For many practically relevant comb sources, the OCNRline is finite, which also impairs the transmission performance. Figure 3.2(b) shows the OSNR at the receiver as a function of OCNRline for various span counts *M*. In this plot, the comb line power is the minimum value required for link-limited transmission, as indicated by the corresponding transition points in Fig. 3.2(a). For low OCNRline , the noise level at the receiver is dominated by the amplified noise background of the comb source, and the OCNRline and OSNR are essentially identical. In this case, the link performance is again source-limited. For high OCNRline , the OSNR is dictated by the accumulated ASE noise of the postamplifier and the in-line amplifiers and is thus independent of the OCNRline . In this regime, the transmission performance is link-limited. Depending on the number of spans, the minimum OCNRline values needed for link-limited transmission range between approximately 25 dB and 35 dB. The transition between both regimes is marked by black squares in Fig. 3.2(b), indicating the points where the OSNR has decreased by 1 dB in comparison to its respective limit at high OCNRline .

Note that finite OCNR can also become relevant at the receiver in case a frequency comb is used as multi-wavelength LO. In a simplified consideration, we may assume that the transmitter and the receiver rely on comb sources with identical OCNR. In this case, the OCNR of the LO comb is always higher than the OSNR of the received signal, which is affected by the ASE noise of the postamplifier at the transmitter, the pre-amplifier at the receiver and the inline amplifiers along the link. In the link-limited transmission regime, the noise accumulated along the link dominates, and the noise of the LO comb can hence be neglected. The only case for which the impact of LO noise becomes important is the source-limited transmission regime, i.e., the left-hand part of Fig. 3.2(b). In this region, the LO comb noise additionally impairs the reception, thereby increasing the OSNR of the data signal that is required for a given BER. This is indicated by the dashed lines for the 400 Gbit/s 16QAM signal and for the 600 Gbit/s 64QAM signal. Neglecting noise-noise beating in the coherent receiver and defining OCNR∞ as the OSNR required for a given BER in case of an ideal noise-less LO comb (dotted line in Fig. 3.2(b)), the OSNR in case of a non-ideal LO-comb with finite OCNRline can be expressed as

$$\text{OSSNR} = \left(\frac{1}{\text{OSNR}\_{\text{os}}} - \frac{1}{\text{OSNR}\_{\text{line}}}\right)^{-1}.\tag{3.9}$$

Note that the underlying BER can only be achieved for OCNR > OSNR line ∞ and that the achievable OSNR is always worse than the OCNRline of the transmitter comb, i.e., OSNR OCNR ≤ line if the transmitter and the receiver rely on comb generators with identical.

## **3.4 OSNR limitations considering frequency combs with line-to-line power variations**

Chip-scale comb sources, relying on different comb generation approaches, have been used in a variety of WDM transmission experiments covering a wide range of data rates, channel counts, and line spacings [12], [16], [101]–[103], [17], [20], [82], [85], [96]–[98], [100]. In these WDM transmission experiments, the line to line variations of *P*line and OCNRline lead to a channel-dependent OSNR. In the following, we will analyze the impact of line-to-line power variations on the transmission performance of the WDM link for different transmission distances. To this end, we consider a Kerr frequency comb generated in a silicon nitride (SiN) microresonator [106] as an illustrative example. Kerr frequency combs are generated by pumping a high-Q microresonator with a strong CW laser, see Fig. 3.3(a). Under appropriate pumping conditions, cascaded four-wave mixing leads to the formation of a multitude of spectral lines. As a technically attractive example, we consider so-called single-Kerr-soliton states, which rely on a double balance of parametric gain and cavity loss as well as second order dispersion and nonlinearity and which consist of a single ultra-short pulse circulating in the micro-resonator [105] This leads to broadband frequency combs providing tens or even hundreds of high-quality tones for massively parallel WDM transmission [96]. Note that single-soliton Kerr combs are considered for illustrative purposes only and that other comb sources or other comb states in Kerr-nonlinear microresonators can also be used for WDM transmission. As an example, Turing rolls and dark solitons can achieve high power conversion efficiencies and have been used in WDM transmission [82], [85]. However, the number of comb lines is rather limited and the line-to-line power variations may be strong. Solitons generated in microresonators with higher-order dispersion, such as quartic solitons [112] may provide frequency combs with broad and smooth spectra and might thus lend themselves to massively parallel WDM transmission.

An example of a measured single-soliton Kerr comb spectrum is shown in Fig. 3.3(b), which is measured after equalizing the residual pump power with a notch filter (not shown in Fig. 3.3). This spectrum comprises around 110 carriers spaced by approximately 100 GHz within the telecommunication C and L band (1530 nm … 1610 nm). The line powers range from – 11 dBm near the center to – 20 dBm at the edges of the telecommunication window, and the OCNR values range from 48 dB to 40 dB, which would safely permit link-limited transmission in realistic WDM systems, see Fig. 3.2. While the on-chip pump power used to generate the comb in the originally experiment was approximately 29 dBm, recent advances in fabrication technology and system design have shown the possibility to significantly reduce the required pump power for soliton generation and increase the power conversion efficiency, e.g., by increasing the quality factor of the microresonator [113] or incorporating the microresonator into the cavity of the pump laser [76]. Using Eq. (3.8) with the *P*line and OCNRline values measured from the carriers of the soliton frequency comb and with the model parameters from Table 3.1 and Table 3.2, we calculate the optical signal-to-noise ratio OSNR , =1…*L*, for each individual channel as a function of the link distance, see Fig. 3.3(c)-3.3(e). For this analysis, we assume an output power of 25 dBm provided by the comb amplifier, which corresponds to a power of approximately 5 dBm per line at the input of the WDM modulation unit. The gain of the post-amplifier is set such that a power per line of 0 dBm is launched into each fiber span.

We investigate three different WDM transmission scenarios, refer to Table 3.2 for the gain *G*0 and *G*1 of the comb amplifier and the post-amplifier for each of these scenarios as well as for the corresponding power transmission factor 0 *g* of the WDM modulation unit. In the first scenario, the comb lines are not equalized in power ("No equalization"), and all amplifiers are assumed to have a spectrally flat gain. Note that this scenario is typically not implemented in practical WDM transmission systems, and it is used here as a reference. In our analysis we assume the power fiber *P* = 0 dBm to be the average signal power per WDM channel at the input of each fiber span. The individual per-channel launch powers vary from – 7 dBm to 3 dBm. In the second scenario, the power per line is equalized at the first amplifier stage of Fig. 3.1 by using, e.g., a wavelength-dependent gain *G*0 such that the comb lines at the edge of the telecommunication windows are amplified more than those at the center to reach a spectrally uniform per-channel launch power of 0 dBm into the first fiber span. This can be achieved, e.g., by adapting the gain profile of the optical amplifiers to the spectral variations of the

**Figure 3.3**. Single-soliton Kerr frequency combs and impact of line-to-line *P*line and OCNRline variations on the OSNR. **(a)** Kerr comb generation: A high-Q Kerr nonlinear microresonator is pumped by a CW laser. Under appropriate conditions, cascaded degenerate and non-degenerate four-wave mixing leads to formation of new spectral lines. For single-soliton states, the superposition of the phase-locked optical tones forms an ultra-short soliton pulse circulating in the cavity. This leads to a comb spectrum with a broadband envelope. **(b)** Spectrum of a single-soliton Kerr frequency comb generated in a SiN microresonator [96]. The comb offers 110 carriers in the telecommunication C and L band (1530 nm … 1625 nm), spaced by approximately 100 GHz. In the center of the spectrum, the comb line power amounts to – 11 dBm, and the OCNR is approximately 48 dB. Towards the wings of the comb, both line power and OCNR decrease. **(c-e)** OSNR as a function of the link distance and the comb line index, , **(c)** without equalizing the power per line ("No equalization"); **(d)** for equalizing the power per line by using a spectrally variable gain in first amplifier stage of Fig. 3.1 ("Variable gain"); **(e)** for equalizing the power per line by introducing individual power attenuations for each channel ("Variable loss") at the WDM modulation unit from Fig. 3.1.

frequency comb. For simplicity, we assume the noise figure of all amplifiers to be wavelength-independent. We refer to this scheme as variable-gain equalization ("Variable gain"). In the third scenario, the power per line is equalized at the WDM modulator stage of Fig. 3.1 by considering a channel dependent power transmission 0 *g* . This can, e.g., be accomplished by using optical attenuators or by adjusting the drive voltages of the IQ modulators, such that the channels at the center of the comb spectrum experience a higher attenuation. In this scenario, we assume again amplifiers with spectrally flat gain and noise figure. The gain *G*1 of the post-amplifier is increased such that fiber *P* = 0 dBm, We refer to this scheme as variable-loss equalization ("Variable loss").

**Table 3.2.** Model parameters for each WDM transmission scenario in Fig. 3.3 and Fig. 3.4. The gain *G*0 of the comb amplifier is adjusted to reach a fixed output power of 25 dBm fed into the WDM modulation unit, while the gain*G*1 of the post-amplifier is adjusted to obtain a power per channel of 0 dBm at the input of the first fiber span. The quantity 0 *g* denotes the power transmission of the WDM modulation unit and of the associated variable attenuators used for spectral flattening.

If no power equalization to the comb lines is performed, strong channel-to-channel OSNR variations can be observed for all transmission distances, see Fig. 3.3(c) "No equalization". Note that these channel-dependent OSNR variations do not decrease with propagation distance since the amplifier noise term in Eq. (3.8) dominates the noise power in the denominator such that the difference in *P*line at the output of the frequency comb will determine the OSNR . If the comb line powers are equalized at the first amplification stage, see Fig. 3.3(d) "Variable gain", all channels will exhibit the same OSNR for large transmission distances. This can be understood by the fact that, at large distances, the accumulated ASE noise from the in-line amplifiers will dominate the noise power in all channels such that the initial OSNR differences become irrelevant. The same is true if the comb line powers are equalized at the WDM modulation stage, see Fig. 3.3(e) "Variable attenuation" – also here the accumulated ASE noise will dominate the noise power with increasing distance. In addition, the initial attenuation of the center channels will decrease the associated OSNR for short transmission distances, but this difference disappears for longer links as the accumulated ASE noise of the in-line amplifiers dominates. As a consequence, the performance of the second and the third transmission scenario converge with increasing transmission distance.

To quantitatively compare the transmission performance of the three different schemes, we estimate the maximum capacity for a given reach [114],

$$C = f\_r \sum\_{\ell=1}^{L} \log\_2 \left( 1 + \text{SNR}\_{\ell} \right), \tag{3.10}$$

where *rf* is the comb line spacing, *L* is the number of comb lines, and SNR is obtained from the OSNR through Eq. (3.1) with a bandwidth *B f* = *r* . Equation (3.9) considers the maximum capacity for each channel which can be theoretically achieved by using an arbitrarily complex modulation format [114]. The link capacity according to Eq. (3.10) for =100 GHz *rf* and *L* = 110, as well as the spectral efficiency, SE =*C Lf* ( *r* ) are indicated as solid lines in Fig. 3.4. The line spacing was chosen to maximize the per-channel symbol rate while still being compatible with the bandwidth of available signal generators [115] and IQ modulators [116].

For Metro links, both the scheme without equalization ("No equalization") and the scheme with spectrally variable gain ("Variable gain") lead to a higher capacity than the scheme based on spectrally variable attenuation ("Variable attenuation"), offering link capacities of around 80 Tbit/s. For longer reach, the capacity decreases, and the differences between the three schemes become negligible. Note that our consideration does not account for the impact of fiber nonlinearity, which might lead to further limitations at longer transmission distances [30].

Another scenario of practical interest is the case where all modulators of the various WDM channels are operated with the same modulation format and same FEC overhead is applied to all channels. The maximum capacity is then dictated by the channel with the lowest SNR, SNRmin , leading to

$$C = Lf\_r \log\_2\left(1 + \text{SNR}\_{\text{min}}\right),\tag{3.11}$$

The results of this consideration are indicated as dashed lines in Fig. 3.4. For metro links, the variable-gain scheme provides the highest SNRmin and thus the highest capacity and spectral efficiency. For longer links, the performance of carriers of a soliton Kerr frequency the variable-gain scheme approaches that of the variable-attenuation scheme. The capacity is then the same as the one obtained from Eq. (3.10). As a comparison, Fig. 3.4 also shows the case of using individual lasers instead of the comb. For this analysis, we have assumed a fixed

**Figure 3.4**. Total capacity and spectral efficiency of a WDM transmission link using individual lasers (black line) single-soliton Kerr frequency combs with *L* =110comb lines and a comb line spacing =100 GHz *rf* (colored traces). Blue traces: No equalization done ("No equalization"). Red traces: Flattening of the frequency by spectrally variable gain in the first amplifying stage ("Variable gain"). Green trace: Flattening of the frequency comb by spectrally variable attenuation in the WDM modulation unit ("Variable attenuation"). Black trace: Individual lasers each with 13 dBm of optical power and 60 dB of OCNR. Solid lines: The capacity is optimized individually for each channel. Dashed lines: The per-channel capacity is derived from the smallest SNR, SNRmin in the WDM link.

power per line of 13 dBm fed directly into the modulator along with an OCNR of 60 dB. For short transmission distances, the performance of the comb-based scheme is source limited due to the low power per line. The analysis also shows that the spectral flatness and the gain flattening technique have a direct impact on the achievable capacity. For longer reach, all schemes with flat spectra approach the same link-limited performance.

