*2.9. Statistical Analyses*

All numerical data were analyzed using Tukey's honestly significant difference (HSD) for parametric analysis and the Mann–Whitney *U* test for non-parametric analyses with R software version 4.0.2. (https://www.r-project.org/ accessed on 23 July 2020). Differences were considered significant when *p*-values were smaller than 0.05.


*2.1. Methodology*

During the experiment, hybrid composite panels reinforced with aramid and carbon fabrics were used. Aramid twill weave fabric used in the experiment with weight of 300 g/m2 was made from Twaron 2200 fibers. The second material used as a reinforcement was carbon twill weave fabric with a weight of 200 g/m2. It was made from Pyrofil TR30 S fibers. Mechanical properties of used fibers [47,48] are shown in Table 1.

**Table 1.** Mechanical properties of used reinforcing fibers.

Hybrid panels consisted of 14 layers of reinforcing fabrics. They were arranged in the following combination: four layers of aramid fabric, one layer of carbon fabric, four layers of aramid fabric, one layer of carbon fabric, and four layers of aramid fabric. Epoxy resin LG285 was used as a matrix. The dedicated by manufacturer HG285 curing agent was mixed with resin with a 100:40 weight ratio. The epoxy matrix's properties declared by the manufacturer [49] are shown in Table 2.

**Table 2.** Properties of epoxy resin LG285 with HG285 curing agent.

The composite panels were manufactured by the hand-laminating method with vacuum support (−68 kPa of vacuum pressure). On the basis of the literature [6,16], four striker geometries were developed. Geometries of those strikers are shown in Figure A1. The adopted geometries allow the strikers to maintain a constant mass and to simulate the impact of various splinters. The required repeatability of the strikers' impact kinetic energy can be achieved because of this. This repeatability is important because the researchers' main goal is to determine the destruction images depending on the geometry of the strikers. They could be compared only when the impact energy was the same. Steel strikers with a mass of 49 g are shown in Figure 2.

**Figure 2.** Strikers used in experiment: A—ogival striker, B—blunt striker, C—hemispherical striker, D—conical striker.

The tests were realized using a hybrid electromagnetic launcher with a pneumatic support [26,50]. Initial air pressure value in an air tank and air valves were set up using a control panel. The test stand is shown in Figure 3.

**Figure 3.** Test stand used in experiment.

The striker velocity was measured using an optical gate connected to the oscilloscope. When the striker breaks the optical beam, the voltage spike could be observed on the oscilloscope. The next voltage spike is observed when the striker ends, breaking the optical beam. The experiments were carried out with 23.5 J of impact kinetic energy. This energy refers to sub ballistic velocities of the impact—such as collisions with fast moving elements [16]. The samples were glued to the 10 mm polyethylene base plate and hit three times by each striker. The polyethylene plate was exchanged with each composite sample. There is no deformation and destruction in the polyethylene plates after impact.


**Contents**

## **About the Editors**

**Maria Antonietta Ferrara** (Dr.) received her M.S. degree in electronic engineering from the University of Naples Federico II, Italy, in 2003 and her PhD degree in electronic engineering from the University "Mediterranea" of Reggio Calabria, Italy, in 2008. Since 2008, she has been a postdoctoral fellow at the Institute for Microelectronics and Microsystems, Naples, where she carried out research on "advanced optoelectronic devices and integrated sources based on nonlinear Raman scattering" and "noncontact optical characterization based on interferometric techniques". In 2012, she became a researcher at the Institute for Microelectronics and Microsystems, and since 2019, she has been affiliated with the Institute of Applied Sciences and Intelligent Systems of the National Research Council of Italy. She is the person in charge for the Imaging and Holography Laboratory. Her research interests are in the fields of digital holography, volume holographic optical elements, nonlinear optics, coherent Raman spectroscopy, and microscopy. She is the author of more than 90 peer-reviewed scientific papers published in indexed journals and 5 book chapters and is the holder of several patents.

**Principia Dardano** (Dr.) received her PhD in fundamental and applied physics in 2008. Since December 2004, she has been working at the Italian National Council of Research (CNR), first at the Institute for Microelectronics and Microsystems (IMM—CNR) and now at the Institute of Applied Sciences and Intelligent Systems (ISASI), in Naples, where she is the head of the photolithographic laboratory. She is responsible for the design, fabrication, and characterization of theranostic and photonic devices and for the imaging of micro/nano biosystems with AFM, EFM, and SEM.

### *Editorial* **Special Issue on Recent Advances and Future Trends in Nanophotonics**

**Maria Antonietta Ferrara \* and Principia Dardano \***

National Research Council (CNR), Institute of Applied Sciences and Intelligent Systems, Via Pietro Castellino 111, 80131 Naples, Italy

**\*** Correspondence<EMAIL_ADDRESS>(M.A.F<EMAIL_ADDRESS>(P.D.)

#### **1. Introduction**

Nanophotonics is an emerging multidisciplinary frontier of science and engineering. Its high potential in contributing to the development of many areas of technology makes nanophotonics a focus of interest for many researchers from different fields.

In light of the above, the present Special Issue of *Applied Sciences* on "Recent Advances and Future Trends in Nanophotonics" gives an overview of the latest developments in nanophotonics and its roles in different application domains. Eleven papers were submitted to this Special Issue, and nine papers were accepted (i.e., an 82% acceptance rate). The presented papers explore innovative trends of nanophotonic science and technology that enable technological breakthroughs in high-impact areas and cover several topics, mainly regarding diffraction elements, detection, imaging, spectroscopy, optical communications and computing.

#### **2. Diffraction Elements**

Diffractive Optical Elements (DOEs) have been expanding for many years and are a stimulant technology that allow for the redirection of redirect light using diffraction rather than refraction. When a photonic structure is realized via holography, we refer to this as Holographic Optical Elements (HOEs), i.e., elements recorded by a specific interference pattern in a photosensitive optical material. Volume HOEs show very high diffraction efficiency in single-order diffraction; however, angular wavelength selectivity and high dispersion still are considerable challenges. In order to achieve a highly efficient HOE with low dispersion, Keshri and co-workers [1] explored a fabrication method regarding a DOE with two separate target wavelengths. Two independently sensitized layers of photopolymer were stacked and used at two different wavelengths in sequential holographic recording. The diffraction peaks of the recorded photonic structures were investigated and compared with those of the designed structures, and then, they were theoretically predicted. The device, illuminated with an expanded divergent beam at both target wavelengths and with white light, showed a strong diffracted beam. This approach could be optimized and useful for potential applications in the fields of illumination, solar collection and displays.

