientation measurements (with a BFS sensitivity of 2.06 MHz/m−1 ) by correlating the difference of BFS between the central core and outer six cores, paving the way to full 3D shape determination using an optical fiber [44]. The interest of an RCF, with an inner and outer core diameter of 7.38 µm and 15.14 µm, respectively, and a ∆ncore-cladding ~0.0131, was demonstrated for measuring distributed small curvature radius by exploiting its excellent bending loss resistance (α < 0.01 dB for a radius of 0.5 cm) in comparison to an SMF that suffers from macro-bending losses (α > 10 dB). In addition to a higher sensitivity than SMFs (with BFS ~ 32.9 MHz for a radius of 0.5 cm), the RCF enables distributed curvature sensing without temperature or axial strain sensitivity by measuring its Brillouin gain variation [54], as shown in Figure 9. *Photonics* **2021**, *8*, x FOR PEER REVIEW 11 of 15

**Figure 9.** (**a**) Optical microscope image of the cross section of an RCF, (**b**) schematic illustration of strain applied in a bent fiber, (**c**) illustration of distributed curvature measurements by winding the RCF around different rod diameters, (**d**) measured Brillouin gain along the RCF including four sections where the RCF is winded. (**e**) Estimation of the curvature from BFS or Brillouin gain measurements versus temperature variations. Reproduced from [54], with the permission of Chinese Laser Press Publishing. **Figure 9.** (**a**) Optical microscope image of the cross section of an RCF, (**b**) schematic illustration of strain applied in a bent fiber, (**c**) illustration of distributed curvature measurements by winding the RCF around different rod diameters, (**d**) measured Brillouin gain along the RCF including four sections where the RCF is winded. (**e**) Estimation of the curvature from BFS or Brillouin gain measurements versus temperature variations. Reproduced from [54], with the permission of Chinese Laser Press Publishing.

*Salinity measurement:* A PM-PCF with a polyimide coating was used to demonstrate salinity measurements based on BOTDA and BDG [59]. This coating shrinks in contact with a NaCl solution. A frequency shift is measured with BDG-BOTDA corresponding to a birefringence variation from modification of the hydrostatic pressure applied on the PM-PCF by the coating depending on the salinity concentration. Linear NaCl sensitivity from 30.1 MHz/(mol/L) to 139.6 MHz/(mol/L) have been reported for different coating thickness *Pressure sensing:* PM-PCF composed of only silica and air, which exhibits a very low thermal sensitivity, was used for hydrostatic pressure sensing by measuring the birefringence changes through exciting and probing the BDG (with a differential pulse-width pair Brillouin optical time domain analysis, DPP-BOTDA) [55]. A linear dependence of the Birefringence BFS difference of about 199 MHz/MPa has been measured for hydrostatic pressure from 0 to 1.1 PM with a measurement error of 0.025 MPa.

ranging from 5 μm to 20 μm, respectively, with a maximum salinity accuracy of 0.072 mol/L (considering a measurement uncertainty less than 10 MHz). This demonstration with a spatial resolution of 15 cm enables distributed salinity sensor with both high accuracy and high resolution. *Refractive index measurements of liquid:* The parameters previously presented are measured by sensing the dependence of the BFS on strain variations applied on the fiber. The linear dependency of the BFS to the effective index of the propagated light into the fiber was exploited for sensing the refractive index of a liquid surrounding a side-polished op-*Characterization of Fiber-Optic Parametric Amplifier (FOPA) and nonlinear optical fibers:* FOPA gain that relies on strict phase-matching conditions imposed by the four-wave mixing process was measured along the length of the highly non-linear fiber by using BOTDA in a novel scheme where the parametric amplification acts on the BOTDA pump [56]. The fluctuation measurements of the zero-dispersion wavelength (ZDW) along the highly nonlinear fiber of a FOPA was also demonstrated (with ZDW fluctuations as low as 0.02 nm along 200 m of the fiber and 2 m longitudinal resolution) [57,58]. These demonstrations offer new possibilities for precisely characterizing the chromatic dispersion along highly

tical fiber [60]. The fraction of evanescent field interacting with the liquid along the sidepolished section of 3 cm was further increased by depositing a thin film with high refrac-

about 293 MHz/RIU around *n* = 1.40. The measurements were realized with a high spatial

*Monitoring dihydrogen diffusion:* The diffusion of dihydrogen (H2) within an SMF was demonstrated with BOTDA measurements. The dependence of the BFS to H2 concentration in the silica was reported with a rate of approximately 0.21 MHz/%H2 [61]. Simultaneous Rayleigh and Brillouin backscattering measurements during H2 diffusion have enabled to decorrelate the BFS induced by a refractive index variation and by a linear increase of acoustic velocity of about 5.2 (m/s)/(%mol H2) with H2 concentration in silica [62]. Further studies are developed to increase the BFS sensitivity to H2 concentration by inserting palladium particles (H2 sensitive material) into specialty optical fibers [63].

resolution BOFDA apparatus.

nonlinear fibers, i.e., including local fluctuation, which is a key parameter for numerous nonlinear optic applications.

*Salinity measurement:* A PM-PCF with a polyimide coating was used to demonstrate salinity measurements based on BOTDA and BDG [59]. This coating shrinks in contact with a NaCl solution. A frequency shift is measured with BDG-BOTDA corresponding to a birefringence variation from modification of the hydrostatic pressure applied on the PM-PCF by the coating depending on the salinity concentration. Linear NaCl sensitivity from 30.1 MHz/(mol/L) to 139.6 MHz/(mol/L) have been reported for different coating thickness ranging from 5 µm to 20 µm, respectively, with a maximum salinity accuracy of 0.072 mol/L (considering a measurement uncertainty less than 10 MHz). This demonstration with a spatial resolution of 15 cm enables distributed salinity sensor with both high accuracy and high resolution.

*Refractive index measurements of liquid:* The parameters previously presented are measured by sensing the dependence of the BFS on strain variations applied on the fiber. The linear dependency of the BFS to the effective index of the propagated light into the fiber was exploited for sensing the refractive index of a liquid surrounding a side-polished optical fiber [60]. The fraction of evanescent field interacting with the liquid along the side-polished section of 3 cm was further increased by depositing a thin film with high refractive index (SU-8 photoresist, *n* = 1.56), leading to a refractive index sensitivity of the BFS about 293 MHz/RIU around *n* = 1.40. The measurements were realized with a high spatial resolution BOFDA apparatus.

*Monitoring dihydrogen diffusion:* The diffusion of dihydrogen (H2) within an SMF was demonstrated with BOTDA measurements. The dependence of the BFS to H2 concentration in the silica was reported with a rate of approximately 0.21 MHz/%H2 [61]. Simultaneous Rayleigh and Brillouin backscattering measurements during H2 diffusion have enabled to decorrelate the BFS induced by a refractive index variation and by a linear increase of acoustic velocity of about 5.2 (m/s)/(%mol H2) with H2 concentration in silica [62]. Further studies are developed to increase the BFS sensitivity to H2 concentration by inserting palladium particles (H2 sensitive material) into specialty optical fibers [63].

#### **4. Prospects and Conclusions**

The flexibilities and functionalities of the specialty optical fibers have demonstrated great potential in sensor performance enhancement and application development for BOTDA systems. In this review, several key aspects of the achievements using the specialty fiber in BOTDA systems are summarized, including the Brillouin gain amplification through the integration of highly nonlinear gas medium into the hollow-core fiber, novel polarization properties of specialty fiber based BOTDA systems, sensitivity enhancements by specially coated optical fibers, discriminative sensing of temperature and strain, multiplexed distributed fiber sensing systems of BOTDA and other systems, and novel sensing parameters enabled by specialty fibers. It is believed that specialty fibers are becoming an important design and implementation considerations of the BOTDA system for distributed sensing applications. In addition, the developments of specialty fibers specially designed for a sensing application, by optimizing the topology (core shape, number of modes, multicores) and by associating material properties (silica/air, gas, highly Ge-doped) such as multi-material fibers, will offer new prospects for further enhancing the performance of BOTDA systems in growing applications areas such as the oil and gas industry, power industry, construction industry, transportation industry and security monitoring [9].

**Author Contributions:** Conceptualization: D.J.J.H., H.D. and H.Z.; writing-original draft preparation, D.J.J.H. and G.H.; writing-review and editing: H.D., H.Z., Q.S. and J.H. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work presented in this paper is a result of the research effort through Enhancing Offshore System Productivity, Integrity and Survivability in Extreme Environments (ENSURE) programme financed by A\*STAR under its RIE 2020 Industry Alignment Fund (Grant No: A19F1a0104). **Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Nomenclature**

The symbols used in the manuscript are listed in the table below.

#### **References**

# *Review* **Review of a Specialty Fiber for Distributed Acoustic Sensing Technology**

**Yixiang Sun , Hao Li, Cunzheng Fan , Baoqiang Yan, Junfeng Chen, Zhijun Yan and Qizhen Sun \***

National Engineering Laboratory for Next Generation Internet Access System (NGIA), Wuhan National Laboratory for Optoelectronics (WNLO), School of Optical and Electronic Information, Huazhong University of Science and Technology, Wuhan 430074, China<EMAIL_ADDRESS>(Y.S<EMAIL_ADDRESS>(H.L<EMAIL_ADDRESS>(C.F<EMAIL_ADDRESS>(B.Y<EMAIL_ADDRESS>(J.C<EMAIL_ADDRESS>(Z.Y.)

**\*** Correspondence<EMAIL_ADDRESS>
**Abstract:** Specialty fibers have introduced new levels of flexibility and variability in distributed fiber sensing applications. In particular, distributed acoustic sensing (DAS) systems utilized] the unique functions of specialty fibers to achieve performance enhancements in various distributed sensing applications. This paper provides an overview of recent preparations and developments of specialtyfiber-based DAS systems and their sensing applications. The specialty-fiber-based DAS systems are categorized and reviewed based on the differences in scattering enhancement and methods of preparation. The prospects of using specialty fibers for DAS systems are also discussed.

**Keywords:** specialty fibers; distributed acoustic sensing; DAS; distributed fiber sensor; scattering enhancement fiber

#### **1. Introduction**

The identification of the internal properties of a medium is an important way to understand nature and explore the world, which can be obtained using both direct and indirect measurements. Regarding acoustic waves, the transmission form of sound travels in different directions with the help of various media in the environment. Therefore, the internal properties of the medium can be recognized by measuring and tracking the information carried by the acoustic field [1–3]. In recent years, acoustic sensing technology has been widely used in the analysis of material properties at different scales, such as in geological structure detection [4], resource exploration [5], structural health monitoring [6], and perimeter security [7].

Acoustic sensors allow people to analyze media through acoustic information. With the increases in the range and scale of acoustic detection, the demand for distributed high-capacity acoustic sensors is also expanding. Furthermore, distributed acoustic sensing (DAS) has become a research hotspot because of its advantages in terms of antielectromagnetic interference, high sensitivity [8], and the small volume and light weight of the systems. DAS is a rising acoustic sensing technology that uses passive optical fibers as the transmission and sensing medium at the same time, squeezing information from optical fiber Rayleigh backscatters to achieve acoustic detection in the surrounding environment. Most DAS systems are based on phase-sensitive optical time domain reflectometry (ϕ-OTDR), since the phase change in Rayleigh backscattered light has a linear relationship with the acoustic wave acting on the optical fiber [9].