Regarding technical realizations of chip-scale WDM transceivers, it should be noted that integration of high-power comb amplifiers might represent a challenge, in particular when it comes to massively parallel transmission with tens of even hundreds of comb lines [96], [97]. For the example of an input power of approximately 3 mW per line measured at the input of the modulator, a highpower semiconductor optical amplifier (SOA) with a saturation output power of 23 dBm [117] could be used to handle approximately 70 lines. For bigger line counts or higher powers per line, the tones have to be amplified in separate groups or fiber amplifiers have to be used. For Kerr combs, another challenge might arise from the fact that the residual pump after the resonator may be much stronger than the other comb tones. Suppressing the pump leads to additional energy loss. Note, however, that in all of these cases, the power consumption of the comb generator and the comb amplifier is shared by all comb lines such that the power consumption per line still remains reasonable [96].

## **3.5 Summary**

We have investigated the influence of the comb line power and optical carrierto-noise ratio (OCNR) on the optical signal-to-noise ratio (OSNR) for combbased WDM transmission systems. We identify two regimes of operation depending on whether the transmission performance is limited by the comb source ("source-limited") or by the link and the associated in-line amplifiers ("linklimited"). Our analysis indicates that, depending on the number of spans, minimum comb line powers between –25 dBm and –15 dBm and minimum OCNRline values between 25 dB and 35 dB are needed for link-limited transmission. In addition, we investigated the impact of line-to-line power variations on the achievable OSNR and the overall link capacity for WDM system that relies on single-soliton Kerr frequency combs as a particularly interesting example. We find that OSNR levels of around 30 dB for Metro links lead to capacities of around 80 Tbit/s. We believe that our findings will help to broadly compare different comb generator types and to benchmark them with respect to the achievable transmission performance.

*[end of paper [J3]]* Equation Chapter (Next) Section 1

# **4 DC-driven quantum-dash modelocked laser diode for Tbit/s WDM transmission**

This chapter details the data transmission experiments performed with a DCdriven quantum-dash (QD) mode-locked laser diode (MLLD) as a multi-wavelength light source at the transmitter. The content of this chapter is taken from a paper that has been published in Optics Express [J2]. In order to fit the structure and layout of this document, it was adapted accordingly.

The idea of the experiment was developed by P. Marin-Palomo and C. Koos. P. Marin-Palomo developed and implemented the experimental setups with the support of J. N. Kemal, P. Trocha, and S. Wolf. K. Merghem, and F. Lelarge developed and fabricated the QD-MLLDs for comb generation, under the supervision of A. Ramdane. The DSP required for the analysis of the received waveforms was performed by the author of this dissertation with the support of S. Randel. The manuscript was written by the author with the support of W. Freude, S. Randel, and C. Koos.

*[start of paper [J2]]*

*Copyright © 2020 Optical Society of America*

**Comb-based WDM transmission at 10 Tbit/s using a DC-driven quantum-dash mode-locked laser diode**

*Optics Express, Volume 27, pages 31110-31129 (2019)* DOI: 10.1364/OE.27.031110

P. Marin-Palomo,1 J. N. Kemal,1 P. Trocha,1 S. Wolf,1 K. Merghem,2 F. Lelarge,3 A. Ramdane,2 W. Freude,1 S. Randel,1 and C. Koos1,4

1 Karlsruhe Institute of Technology, Institute of Photonics and Quantum Electronics, 76131 Karlsruhe, Germany

Chip-scale frequency comb generators have the potential to become key building blocks of compact wavelength-division multiplexing (WDM) transceivers in future metropolitan or campus-area networks. Among the various comb generator concepts, quantum-dash (QD) mode-locked laser diodes (MLLD) stand out as a particularly promising option, combining small footprint with simple operation by a DC current and offering flat broadband comb spectra. However, the data transmission performance achieved with QD-MLLD was so far limited by strong phase noise of the individual comb tones, restricting experiments to rather simple modulation formats such as quadrature phase shift keying (QPSK) or requiring hardware-based compensation schemes. Here we demonstrate that these limitations can be overcome by digital symbol-wise blind phase search (BPS) techniques, avoiding any hardware-based phase-noise compensation. We demonstrate 16QAM dual-polarization WDM transmission on 38 channels at an aggregate net data rate of 10.68 Tbit/s over 75 km of standard single-mode fiber. To the best of our knowledge, this corresponds to the highest data rate achieved through a DC-driven chip-scale comb generator without any hardware-based phase-noise reduction schemes.

## **4.1 Introduction**

With the explosive growth of data rates across all network levels [2], wavelength-division multiplexing (WDM) schemes are becoming increasingly important for short transmission links that connect, e.g., data centers across metropolitan or campus-area networks. In this context, optical frequency combs have emerged as particularly attractive light sources, providing a multitude of narrowband optical carriers at precisely defined frequencies that may replace tens or even hundreds of actively stabilized laser diodes [78], [82], [85], [93]– [97]. Among the various comb generator concepts, chip-scale devices are of special interest, in particular when it comes to short-distance WDM links, for which compactness and cost-efficient scalability to high channel counts is of utmost importance.

Over the previous years, a variety of chip-scale comb generators have been shown to enable high-speed WDM transmission at Tbit/s data rates. The highest performance was achieved by exploiting Kerr nonlinearities in integrated optical waveguides, either for spectral broadening of initially narrowband frequency combs [97] or for Kerr comb generation in high-Q microresonators [82], [85], [96]. While these approaches allow to generate hundreds of spectral lines distributed over bandwidths of 10 THz or more, the underlying setups are rather complex, require high pump power levels along with delicate operation procedures, and still comprise discrete components such as fiber amplifiers or external light sources. Other approaches to chip-scale comb generators rely on gain switching of injection-locked DFB lasers [14], [16], [17], which may be integrated into chip-scale packages with all peripheral components but suffer from the rather small bandwidth of the overall comb, which typically spans less than 500 GHz [14].

These limitations may be overcome by so-called single-section quantum-dash (QD) mode-locked laser-diodes (MLLD) [19], [61], [122]–[125], [69], [70], [101], [102], [118]–[121] These devices combine an inhomogeneously broadened gain spectrum of the QD material with passive mode-locking through fourwave mixing and self-induced carrier density modulation [19], [61], [118] and allow for generation of broadband flat frequency combs without requiring a saturable absorber. QD-MLLD can be operated by a simple DC current while producing combs that can comprise 50 carriers or more, spaced by tens of GHz and distributed over a spectral range of more than 2 THz. However, the devices suffer from large optical linewidth of the individual tones, which strongly impairs transmission of signals that rely on advanced modulation formats [101], [119]– [122]. As a consequence, data transmission demonstrations with QD-MLLD have so far relied on intensity modulation of the optical carriers using, e.g., onoff-keying (OOK) [119] or electrical orthogonal frequency division multiplexing (OFDM) signals [120], were limited to rather simple modulation phase formats such as quadrature phase-shift keying (QPSK) [101], [121], [122], or

required dedicated hardware schemes for reducing the optical linewidth of the comb tones [69], [70], [102], [123].

In this work, we show that the phase-noise limitations of QD-MLLD-based WDM transmission schemes can be overcome by a continuous feed-forward algorithm based on symbol-wise blind phase search (BPS) [53] without the need for any additional optical hardware. Expanding on our earlier demonstrations [121], our concept allows for data transmission using 16-state quadrature amplitude modulation (16QAM), even in the presence of strong phase noise of the QD-MLLD tones. The viability of our concept is demonstrated in a series of transmission experiments. In a first experiment, we transmit 52 channels over 75 km of standard single-mode fiber (SSMF) using QPSK as a modulation format at a symbol rate of 40 GBd. By exploiting polarization-division multiplexing (PDM), we achieve an aggregate line rate (net data rate) of 8.32 Tbit/s (7.83 Tbit/s). In a second experiment, we use 38 carriers to transmit PDM-16QAM signals at a symbol rate of 38 GBd over 75 km of SSMF, leading to an aggregate line rate (net data rate) of 11.55 Tbit/s (10.68 Tbit/s). To the best of our knowledge, this is the highest data rate achieved by a DC-driven chip-scale comb generator that does not require any hardware-based phase-noise reduction schemes. Our investigation is supported by an in-depth analysis of the phasenoise characteristics of the QD-MLLD, revealing a strong increase of the FMnoise spectrum at low frequencies as the main problem that has prevented 16QAM transmission so far. Our results combined with the robustness and the ease of operating QD-MLLD show the great potential of such devices as light sources for highly scalable WDM transceivers.

## **4.2 Quantum-dash mode-locked laser diodes**

The frequency comb sources used in our data transmission experiments consist of InAs/InGaAsP quantum-dash (QD) structures, which are grown by molecular beam epitaxy (MBE) on InP substrates [126]. The active region consists of six stacked layers of InAs QD, embedded into InGaAsP barriers, see Fig. 4.1(a). The InGaAsP composition is designed to have a bandgap corresponding to a photon energy λg = 1.17 µm, and the emission wavelength of the device used in our experiments is approximately 1.55 µm. Details of the dash-in-a-barrier design can be found in [19]. The thickness of the barrier between the QD layers amounts to 40 nm, and the structure is terminated by 80-nm-thick separate confinement heterostructure (SCH) layers of InGaAsP towards the top and bottom InP regions. Electrons are injected into the SCH layer from the *n*-side, corresponding to the bottom contact in Fig. 4.1(a), and are then trapped in the QD, emitting photons with a wavelength of approximately 1.55 µm. The photons are guided in a buried ridge waveguide of 1.5 µm width [19]. Cleaved facets act as broadband front and backside mirrors, thereby forming a Fabry-Perot (FP) laser cavity with a total length of 980 µm, corresponding to a free spectral range (FSR) of approximately 42 GHz. Due to the inhomogeneously broadened gain originating from the shape distribution of the QD, multiple longitudinal modes can coexist in the laser cavity. According to [126], mode-locking in QD-MLLD does not require a saturable absorber, but relies on mutual sideband injection due to four-wave mixing and self-induced carrier density modulation at the FSR frequency – similar to actively mode locked laser diodes, but induced by the signal generated from the beating among the laser cavity modes rather than by an external radio frequency (RF) source. This leads to a comb of equally spaced spectral lines with strongly correlated phases [127], thereby forming a periodic output signal with a period corresponding to the cavity round-trip time. The strong phase correlation of neighboring modes leads to a narrow RF beat note measured at the FSR frequency when detecting the periodic output signal with a high-speed photodetector.

To identify favorable parameters for operating the QD-MLLD in transmission experiments, we performed a thorough characterization of the devices using the setup shown in Fig. 4.1(b). The light emitted by the DC-driven QD-MLLD is collected by a lensed single-mode fiber (LF), which features an anti-reflection coating to avoid distortions by optical back-reflection into the laser cavity. The collected light is sent to an optical spectrum analyzer (OSA) and to a photodiode (PD), which is connected to an electrical spectrum analyzer (ESA) for extracting the RF beat note at the FSR frequency. In our experiment, we swept the pump current and recorded the fiber-coupled output power of the device along with the linewidth of the RF beat note and the optical spectrum, from which we extract the optical carrier-to-noise power ratio (OCNR) and the number of lines within a 3-dB bandwidth of the comb, see Fig. 4.1(c) – 4.1(d). Figure 4.1(c) shows the full width half maximum (FWHM) linewidth of the RF beat note at the FSR frequency and the number of comb lines within the 3-dB bandwidth of the comb as a function of the injection current. The linewidth of the RF beat note decreases with higher injection current and reaches a constant value of approximately 10 kHz at high currents. Note that this decrease of the RF linewidth with injection current has been described in the literature [127], [128] and is attributed to the fact that mode-locking in the QD-MLLD relies on nonlinear interaction of the various modes, e.g., through four-wave mixing and carrier density modulation [126]. This interaction increases for higher optical power levels, i.e., higher injection currents, which leads to a decreased RF linewidth. Figure 4.1(d) shows the fiber-coupled output power and the average OCNR. The OCNR values are first determined individually for each comb line based on the optical spectrum of the frequency comb. As a reference bandwidth for specifying the OCNR, we choose 12.5 GHz, which corresponds to a wavelength span of 0.1 nm at a center wavelength of 1550 nm. Within the 3 dB-bandwidth of the comb, the OCNR of the lines exhibit only small variations of approximately ± 1 dB. The plot in Fig. 4.1(d) shows the mean OCNR averaged over all lines within the 3-dB bandwidth of the comb. The average OCNR increases with injection current and reaches an essentially constant level of approximately 40 dB above 300 mA.