A diffraction grating structure was numerically simulated in the paper authored by Li and coworkers [2], where a guided-mode resonance system with a double-bar dielectric grating was exploited to achieve a multispectral electromagnetically induced transparency (EIT) effect. In this case, the resonance wavelengths of the two EIT peaks could be modified by changing the corresponding structural parameters and could be exploited for dual mode sensor, dual channel slow light, etc. When optimized, two EIT peaks showed ultra-high Q factors of 35,104 and 24,423. Moreover, the dual-mode refractive index sensor based on this system reached figures of merit (FOMs) of 571.88 and 587.42.

**Citation:** Ferrara, M.A.; Dardano, P. Special Issue on Recent Advances and Future Trends in Nanophotonics. *Appl. Sci.* **2022**, *12*, 663. https:// doi.org/10.3390/app12020663

Received: 5 January 2022 Accepted: 6 January 2022 Published: 11 January 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/).

#### **3. Detection, Imaging and Spectroscopy**

The manipulation of light and light-matter interactions have been largely investigated for applications in the fields of detection, imaging and spectroscopy.

In the paper published by Demirer and co-workers [3], the Magneto-Optic Kerr Effect in the guided mode of an unbalanced Mach Zehnder Interferometer (MZI) was designed and simulated to optically detect the magnetization direction of ultra-thin (~12 nm) metal cladding. In fact, the device was an unbalanced MZI based on InP membrane on silicon. The MZI arms were made up of a polarization converter from one side and ferromagnetic thinfilm cladding and a delay line from the other side. The device read a nanoscale memory bit (400 nm × 50 nm × 12 nm) with a signal-to-noise ratio ∼10 dB and tolerated performance reductions that arose during the fabrication. While this hybrid device based on ultra-thin metal membrane on silicon was demonstrated to be an all-optical magnetic memory reading tool, hybrid devices with an ultra-thin conductive layer jointed with semiconductors were presented by Crisci and co-authors [4], such as all-optical Schottky photodetectors that operated at room temperature. In particular, in [4], two Schottky photodetectors based on graphene/n-silicon (Si) and graphene/n-germanium (Ge) Schottky barriers were theoretically investigated and operated at 1550 nm and at 2000 nm, respectively. The responsivity/noise equivalent power (NEP) ratio was analysed, and a strong addiction on the Schottky barrier height of the junction was demonstrated. The authors derived a closed analytical formula for use in maximizing the responsivity/NEP ratio and theoretically discussed how the Schottky barrier height is related to the reverse bias applied to the junction. Moreover, they found that at 1550 nm, the optimized graphene/n-silicon (Si) Schottky PDs with a reverse bias of 0.66 V showed a responsivity and NEP of 133 mA/W and 500 fW/√Hz, respectively. Finally, at 2000 nm, the optimized graphene/n-germanium (Ge) Schottky PDs showed a responsivity and NEP of 233 mA/W and 31 pW/√Hz, respectively.

The detection and imaging of optical signals were investigated and reviewed in this Special Issue. In particular, two innovative imaging techniques were addressed: Polarization-sensitive Digital Holographic Imaging (PDHI) [5] and Stimulated Raman Scattering (SRS) microscopy [6].

Coppola and Ferrara [5] reported a review on the state of the art of PDHI techniques, focusing on the theoretical principles and important applications. The paper not only provided an exhaustive review of applications in several fields, from biology to microelectronics and micro-photonics, but also emphasized the merits of this new technique based on the interference between different polarized optical beams. PSDHI, in fact, simultaneously allows the three-dimensional reconstruction and the quantitative evaluation of the polarization properties of a sample with a resolution on the micrometric scale, a good acquisition speed and the absence of labels/markers.

Sirleto and co-workers [6] measured the spectral resolution of SRS, i.e., the ability to distinguish closely lying resonances, and their paper focused on the spectral splitting of protein and lipid bands in the C-H region, which is of great interest in the field of biochemistry. In particular, the paper addressed the interplay among pump and Stokes bandwidth and the degree of chirp-matching. Moreover, the spectral resolution of femtosecond SRS microscopy was experimentally investigated.

Spectroscopy systems were further reviewed by Althobaiti and Al-Naib [7] in the field of instrumentation working at near-infrared NIR frequencies. The authors discussed NIR spectroscopy systems from the instrumentation point of view with regard to state-of-the-art approaches and the associated challenges. In particular, the authors provided a summary of the recent development of continuous-wave, time-domain and frequency-domain NIR systems and presented an outlook into the future of the design and development of functional near-infrared spectroscopy systems for various medical applications.

#### **4. Optical Communications and Computing**

Nonlinear waveguides can play a key role in optical communication applications, in particular in the 2 μm wavelength band, where interest in mitigating the 'capacity

crunch' is growing. In this context, Tu and co-authors [8] fabricated and characterized silicon-rich nitride (SRN) ridge waveguides with different widths and rib heights. The structures showed a loss of ~2 dB/cm, and the SRN nonlinear refractive index was shown to be ~1.13 × 10−18 m2/W around the wavelength 1950 nm. By optimizing parameters to improve nonlinear performances for the 2 μm band, a maximal nonlinear figure of merit (i.e., the ratio of nonlinearity to loss) of 0.0804 W−1 or a super-broad FWM bandwidth of 518 nm were found. These results pave the way for high-performance on-chip nonlinear waveguides for use in optical communications in the 2 μm wavelength band.

Finally, the review proposed by Cheng and co-authors [9] underlined how the recent development of nanofabrication technologies for the generation, processing and detection of optical signals have paved the way in the field of new analog optical computing. Particular attention was given to metamaterials or metasurfaces, which offer unprecedented opportunities to arbitrarily manipulate light waves at the subwavelength scale, leading to an acceleration of the progress of wave-based spatial analog computing. Furthermore, the authors discussed challenges and future opportunities in high-efficiency signal processing by exploiting quantum behaviors.

**Funding:** This research received no external funding.

**Acknowledgments:** This issue would not be possible without the valuable contributions of all the authors and peer reviewers. We would like to take this opportunity to record our sincere gratefulness to the editorial team of *Applied Sciences*.

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

#### **References**

## *Article* **Development and Testing of a Dual-Wavelength Sensitive Photopolymer Layer for Applications in Stacking of HOE Lenses**

**Sanjay Keshri 1, Brian Rogers 1,2, Kevin Murphy 1, Kevin Reynolds 1,2, Izabela Naydenova 1,2 and Suzanne Martin 1,\***

**Abstract:** Diffractive optical elements (DOEs) have been in development for many years and are an exciting technology with the capability to re-direct light, using diffraction rather than refraction. Holographic Optical Elements (HOEs) are a subset of diffractive optical elements for which the photonic structure is created holographically, i.e., by recording a specific interference pattern in a suitable, photosensitive optical material. Volume HOEs are of particular interest for some applications because of their very high diffraction efficiency and single diffracted order; however, high dispersion and angular wavelength selectivity still present significant challenges. This paper explores a method for producing a compound DOE useful for situations where elements designed for two separate target wavelengths can be advantageously combined to achieve a highly efficient HOE with reduced dispersion. A photopolymer material consisting of two independently sensitized laminated layers is prepared and used in sequential holographic recording at two different wavelengths. The photonic structures recorded are investigated through examination of their diffraction peaks and comparison with the structure predicted by modeling. Finally, the device is illuminated with an expanded diverging beam at both target wavelengths and with white light, and a strong diffracted beam is observed.