Common DAS systems usually use a single-mode fiber (SMF) as the sensing fiber. However, with such fibers the Rayleigh backscattered light is extremely weak and the signal-to-noise ratio (SNR) of the optical sensing signal is low, which leads to a poor SNR of the demodulation phase signal in DAS systems based on ϕ-OTDR [10]. In addition, since a laser pulse with a narrow linewidth and high coherence is injected into the fiber, the

**Citation:** Sun, Y.; Li, H.; Fan, C.; Yan, B.; Chen, J.; Yan, Z.; Sun, Q. Review of a Specialty Fiber for Distributed Acoustic Sensing Technology. *Photonics* **2022**, *9*, 277. https:// doi.org/10.3390/photonics9050277

Received: 29 January 2022 Accepted: 15 March 2022 Published: 20 April 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

interference between the Rayleigh scattering points in one pulse will produce interference cancellation, resulting in coherent fading of the backscattered light, forming a "dead zone" on the sensing fiber [11]. In recent years, in order to solve the defects of the poor SNR values and the sensitivity of phase demodulation in SMF-DAS systems, many suppression technologies for noise have been studied, such as coherent fading, while at the same time the complexity and cost of the systems has increased, leading to sacrifices in terms of the response frequency band and sensing distance [12–18]. Furthermore, it is also important to enhance the performance of the sensing fiber itself. The development of a specialty fiber for DAS technology will have broad prospects. ‐

φ‐

This paper intends to provide a comprehensive review of the different sensing features and performance enhancements provided by the specialty fibers that are used in DAS systems. The principle of the DAS technology is introduced in Section 2, followed by a discussion of the specialty-fiber-based DAS system with enhanced sensing capability and performance in Section 3. Firstly, two types of specialty fibers are introduced, a continuous scattering-enhanced (CSE) fiber and discrete scattering-enhanced (DSE) fiber, with the latter one being more widely used because of its ability to completely suppress coherent fading. Secondly, several fabrication techniques for introducing scattering enhancement points (SEP) into the fiber are summarized, including femtosecond writing and UWFBG inscription. Thirdly, a variety of methods to enhance the performance of DAS systems for discrete scattering are reviewed. Fourthly, the applications of the specialty fiber DAS system are reviewed in Section 4. Lastly, the prospects of using specialty fibers for DAS systems are discussed in Section 5. ‐ ‐ ‐ ‐

#### **2. Fundamental Principle**

#### *2.1. Principle of DAS Technology*

DAS is achieved by measuring the optical phase change caused by the axial strain variation of the optical fiber [19]. When the sound wave acts on the fiber, the fiber will produce axial strain, which changes the phase of the Rayleigh backscattering signal in the fiber. According to the photoelastic effect, there is a linear relationship between the axial strain and the optical phase change: ଶ

$$
\Delta \varphi = \beta \left[ 1 - \frac{n^2}{2} (P\_{12} + 2P\_{11}) \right] \Delta L \tag{1}
$$

where *β* is the propagation constant of light, *n* is the refractive index of the optical fiber, *P*12 and *P*11 are tensor coefficients of the optical fiber, ∆*L* is the change in fiber length from equation ∆*L* = *εsL*, *εs* is the axial strain of the fiber, and *L* is the length of the fiber. Thus, as shown in Figure 1, as long as the changes in the phase difference between the two points A and B of the probe light can be extracted, the changes in axial strain can be known and the quantitative perception of acoustic waves or vibrations can finally be measured. It is crucial for DAS to achieve distortion-free phase demodulation in all positions of the fiber. ଵଶ ଵଶ Δ ∆ ൌ ௦ ‐

**Figure 1.** The sensing principle of the fiberoptic DAS.

Since Rayleigh scattering is an elastic scattering method without any nonlinear effect, and as the Rayleigh scattered light at different positions can be distinguished via the time of reflection back to the fiber launch end, the optical fiber phase extraction technique based on phase-sensitive optical time domain reflection (ϕ-OTDR) is widely used in DAS systems [20,21]. In 2011, using heterodyne coherent detection technology, the phase of the

Rayleigh scattering signal was successfully demodulated for the first time [22]. The scheme of the heterodyne coherent detection is shown in Figure 2. The local oscillator light and the Rayleigh scattering signal at point A can be expressed as: ൌ ൣ2 ൧

‐ φ‐

$$E\_{LO} = A \pounds\_O \exp\left[j\mathbf{j}\,\pi ft \,\mathbf{f} \cdot \mathbf{j}\,\varphi\_L\mathbf{f}\right] \qquad \mathbf{j} \tag{2}$$

$$E\_A = A\_A \exp[j2\pi(f + \Delta f)t + j\varphi\_A] \tag{3}$$

where *ALO* and *AA* are the amplitude of the local oscillator light and the Rayleigh scattering signal at point A, *f* is the frequency of the probe light, ∆*f* is the frequency shift of the pulse modulator, *ϕLO* and *ϕA* are the optical phases of the local oscillator light and the Rayleigh scattering signal at point A, respectively. After these two signals are coupled by a 3 dB coupler and interfere with the photosensitive surface of the balanced photoelectric detector (BPD), the light intensity detected by the BPD can be expressed as: ∆ ை

$$I \propto 2E\_{LO}E\_A \cos\left(\Delta f t + \overline{\phi\_A'}\right) \tag{4}$$

ൌ ∆

where *ϕ* ′ *A* = *ϕA* − *ϕLO* is the phase difference between the two signals. Then, *ϕ* ′ *A* can be calculated using a digital coherent IQ demodulation algorithm. Similarly, *ϕ* ′ *B* can also be calculated at point B by the same algorithm. Through the spatial differential calculation of the phase, the phase difference *ϕAB* between two points A and B can be finally obtained, which linearly shows the axial strain of the optical fiber and finally allows the quantitative perception of sound waves and vibrations. ′

**Figure 2.** Typical heterodyne coherent detection scheme [22].

ை

‐ ‐ In addition to the heterodyne-based coherent detection scheme, researchers have also proposed other phase demodulation schemes, such as the 3 × 3 coupler scheme [23], phasegenerated carrier (PGC) [24], and linear frequency sweeping pulse method [25]. Some representative schemes are shown in Figure 3, all of which can achieve distributed optical phase demodulation.

‐ **Figure 3.** Rayleigh scattering model of the single-mode optical fiber [26].

#### *2.2. Limitations of Single-Mode Fiber (SMF) DAS*

⋯

‐

Despite SMF DAS technology having been applied in many fields, such as geological monitoring, pipeline monitoring, and oil exploration, and with the advantages of

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distributed detection, high spatial resolution, and high sensitivity, it still has been limited by interference fading and poor signal consistency. The reasons are analyzed below.

In particular, when the pulse width is narrow enough, the Rayleigh backscattering signals of point A and B as discussed in Section 2.1 can be obtained according to the arrival time of the Rayleigh backscattering light. In fact, the probe pulse has a certain pulse width, and the Rayleigh scattering signals of different scattering points in the pulse width will interfere with each other because of the high coherence of the probe light. The interference result of the Rayleigh scattering can only represent a section fiber near point A and B. Due to the inhomogeneous doping in the preparation of the optical fiber, the interference phenomenon of the Rayleigh scattering is random, which will inevitably affect the phase demodulation performance. In order to describe the Rayleigh scattering phenomenon in SMF accurately, researchers established a SMF scattering model [26].

The Rayleigh scattering model is shown in Figure 4. First, the SMF is discretized and the nonuniform distribution of impurities in the core is regarded as a series of equivalent Rayleigh scattering points (ERSP) of micron or submicron size, which are numbered as 1, 2, 3, · · · , M, respectively. Each backscattering coefficient and the position of the scattering point can be presented as (*am*, *zm*); that is, the M-th scattering point is on *zm*, while the reflectivity is *am*. Since the ERSP can be regarded as the superposition of multiple scattering points with a smaller scale, its position can be expressed as *zm* = *md* + ∆*d*, where ∆*d* obeys the uniform distribution in h −*d* 2 , *d* 2 i and *am* obeys the Rayleigh distribution. According to the above analysis, the Rayleigh scattering signal received at the *i*-th time can be expressed as the superposition of interference of the Rayleigh scattering signal of a section of fiber:

$$E\_i = \sum\_{z\_{i1} < z\_m < z\_{i2}} A a\_m \cdot \exp\left(j \frac{2\pi}{\lambda} \cdot 2nz\_m\right) \tag{5}$$

where *n* is the refractive index of the fiber, *zi*1 and z*i*2 are related to the pulse width, which satisfies *zi*2 − *zi*1 = *Wc*/2*n*, *W* is the pulse width of the probe pulse, and *c* is the speed of light in vacuum. Researchers have also verified this model [8]; when the interference signal involves interference cancellation, the signal intensity |*Ei* | will become weaker, leading to a worse optical SNR. Further, the light intensity declines to the same level as the acquisition noise and the demodulated phase information will be submerged in the noise, forming a blind detection area, which is called interference fading. In addition, due to the randomness of the reflectivity *am* of the equivalent scattering point, the equivalent positions of the signals received at different times are different. The signal received at time *i* in Equation (5) is taken as an example. Since the scattered signal at this time is the superposition of multiple complex numbers, its intensity *Aam* is the mode of the complex number, and the phase *j* 2*π λ* · 2*nzm* related to position *zm* is the argument for the complex number, so Equation (5) can be expressed as the superposition of multiple vectors. As depicted in Figure 4, when the Rayleigh scattering intensity of the front-end equivalent scattering point is strong, the signal received at time *i* can be regarded as Rayleigh scattering near the *zi*1 position, while when the Rayleigh scattering intensity of the back-end equivalent scattering point is strong, the signal received at the same time can be regarded as Rayleigh scattering near the *zi*2 position.

In general, it is the randomness of the intensity and position of Rayleigh scattering of ordinary single-mode fibers that leads to the problems of interference fading and poor signal time consistency in DAS, making it difficult to perform high-fidelity sound wave tracking when analyzing the internal properties of the medium.

**Figure 4.** Schematic diagram of equivalent scattering positions in pulse interference.

#### **3. Reviews of Specialty-Fiber-Based DAS Technology**

‐ ‐ **‐ ‐** In order to solve the interference fading and poor consistency in SMF DAS, researchers have conducted a series of studies [13,27–30]. Among them, the most effective method is to improve the fibers to enhance the fiber backscattering, such as continuous scatteringenhanced fibers and discrete scattering-enhanced fibers formed by inscribing microstructures into the fibers. In addition, due to the characteristics of microstructure optical fibers, researchers also designed and improved the matching optical scheme to improve the performance of the DAS system. In this section, a comprehensive review of the specialtyfiber-based DAS with enhanced sensing capability and performance is presented.

#### *3.1. Continuous Scattering-Enhanced Fiber-Based DAS*

‐ ‐ Continuous scattering enhancement (CSE) allows the suppression of coherent fading by enhancing the Rayleigh scattering of the whole fiber, whose essence is to enhance the scattering intensity *am* of the ERSP model described in Section 2.2 by doping or writing continuous grating in the fiber, so as to enhance the light intensity after interference superposition, finally allowing the suppression of interference fading.

‐ ‐ *‐ ‐* In 2017, the OFS laboratory in the United States used the phase mask method to efficiently and continuously inscribe Bragg gratings in multicore fibers through ultraviolet (UV) exposure. The backscattering intensity of the fiber was increased by 14 dB, and the reflection spectrum is shown in Figure 5a. Then, in cooperation with Fotech in the UK, CSE fiber was used in a DAS system, and the SNR of 1 km of CSE fiber was increased by 15 dB [31–34]. Although this method effectively improves the SNR, the bandwidth of the Bragg grating reflection spectrum is narrow, and the reflection wavelength will drift with temperature and stress variation. When the external environment changes, the wavelength of the incident light and grating reflection may not correspond to each other, resulting in the loss of the scattering enhancement effect. Therefore, the application range of this kind of fiber is limited and cannot be used in fields where high temperature and high pressure are required on site. In addition to inscribing continuous gratings, changing the fiber doping is another way to increase the intensity of the Rayleigh scattering. In 2018, Butov et al. used nitrogen-doped fiber as the sensing fiber, which increased the SNR of the acoustic wave detection by 3 dB [35]. In the same year, Feng S et al. used an erbium-doped optical fiber for distributed optical fiber sensing, adopted a phase-generated carrier (PGC) optical scheme, which converts homodyne interference into heterodyne interference by modulating the frequency of the signal, decreased the phase noise by 14 dB, and achieved a high-SNR acoustic measurement on 1.9 km optical fiber [36].