From Fig. 4.1(c) and Fig. 4.1(d), we find that the output power, the number of lines and the OCNR monotonically increase with injection current, while the linewidth of the RF beat note decreases. For the transmission experiment, the injection current is hence chosen as high as possible without exceeding the current limit of the diode. As a favorable operation regime, we identify the range between 300 mA and 420 mA, which is shaded in red in Fig. 4.1(c) and Fig. 4.1(d). We repeated the measurement for other temperatures between 20 and 25 °C, observing a similar trend. Figure 4.1(e) shows the resulting frequency comb spectrum for an injection current of 390 mA at a stabilized temperature of 21.2 ºC. Throughout the subsequent experiments, the injection current and operation temperature of the laser are kept constant to avoid drift of the center frequency of the generated combs. The accuracy of this stabilization

**Figure 4.1.** Frequency-comb generation in quantum-dash mode-locked laser diodes (QD-MLLD). **(a)** Top view and cross-section schematic of a QD-MLLD consisting of a ridge waveguide of 1.5 μm width and 980 µm length. The active region comprises six stacked layers of InAs QD separated by 40 nm-thick InGaAsP barriers, see transmission-electron microscope (TEM) image in the Inset [19]. Carriers are injected into the active region through 80-nm-thick separate confinement heterostructure (SCH) layers of InGaAsP, designed to have a bandgap corresponding to a photon energy λg = 1.17 µm. The emission wavelength of the devices used in our experiments is approximately 1.55 µm. **(b)** Setup for frequency comb characterization. The QD-MLLD is driven by a DC current. LF: Lensed fiber. OI: Optical isolator. PD: Photodiode. ESA: Electrical spectrum analyzer. OSA: Optical spectrum analyzer. **(c)** Number of lines within the 3 dB bandwidth of the comb (blue) and FWHM of the RF beat note ("RF linewidth", red) at the FSR frequency of 42 GHz as a function of injection current. **(d)** Optical output power (green) and average OCNR (black) of the comb lines as a function of injection current. Shaded region: Range of favorable operating currents for low RF linewidth, high output power and OCNR, and large number of lines. **(e)** QD-MLLD frequency comb spectrum for an injection current of 390 mA at a stabilized temperature of 21.2 °C.

amounts to ± 0.1 K for the operating temperature and to ± 0.1 mA for the injection current. For coherent communications, the carriers used to transmit data need to have high OCNR and narrow optical linewidths, or, equivalently, low phase noise. The recorded OCNR level would in principle safely allow for

transmission of 16QAM signals at symbol rates of 50 GBd or more [129]. However, the individual comb tones exhibit strong phase noise, which inhibits the use of advanced modulation formats with high spectral efficiency. In the case of strong phase noise, there is a high probability that the induced phase change causes a wrong recovery of the symbol, thus dramatically increasing the biterror ratio (BER), even at high OCNR. In the next section, we present a more detailed analysis of the phase noise for individual carriers of the QD-MLLD, whilst Section 4.4 contains an analysis of the impact of phase noise on the measured BER for QPSK and 16QAM signaling.

## **4.3 Phase noise characteristics of QD-MLLD**

The optical tones of the QD-MLLD are broadened by several effects [130]. Fundamentally, laser linewidth broadening is caused by the coupling of spontaneous emission into the oscillating mode, leading to spectrally white frequency noise. Other effects such as flicker and random-walk frequency noise contribute to linewidth broadening, too, and occur at longer time scales [51], [52], i.e., lower frequencies. Influences of temperature fluctuations and mechanical vibrations happen on an even larger time scale and are disregarded. In the following, we differentiate between short-term and long-term phase noise, leading to a short-term and a long-term linewidth of the comb tone. Short-term phase fluctuations are characterized by a white frequency-noise spectrum and lead to a Lorentzian laser line shape with a FWHM ∆ L*f* , while long-term phase fluctuations lead to a Gaussian spectrum with FWHM ∆ *f*G [51]. For the devices used in our measurements, the long-term linewidth is observed when considering the frequency fluctuations for observation times 0 τ 1 µs, whereas the short-term linewidth is obtained for observation times 0 τ 1 µs, see Section 4.3.1 for a more detailed discussion.

For measuring the short-term and long-term optical linewidths of the individual comb lines, we follow two different heterodyne approaches, which are illustrated in Fig. 4.2(a), Setup I and Setup II. In Setup I, the QD-MLLD output is superimposed with the output of a highly stable tunable local-oscillator laser (LO I) and then sent to a photodetector connected to an ESA for recording the beat-note spectrum and the long-term linewidth. In Setup II, we use a second tunable local oscillator laser (LO II) along with a coherent receiver and highspeed analog-to-digital converter (ADC). The ADC is used to record the RF beat note, from which the intrinsic Lorentzian, i.e., short-term linewidths are extracted by offline processing of the signals [51], see Section 4.3.2. Both LO I and LO II are external-cavity lasers (ECL, Keysight N7714A) with a specified linewidth below 100 kHz, i.e., the LO linewidths are much smaller than the expected linewidth of the comb lines. This is verified by connecting LO I to Input II (Inp II) of Setup II, and LO II to Input I (Inp I) of Setup I and by observing that in both cases the resulting linewidths of the beat notes are much smaller than those obtained from the QD-MLLD tones, see Fig. 4.2(b). Note that these measurements can only reveal the relative phase fluctuations of LO II with respect to LO I, which can be considered as an upper boundary of the phase noise of each of the sources. In the following sections, we detail a quantitative phasenoise model, Section 4.3.1, and use it to extract the QD-MLLD phase-noise characteristics from the measurements obtained from Setup I and Setup II, Sections 4.3.2 and 4.3.3.

#### **Phase-noise and linewidth model**

In the following, we give a short overview on the model used for quantitatively describing the phase noise of the MLLD tones. More details of the underlying theoretical background and a derivation of the mathematical relationships can be found in [131]**.** The complete statistical characteristics of the phase noise or, equivalently, the frequency noise of a laser oscillator can be obtained from the so-called FM-noise spectrum inst *f S* , i.e., the power-spectral-density function of the instantaneous optical frequency fluctuations *f t* inst ( ), which can be modeled by [132], [133]

$$S\_{f\_{\rm inst}} \left( f \right) = S\_{\rm L} + S\_{\rm L} f^{-1} + S\_{\rm L} f^{-2} \tag{4.1}$$

This power spectral density is composed of spectrally constant white frequency noise 0 L*S f* , flicker frequency noise 1 1 − *S f* , and random-walk frequency noise 2 2 − *S f* . In these relations, the quantities L*S* , 1*S* and 2 *S* are constant coefficients quantifying the various frequency noise contributions.

**Figure 4.2.** Linewidth measurement and phase-noise characterization for selected comb lines of the QD-MLLD. **(a)** Experimental setups: In Setup I, the QD-MLLD output is superimposed with the output of a narrowband local oscillator laser (LO I) and detected by a single photodiode (PD) and an electrical spectrum analyzer (ESA) to extract the long-term linewidth ∆ G*f* . In Setup II, a second LO laser (LO II) is used along with a coherent receiver and a high-speed analog-to-digital converter (ADC) for measuring the temporal phase-noise characteristics, from which we extract the FM-noise spectrum that reveals the intrinsic Lorentzian linewidth L ∆*f* . LF: Lensed fiber. OI: Optical isolator. PC: Polarization controller. LO I, LO II: Tunable external cavity lasers (ECL). OH: Optical hybrid. BPD: Balanced photodiodes. Inp I, Inp II: Auxiliary inputs for verification of the LO laser linewidths. **(b)** Long-term and short-term optical linewidths of the different comb lines. The long-term linewidths were recorded with an effective ESA observation time of 0,ESA τ ≈150 μs. **(c)** Power spectra inst *f S* of instantaneous frequency fluctuations (FM noise) along with model fits according to Eq. (4.1). The length of the recorded time-domain beat signal is 125 µs. The data were obtained by testing a QD-MLLD tone with Setup II (QD-MLLD, blue) or by connecting LO I to Inp II of Setup II (LO I/II, red). In both cases, the wavelength of the tested tone was 1547.3 nm. Note that the second measurement can only reveal the relative phase fluctuations of LO II with respect to LO I, which can be considered as an upper boundary of the phase noise of each of the sources. Since the linewidth of LO I is much smaller than that of the QD-MLLD tone, the phase fluctuations in the first measurement can be attributed to the QD-MLLD tone. **(d)** Phase-noise variance 2 σφ as a function of measurement time *τ*, both for LO I and for the QD-MLLD tone. **(e)** Power spectra as a function of the frequency offset from the carrier for LO I and for the QD-MLLD tone (resolution bandwidth δ*f* = 400kHz).

The FM-noise spectrum can be separated into two areas that influence the measured line shape in distinctively different ways, depending on the observation time. For long observation times, the measured linewidth will be dictated by FM-noise components at low Fourier frequencies, where flicker and randomwalk frequency noise dominates. Specifically, the resulting line can be approximated by a Gaussian if the line shape is dominated by frequency noise at Fourier frequencies *f* smaller than a frequency high *f* defined by [131]

$$S\_{f\_{\rm inst}}\left(f\_{\rm high}\right) = \left(8f\_{\rm high}\ln 2\right) / \pi^2. \tag{4.2}$$

The spectral power of the frequency noise beyond this point does usually not influence the center part of the line shape [131]. Towards smaller Fourier frequencies, the lowest frequency *f*low that can be considered in a given measurement is dictated by the observation time τ 0 low =1 . *f* For high low *f f* > 5 , a good approximation of the long-term FWHM linewidth is then [131]

$$
\Delta f\_{\rm G} = \left[ 8 \ln(2) \mathcal{A} \right]^{1/2}, \tag{4.3}
$$

where the parameter *A* corresponds to the spectral power of the frequency noise between *f*low and high *f* ,

$$A = \int\_{f\_{\rm{low}}}^{f\_{\rm{high}}} S\_{f\_{\rm{int}}} \left( f \right) \mathrm{d}f \tag{4.4}$$

Note that in the presence of flicker or random-walk frequency noise, *A* increases with decreasing lower frequency limit *f*low , i.e., the measured long-term linewidth increases with increasing measurement duration τ0 low =1 *f* .

In contrast to that, the observed line shape is Lorentzian if the observation time is chosen short enough, i.e., if the lower frequency limit *f*low is high enough to exclude the impact of flicker and random-walk frequency noise. The relevant part of the FM- noise spectrum can then be considered white, and the intrinsic Lorentzian linewidth ∆ L*f* is directly proportional to the constant spectral power density L*S* of the frequency noise [51],

$$
\Delta f\_{\rm L} = \pi S\_{\rm L} \,. \tag{4.5}
$$

Note that in this case, the measured linewidth is independent of the exact observation time 0 τ.

These considerations allow us to give a more precise definition of the terms "long-term linewidth" and "short-term linewidth" introduced earlier. The longterm linewidth ∆ *f*G is observed for observation times 0 τ low τ =1 high / *f* (usually τ τ 0 low > 5 ), where high *f* is obtained from Eq. (4.2). For 0 τ low τ , the short-term linewidth, i.e., the intrinsic Lorentzian linewidth ∆ L*f* is found. Measuring the FM-noise spectrum of the QD-MLLD tones and fitting Eq. (4.1) to the measurement allows us to obtain both the intrinsic linewidth ∆ L*f* , see Section 4.3.2, the long-term linewidth ∆ *f*G , see Section 4.3.3, and the parameter low τ ≈1µs, which corresponds to the observation time that roughly marks the transition between the two regimes. Alternatively, the long-term linewidth ∆ *f*G can be extracted by means of an ESA that records the beat-note spectrum of the comb tone with the tone emitted by LO I, see Section 4.3.3.

The results of the linewidth measurements are shown in Fig. 4.2(b) with shortterm linewidths ∆ L*f* ranging from approximately 1.5 MHz at the center of the frequency comb to 4 MHz at the edges, and long-term linewidths ∆ *f*G ranging from 7 MHz at the center to 12 MHz at the edges. The increase of the linewidths towards the edges of the comb spectrum is related to the timing jitter of the periodic signal generated by the QD-MLLD [118]. The long-term linewidths in the comb center are in good agreement with the values found in [118].

#### **Short-term linewidth from measured FM-noise spectrum**

The intrinsic Lorentzian linewidth ∆ L*f* for each line of the frequency comb is obtained from the FM-noise spectrum inst *f S* using Eqs. (4.1) and (4.5). To measure inst *f S* , we first recover the in-phase (I) and quadrature (Q) component of the electric field of individual comb carriers with a coherent receiver [51], [134], [135] using Setup II of Fig. 4.2(a). In these measurements, LO II is tuned to generate an I and a Q beat signal with the respective comb line at an intermediate frequency of approximately 1 GHz. This choice of intermediate frequency guarantees that the beat note with an FWHM of the order of a few tens of MHz does not extend to negative frequencies, thereby avoiding impairment by spectral foldback. The time-dependent phase differences between the LO tone and the comb tone are derived from the I and the Q signals, and the frequency offset is removed by fitting the time-dependent increase of the phase with a linear function. The time-dependent random phase fluctuations φ (*t*) are then obtained from the difference of the measurement data and the linear fit. To extract the associated instantaneous frequency fluctuation *f t* inst ( ), we compute the timederivative of the measured phases,

$$2\pi f\_{\rm inst} \left( t \right) = \frac{\mathbf{d} \,\phi \left( t \right)}{\mathbf{d} \, t} \approx \frac{\phi \left( t + \tau\_s \right) - \phi \left( t \right)}{\tau\_s}, \tag{4.6}$$

where s τ =12.5 ps denotes the sampling period of our ADC (Keysight, DSO-X 93204A). The length of the recorded time-domain beat signal is 125 µs. The FM-noise spectrum inst *f S* is obtained by computing the autocorrelation function of *f t* inst ( ) and by taking its Fourier transform [51], see Fig. 4.2(c), blue trace. As a reference, we also record the relative phase fluctuations of LO I with respect to LO II, see Fig. 4.2(c), red trace. The relative phase fluctuations of LO I and LO II are significantly smaller than the phase fluctuations observed in the QD-MLLD measurement, and we can conclude that the linewidth of the LO does not deteriorate our measurements.

To extract the model parameters L*S* , 1*S* and 2 *S* of Eq. (4.1) from our measurements, we perform a parameter fit of the model prediction to the measured data. The fitting procedure comprises several steps: For smoothing the measured FMnoise spectrum, we used a moving-average filter for which the length increases with frequency**.** We start from a filter length of 1 tap, i.e., no averaging, at Fourier frequencies of up to 70 kHz and then increase the filter length exponentially to 800 taps at a Fourier frequency of 100 MHz. This approach was necessary to maintain the strong increase of the FM-noise spectrum towards low frequencies (< 100 kHz) while effectively reducing the uncertainties at higher frequencies (> 1 MHz). Prior to fitting the smoothed data, we re-sample it to obtain points that are equidistant with respect to the logarithm of the Fourier frequency. This avoids a situation where the least-squares errors of the fit are dominated by the noisy high-frequency part of the spectrum while the physically relevant lowfrequency part does not play a role. The results of the fit are robust with respected to the choice of initial fitting parameters and of the tap number that the averaging filter uses towards high frequencies. For the MLLD tone, we obtain

5 L*S* = × 5.9 10 Hz, 11 2 1*S* = × 9.4 10 Hz and 17 3 2 *S* = × 2.3 10 Hz , leading to an intrinsic Lorentzian linewidth ∆ L*f* = 1.9 MHz. We repeat the measurement for different QD-MLLD lines, see Fig. 4.2(b). For the beat of LO I with LO II, we find 3 L*S* = × 4.0 10 Hz, 9 2 1*S* = × 3.2 10 Hz , and 15 3 2 *S* = × 2.2 10 Hz , leading to an intrinsic linewidth of the measured beat note of 12 kHz.