**Keywords:** diffractive elements; holography; photopolymer; holographic optical elements; volume gratings; compound optical elements; stacked gratings

#### **1. Introduction**

Diffractive Optical Elements (DOEs) are photonics structures that focus and redirect light, using diffraction rather than refraction. 'Volume' or 'thick' Diffractive Optical Elements utilize Bragg diffraction and can very efficiently transfer energy from the incident beam into a diffracted beam [1]. DOEs have the potential to replace optical components in a range of applications and have the advantages of being low cost, lightweight and in most cases, much thinner than their refractive counterparts.

The DOE element can be thought of as a set of localized gratings, each potentially having a different slant, orientation and spatial frequency (set by the patterning process) so that the direction and divergence of the diffracted output beam can be chosen as desired [2]. As a result, DOEs can replace standard optical components (e.g., lenses and mirrors) in some applications. Bragg diffraction, however, introduces wavelength and angular selectivity, which can be particularly restrictive if the element/grating is thick [1].

**Citation:** Keshri, S.; Rogers, B.; Murphy, K.; Reynolds, K.; Naydenova, I.; Martin, S. Development and Testing of a Dual-Wavelength Sensitive Photopolymer Layer for Applications in Stacking of HOE Lenses. *Appl. Sci.* **2021**, *11*, 5564. https://doi.org/ 10.3390/app11125564

Academic Editors: Maria Antonietta Ferrara and Principia Dardano

Received: 7 May 2021 Accepted: 10 June 2021 Published: 16 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/).

Photopolymer materials are typically prepared as thin, photosensitive films that polymerize when they absorb light, and can record patterns with very high spatial resolution. They can, therefore, be used to form volume DOEs in a low-intensity, single-exposure step, which is readily customized. Since the patterning step involves holographic recording, they are also often referred to as Holographic Optical Elements or HOEs. Currently, Diffractive Optical Elements are not routinely used with broadband sources. Some practical applications utilizing surface gratings in the management of light are reported in the literature; for example, LED light is re-directed through a 30◦ angle by a binary diffractive lens [3] and broadband multicolor imaging is demonstrated by using multi-level surface holograms [4].

Fabrication of surface gratings is challenging, however, since it requires multiple manufacturing steps—lithography and etching—and the surface of the photonic structures is difficult to protect. Volume photopolymer HOEs [5] offer a significant improvement since they can be patterned (with low intensity exposure) [6] through the volume of the materials, can be laminated [7,8] into a stack, and importantly, they can achieve near 100% re-direction of the incident light into a single output beam [9,10]. This optical patterning can potentially replace the etching and stamping process and facilitate customization and small batches. The main features of surface and volume HOEs are compared, at a glance, in Table 1.

**Table 1.** Comparing surface and volume diffractive optics elements.

Research into beam patterning and shaping with HOEs has continued to advance [11–13], but solutions for broad wavelength sources are needed to increase the application range. Many sources, such as white light LEDs, output a set of wavelength ranges rather than a continuous broad band of wavelengths (as for solar radiation, for example). This paper explores a method for producing a compound element useful for situations where elements that are designed for two separate target wavelengths can be advantageously combined to achieve a highly efficient HOE. The authors previously reported stacked gratings for operation in broader wavelength range by calculating the correct angle of diffraction for each target wavelength and recording at a single wavelength in green in two separate layers that are then stacked after recording [14]. This approach is somewhat limited by the complex modeling and recording arrangements needed for elements such as lenses, as they contain a wide range of spatial frequencies and slants that need to be matched to the different wavelength, as well as the difficulty of assembling the stack after recording without introducing damage and/or shifts in the slant angle.

This paper presents a method of stacking that utilizes selectively pre-sensitized layers stacked together so that dual wavelength recording can take place independently in the two stacked layers and explores the process as a means to combine lens elements. The recordings are independent of one another because the dye sensitizer in each layer is matched to one of the recording laser wavelengths. It is demonstrated here for two layers but has the potential to be developed for additional layers (e.g., red, green, blue).

The stacking/multiplexing approach to correcting for chromatic dispersion is conceptually simple and relies on fabrication and combination of devices tailored to specific wavelength ranges. It has been exploited to multiplex or de-multiplex in diffusers [15] and lenses [16], in stacking meta-surfaces [17], and more recently, to wavelength multiplexing in lens arrays for full color imaging [18] with each layer fabricated of different materials and with different design parameters to optimize it for a specific frequency band. However, these devices are fabricated through lithographic processes or holographically recorded

into a single layer of a pan-chromatic material through multiplexing. Here, we utilize the limited wavelength sensitivity range in the pre-stacked photopolymer layers to exploit the simple full field exposure step to holographically record a compound element at two separate wavelengths, without the need for complex modeling and fabrication techniques.

In the literature, a variation of dye concentration in multilayer photopolymer was used to improve the uniformity in volume gratings [19]. Three dyes were combined in a single layer of photopolymer material for full color display holography [20]. In this work, two photopolymer layers sensitive to two different wavelengths were laminated together and a lens was recorded in each layer by their designed wavelength in sequential manner.

Firstly, a blue-sensitive photopolymer formulation, previously developed for the recording of reflection holograms (at high spatial frequency), was optimized for the low spatial frequency and high layer thickness needed in the proposed off-axis collimating lens transmission-format element. Next, the design considerations for stacked lenses were discussed for the application of off-axis, high-diffraction efficiency collimating HOE elements. Finally, the dual-wavelength sensitive multi-layer structure was prepared by stacking two photopolymer layers and used to successfully record collimating elements for blue and green wavelengths. The local diffraction characteristics of the recorded microstructure were tested and limitations discussed.

#### *1.1. Concept*

Figure 1 shows the basic concept for stacking by recording in a dual-wavelength sensitive multi-layer structure. Holographic recording of lenses is achieved through the interference of two beams that mimic the input and output beams of the lens device. The interference pattern created is recorded in the volume of the photosensitive material as a periodic structure in which the spatial frequency and slant at a particular point are defined by the two wave-vectors normal to the interfering wave fronts at that point. This structure diffracts incoming light of the same wavelength and incident angle to re-create the original beams. In this case, a dual layer is prepared in which each layer responds optimally to a limited range of wavelengths in blue or green. This means that two sequential recordings in blue and green create a stack of two lenses, without the need for repositioning or adjustment of the layer. Due to the high selectivity of volume diffractive lenses, each lens reconstructs only the appropriate wavelength range and the output beams are identical for both wavelengths. This approach has potential in reducing chromatic dispersion in HOE lenses.