‐

‐

‐

‐

2

∙ 2൰

‐

‐ ‐ **Figure 5.** Typical scheme of continuous scattering-enhanced optical fiber [33,36]: (**a**) the backscattering signal distribution of a typical continuous scattering-enhanced fiber; (**b**) scheme of improved Rayleigh scattering achieved by changing the fiber doping; (**c**) scattering spectrum of high Rayleigh scattering fiber.

‐ For the CSE scheme, although it can effectively improve the scattering intensity and suppress the coherent fading noise, the enhanced fiber scattering results in doubling of the light loss, which greatly limits the detection distance. Taking the optical fiber doping scheme as an example, if the front-end SNR is increased by 10 dB, the Rayleigh scattering of the fiber needs to be increased by ten times, which reduces the detectable distance to 1/10. More importantly, the SCE fiber does not fundamentally change the nature of the optical interference in the pulse, and still cannot completely eliminate the coherent fading phenomenon.

#### *3.2. Discrete Scattering-Enhanced Fiber Based DAS*

*‐* In addition to continuous scattering enhancement, more researchers are focusing on the application of discrete scattering-enhanced (DSE) fiber in DAS. As shown in Figure 6, the essence of this fiber is to enhance the scattering intensity of one single ERSP with a certain interval in the model illustrated in Section 2.2. The intensity of the scatteringenhanced points (SEP) is far greater than that of the ordinary ERSP. In this way, the Rayleigh scattering interference light containing the SEP can be expressed as:

$$E\_i = \sum\_{z\_{i1} < z\_m < z\_{i2}, z\_m \neq z\_j} a\_m \cdot \exp\left(j\frac{2\pi}{\lambda} \cdot 2nz\_m\right) + a\_j \cdot \exp\left(j\frac{2\pi}{\lambda} \cdot 2nz\_j\right) \tag{6}$$

‐

 ൌ ∙ ௭భழ௭ழ௭మ,௭ஷ௭ೕ exp ൬ 2 ∙ 2൰ ∙ exp ൬ where the *j*-th ERSP is the scattering enhancement point. Because the scattering intensity of the SEP is much larger than that of the ordinary ERSP, the first term of the above formula can be ignored, which shows that the Rayleigh scattering signal is only determined by the SEP. Through the phase demodulation method in Section 2.1, the phase difference between the two SEP can be accurately obtained, and because of its high scattering intensity and high SNR, the interference fading can be completely eliminated, ensuring the good consistency of the signal.

‐

2

∙ 2൰

‐

‐

‐

‐

‐

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*‐*

‐ **Figure 6.** Schematic diagram of discrete scattering-enhanced fiber.

‐

‐

exp ൬

2

‐ To verify its effectiveness, we have theoretically analyzed the DSE model and the SMF scattering model. According to the parameters shown in Table 1, three SEPs are set at 3, 7, and 11 m on the fiber at intervals of 4 m. Figure 7a,b shows the distribution results of the scattering intensity obtained from the simulation. It can be seen that the DES fiber completely suppresses the random variation of the signal amplitude and interference fading. To further explore the suppression effect of the DSE fiber on the phase noise, we solve the phase differences between 3 and 7 m on the SMF and DSE fibers, respectively, the of which results are shown in Figure 7c. Compared with SMF, the DSE fiber is not affected by the random distribution of ordinary ERSPs, but is determined by the position of the SEPs, so the phase noise is greatly suppressed.

**Table 1.** Parameters of discrete enhanced scattering model.

**Figure 7.** Simulation results of discrete enhanced scattering model: (**a**) reflection distribution of discrete enhanced fiber; (**b**) reflection distribution of single mode fiber; (**c**) phase demodulation result.

#### *3.3. Preparation and Implementation of DSE Fiber*

‐ ‐ At present, there are two ways to manufacture the discrete scattering-enhanced fiber, one is by inscribing the periodic ultra-weak Bragg grating (UWFBG) array [29,37] into the fiber, and the other is by introducing a local wavelength-independent weak reflection array into the fiber [38–40].

‐ ‐ ‐ UWFBG usually involves the use of ultraviolet light [41–43] or a femtosecond laser [44,45] to form a permanent periodic change in the refractive index of the optical fiber, so as to allow the backward reflection of a specific light wavelength. The most classic preparation system is shown in Figure 8a [46]. In the process of fiber drawing, through strict dynamic control, the UWFBG was written using the phase mask method, using periodic interference fringes of the ±1st diffraction light to irradiate the photosensitive fiber and periodically change the refractive index of the fiber core. Additionally, an FBG writing platform was mounted on the draw tower near the first coating to weaken vibrations in the fiber. The preparation results are shown in Figure 8b [47], and the scattering rate of the scattering-enhanced array is much higher than that of the single-mode fiber. However, as a Bragg grating method, UWFBG is sensitive to temperature and stress. When the temperature and strain of the environment are changed, the reflection wavelength of the UWFBG will drift. As shown in Figure 8c, the bandwidth of UWFBG is usually less than

2 nm and the central wavelength is determined according to the light source used in the specific experiment. Due to the limited bandwidth of UWFBG, there may be a mismatch between the reflective spectrum of UWFBG and the wavelength of the detection light when the UWFBG array fiber operates in special environments, such as for large temperature vibrations or high pressure, while the fiber will also suffer from twisting or pulling forces, meaning the reflection power from the UWFBG will degenerate into Rayleigh scattering, resulting in a blind sensing area. This characteristic of UWFBG hinders its application in underground, underwater, and other special environments [48,49].

**Figure 8.** Typical UWFBG preparation method: (**a**) online UWFBG preparation system [46]; (**b**) OTDR measurement results of the UWFBG array [47]; (**c**) reflection spectrum of UWFBG [46].

In recent years, the enhancement scheme of a local achromatic weak reflection array has also been used in DAS [50,51]. In order to prepare a more universal discrete scattering enhancement array, Sun et al. proposed a preparation method for microstructured optical fibers with a colorless reflection point. The mechanism of the microstructure involves the local refractive index change through UV exposure without the help of the phase mask to form a Fresnel reflecting surface. The fabrication system is shown in Figure 9a [52], while the preparation results are shown in Figure 9b–d [53]. A discrete scattering enhancement array with an interval of 5 m and 15 dB enhanced intensity was achieved. When the temperature changes, the scattering intensity of the microstructure is extremely stable. In addition, the University of Southampton and other universities in the UK also used a femtosecond laser to prepare a weak reflection array [40]. The preparation system, scheme, and results are shown in Figure 10. Compared with UWFBG, whose reflection bandwidth is limited, the weak reflection points are directly engraved in the optical fiber, without wavelength selectivity, avoiding the influence of temperature and strain [54].

**Figure 9.** Preparation method for a colorless microstructure array based on UV exposure: (**a**) automatic colorless microstructure preparation system [51]; (**b**) OTDR measurement results of colorless microstructure array [53]; (**c**) spectra of colorless microstructure arrays [51]; (**d**) temperature stability of colorless microstructure arrays [53].

‐ ‐ **Figure 10.** Preparation method for a weak reflection array based on a femtosecond laser [40]: (**a**) weak reflection array preparation system; (**b**) schematic diagram of weak reflection array preparation method; (**c**) OTDR measurement results for the weak reflection array; (**d**) the result of a cut-back measurement on a separate fiber containing 300 reflectors.

#### *3.4. Methods to Improve the Performance of Specialty Fiber DAS*

In the early stages, researchers mainly focused on using UWFBG in various DAS schemes. In 2015, Wang et al. used UWFBG in DAS based on a 3 × 3 coupler demodulation for hydroacoustic testing, which can detect a water pressure of 0.112 Pa [55]. Subsequently, the team at Huazhong University of Science and Technology successively used DSE fiber in various DAS schemes, such as double-pulse, coherent detection, and PGC demodulation schemes [29,39,40,50,56–58]. These schemes are shown in Figure 11. In recent years, more attention has been paid to improving the DAS system performance by using the advantages of discrete scattering enhancement fiber, including low-frequency phase shift compensation, polarization fading suppression, pulse width compression, and system sampling rate expansion. ‐ ‐

**Figure 11.** Representative DAS scheme based on UWFBG: (**a**) scheme using a 3 × 3 coupler [54]; (**b**) PGC scheme [55]; (**c**) heterodyne coherent detection scheme [29].

#### ‐ 3.4.1. Low-Frequency Phase Drift Compensation Technology

‐ ‐ ‐ ‐ ‐ 3.84pε/√Hz The DSE fiber DAS has the potential for extremely low-frequency detection due to its good signal consistency and lac of interference of random Rayleigh scattering. In the DAS system, the low-frequency drift of the laser phase and the slow change of the external temperature will introduce greater low-frequency noise to the system, limiting the accuracy of the low-frequency detection [59]. The phase drift of the laser can be compensated by the auxiliary interferometer. As shown in Figure 12a, the phase noise of the laser is measured in real time by the auxiliary interferometer, and the measurement results are compensated to suppress the low-frequency noise. In this way, Fan et al. achieved a strain resolution of 3.84pε/ √ Hz [60,61] at a frequency of 10 Hz. The team from Huazhong University of Science and Technology proposed a reference fiber compensation scheme via the discrete enhancement of UWFBG. The scheme is shown in Figure 12b, which can

compensate for laser drift and temperature changes at the same time, achieving a resolution of 0.57nε/ √ Hz at a frequency of 0.01 Hz and a resolution of 3.4nε/ √ Hz at a frequency of 10 Hz [62]. Furthermore, the team introduced an LS-SVM operator during demodulation to track and compensate for the hysteresis effect of the temperature, allowing high-precision acoustic measurements in the 0.001 Hz frequency band [63]. 0.57nε/√Hz 3.4nε/√Hz ‐ ‐

‐ **Figure 12.** Representative scheme for low-frequency noise suppression: (**a**) auxiliary interferometer compensation [60,61]; (**b**) reference fiber compensation [62].

#### 3.4.2. Polarization Fading Suppression Technology

‐ ‐ ‐ ‐ In the DSE-fiber-based DAS system, the coherent fading is completely suppressed, while the polarization random fading problem must be urgently solved [16]. The random polarization fading is caused by the random change in polarization states of the two interference lights. When the polarization directions of the two interference lights are parallel, the interference light signal is the largest and the phase noise is the smallest. However, when the directions are orthogonal, the interference light intensity is decreased to zero and the phase information is completely overwhelmed by noise. In order to solve this problem, Zhang et al. improved the dual-wavelength DAS scheme. As shown in Figure 13, the polarization composite double pulse was used as the detection pulse to achieve polarization noise suppression [16,64]. For the coherent detection DAS scheme, Sun et al. used a polarization beam splitter to divide the reflected light into two orthogonal polarization states to interfere with the local oscillator light, so that the random polarization noise was reduced by 9.5 dB [65]. However, in this scheme, when the polarization states of the local oscillator light and the polarization beam splitter do not match, fading may still occur. To resolve this problem, the Huazhong University of Science and Technology team proposed a method for emitting dual-wavelength probe pulses and using the random polarization states of different wavelength parameters to greatly reduce the probability of polarization fading and to reduce polarization noise by 19.2 dB [66].

‐ **Figure 13.** Representative scheme for polarization noise suppression: (**a**) orthogonal polarization scheme [16]; (**b**) multi-parameter scheme [66].

#### 3.4.3. Pulse Width Compression Technology

τ 2 ⁄ ‐ ‐ െ93.16dB re rad/√Hz ‐ In the DAS system, the interval between the SEPs determines the resolution of the system and also limits the width of the detection pulse. Assuming that the interval between the SEPs is d, the detection pulse is limited to τ ≤ 2*dn*/*c* (where n is the refractive index of the fiber and c is the speed of light in the vacuum). In a radar system, a longer detection pulse is usually transmitted and the pulse is compressed at the receiving end, so as to obtain a signal with a high signal-to-noise ratio under the premise of ensuring the resolution. The common schemes are pulse linear frequency sweeping and pulse coding [67–69]. These techniques have also been used in DSE fiber DAS systems. Fan et al. adopted the sweeping pulse transmission scheme, whereby the receiving end compresses the pulses through matched filtering, achieving a noise level of −93.16dB re rad/√ Hz at 500–2500 Hz as shown in Figure 14a [70,71]. Wang et al. successively used pulse coding technology in UWFBG-based DAS systems and improved the systems' SNR values by 6.9 dB as shown in Figure 14b [72].