Note that the intrinsic linewidth ∆ L*f* can also be inferred from the delay-dependent phase differences ∆ = +− φ φ τφ τ (*tt t* ) ( ) ( ) and the associated phasenoise variance [51]

$$
\sigma\_{\Delta\phi}^2(\tau) = \left< \Delta\phi\_\tau(t)^2 \right> . \tag{4.7}
$$

This involves calculating the slope of ( ) 2 σ τ φ close to τ= 0 [51],

$$
\Delta f\_{\rm L} = \lim\_{\tau \to 0} \frac{\sigma\_{\Lambda \phi}^2(\tau)}{2\pi\tau}. \tag{4.8}
$$

To reliably extract this slope, we first fit a parabola to the measured phase-noise variances ( ) 2 σ τ ∆φ of the QD-MLLD (blue) and of LO I/II (red) in Fig. 4.2(d) and then take the derivative of the fitted function at τ = 0 . The values are consistent with the linewidths obtained from the measured FM-noise spectra according to Eqs. (4.1) and (4.5).

### **Long-term linewidth measurement**

The long-term linewidth ∆ *f*G is measured using the heterodyne setup shown in Fig. 4.2(a), Setup I. To this end, we tune LO I close to a comb line of the QD-MLLD and detect the superposition of both on a PD. The spectrum of the resulting photocurrent is centered about the difference frequencies of the comb line and the tone emitted by LO I and is measured using an electrical spectrum analyzer (ESA).

For better comparison of the results obtained from the ESA measurement to the long-term FWHM linewidths extracted from Eq. (4.3), we estimate the effective observation time 0,ESA τ that has to be assigned to the ESA measurement. For a given frequency span ∆ *f* , the effective observation time 0,ESA τthat is needed to record this span using the ESA is dictated by the resolution bandwidth δ *f* [136],

$$
\pi\_{0, \text{ESA}} = \kappa \frac{\Delta f}{\delta f^2}, \tag{4.9}
$$

where κ denotes the proportionality constant that depends on the specific ESA model. For our system (Keysight N9030A), a value between κ = 2 and κ = 3 is specified [136], and we assume κ = 2.5. Thus, for a resolution bandwidth of δ *f* = 400kHz , we obtain an effective observation time of approximately 0,ESA τ =150µs that is needed to record the approximately 10 MHz-wide beat note between the comb tone and LO I.

In our measurements, we select different comb lines by tuning LO I, see Fig. 4.2(b). In these measurements, two important requirements need to be fulfilled: First, the resulting intermediate frequency must be much larger than the expected spectral half width of the investigated comb line. This is ensured by choosing an intermediate frequency of approximately 1 GHz. Second, the phase fluctuations of the LO must be much smaller than those expected for the investigated comb line. The validity of this assumption was already assured when recording the frequency noise spectrum, see Section 4.3.2.

The long-term linewidth is extracted by evaluating the FWHM of a model function that is fit to the measured spectra. In general, the line-shape is described by a Voigt function, i.e., a convolution of a Lorentzian and a Gaussian [52], [137]. This function, however, may be approximated by a Gaussian near the line center [52]. In our analysis we have investigated the impact of fitting both types of curves to the measured data. Both fits lead to virtually the same results for ∆ *f*G with deviations of less than 5 %. The long-term linewidths indicated in Fig. 4.2(b) are obtained from the Voigt function. For a QD-MLLD tone close to 1547.3 nm, we obtain a long-term linewidth ∆ *f*G of approximately 8 MHz, Fig. 4.2(e), blue curve.

As a check, we also re-confirm that the linewidth of LO I can be neglected by measuring the long-term optical linewidth of the beat note between LO I and LO II using Setup I, leading to G ∆ = *f* 0.6 MHz for an ESA resolution bandwidth of δ*f* = 400kHz , see Fig. 2(e), red curve. We further compare the longterm linewidth obtained from the ESA measurement to that extracted from the fitted FM-noise spectrum. To this end, we use Eqs. (4.3) and (4.4) which, for 3 L*S* = × 4.0 10 Hz, 9 2 1*S* = × 3.2 10 Hz , 17 3 2 *S* = × 5.0 10 Hz , low 0,ESA *f* = = 1 8kHz τ , and high low *f* = = 1 2MHz τ lead to a long-term linewidth ∆ *f*G of approximately 14 MHz. This is in good agreement with the width obtained from the directly measured line shape.

## **4.4 Coherent transmission using QD-MLLD**

In this section, we first investigate the effect of the inherent phase noise of QD-MLLD carriers on coherent data transmission for different modulation formats and symbol rates, see Section 4.4.1. We show that symbol-wise blind phase search (BPS) [53], relying on continuous feed-forward estimation and correction of the instantaneous phase difference between the LO tone and the carrier, substantially improves the transmission performance of the QD-MLLD and finally enables the use of 16QAM signaling, see Fig. 4.3. Details of the phase tracking algorithm are described in Section 4.4.2.

As a reference, we use the transmission performance obtained by block-wise carrier phase recovery (CPR) which is part of the Vector Signal Analyzer (VSA) software offered by Keysight Technologies (89600 series VSA software) [138]. In this approach, received symbols are processed in blocks, within which a certain frequency offset and an otherwise constant phase difference between the LO tone and the carrier are corrected. To this end, the phases of symbols in a block are extracted and unwrapped. The frequency offset is then extracted from a linear regression of the time dependence of the unwrapped phases. Details can be found in [138]. Note that this block-wise CPR does not allow for dynamic phase tracking. We further benchmark the results obtained from the MLLD by replacing the comb tone by an ECL carrier with an intrinsic linewidth of approximately 10 kHz. For optical signal-to-noise power ratios (OSNR) of 25 dB or less that are typically found at the receivers of 16QAM transmission links [139], the transmission performance achieved with QD-MLLD tones in combination with BPS is comparable to that offered by high-quality ECL carriers.

In Sections 4.4.3 and 4.4.4, we present a series of transmission experiments demonstrating the ability of the symbol-wise BPS scheme to compensate for the phase noise of the QD-MLLD tones. In a first experiment, we transmit 52 channels spaced by 42 GHz over 75 km of standard single-mode fiber (SSMF) using QPSK as a modulation format, see Section 4.4.3. Using polarization-divisionmultiplexing (PDM), we achieve an aggregate line rate of 8.32 Tbit/s, which reduces to a net data rate of 7.83 Tbit/s when considering a 6.25 % overhead necessary for hard-decision forward error correction (FEC) of BER values below 4.7 × 10−3 [140]. In a second experiment, we use 38 carriers to transmit PDM-16QAM signals over 75 km of SSMF at an aggregate line rate of 11.55 Tbit/s, which corresponds to a net data rate of 10.68 Tbit/s when accounting for a FEC overhead of 6.25 % for 32 channels and of 20 % for the remaining six channels [140], see Section 4.4.4. This corresponds to the highest data rate achieved by a DC-driven chip-scale comb generator without any additional hardware-based phase-noise reduction [69], [70], [102], [123].

### **Influence of comb-carrier linewidth and OSNR on coherent communications**

To quantify the influence of the linewidth of the QD-MLLD comb lines on coherent transmission, we measure the BER at different symbol rates for both QPSK and 16QAM. The experimental setup is depicted in Fig. 4.3(a). After amplification of the frequency comb by EDFA1 to an output power of 17 dBm, we filter the comb line of interest using a programmable optical filter (POF). A 3dB-bandwidth of approximately 10 GHz of the POF is chosen to effectively suppress all neighboring comb lines. The filtered carrier, centered at a wavelength of 1540.4 nm, is amplified to a power of 24 dBm and sent through an IQ modulator. The phase-noise properties of this carrier are essentially the same as those of the carrier at 1547.3 nm, which is analyzed in detail in Figs. 4.2(c) – 4.2(e). The modulator drive signal is synthesized by an arbitrarywaveform generator (AWG) based on a pseudo-random bit sequence (PRBS) of length 211 − 1. The bit sequence is mapped to either QPSK or 16QAM symbols with pulses having a raised-cosine (RC) spectrum with a 5 % roll-off for QPSK and 10 % for 16QAM. PDM is emulated by splitting the data signal and decorrelating the split signals in time by approximately 5.3 ns using a delay line (DL) [82]. Finally, both signals are combined in orthogonal polarization states using a polarization beam combiner (PBC). To adjust the OSNR of the signal, a noise-loading stage (ASE source) is used. The signal is then sent to the receiver, where it is further amplified by EDFA3 and EDFA4. Bandpass filters (BPF) are used to suppress out-of-band noise after each amplifier. The signal is finally detected by an optical modulation analyzer (OMA, Keysight N4391A) acting as a dual-polarization coherent receiver (DP-CR) with built-in local oscillator (LO) laser. The intrinsic linewidth of the LO is approximately 10 kHz. The output of the DP-CR is digitized by a 4-channel 80 GSa/s real-time oscilloscope (two synchronized Keysight DSO-X 93204A) and recorded for offline digital signal processing (DSP). The digitized signal undergoes a number of DSP steps, comprising timing recovery, MIMO equalization, frequency offset compensation, carrier phase compensation, and decoding, see Section 4.4.2 for details.

The measured signal quality parameters are summarized in Fig. 4.3(b) and 4.3(c) for QPSK and 16QAM signals. In these plots, green traces represent the results obtained from using block-wise CPR ('MLLD/block-wise CPR') as implemented in Keysight's VSA software [138]. In this analysis, the block length was varied between 100 and 200 symbols, depending on the symbol rate. The blue traces are obtained using continuous feed-forward symbol-wise BPS algorithm ('MLLD/symbol-wise BPS') [53], see Section 4.4.2 for details. The red traces ('ECL') are obtained by repeating the experiment using a narrowband ECL as an optical source. The ECL is tuned to the same wavelength as the comb tone and has an intrinsic linewidth of approximately 10 kHz, and we can hence assume that the transmission performance is not impaired by phase noise. This is confirmed by observing that block-wise CPR and symbol-wise BPS lead to the same result for the ECL-based transmission. For QPSK, Fig. 4.3(b), the limited recording length did not contain enough errors for a statistically reliable measurement of the BER. We therefore use the error vector magnitude (EVM) rather than the BER as a performance metric [129]. Assuming that the signals are impaired by additive white Gaussian noise only, the measured EVM would correspond to BER values below 10-10 [129]. Note that the EVM can be defined in two different ways depending on the normalization, which either refers to the maximum field in the constellation, or to the average field resulting from

**Figure 4.3**. Influence of phase noise on coherent transmission at different symbol rates, modulation formats, and OSNR values. The analysis relies on using a single comb line with an intrinsic linewidth of 1.9 MHz as a carrier at a wavelength of 1540.4 nm. As a reference, we use a narrowband optical carrier provided by an ECL with an intrinsic linewidth of ~ 10 kHz. The transmission performance of the ECL tone is compared to that of the QD-MLLD tone using either block-wise CPR (MLLD/block-wise CPR) or symbol-wise BPS (MLLD/symbol-wise BPS). **(a)** Experimental setup. EDFA: Erbium-doped fiber amplifier. POF: Programmable optical filter. IQmod: In-phase/quadrature (IQ) modulator. AWG: Arbitrary waveform generator. PDM: Polarization division multiplexing. VOA: Variable optical attenuator. OSNR meas.: Optical signal-tonoise-ratio measurement unit. DL: Delay line. PBC: polarization beam combiner. ASE: Amplified spontaneous emission. BPF: Band-pass filter. LO: Local oscillator. **(b)** Error-vector magnitude (EVM) measured for PDM-QPSK signaling at different symbol rates. For QPSK, we did not find a sufficient number of errors within our limited recording lengths and can hence only provide the EVM. We find that symbol-wise BPS algorithm can essentially overcome the phasenoise-related limitations observed for block-wise CPR and bring the transmission performance of the MLLD tone close to that of a narrowband ECL tone. **(c)** BER results for PDM-16QAM signaling for different symbol rates. In these measurements, the OSNR was around 35 dB. For practically relevant symbol rates beyond 30 GBd, symbol-wise BPS can essentially overcome the phase-noise-related impairments. The measured BER values fit well to the simulation results (dashed lines) labelled "Sim. MLLD" and "Sim. ECL". **(d)** BER results for PDM-16QAM signaling at 38 GBd for different OSNR values. The OSNR values are measured after EDFA 4, see Subfigure (a). For OSNR values of 25 dB or less, symbol-wise BPS allows the QD-MLLD tone to perform nearly as good as a narrowband ECL carrier with OSNR penalties of approximately 0.5 dB.

summing the power of all possible symbols [44]. Here, we refer to the second definition, i.e., we normalize the EVM to the average field. For 16QAM, we measure the BER directly.