**Figure 1.** Schematic diagram for (**a**) recording two lens patterns, using two different wavelengths in a dual-sensitive layer to create stacked lenses. (**b**) Replay process showing that the stacked lenses reproduce the same collimated beam for both input wavelengths.

#### *1.2. Theory*

The characteristics of a beam diffracted from a grating depend not only on its orientation and spatial frequency (photonic structure), but also on the angles and wavelength of the incident beam.

The classical grating equation for transmission [21] can be expressed by Equation (1):

$$k\_i \sin \theta\_0 + k\_d \sin \theta\_{+1} = \frac{2\pi m}{n\Lambda} \tag{1}$$

where, *ki* = 2*π λ*0 and *kd* = 2*π λ*1 are the propagation vector's modulus for the incident and diffracted beams, m = order of diffraction (*m* = 1 for volume HOE), *θ*0 = the angle of incidence in air, *θ*+1 = angle of diffraction in air, *n* = refractive index of the medium, and Λ = period of the refractive index modulation (spatial period).

Volume HOEs work on the principle of Bragg's law [22], and at the Bragg condition, the angle of incidence equals the angle of diffraction (*θ*+1 = −*θ*0 *and λ*0 = *λ*1). Equation (2) defines the wavelength at the Bragg condition.

$$
\lambda = 2n\Lambda \sin\left(\frac{\theta\_{+1} - \theta\_0}{2}\right) \tag{2}
$$

In applications where the re-direction of illumination is important, volume diffractive optics are preferred because of their potential for high diffraction efficiency, meaning that a large proportion of the incident light is diffracted into a single diffraction order in a direction defined by 2. The diffraction efficiency achieved also depends on the material characteristics of the grating, such as refractive index modulation and thickness. The Kogelnik Coupled Wave Theory (KCWT) [1] is a well-established tool for modeling the efficiency of such elements and can predict how the efficiency of Volume HOEs depends on many parameters, such as the illuminating beam incidence angle, replay wavelength, index modulation and grating thickness.

KCWT shows that at Bragg incidence, the diffraction efficiency for the volume grating can be modeled using the following:

$$\eta = \text{Sim}^2\left(\frac{\pi m\_1 d}{\lambda \text{Cos}\theta\_B}\right) \tag{3}$$

where *θB* = Bragg angle inside the layer, d is the thickness of the grating and n1 the refractive index modulation.

The Q factor is used to check whether the grating will function as a volume Bragg grating [23].

$$Q = \frac{2\pi\lambda d}{n\Lambda^2} \tag{4}$$

With the parameters defined as above, a Q factor of > 10 is considered to be in the 'volume' regime, and therefore is expected to have a single diffraction order and behavior that can be predicted using KCWT.

#### **2. Materials and Methods**

The dual-sensitive recording approach was explored here through a combination of modeling, experimental work, materials optimization, fabrication and testing. Firstly, the approximate diffractive lens device requirements (spectral range, thickness, spatial frequency range, refractive index modulation) for each layer were determined though modeling. Then, a previously developed blue-sensitive photopolymer formulation was optimized for the spatial frequency range and thickness needed here. This was achieved through a study of gratings holographically recorded in dry layers coated on glass slides and optically patterned using different exposure energies and inter-beam angles in the overlapping beams. Finally, holographic lens elements were recorded, using both blue (488 nm) and green (514 nm) wavelengths separately and together (in the dual-sensitive

layer stack), and the resulting HOEs were studied through the analysis of theory diffraction behavior, allowing the recorded microstructure to be studied.

#### *2.1. Materials Preparation*

Two separate photopolymer formulations were prepared. First, a polyvinyl alcohol stock solution was prepared as described elsewhere [14] (10 g dissolved into 100 mL). Two separate dye solutions were then prepared, both with 0.11 g of powdered dye (erythrosine B or acryflavin) in 100 mL of deionized water. Next, to make the green-sensitive formulation, the electron donor (triethanolamine (2 mL)) and the monomers (0.6 g acrylamide and 0.2 g methylene bisacrylamide) were added to 17.5 mL of the PVA solution and stirred for one hour. Finally, 4 mL of the erythrosine B solution was added. For the blue-sensitive formulation, triethanolamine (2 mL) and the monomers (0.8 g acrylamide and 0.2 g methylene bisacrylamide) were added to 17.5 mL of the PVA solution and stirred for one hour. Finally, 3 mL of the acryflavin solution was added.

Layers were prepared by using a micropipette to deposit a controlled amount of solution onto either glass microscope slides or high optical quality plastic of the same dimensions on a level surface. After allowing them to dry in a darkroom for 1–2 days, the dual-sensitive layer photopolymer was prepared by laminating the two layers together. For this step, it was important that one of the layers was prepared on a flexible substrate, in this case, Makrolfol of 0.375 mm thickness (flexible glass is also very suitable [14]). This allows for lamination of the two photopolymer surfaces together in a stable layer with no air gaps or bubbles.

#### *2.2. Optical Patterning: Holographic Recording Setup*

An off-axis holographic lens can be recorded by using the setup shown in Figure 2. Two collimated beams are arranged such that they overlap on the photopolymer layer, then a suitable lens is inserted into one of the beams such that it focuses the beam before it reaches the photopolymer as shown. This produces a diverging beam to interfere with the collimated reference beam and a HOE lens is recorded. The numerical aperture of the lens determines the divergence of the beam and the range of the angles of incidence at the photopolymer. This kind of recording was demonstrated previously with both cylindrical and spherical lenses [24]. However, in this instance, a cylindrical lens was used so that the beam only diverged in one axis (horizontal). This simplified the modeling and experimental testing since the grating characteristics varied in only one axis. In the blue sensitive photopolymer formulation optimization work, simple gratings were recorded, and the set-up was identical except for the fact that both beams were collimated, as the cylindrical lens was not present. For some characterization work, a 532 nm and a 473 nm laser were used but for recording in the dual-sensitized layer, an argon ion was used so that both the 514 nm and 488 nm laser lines could be used in the same optical setup.

When recording lenses, the range of angles of incidence which the diverging beam produces determines the inter-beam angles for the interference pattern, and consequently, the spatial frequency and slant at each location of the photopolymer. The cone of rays will be the same (assuming negligible aberrations) for recordings at both green and blue recording wavelengths. However, since the spatial frequency also depends on the wavelength of the incident light, this will lead to a different interference pattern for each recording.

**Figure 2.** Experimental set-up for both the recording of a cylindrical holographic lens in green and probing using a He–Ne laser. NDF—neutral density filter; HWP—half-wave plate; SF–spatial filter; CL—collimator lens; A—variable aperture; BS—beam splitter.