#### 3.4.4. Sampling Frequency Expansion Technology

In DAS system, the sampling rate is mainly limited by the length of the sensing fiber. After the system transmits the probe pulse into the optical fiber, it needs to ensure that the Rayleigh backscattering signal transmitted to the farthest end of the pulse returns to the receiving end before transmitting the next pulse, otherwise crosstalk will occur. However, during railway safety detection and power grid partial discharge detection applications, it is necessary for the DAS system to perform long-distance and high-frequency detection simultaneously. The way to solve these problems is to transmit multiple probe lights in parallel and distinguish them through a certain feature to avoid crosstalk. By transmitting pulses with different frequencies into the optical fiber and distinguishing them by using different pulse frequencies, Zhang et al. achieved a sampling rate of 440 kHz on a 330 m optical fiber and expanded the distance bandwidth product by three times [73]. Sun et al. put forward a time slot multiplexing scheme. As shown in Figure 15, multiple pulses are inserted into the time slot between two adjacent SEPs of an optical fiber, with a sampling rate of 300 kHz being achieved on a 1020 m optical fiber, expanding the distance bandwidth product by six times [74].

‐

െ93.16dB re rad/√Hz

**Figure 14.** Representative scheme for pulse width compression: (**a**) orthogonal polarization scheme [70,71]; (**b**) multi-parameter scheme [72].

τ 2 ⁄

‐ ‐

‐

**Figure 15.** Time slot multiplexing scheme [74]: (**a**) principle; (**b**) demodulation algorithm.

 Above, the two specialty fibers, namely CSE fiber and DSE fiber, are analyzed and compared in terms of SNR enhancements, sensing distance, and methods to improve the performance. As shown in the Table 2, it can be seen that the DSE fiber performs significantly better than the CSE fiber in terms of the sensing distance, while the greater number of matching DAS schemes also further improves the performance of DAS system in multiple dimensions.

**Table 2.** Performance summary for CSE and DSE fibers.

#### **4. Significant Application Progress**

With the continuous improvement and development of the DAS system based on the specialty scattering-enhanced optical fiber, researchers have applied the system to practical engineering applications in many fields, including geological and resource exploration, structural health monitoring, and hydroacoustic exploration. ‐

#### *4.1. Geological and Resource Exploration*

The vertical seismic profile (VSP) is a commonly used parameter for petroleum exploration seismic observations. With the development of DAS technology, fiberoptic logging has become a research hotspot.

Sun et al. conducted a walkaway VSP experiment using a self-made microstructure fiber DAS system [75]. The microstructure fiber is arranged vertically in the test well and the explosive source is artificially introduced on the ground to generate seismic waves, which are transmitted along the stratum to generate direct waves and reflected waves. Figure 16 shows the VSP results recorded at the "zero bias" position and 2.5 km away from the "non-zero bias" position. Figure 16a is the seismic wave transmission diagram recorded by the microstructure fiber DAS system under the condition of "zero bias". The specific details are enlarged, as shown in Figure 16b. It can be observed that clear direct transmission of the p-wave and s-wave is demonstrated, and that the peaks and troughs of multi-channel signals correspond to each other, highlighting the phase difference caused by the transmission time, which proves the high consistency of the microstructure fiber DAS system. In addition, as shown in Figure 16c, for the "non-zero biased" signal away from 2.5 km, the microstructure fiber DAS can also record direct waves and reflected waves with high SNR values. The DAS system based on microstructure fiber has the advantages of a high SNR, high signal consistency, and high reliability, meaning it could become an efficient, fast, and reliable acquisition tool for oil data acquisition, potentially allowing intelligent resource exploration.  VSP test results for the microstructure fiber DAS system [75]: (**a**) "zero bias" test results; (**b**) schematic diagram of signal consistency; (**c**) "non-zero bias" test results; (**d**) "zero bias" spectrum diagram; (**e**) "non-zero bias" spectrum.

In 2019, Yang built a DAS system based on a UWFBG array [76], using UWFBG to enhance the intensity of the fiber's backscattered signal as shown in Figure 17. In the experiment, the results measured by optical fiber were compared with the waveforms measured

by geophone, and the time-frequency results were in good agreement. Furthermore, it was applied to VSP logging, and a clear VSP waveform with a high SNR was obtained without any data processing. ‐

**Figure 17.** (**a**) The VSP test site. (**b**) The VSP test result [76].

#### *4.2. Structural Health Monitoring*

‐ The health status of various infrastructure, such as railways, tunnels, and pipelines, is related to operational safety, the national economy, and social production. The DAS system based on scattering-enhanced fibers was applied to the field of structural health monitoring to ensure high reliability.

#### 4.2.1. Pipeline Monitoring

The transportation of resources such as oil and natural gas is closely related to the national economy and people's lives, but transmission pipelines may fail due to external invasion, corrosion, and other reasons, threatening the safety of personal, profits, and property. The DAS system based on discrete enhanced optical fibers was applied for pipeline safety monitoring due to its high SNR and high stability [77,78].

‐ ‐ ‐ ‐ A team from the University of Pittsburgh [79] used femtosecond writing technology to artificially introduce optical fiber SEPs. As shown in Figure 18, the high-SNR DAS system tracks the propagation characteristics of soundwaves in the pipeline, combined with neural-network-based machine learning algorithms, and the data collected by the DAS system are analyzed to identify external intrusion events and the internal corrosion status of the pipeline. The system's recognition accuracy for different external intrusion events exceeds 85%, the defect recognition accuracy rate exceeds 94% under supervised learning conditions, while the recognition accuracy rate reaches 71% under unsupervised learning conditions. Furthermore, the team also conducted a test of the sand content and the solid–liquid two-phase flow of the pipeline by laying a discrete scattering enhancement fiber on the pipeline wall. By tracking the acoustic emission signals induced by the sand particles in the liquid hitting the pipe wall, the measurement of different sand particle concentrations was achieved.

**Figure 18.** Schematic diagram of a pipeline survey [79]: (**a**) schematic diagram of DAS system for pipeline protection; (**b**) architectures of neural networks in the pipeline protection system; (**c**) the confusion matrix of four acoustic events.

‐

#### 4.2.2. Track Defect Monitoring

‐ ‐ ‐ With the development of high-speed railway technology, track defect monitoring has become more important. A variety of mature detection methods have been developed, but most of them involve electromagnetic sensors, which are vulnerable to harsh environments [80]. In 2019, Sun et al. used a DAS system based on scattering-enhanced fibers for distributed detection of a railway defect [81]. As shown in Figure 19, the scatteringenhanced fiber is set in the middle of the rail. At the position where the defect occurs, the interaction between the wheel and rail will form an impact sound signal, which is transmitted along the two directions of the track. The DAS system is used to track the transmission signal, and then the accurate positioning of the defect is identified through the positioning algorithm, the results of which show that the maximum error of the defect is only 2.1 m. This method can provide an effective and reliable solution for rail health monitoring. ‐ ‐

**Figure 19.** Rail defect detection based on DAS system [80]: (**a**) the process of detecting and analyzing sound waves based on fiber DAS; (**b**) photographs of the field test environment; (**c**) sound distribution measured by DAS.

#### 4.2.3. Tunnel Safety Monitoring

In addition, the health of infrastructure such as tunnels is related to the traffic operation safety. An optical fiber DAS system can also be used for safety detection in tunnels, such as in subways and highways. However, the effectiveness of the reinforcement segment and steel loop in the tunnel structure maybe be a problem. The partial separation of the segment and steel loop will mean the steel loop is unable to effectively support the segment, resulting in potential safety hazards. A resonant cavity will be formed between the segment and the steel loop due to the separation, with different degrees of invalidity corresponding to the different resonant frequencies. In 2021, Sun et al. carried out intelligent monitoring of a tunnel steel loop structure based on a scattering-enhanced optical fiber DAS system [81]. As shown in Figure 20, the sensing fiber is laid on the steel loop structure to obtain the resonant frequency changes induced by the active sound source. Furthermore, the machine learning algorithm based on the BP neural network is used to effectively classify different failure levels, so as to achieve the online detection of the bonding state of the reinforced steel loop. The experimental results show that the system has a recognition rate of up to 97.8%. ‐

**Figure 20.** (**a**) Tunnel steel loop detection system based on DAS. (**b**) Schematic diagram of an invalid steel loop. (**c**) BP neural network. (**d**) Relationship between the degree of invalidity and the frequency deviation, (**e**) Relationship between the degree of invalidity and the energy distribution. (**f**) Power spectrum under different degrees of invalidity. (**g**) Wavelet energy transformation under different degrees of invalidity. (**h**) Recognition rate [81].

#### 4.2.4. Geological Structural Monitoring

‐ ‐ ‐ ‐ ‐ ‐ In recent years, DAS monitoring has been used for geological structures [82]. In 2017, a team from the University of California Berkeley transformed fiberoptic telecommunication cables into sensor arrays enabling meter-scale recording over tens of kilometers of linear fiber length to record the nearly vertically incident arrival of an earthquake from the Geysers Geothermal Field and to estimate its backazimuth and speed [83]. In 2018, Jousset et al. demonstrated the possibility of dynamic strain determination with conventional fiber cables deployed for telecommunication [84]. Then, by using DAS, they recorded seismic signals from natural and man-made sources with 4 m spacing along a 15-km-long fiber cable, identifying new dynamic fault processes with unprecedented resolution, opening a new path for earth hazard assessments and the exploration of structural features. In 2019, Sladen et al. reported measurements on a 41.5-km-long telecom cable that was deployed offshore of Toulon, France, demonstrating the capability to monitor the ocean's solid earth interactions from the coast to the abyssal plain [85]. In the same year, Lindsey et al. reported the use of an optical fiber cable with a DAS operating onshore, creating a ~10,000-component, 20-km-long seismic array. As depicted in Figure 21, they recorded

a minor earthquake wavefield, identified multiple submarine fault zones, and tracked sea-state dynamics during a storm cycle in the northern Pacific Ocean [86]. ‐

‐ ‐ ‐

‐ **Figure 21.** (**a**) Map of Monterey Bay, CA, showing the Monterey Accelerated Research System (MARS) cable (DAS, pink portion), mapped faults, the Gilroy earthquake (red and white beach ball), and major bathymetric features. (**b**) Cross-section illustration of the MARS cable used for DAS. (**c**) The 10 min average wave height and spectral wave density (SWD) measurements outside Monterey Bay, which were measured using a buoy. (**d**) Seafloor DAS strain from a 2 km cable location averaged over a 15 min sliding window. (**e**) North component of ground velocity from an onshore broadband inertial seismometer averaged over a 15 min sliding window [86].

#### *4.3. Hydroacoustic Exploration*

‐ ‐ ‐ ‐ − − Ocean exploration is of great significance to homeland security and resource exploration. The acoustic medium can carry a wealth of information and can transmit signals for long distances underwater, so hydrophones are an important tool for underwater information acquisition. Optical fiber sensors have been preliminarily used in the field of underwater acoustic measurement due to their unique advantages. Single-point sensors and hydrophone arrays based on FBG and interferometers were common methods used for early optical fiber hydrophones. However, due to the limited multiplexing capacity, it is difficult to meet the requirements for large-scale exploration in the ocean and other application environments. In recent years, the DAS system has been well applied in the field of terrestrial acoustic detection. Because of its distributed, long-distance, and high-sensitivity characteristics, the DAS system has been introduced into the field of hydrophones. In the preliminary stage, researchers measured the underwater acoustic sensitivity and other parameters of an optical fiber in the laboratory. Usually, a distributed underwater acoustic sensing system is built based on a UWFBG array and unbalanced interferometer demodulation structure [54,87]. The underwater acoustic signal is obtained by demodulating the change in phase difference between two adjacent UWFBGs, in which the sensitivity obtained usually reaches about −160~−150 dB re rad/µPa.