Generally, the impact of phase noise increases with decreasing symbol rates, i.e., longer optical symbol periods, which leads to an increase of the EVM or the BER at low symbol rates for the QD-MLLD experiments with block-wise CPR, see green traces in Fig. 4.3(b) and 4.3(c). At high symbol rates, the signal quality is impaired by the decreasing SNR and by the bandwidth limitations of our AWG, leading to higher EVM and BER. Using the symbol-wise feed-forward BPS, the impact of phase noise can be greatly reduced, both for QPSK and 16QAM, see blue traces. For QPSK, the transmission performance comes close to that of the narrowband ECL, illustrated by the red trace. 16QAM is generally more sensitive to phase noise than QPSK, since more phases need to be discriminated. In this case, at low symbol rates, even the symbol-wise BPS is not capable of compensating the complete impact of phase noise. Still, the performance of the QD-MLLD experiments with symbol-wise BPS does not show any substantial penalty compared to that of the ECL-based transmission at practically relevant symbol rates of 30 GBd or more.

To quantitatively confirm the results depicted in Fig. 4.3(c), we have performed simulations of 16QAM transmission at different symbol rates. In these simulations, we neglect low-frequency FM noise and only consider the spectrally white part of the FM-noise spectrum. To this end, we model the underlying phase fluctuations as a Wiener process where the variance of the stochastic phase increments is chosen to produce an intrinsic linewidth of 1.9 MHz for the QD-MLLD carrier and of 10 kHz for the ECL carrier. We further consider additive white Gaussian noise (AWGN), modeling the noise contributions of the optical amplifiers and the receiver electronics. The AWGN level used in each simulation is obtained from the signal-to-noise ratio (SNR) of the measured data signals. The dashed lines in Fig. 4.3(c) show the simulation results, which are in good agreement with their measured counterparts.

Finally, we measure the BER as a function of the OSNR, see Fig. 4.3(d), for 16QAM and a symbol rate of 38 GBd, which is used for the high capacity WDM transmission experiment, see Section 4.4.4. In this measurement, we again compare the QD-MLLD with block-wise phase recovery (green trace) and symbol-wise phase tracking (blue trace) as well as the ECL reference (red trace). For a BER of 4.7 × 10−3 , corresponding to the threshold for hard-decision FEC with 6.25 % overhead [140], the implementation penalty amounts to approximately 0.9 dB for ECL-based transmission and to approximately 1.4 dB for the MLLD tone. The penalty of the MLLD tone with respect to the ECL carrier hence amounts to approximately 0.5 dB. This value is not only found at the FEC threshold, but more generally for all OSNR values of less than 25 dB. Thus, under realistic transmission conditions [139], the carriers of the QD-MLLD comb source perform similarly as a high-quality individual ECL carrier. The slightly lower performance of the MLLD tone observed at high OSNR beyond 25 dB, see Fig.4.3(d), is attributed to residual phase noise that is still left after phase tracking [53]. This is confirmed by the simulation results shown in Fig. 4.3(c), which reproduce the measured BER performance both for the MLLD and the LO carrier by accounting for the measured linewidth of the respective carrier and by assuming OSNR levels between 20 dB and 25 dB. For the simulation, the OSNR level of each channel is derived from the SNR of the measured data signal.

### **Data recovery using feed-forward symbol-wise blind phase search**

The continuous feed-forward algorithm for symbol-wise phase tracking was implemented in Matlab following the scheme introduced by Pfau *et al.* [53]. It is part of a multi-step DSP procedure, see Inset of Fig. 4.3(a). First, the signal is resampled to two samples per symbol followed by timing recovery [37], [38]. A 30-tap MIMO equalizer based on the constant-modulus algorithm (CMA) is then used to demultiplex the two orthogonal polarizations of the signal and to compensate for linear transmission impairments [39]. The received symbols from the MIMO equalizer then undergo frequency-offset correction [141]. For QPSK, the 4th-power of the received symbols is calculated to remove the information of the modulated phase. This leaves only the rapidly increasing phase caused by the frequency offset between signal carrier and LO. The frequency offset is then corrected by fitting a linear curve to the unwrapped phase as a function of time and by subtracting the fitted curve from the measured phase

offset. For the case of 16QAM signaling, the 4th-power scheme can be adapted by QPSK-partitioning [40]. Once the carrier frequency offset is compensated, carrier phase noise compensation is carried out based on a "symbol-wise" BPS algorithm [53]**.**

The BPS algorithm starts with selecting a group of *N* complex symbols which are centered around the symbol of interest. The phases of these complex symbols are then modified by adding identical test phases φ t . The test phases are varied, and the sum of the squares of the *N* Euclidean distances of the measured symbols to their closest constellation points in the complex plane is measured. The optimum phase is determined by searching the minimum value of this sum [53]. Note that for symbol-wise BPS, the group of symbols used for phase estimation is slid along with the symbol of interest such that an individual phase correction term is computed for each symbol. This is in contrast to "block-wise" phase recovery, where all symbols within a block are treated with the same phase-correction parameter. For evaluating our measurements, we apply 45 equidistant test phases for covering an unambiguity range of ± ° 45 for an *M*-QAM signal with a quadratic constellation.

As a rough estimate, a symbol-wise phase tracking technique relying on averaging of measured phases over a moving group of *N* symbols can effectively suppress frequency noise components occurring at Fourier frequencies up to S *f NT* =1 , where *T*S corresponds to the symbol duration. This is confirmed by simulating 16QAM transmission at a symbol rate of 38 GBd, an intrinsic linewidth of the carrier of L ∆ = *f* 1.9 MHz , and an OSNR of 35 dB, see Fig. 4.4. In this simulation, we perform BPS with different averaging lengths *N* and then extract the residual phase error of the various symbols with respect to the respective ideal constellation point. The residual instantaneous frequency fluctuations *f t* inst ( ) are then extracted from this time series of phase errors using the relation given in Eq. (4.6), and the FM-noise spectrum is derived by taking the Fourier transform of the autocorrelation function of *f t* inst ( ). The FM-noise spectra for different averaging lengths are then compared to the FM-noise spectrum of the carrier prior to modulation, indicated by a blue trace in Fig. 4.4. For *N* = 10 (red trace) we find that the frequency noise is effectively suppressed for Fourier frequencies smaller than approximately 4 GHz, whereas for *N* = 100 symbols (green trace), the suppression is only effective up to approximately 400 MHz, thus confirming the above-mentioned rule. Note that for *N* = 10, we observe a slight increase of the frequency noise level towards higher Fourier frequency. We attribute this to the impact of additive white Gaussian noise which may distort the phase recovery for small *N*. Note that Flicker and randomwalk frequency would occur at Fourier frequencies below 1 MHz, see Fig. 4.2(c), and would hence also be effectively suppressed by BPS.

**Figure 4.4**. FM- noise compensation by blind-phase search (BPS) for different averaging lengths *N*: In the simulation, we assume 16QAM transmission at a symbol rate of 38 GBd, an intrinsic linewidth of the carrier of L ∆ = *f* 1.9 MHz, and an OSNR of 35 dB. The traces show the residual FM-noise spectrum of the received signal after blind phase search, relying on averaging of measured phases over a moving group of *N* =10 (red trace) and *N* = 100 (green trace) symbols. The blue trace indicates the spectrally white FM-noise spectrum of the carrier prior to modulation. As a rough estimate, BPS relying on a moving group of *N* symbols can effectively suppress frequency noise components occurring at Fourier frequencies up to S *f NT* =1 , where S*T* ≈ 26ps corresponds to the symbol duration. Flicker and random-walk frequency would occur at Fourier frequencies below 106 Hz and would hence also be effectively suppressed by BPS.

For a carrier with given phase noise and a fixed OSNR, an optimum number *N* of symbols within a group exists that provides an ideal trade-off between strong resilience to noise when averaging over many symbols for large *N* and the ability to track fast phase fluctuations, which requires small *N*. For a symbol rate of 38 GBd, an intrinsic linewidth of the QD-MLLD tone of 1.9 MHz, and OSNR levels of approximately 25 dB, best values of *N* are typically between 20 and 40. For *N* = 40 and symbol rates of 2 GBd or more, the overall averaging time of the phase-tracking scheme amounts to at most 20 ns. This is much shorter than the limit τ low ≈1µs of the observation time, beyond which flicker and random-walk frequency noise start to become noticeable, see Section 4.3.1. We may hence conclude that the phase-noise-related impairments that remain after symbol-wise phase tracking are solely dictated by the intrinsic (short-term) linewidth of the device related to the spectrally white component of the FM-noise.

Note that there is a residual probability that cycle slips occur in the BPS algorithm. To check this aspect, we have investigated our 16QAM recordings with OSNR values of 19.8 dB, 20.6 dB and 21.3 dB and with lengths of 6 × 105 symbols without finding any cycle slips. We hence conclude that the BPS phase recovery is able to reliably track the phase over long symbol sequences. In a real system, this might have to be backed up by advanced FEC schemes [41] or pilot symbols [42].

In our experiments, the length of the PRBS was limited to 211 – 1 due to the memory size and the memory granularity of the arbitrary waveform generator (AWG) that was used to generate the data signals. However, we do not expect that a longer PRBS would lead to different results. For a symbol rate of 38 GBd, the duration of a single PRBS sequence amounts to 50 ns. In comparison to that, the averaging time used for BPS is much shorter and amounts to less than 1 ns (*N* < 40). Any phase drifts occurring over a longer time scale will be suppressed by the phase-noise compensation, and the associated signal impairments will vanish. Increasing the PRBS length beyond the currently used 50 ns will hence not have any impact on the phase-noise-related signal impairments.

Note that BPS is not the only phase tracking technique that allows to compensate impairments introduced by optical carriers with strong phase noise. Comparative study of other phase-tracking techniques such as digital phase-locked loops, Viterbi & Viterbi phase estimation, or algorithms based on Kalman filtering can, e.g., be found in Refs. [142]–[144]. In these studies, one conclusion is that feed-forward techniques such as BPS are more phase-noise tolerant and better suited for high symbol rates than feedback phase tracking such as digital phase-locked loops or algorithms based on Kalman filtering. Regarding feedforward methods, it has also been shown that BPS outperforms other algorithms such as Viterbi & Viterbi phase estimation in terms of phase-noise tolerance, and previous studies indicate that the Viterbi & Viterbi algorithm is not well

suited for compensating the phase noise of QD-MLLD carriers at rather low symbol rates of 12.5 GBd [101].

It should also be noted that the performance advantages of symbol-wise BPS come at the price of increased computational complexity when compared to block-wise phase recovery. A more detailed discussion of the trade-off between the computational effort and the performance of BPS can, e.g., be found in [144]. Despite this complexity increase of the phase-tracking algorithm, the overall DSP complexity at the receiver does not change to a substantial degree, since the computational effort is mainly dominated by chromatic-dispersion (CD) compensation and FEC decoding [145].

### **42 GBd PDM-QPSK 7.83 Tbit/s data transmission**

To demonstrate the viability of QD-MLLD in WDM transmission, we perform an experiment at a symbol rate of 40 GBd using QPSK as modulation format. The experimental setup is shown in Fig. 4.5(a). The total QD-MLLD output power is boosted by EDFA1 to 17 dBm. Using a programmable optical filter (POF), we select 52 tones from the frequency comb, marked in blue in Fig. 4.5(b), and separate them into odd and even carriers. The two sets of carriers are later encoded with independent data streams to emulate a realistic WDM signal [82], [95]. The POF additionally flattens the power spectrum of the carriers. After amplification and flattening, the OCNR of the comb lines amounts to approximately 35 dB. The even and odd carriers are amplified by subsequent EDFA2 and EDFA3 and sent through a pair of IQ modulators. Both modulators are driven by QPSK signals with RC spectrum pulses with a 5 % roll-off, generated by an AWG using a PRBS of length 211−1 at a symbol rate of 40 GBd. After combining the signals, PDM is emulated by a split-and-combine method, described in Section 4.4.1. The data stream is amplified and transmitted over 75 km of SSMF, see Fig. 4.5(c) for the power spectrum before and after modulation. At the receiver, we amplify the signal and select each channel using a 0.6 nm tunable BPF followed by EDFA6 and a second tunable 1.5 nm BPF to suppress out-of-band ASE noise. The signal is detected with a DP-CR and

**Figure 4.5**. PDM-QPSK data transmission with QD-MLLD. **(a)** Experimental setup used to emulate the WDM transmission experiment. EDFA: Erbium-doped fiber amplifier. POF: Programmable optical filter. AWG: Arbitrary-waveform generator. PDM: Polarization division multiplexing. VOA: Variable optical attenuator. DL: Delay line. PBC: Polarization beam combiner. SSMF: Standard single-mode fiber. BPF: Band-pass filter. LO: Local oscillator. **(b)** Optical spectrum of the QD-MLLD frequency comb. The 52 lines selected for WDM experiment are colored in blue. **(c)** Top: Superimposed spectra of odd and even carriers before modulation. Bottom: Spectrum of 52 modulated carriers. **(d)** EVM of the transmitted WDM channels. The maximum recording length of 2 × 106 bit leads to a minimum BER of 6.5 × 10–6 that can be measured in a statistically reliable way. This corresponds to an EVM of 22.9 %. Below this value, the expected BER is smaller and cannot be measured within our recordings of 10 6 symbols – the associated range of EVM values is shaded in green. Importantly, all 52 channels fall below an EVM of 38.5 %, which corresponds to a BER of 4.7 × 10−3 , representing the threshold for hard-decision FEC with 6.25 % overhead [140].

undergoes a number of DSP steps, as described in Sections 4.4.1 and 4.4.2. To undo the dispersive effect of the 75 km-long fiber link, we additionally perform CD compensation.