#### *2.3. Testing the Recorded Lenses*

The recorded lenses were tested at three locations on the lens: at the center of the lens, 3 mm to the left of the center and 3 mm to the right of the center. Figure 3 illustrates how the Bragg positions for the two gratings vary because of the different wavelengths, and how they differ at the three probing positions. Testing involved illumination with an unexpanded He–Ne beam of about 1 mm in diameter and rotation of the sample through a wide angular range while monitoring the intensity changes in the transmitted or first-order beam. Since in all cases studied here, higher order beams are negligible, it was often more useful to monitor the zero order or transmitted beam so that the angular position, diffraction efficiency and FWHM information was available in a single scan. Except where otherwise stated, all tests were carried out in a computer-controlled system with a Newport rotation stage and photodetector and a λ = 633 nm He–Ne probe laser. Figure 3 shows an illustration of the different conditions for Bragg matching at three positions on the lens. The wave vectors for the input and output beams at both wavelengths are shown along with the grating vector for each position on the lens for each of the two wavelengths.

**Figure 3.** (**a**) Ewald Sphere illustration of the different conditions for Bragg matching at three positions on the lens and (**b**) Bragg matching condition for each position, −3 mm, center and +3 mm shown separately for clarity.

#### *2.4. Modeling the Recorded Microstructure—Calculation of Slant and Spatial Frequency*

In order to fabricate a HOE lens which collimates an off-axis diverging beam, a photonic structure is needed that will be on-Bragg everywhere for rays diverging from the off axis focal point and will re-direct them (through diffraction) into a collimated beam with a defined angle with respect to the HOE plane. At each location, the desired input beam angle can be defined, using the position of the focal point relative to that location. The desired output beam angle is known and is the same everywhere on the element (for the collimated output). Once the angles of the two beams, θ1 and θ2, are known, the slant angle (θs=(θ2 + θ1)/2) and Bragg angle (θB = (θ2 − θ1)/2) at that location are determined from geometry, and the spatial frequency needed to obtain such a Bragg angle at the design wavelength is calculated from Equation (2) above. Figure 4 depicts this procedure for a single point on the DOE lens. Once the slant angle and spatial frequency are known, one can calculate, for every point on the lens, the interference pattern required to fabricate the desired structure at a given wavelength. If the recording wavelength is close to the design wavelength, however, this process becomes extremely convenient, as θ1 and θ2 become the recording angles. Then the process involves using the desired input beam as one of the recording beams, made to interfere in the plane of the polymer material with the other recording beam, which has the characteristics of the desired output beam. The dual-sensitive polymer layer enables this convenient process to be exploited at two separate wavelengths in one device.

**Figure 4.** Simple geometrical model used to calculate the required grating slant and spatial frequency for the grating needed to re-direct Beam 1 into Beam 2 (at each specific location on the DOE lens). For simplicity, refraction at the medium boundaries are not shown here, but are taken into account in the calculations. θB is the Bragg angle; θ1 is the incident angle of the input Beam 1 and θ2 is the angle of the output Beam 2. θS denotes the slant angle of the fringes.

#### **3. Results**

#### *3.1. Modeling and Design of the Diffractive Optical Elements*

The stack envisaged consists of two off-axis lens elements, one designed for a blue target wavelength, and one designed for a green, both having a focal point of 5 cm from the plane of the photopolymer element.

The design considerations are as follows:

Target wavelengths [25] 514 nm and 488 nm were chosen to mimic typical green and blue peaks in a white LED spectrum for which close laser wavelengths were available for holographic recording. The design is based on high efficiency with the assumptions that higher diffracted orders are negligible, the grating is uniform though the depth of the polymer layer, and the polymer faithfully records the interference pattern (zero dimensional changes during recording).

As discussed above, each element consists of a range of grating spatial frequencies, which will change with the design wavelength, the off-axis angle and the aperture and focal length of the lens. In turn, the set of spatial frequencies recorded in the lens influences all of the above design considerations. On-axis elements are not suitable here because of well-understood issues around the limits of volume diffraction [2] that arise where the diffraction angle is very small (near zero spatial frequency). Off-axis elements are, therefore, used to focus light for these applications, so the first design step was to choose an offset angle, or central spatial frequency, that would avoid this. For transmission elements, high spatial frequencies (large offset angles) are less challenging to record so the limits of the low spatial frequency range are explored here.

#### 3.1.1. Green Lens Design

First, the range of spatial frequencies expected to be recorded across the lens for a recording wavelength of 514 nm was calculated for a number of different off-axis angles (different central spatial frequencies). The calculated range of spatial frequencies for lenses having central spatial frequencies of 300, 400, 455 and 500 L/mm are shown in Figure 5a. Figure 5b shows the calculated Q values for the lowest spatial frequency occurring in each lens from Figure 5a for different thicknesses. It was decided to choose the lens with the lowest off-axis angle (and spatial frequency range) that would ensure volume Bragg grating behavior (Q > 10) across the whole lens aperture for 150 microns in thickness. This ensures that higher orders are negligible. A minimum of 140–150 micron-thick gratings were shown to be needed to avoid crosstalk in previous work [14]; thickness above 150 microns can be more challenging to prepare without compromising layer optical quality. The lens chosen was, therefore, Lens 3, with 150 μm layer thickness and 455 L/mm central spatial frequency.

**Figure 5.** (**a**) Local grating spatial frequency across the diameter of four lenses with different central spatial frequencies, design wavelength 514 nm, focal length 5 cm, lens diameter 14 mm and (**b**) the Q value for the lowest spatial frequency in each lens for a range of grating thicknesses. The green horizontal line indicates where Q = 10, i.e., the minimum Q value to ensure a single diffracted order.

#### 3.1.2. Blue Lens Design

The next step was to design a second lens, which would produce the same output angle across the whole lens aperture for a 488 nm design wavelength with the same range of input and output angles. The Q value for the lowest spatial frequency was 11.4, for a 150 micron layer, ensuring volume diffraction here, too. Since 150 micron layers were used, the capability of achieving sufficient grating strength was assured for the green sensitive formulation (100% can, in fact, be achieved in much thinner layers [26]). Figure 6 shows the range of spatial frequencies across this lens, which has the same angular offset and focal length as Lens 3 but is designed for operation at λ = 488 nm.

**Figure 6.** The range of spatial frequencies across the lens designed for 488 nm, diameter = 14 mm with the same angular offset and focal length as Lens 3 but for operation at λ = 488 nm.

The refractive index modulation needed to maximize the diffraction efficiency was controlled through exposure during recording, as detailed in the experimental section. Some characterization was needed in order to achieve this for the blue-sensitive formulation, which had not been as widely studied as the standard green (eythrosine B) formulation.