μ ‐ − μ ‐ ‐ In 2021, Sun et al. designed a lightweight and fully distributed hydroacoustic optical sensing cable [88]. An acoustic sensitizing layer is superimposed on the inner core layer, the microstructure scattering-enhanced fiber is wound on the sensitizing layer, and a further protective layer is added to the outermost layer. As depicted in Figure 22, the coherent detection system has been utilized to conduct experiments, with the results showing that the hydroacoustic detection sensitivity is as high as −127 dB re rad/µPa with a flat frequency response range of 100–2000 Hz. Furthermore, the team conducted an on-site lake test, the results of which are depicted in Figure 23.

‐ ‐ **Figure 22.** (**a**) Fully distributed underwater acoustic sensor system. (**b**) Lightweight fully distributed underwater acoustic fiberoptic cable based on scattering-enhanced fiber. (**c**) The relationship between the phase demodulation change and acoustic pressure. (**d**) The frequency response curve within the frequency range of 100–2000 Hz [88]. ‐ ‐

**Figure 23.** The underwater acoustic test: (**a**) the setup for the field test; (**b**) picture of the sensitized optical cable; (**c**) the static test results for the sound source; (**d**) motion trajectory tracking of the sound source.

#### **5. Conclusions and Prospects**

‐ ‐ ‐ ‐ ‐ ‐ The variability and functionality of specialty optical fibers have demonstrated their major potential for sensing performance enhancement and application development for DAS systems. In this review, the scattering characteristics and noise suppression principles of specialty optical fibers are analyzed, and the fabrication technologies used for DSE are introduced. Based on the discrete scattering-enhanced fiber, the performance enhancement technologies of the DAS system are summarized, including the low-frequency phase noise compensation, polarization fading suppression, pulse width compression, and system sampling rate expansion. Further, due to the unique advantages of the scattering-enhanced fiber, the DAS system has been widely applied in various fields, such as in resource

exploration, structural health monitoring, and for distributed hydrophones. Looking to the future, the research on the specialty-fiber based DAS will develop rapidly for many aspects, such as the doping of new materials for high sensitization, the development of fabrication techniques for higher efficiency, the introduction of AI techniques for higher measurement accuracy, and the exploration of wider application fields. Owing to the distinct advantages, it is believed that the specialty-fiber-based DAS system will have bright market prospects in geological, resource, and hydroacoustic exploration, as well as structural health monitoring.

**Author Contributions:** Conceptualization, Q.S. and Z.Y.; methodology, H.L. and C.F.; formal analysis, Y.S. and J.C.; investigation, B.Y.; writing—original draft preparation, Y.S.; writing—review and editing, Y.S.; funding acquisition, Q.S. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was supported by National Natural Science Foundation for Distinguished Young Scholars through Grant No. 61922033; the Marine economic development project of Guangdong Province through Grant No. GDNRC 2020(045); the National Natural Science Foundation of China through Grant No. 61775072; and the Innovation Fund of WNLO.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

# *Review* **Transmission and Generation of Orbital ANGULAR Momentum Modes in Optical Fibers**

**Zhuo Wang 1,2 , Jiajing Tu 3 , Shecheng Gao 3 , Zhaohui Li 4 , Changyuan Yu 1,2, \* and Chao Lu 1,2**

**Abstract:** The orbital angular momentum (OAM) of light provides a new degree of freedom for carrying information. The stable propagation and generation of OAM modes are necessary for the fields of OAM-based optical communications and microscopies. In this review, we focus on discussing the novel fibers that are suitable for stable OAM mode transmission and conversion. The fundamental theory of fiber modes is introduced first. Then, recent progress on a multitude of fiber designs that can stably guide or generate OAM modes is reviewed. Currently, the mode crosstalk is regarded as the main issue that damages OAM mode stability. Therefore, the coupled-mode theory and coupled-power power theory are introduced to analyze OAM modes crosstalk. Finally, the challenges and prospects of the applications of OAM fibers are discussed.

**Keywords:** orbital angular momentum; optical fiber; fiber mode crosstalk; vortex mode generator

**Citation:** Wang, Z.; Tu, J.; Gao, S.; Li, Z.; Yu, C.; Lu, C. Transmission and Generation of Orbital ANGULAR Momentum Modes in Optical Fibers. *Photonics* **2021**, *8*, 246. https:// doi.org/10.3390/photonics8070246

Received: 24 May 2021 Accepted: 22 June 2021 Published: 30 June 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

#### **1. Introduction**

A photon can carry spin angular momentum (SAM) and orbital angular momentum (OAM). The SAM of light is associated with the spin of a photon, and it can be characterized as the circular polarization of a light beam [1]. The values of SAM are ±*h*¯ per photon, which correspond to left- and right-handed circularly polarized states, respectively. Different from the SAM, the OAM of light originates from the azimuthal phase distribution at the wave front [2]. In 1992, Allen et al. first recognized that a light beam having a helical phase exp(*ilφ*) can carry OAM with the value *lh*¯ per photon [3]. After this groundbreaking work, detailed studies on optical OAM were constantly carried out [4] and have given rise to developments in many application areas including trapping and guiding atoms with optical OAM [5–7], OAM states' entanglement [8], high-dimensional cryptography [9], vortex beam assisted microscopy [10,11]. and optical communications [12–15].

At present, the high growth rate of the demand for data transmission capacity leads to a huge challenge for the optical communication community. Space-division multiplexing (SDM) is considered as an effective method to solve the problem of capacity crunch in the f long term [16]. It is obvious that, by using multiple space channels, the nominal data transmission capacity can be increased greatly. Fortunately, the optical OAM provides a new degree of physical dimension for SDM [13,14]. OAM modes can be generated by using spatial light modulators (SLMs) [12], spiral phase plates [17], log-polar mapping [18,19], angular gratings [20], fiber couplers [21,22], and fiber gratings [23–27]. These methods provide various choices for loading information onto OAM beams. In addition, Dammann vortex gratings give a feasible way for the wide-range detection of OAM modes [28] and for the multiplexing and demultiplexing of massive OAM channels [29]. In addition, the

technique of multi-plane light conversion provides another effective way to multiplex and demultiplex OAM modes [30,31]. However, the stable long-distance transmission of massive OAM modes is still an open issue. In the case of free-space-optics (FSO) data transmission, the atmospheric turbulence can cause the fluctuation of the refractive index of air, which damages the intensity profile and the transverse phase structure of OAM modes [32]. In addition, the diffraction of OAM beams limits the FSO data transmission in long-distance situations. Another way for OAM mode propagation is using optical fiber. The OAM modes form a set of orthogonal bases, which is equivalent to the basis of vector modes in optical fibers. Because of the orthogonality, each OAM mode can carry information independently under ideal conditions. However, the fiber defects introduced in the fabrication and the irregular bending in the application will break the orthogonal condition of fiber modes and cause inter-mode crosstalk [33]. Therefore, the novel designs to reduce the crosstalk of OAM modes in optical fiber and the signal processing algorithm to compensate the overall crosstalk at the receiving end attract extensive attention.

In 2009, Ramachandran et al. first demonstrated a kind of ring-core fiber (RCF) in which the first-order vector modes can be transmitted with outstanding stability [34]. Later, a fiber with ring-core structure was used to transmit OAM modes, achieving terabit-scale SDM [14]. To further increase the stability of OAM modes, a kind of air-hole ring-core fiber (AH-RCF) was proposed and tested [35]. It shows good ability to conserve OAM modes even in the presence of strong bend perturbations. Using this kind of fiber, a 13.4 km OAM state transmission was demonstrated [36]. At the same time, a kind of ring-core photonic crystal fiber (RC-PCF) was designed for OAM mode transmission with ultra-low confinement loss and wide bandwidth [37]. In addition, Wong et al. found that helically twisted PCF can preserve the chirality of OAM modes [38]. These works provide good references for the long-distance transmission of OAM modes.

Our group also attaches great importance to the study of OAM-related optical fibers and fiber devices. A kind of microstructure RCF employing negative curvature cladding structures was proposed and fabricated [39,40]. Under experimental test, it showed low transmission loss of the first-order OAM modes with the value of 0.095 dB/m. In addition, all-fiber OAM generators based on asymmetric long-period fiber gratings (LPFGs) were fabricated. Experiments demonstrated that the generation efficiencies from the fundamental mode to second- and third-order OAM modes were 99.7% [24] and 99.8% [25], respectively. Furthermore, we are currently doing the simulation and fabrication of low crosstalk muli-ring-core fibers (MRCFs) for dense SDM.

This paper introduces the fiber-guided OAM modes from the principle of fiber mode theory and highlight the advances in design, fabrication, and application of OAM fibers including conventional solid optical fibers and microstructure optical fibers. The crosstalk of OAM modes under fiber deformations is discussed using coupled-mode theory [33] and coupled-power theory [41]. Additionally, we also review the progress of all-fiber OAM generation techniques. The technical challenges and application prospects of OAM fibers are discussed at the end.

#### **2. OAM Modes in Regular Solid Optical Fibers**

Optical fiber is a kind of circularly symmetric waveguide; thus, the electric and magnetic fields of eigenmodes can be expressed in the form of separating variables as

$$\mathbf{E}(r,\phi,z) = \left[\mathfrak{f}e\_{l}(r)\cos(v\phi+\phi\_{0}) - \mathfrak{f}e\_{\phi}(r)\sin(v\phi+\phi\_{0}) + 2\varepsilon\_{2}(r)\cos(v\phi+\phi\_{0})\right] \exp(i\beta z),\tag{1a}$$

$$\mathbf{H}(r,\phi,z) = \left[\hbar h\_{\mathbf{r}}(r)\sin(\mathbf{r}\phi + \phi\_0) + \hat{\phi}\hbar\_{\Phi}(r)\cos(\mathbf{r}\phi + \phi\_0) + 2\hbar\_{\mathbf{z}}(r)\sin(\mathbf{r}\phi + \phi\_0)\right] \exp(i\mathbf{j}\xi z),\tag{1b}$$

where *r*ˆ, *φ*ˆ, and *z*ˆ are unit vectors in the radial, angular, and longitudinal directions of an optical fiber. *β* is the propagation constant. Shown by the vector mode category in Figure 1, the fiber eigenmodes can be classified into HE*l*,*v* , EH*l*,*v* , TE0,*v*, and TM0,*v* modes [42], where *l* and *v* (= 1,2,3· · · · · · ) represent azimuthal order and radial order of modes, respectively. Commonly, the constant phase *φ*0 in Equation (1) is chosen as 0 or *π*/2 to represent even or

odd polarization state. The superposition of even and odd states of each HE and EH mode with a ±*π*/2 phase difference can form OAM modes as [43]

$$\text{OAM}^{\pm}\_{\pm(l-1),\nu} = \text{HE}^{\text{e}}\_{l,\nu} \pm i \text{HE}^{\text{o}}\_{l,\nu'} \tag{2a}$$

$$\text{OAM}^{\mp}\_{\pm(l+1),\nu} = \text{EH}^{\text{e}}\_{l,\nu} \pm i \text{EH}^{\text{o}}\_{l,\nu'} \tag{2b}$$

where "e" and "o" represent even and odd polarization states and the superscripts "+" and "−" correspond to left- and right-handed circular polarization, respectively. The elements *l* − 1 and *l* + 1 are the absolute values of OAM topological charge. When *l* = 1, the HE modes can only form a circularly polarized state without carrying OAM. In addition, because TE0,*v* and TM0,*v* modes are intrinsically non-degenerate [43], their relative phase difference will vary periodically with propagation; consequently, they can not form stable OAM modes. Therefore, the synthetic modes constructed by TE0,*v* and TM0,*v* are excluded from the category of OAM modes in Figure 1. When a fiber is in the weakly guiding condition, the effective index difference (∆*n*eff ) between the near-degenerate modes are too small to be distinguished. In this case, mode coupling can easily happen, and the superposition of near-degenerate vector modes can form linearly polarized (LP) states, which is shown by the category in the left side of Figure 1. Mathematically, the LP modes are the solutions of scalar Helmholtz equations under the weakly guiding approximation. Since the polarization effects at the refractive index step are ignored, all the polarization states in the same LP mode group have an identical effective index (*n*eff ).