The measured EVM values are shown in Fig. 4.5(d). For evaluating the recorded signals, the averaging length *N* used for BPS is optimized individually for each channel, and amounts to approximately 30 symbols. For QPSK transmission, the signal quality is comparatively high with EVM levels down to 16 %, which would correspond to a BER of 2 × 10−10 assuming that the signals are impaired by additive white Gaussian noise (AWGN) only. To measure a statically reliable BER reaching a confidence level of 99 % within a confidence interval of 100 %, at least 13 erroneous bits have to be found in each recording [44]. This would lead to recording lengths of more than 6 × 1010, which is far beyond the storage capabilities of our oscilloscope. We hence limited our recordings to a practically well manageable length of approximately 2 × 106 bit and rely on the EVM as a quality metric. For this length, the smallest BER that can be measured with the above-mentioned confidence amounts to 6.5 × 10−6 , which would correspond to an EVM of approximately 22.9 %. Recordings with EVM values below this value are not accessible to direct BER measurements and fall into the green shaded area in Fig. 4.5(d). A statistically reliable measurement of the BER was hence only possible for the two channels at the lowest carrier frequency – the measured BER values are indicated in Fig. 4.5(d) and are in good agreement with the BER estimated from the EVM assuming that the signals are impaired by AWGN only. Importantly, all 52 channels fall below an EVM of 38.5 %, which corresponds to a BER of 4.7 × 10−3 [44], representing the threshold for hard-decision FEC with 6.25 % overhead [140]. This leads to an aggregate line rate of 8.32 Tbit/s and a net data rate of 7.83 Tbit/s, transmitted over 75 km of SSMF with a net spectral efficiency of 3.8 bit/s/Hz.

#### **38 GBd PDM-16QAM 10.68 Tbit/s data transmission**

We also perform a 16QAM transmission demonstration to prove the viability of symbol-wise blind phase search (BPS) for more complex modulation formats. We use the same setup as for the QPSK experiments, see Fig. 4.5(a). The symbol rate amounts to 38 GBd, and we use 38 carriers from our QD-MLLD frequency comb for WDM transmission, see Fig. 4.6(a) for the flattened power spectrum before and after modulation. We use pulses with RC spectrum having a 10 % roll-off. The WDM transmission experiments relies on the central 38 comb lines, which offer a spectral flatness of better than 3 dB. The measured BER for each of the transmitted WDM channels is depicted in Fig. 4.6(b). For each channel, five signal sequences were recorded, each containing 106 bit. This recording length is sufficient to provide more than 100 erroneous bits in each of our measurements, hence allowing for a statistically reliable BER estimation, see Section 4.4.3. Also here, the averaging length *N* used for BPS is optimized for each channel, see Section 4.4.2. Out of the 38 channels, 32 fall below the

**Figure 4.6**. Data transmission results of 38 channels carrying PDM-16QAM signals at 38 GBd. **(a)** Top: Combined odd and even carriers prior to modulation. Bottom: 38 modulated carriers prior to transmission. The line rate amounts to 304 Gbit/s per channel. **(b)** Measured BER of the transmitted channels. The BER increase towards lower carrier frequencies is attributed to an increase of the noise figures of EDFA5 and EDFA6 with decreasing optical frequency. **(c)** Exemplary constellation diagrams recorded at different optical carrier frequencies.

BER threshold of 4.7 × 10-3 for hard-decision FEC with 6.25 % overhead, while the remaining six channels fall below the BER threshold of 1.44 × 10−2 for FEC with 20 % overhead [140]. This leads to an aggregate line rate of 11.55 Tbit/s and a net data rate of 10.68 Tbit/s with a net spectral efficiency of 6.7 bit/s/Hz. To the best of our knowledge, our experiments represent the first demonstration of optical 16QAM signal transmission using multiple carriers from a DC-driven chip-scale comb generator without any hardware-based phase-noise reduction schemes, leading to the highest data rate achieved in such an experiment. From Fig. 4.6(b) one can observe that channels at higher frequencies have a better signal quality. This is due to the fact that our preamplifiers EDFA5 and EDFA6 have a higher noise figure for decreasing optical frequency. Exemplary constellation diagrams for dual polarization channels at carrier frequencies 195.46 THz and 194.64 THz are shown in Fig. 4.6(c).

Note that the FSR of 42 GHz of the MLLD comb generator was deliberately chosen for our experiments to enable transmission at maximum spectral efficiency with the available transmitter equipment. Specifically, the AWG (Keysight M8195) used for driving the I/Q modulators was limited to a bandwidth of approximately 20 GHz, which led to high penalties when utilizing 16QAM at symbol rates beyond 40 GBd, see Fig. 4.3(c). Other FSR can be obtained by cleaving the devices at a different length to achieve line spacings of, e.g., 25 GHz [122] or 50 GHz that comply to ITU standards.

## **4.5 Summary**

Equation Chapter (Next) Section 1

We have shown that the strong low-frequency FM noise of QD-MLLD can be overcome by feed-forward symbol-wise phase tracking, thus making the devices usable as particularly simple and attractive multi-wavelength light sources for WDM transmission at data rates beyond 10 Tbit/s. We perform an in-depth analysis of the phase-noise characteristics of QD-MLLD, which reveals a strong increase of the FM-noise spectrum at low frequencies as the main problem that has prevented the use of higher-order modulation formats such as 16QAM so far. To overcome these limitations, we implement and test a digital phase tracking technique using a symbol-wise blind phase search (BPS) technique that finally allows transmission of 38 GBd dual-polarization (DP) 16QAM signals on a total of 38 carriers. This leads to a line rate of 11.55 Tb/s and a net data rate of 10.68 Tbits/s. To the best of our knowledge, this is the highest data rate so far achieved by a DC-driven chip-scale comb generator without any hardwarebased phase-noise reduction schemes. We show that under realistic transmission conditions the QD-MLLD tones show a penalty of less than 0.5 dB with respect to a 10 kHz-wide high-quality laser carrier.

# **5 Microresonator-based Kerr comb generators for massively parallel coherent optical communications**

This chapter devotes itself to the demonstration of massively parallel WDM coherent communications using the tones of microresonator-based dissipative Kerr solitons (DKS) both at the transmitter and at the receiver. The contents of this chapter correspond to the publication [J1], which was published with equal contribution from me, Juned N. Kemal, and M. Karpov. In this work, I contributed and lead the DKS generation and the data transmission experiments using DKS generators as multi-wavelength light sources at the transmitter, see Sections 5.2 and 5.3., and to the analysis of the power conversion efficiency of DKS in Section 5.5. To maintain a logical structure of the contents of this thesis, the complete publication is reproduced in this chapter. In order to fit the structure and layout of this document, the content of the publication was adapted accordingly. Methods and Supplementary Information associated with this publication are to be found in Appendix B.

In this publication, the author of this thesis, Juned N. Kemal and M. Karpov contributed equally. The idea of the experiment was developed jointly by the author together with J. Kemal, and C. Koos. The author of this thesis and J. N. Kemal jointly developed and implemented the experimental setups, discussed in detail in Appendices B.3, B.4 and B.5, with the support of P. Trocha, S. Wolf, R. Rosenberger, J. Pfeifle, and K. Vijayan. The transmission experiments with DKS combs as multi-wavelength carrier source at the transmitter, Section 5.3, were lead by the author of this thesis, while the transmission experiment using DKS solitons both as multi-wavelength carriers and multi-wavelength LO was lead by J. N. Kemal. The investigation of power conversion efficiency of the DKS source, Section 5.5, was developed by the author together with J. N. Kemal with the support of C. Koos, M. Karpov, M.H.P. Pfeiffer, V. Brasch, M. H. Anderson, and A. Kordts from the Laboratory of Photonics and Quantum Measurements at École Polytechnique Fédérale de Lausanne (EPFL) developed,

fabricated, and characterized the Kerr-nonlinear microresonators for comb generation as well as the soliton-generation technique described in Appendices B.1 and B.2. Section 5.2 and Appendix B.7 under supervision of T. J. Kippenberg. The DSP required for the analysis of the recordings was performed by the author of this dissertation together with J. N. Kemal. Sections 5.2, 5.3, and 5.5 were written by the author with the support of J. N. Kemal, W. Freude, and C. Koos. The work was jointly supervised by W. Freude, T.J. Kippenberg, and C. Koos.

*[start of paper [J1]]*

#### **Microresonator solitons for massively parallel coherent optical communications**

*Nature, Volume 546, Issue 7657, pp. 274-279, 2017 DOI: 10.1038/nature22387*

Pablo Marin-Palomo1,† , Juned N. Kemal1,† , Maxim Karpov2,† , Arne Kordts2 , Joerg Pfeifle1 , Martin H. P. Pfeiffer2 , Philipp Trocha1 , Stefan Wolf 1 , Victor Brasch2 , Miles H. Anderson2 , Ralf Rosenberger1 , Kovendhan Vijayan1 , Wolfgang Freude1,3, Tobias J. Kippenberg2 , Christian Koos1,3

Optical solitons are waveforms that preserve their shape while propagating, relying on a balance of dispersion and nonlinearity [146], [147] Soliton-based data transmission schemes were investigated in the 1980s, promising to overcome the limitations imposed by dispersion of optical fibers. These approaches, however, were eventually abandoned in favor of wavelength-division multiplexing (WDM) schemes that are easier to implement and offer improved scalability to higher data rates. Here, we show that solitons may experience a comeback in optical communications, this time not as a competitor, but as a key element of massively parallel WDM. In-stead of encoding data on the soliton itself, we exploit continuously circulating dissipative Kerr solitons (DKS) in a microresonator [21], [148]. DKS are generated in an integrated silicon nitride microresonator [149] by four-photon interactions mediated by Kerr nonlinearity, leading to low-noise, spectrally smooth and broadband optical frequency combs [75]. In our experiments, we use two interleaved soliton Kerr combs to transmit a data stream of more than 50 Tbit/s on a total of 179 individual optical carriers that span the entire telecommunication C and L bands. Equally important, we demonstrate coherent detection of a WDM data stream by using a pair of microresonator Kerr soliton combs – one as a multi-wavelength light source at the transmitter, and another one as a corresponding local oscillator (LO) at the receiver. This approach exploits the scalability advantages of microresonator soliton comb sources for massively parallel optical communications both at the transmitter and receiver side. Taken together, the results prove the significant potential of these sources to replace arrays of continuous-wave lasers in high-speed communications. In combination with advanced spatial multiplexing schemes [94], [150] and highly integrated silicon photonic circuits [151], DKS combs may bring chip-scale petabit/s transceivers into reach.

### **5.1 Introduction**

The first observation of solitons in optical fibers [147] in 1980 was immediately followed by major research efforts to harness such waveforms for long-haul communications [146]. In these schemes, data was encoded on soliton pulses by simple amplitude modulation using on-off-keying (OOK). However, even though the viability of the approach was experimentally demonstrated by transmission over one million kilometers [152], the vision of soliton-based communications was ultimately hindered by difficulties in achieving shape-preserving propagation in real transmission systems [146] and by the fact that nonlinear interactions intrinsically prevent dense packing of soliton pulses in either the time or frequency domain. Moreover, with the advent of wavelength-division multiplexing (WDM), line rates in long-haul communication systems could be increased by rather simple parallel transmission of data streams with lower symbol rates, which are less dispersion sensitive. Consequently, soliton-based communication schemes have moved out of focus over the last two decades.

More recently, frequency combs were demonstrated to hold promise for revolutionizing high-speed optical communications, offering tens or even hundreds of well-defined narrowband optical carriers for massively parallel WDM [93]– [95]. Unlike carriers derived from a bank of individual laser modules, the tones of a comb are intrinsically equidistant in frequency, thereby eliminating the need for individual wavelength control and for inter-channel guard bands [94], [95]. In addition, when derived from the same comb source, stochastic frequency variations of optical carriers are strongly correlated, permitting efficient compensation of impairments caused by nonlinearities of the transmission fiber [34].

For application in optical communications, frequency comb sources must be compact. In recent years, a wide variety of chip-scale comb generators have been demonstrated [12], [16], enabling transmission of WDM data streams with line rates of up to 12 Tbit/s [123]. Transmission at higher line rates however, requires more carriers and lower noise levels, and still relies on spectral broadening of narrowband seed combs using dedicated optical fibers [93]–[95] or nanophotonic waveguides [97]. In addition, generating uniform combs with a broadband spectral envelope often requires delicate dispersion management schemes, usually in combination with intermediate amplifiers [93]. Such schemes are difficult to miniaturize and not readily amenable to chip-scale integration. Moreover, with a few exceptions at comparatively low data rates [17], all advanced comb-based transmission experiments exploit the scalability advantages only at the transmitter, but not at the receiver, where individual continuous-wave (CW) lasers are still used as optical local oscillators (LO) for coherent detection.

In this paper, we show that dissipative Kerr solitons [21] (DKS) generated in integrated photonic microresonators via Kerr-nonlinear four-photon interactions, allow for generation of highly stable broadband frequency combs that are perfectly suited to overcome scalability limitations of massively parallel optical transmission both at the transmitter and receiver. Microresonator-based Kerr comb sources [153], [154] intrinsically offer unique advantages such as small footprint, large number of narrow-linewidth optical carriers, and line spacings of tens of GHz, which can be designed to fit established WDM frequency grids. However, while these advantages were recognized, previous transmission experiments were limited to aggregate line rates of 1.44 Tbit/s due to strong irregularities of the optical spectrum associated with the specific Kerr comb states [82].