#### *3.2. Optimization of the Acriflavine Based Photopolymer Layer*

In the literature, acriflavine sensitized photopolymer material was used in the development of a panchromatic photopolymer for holographic recording applications [20]. Previously, the characterization of a 60 μm thick transmission grating with high spatial frequencies was reported [27]. In this work, a similar composition is optimized for the range of spatial frequencies polymer layer thickness needed in this application. Figure 7a shows the composition of the layers and Figure 7b, the absorption spectrum for this acriflavine-sensitized photopolymer.

**Figure 7.** (**a**) The relative mass of the components of the acriflavine-sensitized dry photopolymer layer. (**b**) The absorption spectrum of the acriflavine-sensitized photopolymer (composition as outlined in (**a**)). (**c**) On-Bragg diffraction efficiency growth curve of 60 μm thick gratings recorded at various spatial frequencies, with recording intensity = 5 mW/cm2 (**d**) with recording intensity = 1.5 mW/cm2.

3.2.1. Optimization for Spatial Frequency

Figure 7 shows the optimization of the recording conditions for a range of spatial frequencies in Figure 7c,d. This study was carried out using 60 micron layers so that detailed information about the grating growth dynamics could readily be obtained using on-Bragg dynamic measurements of the diffraction efficiency during recording. High angular selectivity makes on-Bragg illumination during recording more challenging for 150 micron layers.

Using two different recording intensities, and monitoring on Bragg at 633 nm, the recording dynamics were observed for spatial frequencies from 200 to 2000 lines/mm (equivalent to 5 micron to 0.5 micron fringe spacing). It should be noted that the zero-order transmission was monitored and the raw data from the zero-order transmittance were transformed into the first-order efficiency. In the diffraction efficiency curves the growth dynamics are very similar for all spatial frequencies across the range, except for the two extremes of 200 and 2000 lines/mm. At the higher end, the 2000 lines/mm curves are observed to fall slightly below the mid-range curves. At 200 lines/mm, a significantly slower grating growth is observed, although the diffraction efficiency is similar after 200 s for the higher intensity recording. The photopolymer material composition and the absorption spectrum are also shown.

#### 3.2.2. Optimization for 150 Micron Thick Layers

Real-time monitoring of the diffraction efficiency during grating recording is considerably more challenging at 150 microns, so a stepwise recording with multiple samples is sometimes needed to properly examine the grating growth, especially at higher spatial frequencies (due to the high angular selectivity). In this section, a combination of real time recording and multiple Bragg curves is used to study blue-sensitive layers of 150 micron thickness. Firstly, real-time recording was done for 200 L/mm spatial frequency with higher (5 mW/cm2) and lower (1.5 mW/cm2) intensities. The growth curves of first-order efficiencies are shown in Figure 8a.

**Figure 8.** Diffraction efficiency growth for 150 micron thick blue-sensitive layers. (**a**) On-Bragg efficiency growth curve of for gratings recorded with spatial frequency 200 L/mm, (**b**) a series of zero-order Bragg selectivity curves for grating recorded with 500 L/mm, for a range of exposure times, measured at 633 nm. (**c**) On-Bragg diffraction efficiency values obtained from (**b**). The equivalent diffraction efficiency that would be expected at 488 nm is also shown so that the optimal recording time can be identified.

For 500 L/mm, individual gratings were recorded at a constant intensity (5 mW/cm2) but with different exposure times. The recording time for each gratin g was increased from 10 to 40 s with an interval of 5 s. Figure 8b shows the results obtained in the form of zeroorder Bragg selectivity curves, when the individual gratings were probed after recording by a He–Ne laser. Each curve graphs a set of data obtained by rotating the probe beam though a range of angles while monitoring the diffraction efficiency. The curves are arranged in Figure 8b according to the exposure time used to create the grating. They show gratings of increasing strength up to the optimum exposure and then the characteristic indications of overmodulation (growing sidelobes). The minimum value from each zero-order Bragg selectivity was taken to obtain the growth curve, which is shown in Figure 8c, along with theoretical values for the efficiency, which is for the same strength grating at 488 nm (using Equation (3)). Considering the growth of diffraction efficiency for both 200 L/mm and 500 L/mm spatial frequencies, the optimized time to record gratings with 5 mW/cm2 for λ = 488 nm is estimated ≈16–20 s. As seen in Figure 6, the holographic lens to be recorded covers the range of spatial frequencies from 198 L/mm to 790 L/mm.

#### *3.3. Optimization of the Holographic Recording Conditions for the Fabrication of Individual Lenses at Blue and Green Wavelengths*

The next step was to record and test the individual lenses. As lenses consist of many spatial frequencies and slant angles in a single element, it is necessary to determine the optimal recording conditions for each lens, as well as to analyze the overall diffraction behavior to ensure that the expected microstructure is recorded. This makes it possible to (i) confirm experimentally which exposure conditions (from the range identified above) give the best performance across the lens aperture and (ii) to provide performance data of individual lenses as a comparator for the stacked lenses.

#### 3.3.1. Recording and Characterization of Holographic Lens Designed for 488 nm

Individual lenses were recorded at a constant recording intensity with a number of different exposure times. Each lens was then characterized by probing it at three positions across the element through a wide angular range in order to measure the local DE and angular positions of the diffraction peaks (troughs). This allowed for fine tuning of efficiency and uniformity across the lens aperture as well as investigation of the local spatial frequency and slant of the recorded photonic structure. The spatial frequency at each location is indicated by the angle between the two diffraction maxima (minima) in the intensity values of the zero-order wide angular scan, and the slant can be estimated from their offset from 0◦ at each location. For convenience, this is done at a single wavelength (633 nm).

The recording of these individual lenses was done at a constant recording intensity of 3.6 mW/cm2 with 17, 27 and 37 s exposure times, thereby achieving total exposure energies of 61, 97 and 130 mJ/cm2, respectively. After recording, the lenses were probed at three positions across the element (the center of the lens and +/− 3 mm either side). The zero order and first order intensity curves are shown in each case for a range of incident angles in Figure 9. The latter is useful because it is a direct confirmation that the light diffracted from the zero-order curve appears in the first order, validating the assumption that volume gratings/Bragg diffractions as beams other than those of the first-order are of negligible intensity. A number of observations can be made from these results. Firstly, the uniformity of the diffraction efficiency is an important factor in the performance of the collimating device so by looking at the diffraction behavior at three known locations, the recording can be optimized for uniformity as well as the magnitude of the diffraction efficiency. Secondly, the spatial frequency of the grating can be examined by studying the separation of the diffraction peaks/troughs. From Table 2 below, we can see that the separations expected for a 633 nm probe beam for the lens element G1 (designed for 488 nm light) are 13.4◦, 18.0◦ and 22.5◦ respectively. Taking Figure 9a as an example, we observe separations of 12.1◦, 16.8◦ and 22.8◦. These match the expected values to within 1.2◦. The differences are probably due to errors in positioning of the probe beam and an averaging effect caused

by the probe beam spanning a non-zero range of locations/grating periods. There is also some variation between the three samples.