**Figure 1.** The schematic diagram of mode classification categories in optical fiber.

#### *2.1. OAM Modes in Circular-Core Fibers*

The refractive index profile of a conventional step-index circular-core fiber (SI-CCF) is shown in Figure 2a. The fiber guiding condition is determined by the values of core refractive index (*n*co) and core radius (*r*co). Vector modes in the SI-CCF can be obtained by solving Helmholtz equations with the tangential continuous boundary conditions. Using Equation (2), the OAM modes having a helical wave-front phase can be formed by the superposition of vector modes. As an example, Figure 1 shows the wave-front phase and circularly polarized chirality of OAM± ±1,1 , OAM± ±2,1 and OAM∓ ±2,1 ; these modes are formed by HE e/o 2,1 , HE e/o 3,1 , and EH e/o 1,1 , respectively. The variation of *n*eff for vector modes versus fiber core radius is shown in Figure 2b. We can see that radial higher-order modes (HOMs) such as HE1,2, TE0,2, and TM0,2 will by accompanied by the azimuthal HOMs. These undesired radial HOMs will increase the complexity of mode coupling and decrease the stability of OAM modes in transmission.

**Figure 2.** (**a**) The refractive index profile of SI-CCF. (**b**) The variation of *n*eff versus *r*co when (*n*co − *n*cl )/*n*co = 0.6% at the wavelength of 1550 nm.

In addition, near-degenerate vector modes such as TE0,1, HE2,1, and TM0,1 have almost the same *n*eff . The ∆*n*eff around 1 × 10 −5 is too small to avoid the accidental phase matching between the near-degenerate modes. Referring to the experiment of polarization maintaining fibers, the ∆*n*eff should be greater than 1 × 10 −4 to maintain a polarization state of the HE1,1 mode in length scales exceeding 100 m [43]. Thus, in practice, the fiber index profile deformation and fiber bending can easily cause mode coupling between the near-degenerate vector modes or OAM modes. The superposition of near-degenerate vector modes can form LP modes. As shown in Figure 3, because of strong mode coupling, the intensity patterns of LP modes can be observed at the fiber output end, even though the inputs are true vector modes.

**Figure 3.** Intensity patterns of the first higher-order mode group in a SI-CCF. Arrows show the polarization of the modal electric field. The left column shows the input exact vector modes, while the right column shows the resultant modes at the output end. Specific linear combinations of mode pairs in the left column, resulting in the variety of LP1,1 modes, are shown by colored lines.

Graded-index circular-core fibers (GI-CCFs) were also studied for OAM mode transmission [44–46]. Because the gradient of the graded-index profile is much slower than the step-index profile, the OAM modes have a higher mode purity in GI-CCFs. In [44], the authors presented a specially designed GI-CCF that can support OAM modes having a purity higher than 99.9%. This kind of design can effectively decrease the intrinsic crosstalk between OAM modes. The possibility of OAM mode transmission in commercially available graded-index multimode fiber was discussed by Chen [45]. Recently, all-fiber OAM (de)multiplexing devices based on graded-index multimode fiber were demonstrated with high excitation purity of over 90% [46].

Although GI-CCF shows better potential for OAM mode transmission than SI-CCF, no experiment demonstrates the long-distance transmission of OAM modes in circularcore fibers so far. OAM modes may easily transform into LP modes under the external disturbance in practice. Such instability is the main barrier for long-distance OAM modes propagation in CCFs. Therefore, new types of optical fiber are required to enhance the OAM mode stability.

#### *2.2. OAM Modes in Ring-Core Fibers*

The azimuthal higher-order vector modes or OAM modes in circularly symmetrical optical fiber have a donut-shaped intensity pattern. One may be inspired to think that the waveguide index profile mimicking the donut shape may provide a more stable environment for the transmission of OAM modes. The pioneering works on the stable transmission of vector modes were done by Ramachandran et al., who adopted a first-order perturbation analysis to provide physical insight into the degeneracy of vector modes. Taking the first-order vector modes as an example, the propagation constant of each mode can be expressed by adding a vector correction to the scalar propagation constant *β*e, that is [34]

$$
\beta\_{\rm TE01} = \tilde{\beta}, \quad \beta\_{\rm TM01} = \tilde{\beta} - \Im(\delta\_1 + \delta\_2), \quad \beta\_{\rm HE21} = \tilde{\beta} + (\delta\_2 - \delta\_1), \tag{3}
$$

where

$$\delta\_1 = \frac{\Delta n\_{\text{max}}}{2a^2 n\_{\text{co}} \beta} \int\_0^\infty r E(r) \frac{\partial E(r)}{\partial r} \frac{\partial (\Delta n(r) / \Delta n\_{\text{max}})}{\partial r} dr \tag{4a}$$

$$\delta\_2 = \frac{\Delta n\_{\text{max}}}{2a^2 n\_{\text{co}} \beta} \int\_0^\infty E^2(r) \frac{\partial (\Delta n(r) / \Delta n\_{\text{max}})}{\partial r} dr \,\tag{4b}$$

where *r* is the radial coordinate, *E*(*r*) is the electric field for the scalar mode, *a* is the size of the fiber core, ∆*n*(*r*) is fiber refractive index profile relative to the cladding index, and ∆*n*max is the highest refractive index difference. The expressions of *δ*1 and *δ*2 indicate that, when the electric field has a high changing rate and large amplitude in the region of refractive index discontinuities, the polarization orientation of modes will cause a large additional propagation constant. Since a ring core has inner and outer discontinuous boundaries of refractive index, the ∆*n*eff between the near-degenerate vector modes can be effectively enlarged. Figure 4a shows the index profile of a fabricated novel RCF and the simulated intensity distribution of the first higher-order mode group (HOMG). Although the fiber has a high refractive index core at the center, it does not damage the guidance of the first HOM in the ring core. Most of the mode energy is guided in the ring core, which is the case expected to help with mode stability. The *n*eff of TE0,1, HE2,1, and TM0,1 measured by recording grating resonance wavelength are shown in Figure 4b. We can see that the *n*eff for each pair of modes is separated well. The minimum ∆*n*eff between TM0,1 and the other modes is no less than 1.8 × 10−4 ; it is much higher than the value in conventional CCFs, which is of the order of 10−5 . The stability of the first-order vector modes in this RCF was measured. Under the perturbations of multiple twists and bends with bending radius down to 1 cm, the mode purity can remain 99.8% after transmitting through the 20 m long fiber.

Later, the stable transmission and manipulation of the first-order OAM modes were achieved in RCF [47]. Theoretically, using the same design philosophy, more stable OAM modes can be accommodated into a RCF by increasing the core size and refractive index contrast. However, the radial HOMs may access fiber accompanying the azimuthal HOMs. To eliminate the mode coupling caused by undesired radial HOMs, an optimized design can be applied to RCF to suppress radial HOMs without damaging azimuthal HOMs [48]. Since a radial HOM has a multi-layer ring intensity pattern, narrowing down the ring core thickness can effectively suppress the existence of radial HOMs. Figure 5a shows the refractive index profile of a RCF; the ring core thickness is determined by *r*1 and *r*2. The cutoff curves of OAM mode groups are shown in Figure 5b. Actually, the cutoff condition of

a mode group OAM*l*,*v* consists of cutoff curves of a set of near-degenerate modes OAM± ±*l*,*v* and OAM∓ ±*l*,*v* ; however, they are too close to be clearly distinguished when the relative index difference between the core and cladding is small ((*n*co − *n*cl )/*n*co < 2%). Thus, only one cutoff curve is displayed for each OAM mode group. These cutoff conditions define boundaries of parameter regions where a specific number of modes is supported in the fiber. The curve of OAM0,2 forms a design boundary for eliminating all the radial HOMs. In the region above this cutoff curve (unshaded region), the radial order of all modes is one. In the gray shaded region below the cutoff curve, the modes with *v* > 1 become guided in the fiber. Therefore, by tuning the values of *r*2 and *r*1/*r*2, a fiber can support a targeted number of OAM*l*,1 without introducing radial HOMs.

**Figure 4.** (**a**) Measured index profile of the fabricated fiber and simulated intensity distribution of the LP11 mode. (**b**) Measured *n*eff of TE0,1 , HE2,1 , and TM0,1 of the fiber shown in (**a**). Reprinted with permission from Ref. [34] © The Optical Society.

**Figure 5.** (**a**) The refractive index profile of RCF and (**b**) the cutoff conditions of different order OAM mode groups when (*n*co − *n*cl )/*n*co = 0.6% at the wavelength of 1550 nm.

The stable propagation of multiple azimuthal higher-order OAM modes in a RCF was first demonstrated in 2013 [49]. The authors designed and fabricated a RCF with a central air-hole which maximizes the refractive index gradient at the inner boundary of the ring core. This large refractive index gradient coincides with modal field gradient yields large ∆*n*eff of OAM modes. The best propagation stability was measured on the eighth-order OAM mode, which had ∼20 dB mode purity at the output end of a 1 km long fiber. After that, many research works were done to optimize the design and fabrication of AH-RCFs [35,50–52]. An interesting phenomenon found in AH-RCFs was that the OAM longevity increases with mode order [35], which is contrary to the common intuition that fundamental states of systems are the most stable. To test modal stability, circularly polarized OAM modes were generated by a SLM and a quarter-wave plate and then were coupled into a 10 m long AH-RCF. The output OAM modes purities were measured under the condition of arbitrary fiber bending and twisting, as schematically illustrated

in Figure 6a. The air-hole radius of the under test AH-RCF is 3 µm, and the outer radius of the ring core is 8.25 µm shown in Figure 6b. The central air-hole forces the modes to distribute more intensity at the outer boundary of the ring core, and modes will "feel" more of the large refractive index difference between the ring core and cladding. Hence, the *n*eff of modes with OAM and SAM aligned (having the same handedness) will be separated from those with OAM and SAM anti-aligned (Figure 6c). Furthermore, the separation level of *n*eff increases with the OAM order. A ∆*n*eff around 10 −4 is considered reasonable for OAM mode propagation [43]; in this fiber, the OAM modes with |*L*| = 5, 6 and 7 can meet the requirement, as indicated in Figure 6d. In addition, the perturbation has weaker effects on modes with the increase of mode order [35]. The perturbation of fiber bends and geometrical deformations can be expanded into Fourier series, where the azimuthal factor of each element can be expressed as *fp*(*r*) exp(*ipφ*). Since the coupling coefficient is determined by the inner product between the first OAM mode *E*1(*r*) exp(*iL*1*φ*), the perturbation factor and the second OAM mode *E*1(*r*) exp(*iL*2*φ*), mode coupling mainly happens when *p* = *L*1 − *L*2. For the near-degenerate OAM modes with |*L*|, because of the requirement of spin alignment, the perturbation can cause mode coupling when *p* = 2|*L*|. However, the *fp*(*r*) becomes increasingly negligible for large *p*. Therefore, the higher-order OMA modes gain better stability.

**Figure 6.** (**a**) Schematic picture of OAM mode transmission through a randomly bended and twisted AH-RCF conserving their original states. Each state has a total angular momentum *J* that consists of orbital component *L* and spin part *s*. (**b**) Cross section image (top) and measured refractive index profile (bottom) for the AH-RCF. (**c**) Example of *n*eff separation between near-degenerate OAM modes. (**d**) The splitting of *n*eff for near-degenerate OAM modes among different OAM mode groups and the modal interference images when |*L*| = 5, 6 and 7. Reprinted with permission from Ref. [35] © The Optical Society.