These limitations can be overcome by using DKS combs generated in a CWdriven microresonator. The technique exploits four-wave mixing, a process that converts two pump photons into a pair of new photons. In a microresonator, the strength of this interaction is given by the single-photon Kerr frequency shift of = ℏ0 22 2 ⁄ eff, where 2 (*n*) is the nonlinear (linear) refractive index, *c* the speed of light in vacuum, ℏ the reduced Planck constant, eff the nonlinear optical mode volume and 0 the angular frequency of the pump mode. For pump powers that cause the cavity Kerr frequency shift to exceed the linewidth of the resonance, parametric oscillations lead to the emergence of Kerr frequency combs (modulation instability, MI Kerr combs). Bright DKS can be formed in this process when the microresonator has a locally anomalous group velocity dispersion (i.e. a Taylor expansion for cavity modes = 0 + ∑ ⁄! ∞ =1 has 2 > 0 ) and a CW laser excitation (frequency ) that is red detuned from the cavity resonance (i.e. = 0 − > 0). Mathematically, DKS states appear as specific solutions of the Lugiato-Lefever equation [155] and consist of an integer number of discrete secant-hyperbolic-shaped pulses on a CW background circulating in the cavity [21]. Stability of such states relies on the double balance of dispersion and Kerr nonlinearity as well as of nonlinear parametric gain and cavity loss. Theoretically predicted in Ref. [148] and first reported to spontaneously form in microresonators made from crystalline MgF2 [21], DKS have been observed in different types of material systems including silica-on-silicon [156] and silicon nitride [75] (Si3N4) as well as silicon [157]. Of particular interest are single-soliton states, which consist of only one ultrashort pulse circulating around the cavity, leading to a broadband comb spectrum with a smooth and numerically predictable envelope given by

$$p(\mu) \approx \frac{\kappa\_{\rm ev} D\_2 \hbar o\_o}{4g} \text{sech}^2 \left(\frac{\pi \mu}{2} \sqrt{\frac{D\_2}{2 \delta o}}\right) \tag{5.1}$$

where represents the external coupling rate to the bus waveguide [21] (see Appendix B.6.2 for more details). DKS have already been used in applications such as self-referencing of optical frequency combs [11], [158], low noise microwave generation [159] and dual soliton comb spectroscopy [156], [160].

Our demonstration comprises a series of three experiments that exploit the extraordinarily smooth and broadband spectral envelope and the inherently low phase noise of DKS combs for massively parallel coherent communications. In a first experiment, we transmit data on 94 carriers that span the entire telecommunication C and L bands with a line spacing of ~ 100 GHz. Using 16-state quadrature amplitude modulation (16QAM) to encode data on each of the lines, we achieve an aggregate line rate of 30.1 Tbit/s. In a second experiment, we double the number of carriers by interleaving two DKS combs. This gives a total of 179 carriers and an aggregate line rate of 55.0 Tbit/s transmitted over a distance of 75 km – the highest data rate achieved to date with a chip-scale frequency comb source. In a third experiment, we demonstrate coherent detection using a DKS comb as a multi-wavelength LO. We use 93 carriers to transmit and receive an aggregated line rate of 37.2 Tbit/s. In these experiments, the LO comb is coarsely synchronized to the transmitter comb, and digital signal processing is used to account for remaining frequency differences. The results prove the tremendous potential of Kerr soliton combs, both as multi-wavelength optical sources and as LO for massively parallel WDM transmission.

## **5.2 Generation of dissipative Kerr soliton frequency combs in SiN microresonators**

Our work relies on integrated Si3N4 microresonators for generation of DKS frequency combs [21], cf. Fig. 5.1(a). The Si3N4 platform is chosen due to its low optical losses and its compatibility with large-scale silicon-based processing [149]. The microresonators feature a waveguide height of 800 nm to achieve anomalous group velocity dispersion (GVD) and are fabricated using the photonic Damascene process [161]. Neighboring resonances are spaced by 100 GHz while featuring intrinsic *Q*-factors exceeding 106 . DKS combs are obtained by sweeping of the pump laser through the resonance from a blue-

**Figure 5.1**: Broadband frequency comb generation using dissipative Kerr solitons in high-Q silicon nitride (Si3N4) microresonators. **(a)** Principle of soliton frequency comb generation: The integrated photonic microresonator is pumped by a tunable CW laser amplified by an erbium-doped fiber amplifier (EDFA). Lensed fibers are used to couple light to the chip (FPC – fiber polarization controller). After the microresonator, a notch filter (NF) suppresses the remaining pump light. The insets show scanning electron microscopy images of a Si3N4 microresonator with a radius of 240 μm. Right inset: Top view. The checker-board pattern results from the photonic Damascene fabrication process [161], see Appendix B.1. Left insets: Cross sections of the resonator waveguide (dimensions 0.8 × 1.65 μm2 ) at the coupling point (top) and at the tapered section (bottom, dimensions 0.8 × 0.6 μm2 ). The tapered section is used for suppressing higher order modes families [162], while preserving a high optical quality factor (*Q* ~ 106 ), see Appendix B.1**. (b)** Pump tuning method for soliton generation in optical microresonator, showing the evolution of the generated comb power versus pump laser wavelength: (I) The pump laser is tuned over the cavity resonance from the blue-detuned regime, where high-noise modulation instability (MI) combs are observed, to the red-detuned regime, where cavity bistability allows for the formation of soliton states (here a multiple soliton state); (II) Upon having generated a multiple soliton state, the pump laser is tuned backwards to reduce the initial number of solitons down to a single one. The insets on the right schematically show the corresponding intracavity waveforms in different states (MI, multiple and single soliton state). **(c)** Measured spectrum of a single-soliton frequency comb after suppression of residual pump light. The frequency comb features a smooth spectral envelope with a 3 dB bandwidth of 6 THz comprising hundreds of optical carriers extending beyond the telecommunication C and L bands (blue and red, respectively).

detuned wavelength to a predefined red-detuned wavelength [21], [75]. This leads initially to the generation of MI Kerr combs followed by DKS states once the resonance is crossed, cf. Fig. 5.1. Importantly, once a multiple-soliton comb state is generated, the transition to a single-soliton state can be accomplished in a reliable and deterministic manner by adjusting the laser frequency [22], cf.

Fig. 5.1(a),(b) and Appendix B.1. The measured power spectrum of the DKS comb state is shown in Fig. 5.1(c), which exhibits a 3dB spectral bandwidth of ~ 6 THz. The soliton comb states are remarkably stable for many hours in a laboratory environment, which is key to the transmission experiments presented in this work. Massively-parallel data transmission using dissipative Kerr solitons.

## **5.3 Soliton Kerr comb generators for as multiwavelength carriers for WDM transmission**

The general concept of massively parallel data transmission using a frequency comb as a multi-wavelength light source is depicted in Figure 5.2(a). For emulating massively parallel WDM transmission in our laboratory, we rely on a simplified scheme using only two independent data streams on neighboring channels along with an emulation of polarization division multiplexing, see Appendix B.3 for details. We use 16QAM at a symbol rate of 40 GBd along with band-limited Nyquist pulses that feature approximately rectangular power spectra, Figure 5.2(b). At the receiver, each channel is individually characterized using a CW laser as LO and an optical modulation analyzer, which extracts signal quality parameters such as the error-vector magnitude (EVM) or the biterror ratio (BER). The BER of the transmission experiment are depicted in Figure 5.2(e) with different BER thresholds indicated as horizontal dashed lines. Out of the 101 carriers derived from the comb in the C and L band, a total of 94 channels were used for data transmission. This leads to a total line rate of 30.1 Tbit/s, see Appendix B.1 for details on data rate calculations. The transmission capacity is restricted by the fact that the line spacing of ~ 100 GHz significantly exceeds the signal bandwidth of ~ 40 GHz, leading to unused frequency bands

**Figure 5.2**: Data transmission using microresonator soliton frequency comb generators as optical sources for massively parallel WDM. **(a)** Principle of data transmission using a single DKS comb generator as optical source at the transmitter. A demultiplexer (DEMUX) separates the comb lines and routes them to individual dual-polarization in-phase/quadrature (IQ) modulators, which encode independent data on each polarization. The data channels are then recombined into a single-mode fiber using a multiplexer (MUX) and boosted by an erbium-doped fiber amplifier (EDFA) before being transmitted. At the receiver, the wavelength channels are separated by a second DEMUX and detected using digital coherent receivers (Coh. Rx) along with individual CW lasers as local oscillators (CW LO). In our laboratory experiment, we emulate WDM transmission by independent modulation of even and odd carriers using two IQ modulators, see Appendix B.3. We use 16-state quadrature amplitude modulation (16QAM) at a symbol rate of 40 GBd per channel. (Caption continued on next page)

**Figure 5.2 continued**: **(b)** Section of the optical spectrum of the WDM data stream. Nyquist pulse shaping leads to approximately 40 GHz wide rectangular power spectra for each of the carriers, which are spaced by approximately 100 GHz. **(c)** Principle of data transmission using interleaved DKS combs. At the transmitter, two combs of practically identical line spacing are interleaved. The resulting comb features a carrier spacing of approximately 50 GHz, which enables dense spectral packing of WDM channels and hence high spectral efficiency. At the receiver, this scheme still relies on individual CW lasers as LO for coherent detection, see Appendix B.3 for details. **(d)** Section of the optical spectrum of the WDM data stream. **(e)** Measured biterror ratios (BER) of the transmitted channels for the single-comb and the interleaved-comb experiment, along with the BER thresholds for error-free propagation when applying forward error correction schemes with 7% overhead (4.5 × 10-3, dashed orange line) and 20 % overhead (1.5 × 10-2, dashed blue line) [43], see Appendix B.1 for details. For the interleaved-comb experiment, the outer 14 lines at the low-frequency edge of the L band were modulated with quadrature phase-shift keying (QPSK) signals rather than 16QAM due to the low OSNR of these carriers. **(f)** Measured BER vs. optical signal-to-noise ratio OSNR of three different channels derived from a DKS frequency comb (blue) and a high-quality ECL (red), all with 16QAM signaling at 40 GBd. A total of 106 bits were compared. The comb lines do not show any additional penalty in comparison the ECL tones. Similar results were obtained at other symbol rates such as 28 GBd, 32 GBd, or 42.8 GBd. **(g)** Constellation diagrams obtained for an ECL and DKS comb tone at 193.56 THz.

between neighboring channels, see Figure 5.2(b), and hence to a rather low spectral efficiency (SE) of 2.8 bit/s/Hz. These restrictions can be overcome by using interleaved frequency combs, see Figure 5.2(c). The scheme relies on a pair of DKS combs with practically identical line spacing, but shifted with respect to each other by half the line spacing by thermal tuning. At the receiver, this scheme still relies on individual CW

lasers as LO for coherent detection. The interleaved comb features a line spacing of ~ 50 GHz, which allows for dense packing of 40 GBd data channels in the spectrum, see Fig. 5.2(d). The BER results of the transmission experiment are depicted in Fig. 5.2(e) with different thresholds indicated as horizontal dashed

lines. For a given forward-error correction (FEC) scheme, these thresholds define the maximum BER of the raw data channel that can still be corrected to a BER level below 10-15, which is considered error-free [43], see Appendix B.1

We find a total of 204 tones in the C and L band, out of which 179 carriers could be used for data transmission. The remaining channels were not usable due to technical limitations, see Appendix B.1. The transmission performance is slightly worse than in the single-comb experiment since twice the number of carriers had to be amplified by the same EDFA, which were operated at their saturation output power such that the power per data channel reduced accordingly. Nevertheless, data was successfully transmitted over 75 km of standard single-mode fiber at a symbol rate of 40 GBd using a combination of 16QAM and QPSK. The total line rate amounts to 55.0 Tbit/s, and the net data rate is 50.2 Tbit/s. This is the highest data rate so far achieved with a chip-scale frequency comb source, and compares very well to the highest capacity of 102.3 Tbit/s ever transmitted through a single-mode fiber core using more than 200 discrete DFB lasers as optical sources at the transmitter [163]. In addition, we achieve an unprecedented spectral efficiency of 5.2 bit/s/Hz, owing to the densely packed spectrum, Fig. 5.2(d). In the experiments, limited saturation output power of the employed EDFA is the main constraint of signal quality and BER, see AppendicesB.3 and B.6.3 for details. The presented data rates are hence not limited by the DKS comb source, but by the components of the current transmission setup, leaving room for further improvement.

To confirm the outstanding potential of DKS combs for data transmission, we compare the transmission performance of a single comb line to that of a reference carrier derived from a high-quality benchtop-type external-cavity laser featuring an optical linewidth of approximately 10 kHz, an optical output power of 15 dBm, and an optical carrier-to-noise power ratio (OCNR) in excess of 60 dB. As a metric for the comparison, we use the OSNR penalty at a BER of 4.5 × 10- 3 , which corresponds to the threshold for FEC with 7 % overhead [43]. The results for 40 GBd 16QAM transmission are shown in Fig. 5.2(f) for three different comb lines and for ECL reference transmission experiments at the corresponding comb line frequencies. The OSNRref values are defined for a reference bandwidth of 0.1 nm, see Appendix B.4. As shown, no additional OSNR penalty is observed for the frequency comb when compared with the high-quality ECL: For both sources, we observe an OSNR penalty of 2.6 dB with respect to the theoretically required OSNR (black line) for a BER of 4.5 × 10-3. DKS-based light sources can hence dramatically improve scalability of WDM systems without impairing the signal quality under realistic transmission conditions. The error floor in Fig. 5.2(f) is attributed to transmitter nonlinearities and electronic receiver noise in our setup. Fig. 5.2(g) shows the measured constellation diagrams for the ECL and the comb line at 193.56 THz, both taken at the same OSNR of 35 dB.