**Figure 9.** Experimental data for (**a**) zero-order transmission and (**b**) first-order diffraction efficiency at three points across the lens fabricated in acriflavine-sensitized photopolymer layer, using exposure 61 mJ/cm2, exposure 97 mJ/cm2 (**c**) and (**d**) exposure 130 mJ/cm2 (**e**) and (**f**).

**Table 2.** The measured diffraction angle (angular separation of +1 and −1 diffraction orders) in comparison to the theoretical diffraction angles for the 4 samples at 633 nm wavelength.

3.3.2. Recording and Characterization of Holographic Lens Designed for 514 nm

The process described in Section 3.3.1 was repeated for a holographic lens, designed to operate at 514 nm, and recorded in an erythrosine-B-sensitized photopolymer layer. This time, the recording wavelength was 514 nm and recording energies of 98 mJ/cm2 and 70 mJ/cm2 were used. From Table 2 below, we can see that the separations expected for a 633 nm probe beam for the lens element G2 (designed for 514 nm light) are 11.9, 16.0 and 20.0. Taking Figure 10a as an example, we observe separations of 10.5◦, 15.0◦ and 20.3◦. These match the expected values to within 1.4◦. However, the match appears to be poorer in Figure 10c.

**Figure 10.** Experimental data for (**a**) the zero-order transmission and (**b**) the first-order diffraction efficiency at three points across the lens fabricated in a 150 μm thick eythrosine-B sensitized photopolymer layer. (Exposure energy = 70 mJ/cm2) and for (**c**) and (**d**) with exposure energy = 98 mJ/cm2.

#### *3.4. Two Lenses in Stacked in Dual-Sensitive Photopolymer Layer*

For the final device, the dual-sensitized layer was prepared as described above. Two lenses were then recorded sequentially using the same optical set-up (described above) but switching an Ar-Ion lasers lasing wavelength from 514 nm and 488 nm between the recording, using the lasers coupling prism. For each exposure, the intensity and duration followed the optimized conditions found in the previous sections. In the object beam, a conventional cylindrical lens was introduced to create a diverging beam in one axis, which interfered with a collimated reference beam. The resulting interference pattern was recorded in each photopolymer layer. Firstly, a laser (λ = 514 nm) records the lens pattern in the erythrosine-B-sensitized photopolymer layer, which is the second layer in the stack. Secondly, the laser at 488 nm records the lens in the acriflavine-sensitized photopolymer material, which is the first layer in the stack. After recording, the stacked lenses were probed at three positions (center, +3 mm and −3 mm), over a wide range of angles using a 633 nm wavelength laser to obtain the zero-order transmission angular selectivity curve. A set of four stacked lenses were recorded with the same optimized recording conditions (from Section 3.3) and their results are shown in Figure 11.

**Figure 11.** Zero-order transmission angular selectivity curves when the stacked lens is probed by a He–Ne laser at three positions. (**a**), (**b**), (**c**) and (**d**) show the results for samples (1), (2), (3) and (4) respectively.

In Table 2, the angular separation of the incident angles at which maximum diffraction occurs for 633 nm light is tabulated for the three positions in all four samples. A theoretical angular separation is also shown, based on the diffraction angle expected for the recorded spatial frequency at that location. Neither lens is designed for 633 nm light, which is why some secondary peaks were observed (not noted in the table). The peak positions are closer to the positions for the lens designed for blue light, except in the case of sample 2, possibly because this is the lens that the incident beam meets first in the stack.

In order to examine the diffraction angles at the target wavelengths, sample 1 was then tested at the design/recording wavelengths. Using a manual rotation stage, the angular position of the diffraction peaks was obtained, and the angular separation or full diffraction angle was calculated. Table 3 shows the measured diffraction angle (angular separation of +1 and −1 diffraction orders) in comparison to the theoretical diffraction angles for both gratings in the stack while probing at the recording/design wavelengths. In most cases (+3 mm G1 is the exception) there is better than 0.5◦ agreement between the measured diffraction angle for the stack with the expected diffraction angle for that wavelength.

**Table 3.** Table showing the measured diffraction angle (angular separation of +1 and −1 diffraction orders) in comparison to the theoretical diffraction angles for both gratings in the stack while probing at the recording/design wavelengths.

> The stack was then illuminated with laser light. The input beam was a horizontally diverging beam produced by the cylindrical lens (the same lens that was used in recording). It was arranged that this be incident on the stack at the appropriate angle and the laser was then switched between wavelengths of 488 nm and 514 nm. In both cases, an intense diffracted beam was clearly observed (to the right in Figure 12). While the transmitted portion of the input beam (seen on the left in each figure) was highly diverging, the diffracted output beam was observed to have much lower divergence and to have a circular cross-section. This demonstrates that the stack functions well for both wavelengths. As shown in Figure 12c, the process was repeated with a white light which was collimated and passed through the same cylindrical lens. Again, the stack produced a strong diffracted beam with a circular cross section (to the right in the image). Of course, some dispersion of the colors in the white light source is also evident, especially for the red and violet colors at the extreme ends of the visible spectrum.

**Figure 12.** Demonstration of the stacked lens producing a collimated beam when illuminated with a cylindrically expanding laser beam at (**a**) 488 nm and (**b**) 514 nm and (**c**) with a white LED passing through a cylindrical lens.

#### **4. Discussion**

The exposure optimization work for blue recording showed the viability of using this blue-sensitized photopolymer for recording low spatial frequency gratings in layers as thick as 150 microns. High diffraction efficiencies were obtained with a range of exposures. This material had not previously been characterized in this range. The recording of the DOE

lenses holographically in individual layers showed the challenges of equalizing efficiency across a DOE that contains a range of spatial frequencies, but 80–90% was achieved for green recording and greater than 90% for the blue recordings. With optimization, this could be improved further. It should be noted that the results indicate that two structures were recorded with the microstructure that matched well to the theoretical modeling. However, because the two gratings were designed to have overlapping input and output beams when they function properly, it is not possible to resolve the two individual sets of grating structures. Even at wavelengths far from the design wavelengths, modeling showed that the peaks for G1 and G2 would be less than 0.5◦ apart. In addition, limitations in repeatable positioning of the probe beam on the lens meant that there were relatively large errors in the actual peak positions as well as some averaging over a range of neighboring locations. This will be improved by using a smaller diameter probe beam and devising a system of fiducial marks to properly locate the recording center.