The inter-mode crosstalks of the AH-RCF were measured on a multitude of fiber lengths [36]. Figure 7a illustrates the crosstalks versus fiber length for the |*L*| = 5 and |*L*| = 7 OAM modes. The insets show the modal images at the output end of different fiber lengths. The mode intensities gradually evolve from a donut shape into periodical bright spots in the azimuthal direction with the increase of integrated crosstalk. Longer fiber length leads to heavier crosstalk; the growth rate is 1.5 % per kilometer for the |*L*| = 7 modes and 15 % per kilometer for the |*L*| = 5 modes. The |*L*| = 7 modes maintain better mode purities which have crosstalks lower than −10 dB when the fiber length is up to 5.5 km. The measured results are coincident with the prediction of a tanh(*hz*) (where *h* is the mode coupling coefficient) dependent crosstalk based on coupled-power theory [53]. Similarly, in Figure 6b, the crosstalks of |*L*| = 6 modes measured in a 1 km long fiber fit the crosstalk curve with an *h* value of ∼ 4.1 × 10 −2 km−1 .

**Figure 7.** (**a**) Measured crosstalks for |*L*| = 5 and |*L*| = 7 modes in an AH-RCF (stars), and theoretical crosstalks which have the minimum mean-squared error from the measured data (dashed lines). (**b**) Measured and theoretical crosstalks for |*L*| = 6 modes. Insets are modal images at the output of fiber with different length. Reprinted with permission from Ref. [36] © The Optical Society.

Another novel inverse-parabolic graded-index fiber (IP-GIF) was proposed in 2014 [54]. Similar to the RCFs, the IP-GIF has a refractive index valley at the center of cross section; therefore, the fiber modes can feel large refractive gradient in the fiber. Numerical simulation showed that the specially designed IP-GIF enables a large ∆*n*eff over 2.1 × 10 −4 between the vector modes TE0,1, HE1,1 and TM0,1. Then, the authors experimentally demonstrated the stable transmission of OAM± ±1,1 modes in the 1.1 km long IP-GIF.

The IP-GIFs and RCFs, especially the one assisted by a central air-hole, show good ability to separate the *n*eff of near-degenerate OAM modes. It greatly enhances the stability of OAM modes which is hardly achieved in conventional CCFs. These designs are beneficial to increase fiber transmission capacity via adding spatial modes without resorting to digital signal processing or adaptive optics.

#### **3. Microstructure Optical Fibers Supporting OAM Modes**

Photonic crystal fibers (PCFs) which have periodic transverse air-hole arrangements were first proposed and fabricated in 1996 [55]. With the improvement of manufacturing technique, the accuracy of microstructure can reach 10 nm on the scale of 1 µm [56]. The design of PCFs is more flexible than conventional solid optical fibers, which allows effective control of key modal properties such as dispersion, birefringence, nonlinearity and cutoff conditions. Inspired by the success of PCFs, other kinds of microstructure fibers such as photonic band gap fibers (FBGFs) [57], Kagome fibers [58,59], and negative-curvature fibers [60,61] were proposed to guide optical modes in an air core. These novel guiding mechanisms of microstructure fibers can be adopted to design special OAM fibers.

#### *3.1. Photonic Crystal Fibers Supporting OAM Modes*

The common structure of a PCF is to arrange a regular hexagonal lattice of air-holes symmetrically around a central pure silica core. The equivalent refractive index of the cladding is lower than that of the core due to the air-holes. Thus, optical modes can be well confined in the core. When a PCF is periodically twisted in the longitudinal direction, the cladding light will be guided in the helical lattice of air-holes [62]. The spiral path regulated by air-holes (Figure 8a) will transfer a fraction of the axial momentum into angular momentum, causing the formation of cladding orbital angular momentum states. Furthermore, the wavelengths of the cladding OAM modes vary linearly with the twist rate. However, in this fiber, no stable OAM modes can be transmitted in the core region.

Later, a phenomenon of OAM preservation was detected in a helically twisted PCF with a three-bladed Y-shaped core [38]. The schematic pattern and scanning electron micrograph of fiber cross section are shown in Figure 8b,c, respectively. Based on a helicoidal extension of Bloch wave theory, the authors developed a scalar analysis for the modes in the twisted PCF. Figure 8d shows the calculated axial energy flow of a ring mode when the fiber twist rate is 1.26 rad/mm. In the same fiber, the calculated axial Poynting vector of the fundamental mode is shown in Figure 8e. An experiment showed that the chirality of the +1 order OAM mode was preserved rather than coupled into the −1 order OAM mode, and vice versa in the twisted PCF, which is in agreement with the theoretical prediction.

**Figure 8.** (**a**) The perspective of a helical PCF in a twisting period (blues rods are the air-holes passing through the silica fiber). Adapted with permission from Ref. [62] © AAAS. (**b**) Schematic structure of a Y-shaped core PCF. (**c**) Scanning electron micrograph of the Y-shaped core PCF. (**d**) Calculated axial Poynting vector of a ring mode at the wavelength of 800 nm in the fiber with a twist rate of 1.26 rad/mm. (**e**) Calculated axial Poynting vector of the fundamental mode which carries no OAM modes. Adapted with permission from Ref. [38] © The Optical Society.

In addition to the twisted PCFs, a family of RC-PCFs was proposed for OAM mode transmission [37,63–66]. As shown in Figure 9, the RC-PCFs all adopt circularly symmetric air-hole arrangement, so that the even and odd polarization states of a vector mode will keep well degenerate hence making sure the stability of the combined OAM modes. In [64], three layers of air-holes were used to form the cladding region (Figure 9a). The authors proved that the ∆*n*eff between the even and odd polarization states are around 10 −9 when the number of air elements in each layer is no less than 24. In this case, the fiber structurecaused circular asymmetry is negligible compared with the deformations that arise from external perturbation such as bending and twisting. In the same year, RC-PCFs supporting 14 [37] and 26 [65] OAM modes were designed and analyzed, successively (Figure 9b,c). In these works, identical air-holes were used to construct four circular cladding layers. This design contributes to keeping a similar swelling force in each air-hole, which helps to maintain ideal cross section geometry during the fabrication. The high air-hole filling ratio of the cladding region leads to an equivalent refractive index much lower than that of pure silica; therefore, both inner and outer boundaries of the ring core have very large index gradients. The electric field of modes with a relatively lower-order concentrate and vary rapidly in the vicinity of the inner refractive index step, thus the ∆*n*eff of near-degenerate modes such as (HE2,1, TE0,1, TM0,1) is very large. However, with the increase of mode order, the ∆*n*eff first reduces, and then rebounds to grow after a certain order. Because the modal fields move to the outer region of the ring core with the increase of mode order, the great index step at the outer core boundary becomes dominant to cause large ∆*n*eff between near-degenerate modes in the HOMGs.

In 2019, a PCF with cladding consists of a circular layer of air-hole and three hexagonal layers of air-hole were designed and fabricated [66]. Figure 9d shows the designed fiber cross section. The circular arrangement of the first layer air-holes can help to minimize the ∆*n*eff between the even and odd polarization states of the same vector mode. Furthermore, three outer layers of air-holes contribute to increasing the light confinement in the ring core. The hexagonal arrangement of the outer air-holes makes the fiber easier to be

manufactured by the stack-and-draw method. The scanning electron micrograph of the fabricated RC-PCF is shown in Figure 9e. The ring core maintains a good circular symmetry. However, the fabricated fiber has a relatively large transmission loss of 50 dB/km, and only the transmission of the first- and second-order OAM modes was demonstrated in the experiment.

**Figure 9.** The cross sections of PCFs supporting OAM modes. (**a**) Heterogeneous air-hole cladding design. Adapted with permission from Ref. [64] © IEEE. RC-PCFs with cladding constructed by identical air-holes supporting (**b**) 14 and (**c**) 26 OAM modes. Adapted with permission from Ref. [37] © IEEE and Ref. [65] © Elsevier. (**d**) A design of RC-PCF with cladding that consists of a circular layer of air-holes and three hexagonal layers of air-holes. (**e**) The fabricated RC-PCF based on the design in (**d**). Adapted with permission from Ref. [66] © The Optical Society.

#### *3.2. Negative-Curvature Ring-Core Fibers for OAM Modes Transmission*

In 2011, Wang et al. proved that a hypocycloid-shaped core structure can enhance light confinement in Kagome fibers [59]. Furthermore, by simplified the Kagome cladding into a layer of silica tubes, a kind of negative-curvature fiber was proposed to guide light in a quasi-air environment with ultra-wide bandwidth, low scattering loss, and weak nonlinearity [60,61,67–69]. These designs provide valuable references to improve the cladding structure of RC-PCFs.

Enlightened by the negative-curvature fibers, our group studied a new kind of negativecurvature ring-core fiber (NC-RCF). The loss comparison between the multi-layered hollowcore fiber and negative-curvature hollow-core fiber is shown in Figure 10a [39]. When the number of air–silica interfaces is the same (four layers), the confinement loss of negativecurvature hollow-core fiber is much lower. Therefore, to increase the number of supported OAM modes with achieving ultra-low loss for the HOMs, an NC-RCF (Figure 10c) was proposed that originate from RC-PCF (Figure 10b). The thickness of the cladding tubes should meet the antiresonant condition for the central wavelength of the transmission band that [69–71]

$$t = \frac{\lambda (M - 0.5)}{2\sqrt{n\_{\text{g}}^2 - 1}} \,\text{}\,\text{}\,\tag{5}$$

where *λ* is the free space wavelength, *n*g is the refractive index of silica glass, and *M* represents the order of antiresonance (= 1, 2, 3 . . .).

**Figure 10.** (**a**) Loss comparison between multi-layered annular fiber and negative-curvature fiber. (**b**) RC-PCF. (**c**) Improved NC-RCF. (**d**) Dependence of the confinement loss on the wavelength for (**e**) silica cladding design, (**f**) negative curvature tube cladding with tube thickness of *t* = 2 µm, (**g**) negative curvature tube cladding with tube thickness of *t* = 2.5 µm, and (**h**) air cladding model. Adapted with permission from Ref. [39] © The Optical Society.

Another interesting property of NC-RCF is that the modes formed in the thin membranes of the cladding tubes can couple with certain core modes. Then, the undesired core modes can be effectively filtered out by the coupling caused the large loss. In Figure 10e–h, red regions represent silica and white regions represent air. The simulated confinement losses of the HE3,1 mode in the four designs are shown in Figure 10d. It is easy to understand that the silica cladding and air cladding designs have the highest and lowest confinement loss, respectively. The green and black lines in Figure 10d show the confinement losses of NC-RCF when *t* = 2.5 µm and *t* = 2 µm, respectively. When *t* is 2 µm, the confinement ability of negative curvature tubes is very close to that of air cladding. However, when *t* increases to 2.5 µm, antiresonant and inhibited coupling conditions are not satisfied. Hence, a lot of energy was coupled into the tube membrane modes and caused a very high loss, which can be understood by observing the electric field distribution of HE3,1 mode shown on the right side of Figure 10d.

The detailed structure of NC-RCF and the descriptions of the parameters are illustrated by Figure 11a,b. We took *r* = 7 µm, *ρ* = 0.65, *t* = 1.2 µm, and *d*/Λ = 0.8 as an example to discuss the fiber properties. To prevent the HE- and EH-synthesis OAM modes coupling into LP modes during the propagation, ∆*n*eff should be larger than 10 −4 , which is the minimum modal birefringence of the polarization-maintaining fibers. Figure 11c shows the simulated spectra of ∆*n*eff between the adjacent vector eigenmodes in an OAM mode group. As the TE0,1 and TM0,1 are filtered out, only HE2,1 mode remains in OAM Mode Group #1. Therefore, the case of Group #1 is excluded in Figure 11c. It can be seen that the requirement of >1 × 10 −4 is met in the wavelength band from 1.4 to 1.8 µm for OAM Mode Groups #2, #3, #4, #5, #6, and #8. In this fiber, the ∆*n*eff within a mode group decreases with the order of mode group (except for the Mode Group #8). Such variation trend of ∆*n*eff is opposite to that in the AH-RCF illustrated in Section 2.2. It is because the equivalent refractive index of cladding of our designed fiber is close to 1, thus the large core/cladding refractive index difference makes the lower-order mode group distribute approaching the inner air–silica boundary, and hence generates a higher ∆*n*eff between vector eigenmodes in the mode group. This property will be good for the use of lower-order OAM modes. Figure 11d shows the minimum ∆*n*eff between the adjacent OAM mode groups over the wavelength from 1.2 to 2.0 µm. The eigenmodes used for calculating the minimum intermode-group ∆*n*eff are described in Figure 11(b2). The values increase with the order of

OAM mode group and wavelength. When the wavelength is larger than 1.2 µm, all the inter-mode-group ∆*n*eff exceed 1 × 10 −3 . Consequently, in theory, the designed NC-RCF can stably support 26 OAM states in the telecommunication wavelength band, including OAM Mode Groups #1 (two states), #2 (four states), #3 (four states), #4 (four states), #5 (four states), #6 (four states), and #8 (four states).