#### **5. Conclusions**

In this paper, two photopolymer layers sensitive to two different wavelengths were stacked together and lenses were recorded in each layer. Initially, a theoretical design was developed in order to determine the recording conditions needed to achieve an efficient element. An acriflavine-sensitized photopolymer material was characterized so as to find the recording conditions for the expected range of spatial frequencies. Holographic lenses were then recorded in individual layers at blue and green wavelengths (in the appropriately sensitized photopolymer), which demonstrated uniform and high efficiency at the optimized exposure energies. Dual-wavelength sensitive stacks were then assembled and the sequential recording of stacked lenses was carried out. A set of four stacked lenses were recorded and tested by probing by a He–Ne laser at a wide range of angles for three positions across the element. The angular separation of +1 and −1 order maximum diffraction positions were analyzed. It was found that experimental angular separation matched well with theoretical values for the lenses. It was not possible to resolve the separate diffraction peaks from the blue and green lenses, as they were designed to coincide for blue and green wavelengths; even at 633 nm, the angular separation is expected to be < 0.5◦. Initial tests performed with cylindrically diverging beams showed strong diffraction into collimated off-axis beams for blue, green and white light. With some optimization, this approach could be used to develop stacked DOEs that can re-direct and collimate light with multiple wavelength ranges for potential applications in illumination, solar collection and displays.

Future work will involve investigating the dual-wavelength layer stacking approach for lenses with different off-axis angles and numerical apertures as well as a more detailed study of the independent photonic structures recorded by this method by deliberately separating the positions of the diffraction peaks.

**Author Contributions:** S.K. carried out most of the experimental work and developed aspects of the methodology as well as preparing the original draft. He acquired the funding for the work as part of a PhD scholarship. B.R. contributed to the experimental work in the final section. K.M. helped develop the methodology and contributed to draft preparation and data analysis. He is a co-supervisor of this work. K.R. assisted with the modeling and data analysis. I.N. helped develop the concept, methodology and materials. She is a co-supervisor of this work. S.M. helped develop the concept methodology and materials. She is the lead-supervisor of this work. All supervising authors contributed to reviewing and editing. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by TU Dublin Fiosraigh PhD Scholarship fund. This research received no funding external to TU Dublin.

**Acknowledgments:** The authors would like to acknowledge Vincent Toal for his advice and the FOCAS research Institute for facilities and support.

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

#### **References**


2. Simulation works on the PECVD using MCS and MDS

The PECVD is the most widely used technique to produce hydrogenated amorphous silicon thin films (a-Si:H) for solar cells and for film transistors and electronic devices [8, 9]. Reactions during plasma deposition are complex and are not understood completely.

Gorbachev et al. [10–12] have developed a model that is based on chemical reactions and different processes in a PECVD reactor. The model takes into account the formation of SinHm oligomers (n ≤ 5). It presents a simulation of the growth of the films. Gorbachev et al. found that Si2H5 and Si3H7 strongly influence the growth of the film [11].

Valipa et al. [13] calculated the β reactivity of the SiH3 radical on a surface of a silicon lattice plane during the growth of a-Si:H using MDS. The mechanisms of physical and chemical interactions of low temperature plasmas with surfaces can be explored using MDS [14].

For a CH4/H2 mixture, Farouk et al. used the Monte Carlo method (PIC/MC); they calculated the ionization rate of the plasma and the deposition rate of the thin layer [15]. Rodgers et al. [16] have developed three-dimensional Monte Carlo simulations of diamond (100) surface CVD. Other works on MCS are in [17–19].

In our previous works [20–24], we were interested in the study of the gas phase and the interaction of plasmas with the surface, for SiH4/H2 and CH4/H2 gas mixtures during PECVD processes. The used numerical simulation techniques were MCS and MDS. To complete the studies, we used the fluid model [25].

## 3. General rules for numerical simulation methods

The starting point of numerical simulation is a physical phenomenon; its purpose is to obtain useful physical results. Between these two points, several steps can be identified. These steps are general and they are applicable for MCS. The steps can be summarized as follows:

#### 3.1 Definition of the physical phenomenon and main hypothesis

The physical phenomenon must be defined by the description of the dominant domain of physics. The main assumptions and simplifying approximations are necessary to understand the physical phenomenon and the design of the first model. How to Use the Monte Carlo Simulation Technique? Application: A Study of the Gas Phase… DOI: http://dx.doi.org/10.5772/intechopen.88559


12. Discussion and conclusions

Sustainable growth and responsible business management are not possible to achieve by linear way but adaptive way. Figure 10 describes the conceptual model of adaptive development toward successful well-being operations and home care services. Value chain management, proper digitalization, and data management are the key developing features. The objective of well-being economy is resource efficiency and maintaining ethical values on all operations. Continuous digitalization increases effectiveness on optimized services. Value partners need to streamline effectiveness of leadership and interface processes. The trend on well-being service innovation in home care environment is that ethical care pathway, digitalization, and value network development are increasingly overlapping. The increasing digitalization and manage-

Succeeding co-innovation on well-being and home care requires data mining practices, datato-service management process, and creation of adaptive multidisciplinary cooperation model for common semantic infrastructure and solution development. The experts making applied research with customers have to have content on individual nursing of older persons and home care process knowledge at customer site; they have to be capable to work in teams on distributed way with other experts in value network and have to have certain collaborative

The study followed good scientific practice and guidelines [23, 24, 25]. The clients and all professionals volunteered to participate to the research. Ethical questions related to the

ment on data-to-service process are key enablers in business coevolution.

Figure 10. Proper implementation leading on more intensive overlapping.

skills to work together.

120 Data Mining

11. Ethical considerations

Combining the principles of home care service to value network thinking and digitalization with data mining practices gives opportunity for remarkable competitive performance on whole the well-being environment. Recognition of older persons creating actual customer needs combined with life cycle calculation creates opportunities for life cycle services on home care environment.

Experiences on executed TELI-project show that it is essential to engage municipal authorities and public sector on conceptual development work when creating services for home care environment. It is also relevant to develop acceptable legislation, which enables the use of new digital equipment and delivering of created new services.

Universities can support municipal officers and technology application providers to provide and maintain research and learning environments for continuous piloting of new technologies and preparation of new business models on home care environment. Häme University of Applied Sciences supported demonstration of digitalization of versatile home care environment in Finland at Forssa municipal facility and Hämeenlinna Home Care division.

The data gathered through digital equipment can be used in optimizing service processes. It is important to have generic data as common ontology of service process and semantic architecture to route the gathered data. In this article is introduced, what type of ontology-based sematic architecture could be used in social and health care and how geriatric data should be integrated in caring elderly people. This article introduces experiences on co-innovation of home care services cooperatively together with public and private organizations.

This article introduces experiences on responsible business leadership. Older people like to live meaningful life at their own home. Clients of home care have self-determination about their life and care activities. Living at home has to be the person's own choice. Elderly want the right to decide whether or not to use the digital services.

The study followed good scientific practice and guidelines. The clients and all professionals volunteered to participate to the research. Ethical questions related to the research were evaluated. Target organizations gave research permissions and decisions based on ethical evaluations. All students have signed a separate confidentiality agreement.