**Figure 11.** (**a**) The cross section of the proposed NC-RCF. (**b1**) The description of each structure parameter. (**b2**) The modes used to calculate the minimum ∆*n*eff in (**d**). (**c**) The ∆*n*eff between the adjacent vector eigenmodes in each OAM mode group when *r* = 7 µm, *ρ* = 0.65, *t* = 1.2 µm, and *d*/Λ = 0.8. (**d**) The minimum ∆*n*eff between OAM mode groups. Adapted with permission from Ref. [39] © The Optical Society.

The fabrication procedure of the NC-RCF is illustrated in Figure 12a. It includes four steps: (1) stack the center preform; (2) draw the center cane; (3) stack the fiber preform; and (4) draw the fiber. In the second and fourth steps, the cane and tubes should be sealed at one end to keep positive air pressure in the hollow holes for maintaining the fiber structure during drawing. Furthermore, in Step 4, a vacuum pump should be used to help reserve the hollow structure during the fiber drawing. Figure 12e,f shows the fibers fabricated under the vacuum level of ∼60 kPa at the temperature around 1880 ◦C and ∼40 kPa at the temperature around 1895 ◦C, respectively. We can see that the intervals between the cladding tubes and the central casing tube are filled in by silica; therefore, the fabricated fibers have much higher confinement loss than that predicted in simulation. The minimum transmission losses of OAM1,1 in Fibers (e) and (f) are 0.3 and 0.095 dB/m, respectively. The higher loss in Fiber (e) is caused by the relatively thicker silica layer surrounding the core, which leads to the leakage of energy from the ring core to the cladding silica through mode coupling.

**Figure 12.** Fabrication of the proposed NC-RCF. (**a**) Schematic figure of the fabrication process using stack-and-draw method. (**b**) Stacked preform of the central cane. (**c**) Cross section of the intermedia cane. (**d**) Stacked preform of the NC-RCF. Scanning electron microscopic photo of the fabricated NC-RCF with (**e**) the thickness of ring core around 2.45 µm, Adapted with permission from Ref. [39] © The Optical Society, and (**f**) the thickness of ring core around 2.65 µm. Adapted with permission from Ref. [40] © IEEE.

Finally, we compare the different kinds of fibers supporting OAM mode in Table 1. The recorded number of OAM mode transmissions is 36, achieved by a AH-RCF in 2014. In addition, the maximum transmission length of OAM modes is 13.4 km using a loop of AH-RCF in 2016. Although, theoretically, RC-PCFs and NC-PCFs provide a larger ∆*n*eff between the near-degenerate modes, which help to enhance the mode stability, no experiment demonstrates the long-distance stable transmission of OAM modes in these two kinds of fibers. The main reason is that RC-PCFs and NC-PCFs may suffer relatively large geometrical deformation during the fabrication. Then, the refractive index fluctuation will cause severe mode coupling. We believe that the performance of RC-PCFs and NC-PCFs will be improved with the progress of the fabrication technique.

**Table 1.** Comparison among the reported fibers supporting OAM modes.

#### **4. Crosstalk Analysis of OAM Modes in Optical Fibers**

Multi-core fiber (MCF) is regarded as a good solution for increasing data transmission capacity and saving fiber consumption for the next generation of fiber-optic networks. When the mode coupling between fiber cores is sufficiently small, each core can be regarded as an independent signal channel. Many studies have been done for reducing the inter-core crosstalk, including the studies on heterogeneous and trench-assisted MCFs [72–76]. By optimizing the core structure and arrangement, ultra-low inter-core crosstalk and high core density can be achieved simultaneously [75].

Those experiences in designing MCFs provide good references for the design of MRCFs. Figure 13a shows the refractive index profile of a step-index trench-assisted MRCF. The design region of the size of ring core for supporting a certain number of OAM mode groups can be tuned by changing the central refractive index (*n*ce) and the core refractive index (*n*co). Figure 13b illustrates the design region for supporting mode groups from OAM0,1 to OAM4,1 and cutting off all the radial HOMs in the C+L band (from 1.53 µm to 1.625 µm). The boundaries of each design region are formed by the cutoff curves of OAM0,2 and OAM5,1 at the wavelength of 1.53 µm and OAM4,1 at the wavelength of 1.625 µm, respectively. When the relative index difference of the core (∆co = (*n*co − *n*cl )/*n*co) increases, the available values of the outer radius of ring core (*r*2) decreases. The smaller core size is beneficial to the compact design of MRCFs. In addition, the negative relative index difference of the central area (∆ce = (*n*ce − *n*cl )/*n*ce) can force the *n*eff of OAM0,2 fall to the cladding refractive index more quickly. As shown in Figure 13b, the cutoff curve of OAM0,2 occurs at a smaller value of *r*1/*r*2 when ∆ce decreases, which indicates that the available width of the ring core can be extended. In the experiment, a relatively thicker ring core can help to increase the mode stimulation efficiency at the fiber input end and improve modal stability during transmission.

**Figure 13.** (**a**) The schematic refractive index profile of a trench-assisted MRCF. (**b**) The design regions for supporting 5 OAM mode groups in C+L band.

The inter-core coupling is an essential issue in MRCF. When the core-to-core interval is sufficiently large, the adjacent cores can be regarded as refractive index perturbations of each other. Based on coupled-mode theory, the inter-core mode coupling coefficient of mode *m* in core *i* caused by mode *n* in core *j* can be calculated by an overlap integral as [33]

$$\mathbf{c}\_{\text{mn}}^{(i)(j)} = \frac{\omega \epsilon\_0 \iint\_{A\infty} (\mathbf{n}^{(j)2} - \mathbf{n}\_{\text{cl}}^2) \mathbf{e}\_{\text{m}}^{(j)} \cdot \mathbf{e}\_{\text{n}}^{(j)\*} \, \text{d}A}{\sqrt{\iint\_{A\infty} \hat{z} \cdot (\mathbf{e}\_{\text{m}}^{(i)} \times \mathbf{h}\_{\text{m}}^{(j)\*} + \mathbf{e}\_{\text{m}}^{(i)\*} \times \mathbf{h}\_{\text{m}}^{(j)}) \text{d}A \iint\_{A\infty} \hat{z} \cdot (\mathbf{e}\_{\text{n}}^{(j)} \times \mathbf{h}\_{\text{n}}^{(j)\*} + \mathbf{e}\_{\text{n}}^{(j)\*} \times \mathbf{h}\_{\text{n}}^{(j)}) \text{d}A}},\tag{6}$$

where *n* (*j*) is the refractive index profile of core *j*, *n*cl is the cladding refractive index, and **e** and **h** are the electric and magnetic components of modes. However, in the case that the cores are not identical, the conventional mode coupling coefficient are not symmetric. Therefore, when only considering the forward propagation modes, the total power may not be conserved. To satisfy the law of power conservation, redefined mode coupling

coefficients *C* (*i*)(*j*) *mn* and *C* (*j*)(*i*) *nm* were used; their definitions are the average of the usual mode coupling coefficients [77]

$$\mathbb{C}^{(i)(j)}\_{mn} = \frac{\mathfrak{c}^{(i)(j)}\_{mn} + \mathfrak{c}^{(j)(i)}\_{nm}}{2} = \mathfrak{C}^{(j)(i)}\_{nm}.\tag{7}$$

Because real optical fiber is not perfect, there is a random phase difference between fiber modes, which is a function of propagation length *δ f*(*z*). To consider the effect of the random phase difference, the fiber is divided into finite segments in the longitudinal direction. Furthermore, uniform random phase offsets are applied to all cores in each segment. The overall mode coupling can be obtained by calculating coupled-mode equations in each segment in order.

On the other hand, the inter-core crosstalk can be calculated by coupled-power theory as well [41,77]. Based on the assumption that the random phase fluctuation along the fiber is a stationary random process, it has an autocorrelation function: *R*(∆*z*) = h*δ f*(*z* + ∆*z*)*δ f* ∗ (*z*)i. It has been demonstrated that the calculation based on exponential autocorrelation can obtain crosstalk that agrees well with the experiment results in a single-mode MCF. Furthermore, the power coupling coefficient can be expressed by the Fourier transformation of exponential autocorrelation function as [77]

$$h\_{mn}^{(i)(j)}(z) = \frac{(\mathbb{C}\_{mn}^{(i)(j)})^2 L\_{\mathbb{C}}}{1 + [\Delta \beta\_{mn}^{(i)(j)}(z)L\_{\mathbb{C}}]^2} \, \tag{8}$$

where ∆*β* (*i*)(*j*) *mn* (*z*) represents local propagation constant difference of mode *m* in core *i* and mode *n* in core *j* and *L*c is the correlation length of *R*(∆*z*). To take into account the effects of fiber bending and twisting without using numerical solutions, a closed-form average power coupling coefficient was proposed for estimating the inter-core crosstalk in MCFs [78]. It represents the average power coupling coefficient over a twist pitch as

$$h\_{mn}^{(i)(j)} = \frac{\gamma}{2\pi} \int\_0^{2\pi/\gamma} h\_{mn}^{(i)(j)}(z) \,\mathrm{d}z,\tag{9}$$

where *γ* is the rate of fiber twisting. By solving power coupling equations, the crosstalk between the two modes can be expressed as

$$\text{NT}\_{mn}^{(i)(j)} = 10 \log\_{10} [\tanh(\bar{h}\_{mn}^{(i)(j)} z)]. \tag{10}$$

The crosstalk values calculated by using the average power coupling coefficient were demonstrated to agree well with experimental results [78]. It provides a fast and accurate method for estimating inter-core crosstalk in bent and twisted MCFs.

Using the average power coupling coefficient, we can analyze the variation trend of inter-core crosstalk in MRCFs. Figure 14a illustrates the inter-core crosstalk between two identical fiber cores. Each fiber core can support up to the fourth-order OAM mode group. We can find that the relatively heavy crosstalk exists between the modes in the same mode group, which is because modes having similar ∆*n*eff easily meet the phase-matching condition. In addition, the crosstalk increases with the mode order. As the higher-order OAM mode has a larger fraction of energy distribution in the cladding region, it can "feel" more of refractive index perturbation from the adjacent cores. Therefore, the overlapping integration is greater between the higher-order OAM modes. The maximum crosstalk exist between OAM+ +4,1 and OAM+ −4,1 with the value of −47 dB/m. The variation of the maximum inter-core crosstalk versus the size and position of the trench in the 5-modegroup MRCF is shown in Figure 14b. It is shown that increasing the width of the trench can rapidly reduce the crosstalk, and the gap between core and trench also helps to decrease the crosstalk.

**Figure 14.** Inter-core crosstalk analysis at the wavelength of 1550 nm when the core-to-core interval is 40 µm. (**a**) The crosstalk between modes in two ring cores with the parameters r1 = 4.95 µm, r2 = 9 µm, r3 = 11 µm, r4 = 16 µm, ∆co = 1%, ∆ce = 0%, and ∆tr = −0.7%. (**b**) The variation of crosstalk between OAM+ +4,1 and OAM+ −4,1 in two identical adjacent cores versus the core-trench gap (*r*3 − *r*2) and the trench width (*r*4 − *r*3).