## **5.4 Data transmission using DKS combs both at the transmitter and at the receiver**

To demonstrate the potential of DKS frequency combs as multi-wavelength LO at the receiver, we perform a third experiment shown schematically in Fig. 5.3(a). At the transmitter, a first DKS comb generator with an FSR of ~ 100 GHz serves as an optical source. At the receiver, a second DKS comb source having approximately the same FSR is used to generate the corresponding LO tones, each featuring an optical linewidth below 100 kHz. Fig. 5.3(b),(c) show a section of the transmitted data spectrum along with the corresponding section of the LO comb. As a reference, the same experiment was repeated using a high-quality ECL with a 10 kHz linewidth as an LO for channel-by-channel demodulation. Overall, an aggregate data rate of 34.6 Tbit/s is obtained. The resulting BER values of all 99 channels for both methods are shown in Fig. 5.3(d). Some of the channels showed signal impairments due to limitations of the available equipment, see Appendix B.1. However, we cannot observe any considerable penalty that could be systematically attributed to using the DKS comb as an LO.

## **5.5 Power conversion efficiency of dissipative Kerr solitons**

While frequency combs offer fundamental technical advantages compared to discrete lasers, they can also contribute to reduce the power consumption of the transmission system. In this context, the power conversion efficiency of the DKS comb generator is an important metric, defined as the ratio between the power of the pump and that of the generated comb lines. The power conversion efficiency of our current comb sources is limited to rather small values between 0.1 % and 0.6 % due to the fundamental principle that bright soliton generation

**Figure 5.3**: Coherent data transmission using microresonator soliton frequency combs both at the transmitter and at the receiver side. **(a)** Massively parallel WDM data transmission scheme using DKS frequency combs both as multi-wavelength source at the transmitter and as multiwavelength local oscillator (LO) at the receiver. In contrast to Figure 5.2, a single optical source provides all required LO tones for coherent detection. An extra DEMUX is used to route each LO tone to the respective coherent receiver (Coh. Rx). **(b)** Section of the spectrum of the transmitted channels. **(c)** Corresponding section of the spectrum of the LO frequency comb. Note that the comparatively large width of the depicted spectral lines is caused by the resolution bandwidth of the spectrometer (RBW = 0.1 nm) and does not reflect the sub-100 kHz optical linewidth of the LO tones. **(d)** Measured BER for each data channel. Blue squares show the results obtained when using a DKS comb as multi-wavelength LO, and red triangles correspond to a reference measurement using a high-quality ECL as LO. Dashed lines mark the BER thresholds of 4.5×10–3 (1.5×10–2 ) for hard-decision (soft-decision) FEC with 7 % (20 %) overhead. Black circles show the channels with BER above the threshold for 7 % FEC and specify the reasons for low signal quality: low OCNR of the carriers from the LO comb ("LO") and the signal comb ("Signal"), as well as bandwidth limitations of the C-band EDFA ("EDFA"), see Appendix B.1 for more details.

only occurs with the pump laser being far detuned from the optical resonance. Still, the overall power consumption can already now compete with massively parallel arrays of commercially available integrated tunable laser assemblies (ITLA), see Appendices B.1 and B.6 for details. The analysis also shows that

improvement of more than one order of magnitude compared to ITLA is possible by optimizing the microresonator dispersion, by making use of tailored amplifiers with optimum efficiency, and by increasing the power conversion efficiency via recently demonstrated high-*Q* Si3N4 microresonators with *Q*-factors of 6 × 106 .

## **5.6 Summary**

In summary, we have demonstrated the potential of chip-scale DKS frequency combs for massively parallel WDM at data rates of tens of terabit/s. We use them both as multi-wavelength source at the transmitter and as LO at the receiver, and we show in both cases that that there is no systematic penalty compared to using high-quality ECL. While our experiments achieve the highest data rate with chip-scale frequency comb sources to date, there is still room for increasing the transmission capacity by optimizing the transmission system or by using the adjacent S and U bands for telecommunications in the near infrared. For long transmission distances, comb-based transmission schemes might allow for compensation of nonlinear impairments and hence lead to an improved signal quality compared to conventional WDM schemes [34]. The results prove the tremendous potential of DKS comb generators for high-speed data transmission, both in petabit/s intra-datacenter networks [164] and in inter-datacenter connections.

*[end of paper [J1]*

# **6 Summary and Outlook**

## **6.1 Summary**

This thesis aims at investigating and verifying the potential of chip-scale frequency comb sources for coherent WDM transmission both from a fundamental and an experimental approach.

In this context, a holistic model is derived to estimate the transmission performance of comb-based WDM links. The findings extracted from this model helped to compare different comb generator types and to benchmark them against the achievable transmission performance. When using chip-scale comb sources both at the transmitter side and at the receiver side, the analysis leads to transmission capacities reaching 80 Tbit/s for metropolitan-area links of up to 400 km.

From an experimental standpoint, two highly-promising chip-scale comb sources are characterized and their potential for massively parallel WDM transmission is verified by performing various data transmission experiments. These comb generators are the so-called quantum-dash mode-locked laser diode (MLLD) and the microresonator-based Kerr comb generator which consists of a Kerr-nonlinear silicon nitride (SiN) microresonator driven by a continuouswave (CW) laser.

The main properties of these comb generators and the key data transmission achievements are summarized below.

*Quantum-dash mode-locked laser diodes (QD-MLLD)* stand out due to their compactness and simple operation by a direct current along with the ability to generate a flat and broadband frequency comb comprising dozens of equidistant lines spaced by tens of GHz and distributed over more than 2 THz. These properties make QD-MLLD devices promising candidates to be used as multi-wavelength light sources in WDM links. However, these devices suffer from the large optical linewidth of the individual carriers, which impairs the signal quality and

limits their use to rather low spectral efficient modulation formats. This thesis demonstrates spectrally efficient coherent transmission with QD-MLLD by using a dedicated digital phases tracking technique that can deal with the strong phase noise fluctuations of the comb lines. With this technique, a data stream of 11.55 Tbit/s was transmitted over 75 km of single-mode fiber by using 16QAM symbol at a symbol rate of 38 GBd.

*Microresonator-based Kerr comb generators* stand out due to their ability to produce a stable ultra-short pulse sequence, or soliton train, which corresponds to a broadband frequency comb, so-called dissipative Kerr soliton (DKS) comb, with hundreds of comb lines which are distributed over more than 10 THz. The tones of a DKS comb feature low phase noise levels which allow them to be used to transmit spectral efficient modulation formats without dedicated phase tracking techniques. Using DKS combs, a 55 Tbit/s data stream spanning the entire telecommunication C and L band is transmitted over a fiber length of 75 km, corresponding to the highest data rate with any chip-scale frequency comb source at the time of the publication.

Taken together, these results demonstrate the significant potential of these two comb sources to replace arrays of continuous-wave lasers in multi-Tbit/s communications.

## **6.2 Outlook**

The transmission experiments performed in this thesis relied on the use of a coherent receiver with an external cavity laser (ECL) as a local oscillator (LO). To leverage the full potential of the chip-scale comb sources investigated in this thesis, a second chip-scale comb source should be used at the receiver as multiwavelength LO, as depicted in Fig. 1.2. For Kerr comb sources, a first proof-ofprinciple transmission experiment has been demonstrated using two DKS combs, one as a multi-wavelength carrier at the receiver and another as a multiwavelength LO at the transmitter. The results of the transmission experiment are discussed in Section 5.4 and are part of the work of Juned N. Kemal. Similarly, QD-MLLD devices have been also used in a transmission experiment both as multi-wavelength carrier source and multi-wavelength LO source [J7]. In these two demonstrations, the LO comb is coarsely synchronized to the transmitter comb, and digital signal processing is used to account for the remaining frequency differences between the carriers and the corresponding LO tones. In this context, further investigations are necessary to continuously synchronize the center frequency and the free spectral range of the receiver comb to the transmitter comb.

In this thesis, the DKS comb is generated by driving a silicon nitride (SiN) microresonator with high optical powers of more than 1 W. Such high optical powers are achieved by amplifying the output from an ECL with a high-power optical amplifier. Future investigations towards Kerr-comb-based multi-Tbit/s transceivers should focus on the co-integration of the CW laser source and the microresonator. For this to happen, the threshold power for DKS generation should be reduced considerably. In this context, recent improvements of the microresonator technology by the group of T. J. Kippenberg,10 and the group of M. Lipson and A. L. Gaeta,11 has demonstrated DKS generation with optical powers below the 50 mW [76], [113]. Such advances lead to the first demonstrations of packaged Kerr-comb generators co-integrating the CW laser with the microresonator [23], [24]. In these demonstrations, however, the tones of the associated frequency combs feature comparatively low optical powers, which would impact data transmission performance considerably. The small optical powers are associated with the low power conversion efficiency from the pump laser to the comb lines, which is characteristic of DKS generation. Further investigations could focus on the use of so-called dark-solitons, which offer improved power conversion efficiencies [86], or on the use of quartic solitons, which are solitons generated in a microresonator with quartic group velocity dispersion (GVD) and lead to frequency combs with smoother spectra [112].

Future investigations regarding the use of QD-MLLD devices in WDM transceivers should focus on further paths to reduce the phase noise of the comb lines. In this context, the group of J. Witzens,12 has demonstrated RF linewidth

10 At the *Ecole* Polytechnique Fédérale de Lausanne, https://www.epfl.ch/labs/k-lab/

11 At the Columbia University, https://lipson.ee.columbia.edu/

12 At RWTH Aachen University, http://www.iph.rwth-aachen.de/

and optical linewidth reduction with optical feedback from a photonic integrated chip (PIC) [73]. Further investigations are required to understand the limitations of this approach, and its applicability for massively-parallel WDM transmission is the subject of ongoing research.

The focus of future work should be placed on packaged comb-based coherent WDM transceivers. For example, on the transmitter side, this would require multi-chip integration of modulators, (de)multiplexers and light sources. In this context, the group of C. Koos,13 has demonstrated coherent data transmission with a silicon photonics transmitter, where the silicon photonics modulators are connected to InP lasers by employing 3D nano-printing of freeform optical waveguides, so-called photonic wire bonding, for efficient coupling between the photonic chips [165]. Multi-chip integration of a frequency comb source with modulators and multiplexers is the subject of ongoing research. Future work could thus build upon the investigations presented in this thesis.

13 At the Karlsruhe Institute of Technology, https://www.ipq.kit.edu/index.php

# **Appendices**

Equation Chapter 1 Section 1

# **A. Performance of chip-scale optical frequency comb generators in coherent WDM communications: Additional information**

This section includes additional information on the underlying models introduced in Chapter 3.

## **A.1 OSNR penalty when using frequency comb sources at the receiver side**

This section details the derivation of Eq. (3.9) in Section 3, which describes the OSNR penalty of using a frequency comb source as a multi-wavelength local oscillator at the receiver side. The impact of the local oscillator is typically neglected, however, when using a frequency comb, the impact of a finite OCNR of the tones can become relevant.

Equation (3.9) is derived considering the coherent receiver from Fig. A.5, and assuming the signal is impaired by additive white Gaussian noise: The signal and the LO can be expressed as

$$\begin{aligned} \underline{E}\_1 &= \underline{E}\_s + \underline{\eta}\_s \\ \underline{E}\_2 &= \underline{E}\_{\rm LO} + \underline{\eta}\_{\rm LO} \end{aligned} \tag{A.1}$$

where s *E s n* and *E*LO LO *n* . Similar to Eq. (2.11), the photocurrent at the output of the tow BPDs can be expressed as

A Performance of chip-scale optical frequency comb generators in coherent WDM communications: Additional information

$$\begin{aligned} \underline{i}\_{I} - \mathrm{Re}\left\langle \underline{E}\_{1} \underline{E}\_{2}^{\*} \right\rangle &= \mathrm{Re}\underbrace{\left\langle \underline{E}\_{s} \underline{E}\_{\mathrm{LO}}^{\*} \right\rangle}\_{\mathrm{signal}} + \underbrace{\underline{E}\_{s} \underline{n}\_{\mathrm{LO}}^{\*} + \underline{E}\_{\mathrm{LO}}^{\*} \underline{n}\_{\mathrm{s}} + \underline{n}\_{s} \underline{n}\_{\mathrm{LO}}^{\*}}\_{\mathrm{noise}} \\ \underline{i}\_{Q} - \mathrm{Im}\left\langle \underline{E}\_{1} \underline{E}\_{2}^{\*} \right\rangle &= \mathrm{Im}\underbrace{\left\langle \underline{E}\_{s} \underline{E}\_{\mathrm{LO}}^{\*} \right\rangle}\_{\mathrm{signal}} + \underbrace{\underline{E}\_{s} \underline{n}\_{\mathrm{LO}}^{\*} + \underline{E}\_{\mathrm{LO}}^{\*} \underline{n}\_{\mathrm{s}} + \underline{n}\_{s} \underline{n}\_{\mathrm{LO}}^{\*}}\_{\mathrm{noise}} \end{aligned} \tag{A.2}$$

Neglecting the noise-noise mixing terms \* *s* LO *n n* and adding the photocurrents from both BPDs, the complex value signal can be constructed as

$$
\underline{i} \vdash \underline{E}\_s \underline{E}\_{\text{LO}}^\* + \underline{E}\_s \underline{\eta}\_{\text{LO}}^\* + \underline{E}\_{\text{LO}}^\* \underline{\eta}\_{\text{s}} \,. \tag{A.3}
$$

Equation (A.3) can be separated into signal intensity \* signal = *s* LO *i EE* and noise intensity \* \* noise LO s = + *s* LO *i En E n* . Next, the signal and noise powers are computed. Assuming that the noise terms are uncorrelated, the powers are added, resulting in

$$\begin{aligned} \boldsymbol{\dot{n}}\_{\text{signal}}^2 &\sim \left| \underline{\boldsymbol{E}}\_s \underline{\boldsymbol{E}}\_{\text{LO}}^\* \right|^2\\ \boldsymbol{\dot{n}}\_{\text{noise}}^2 &\sim \left| \underline{\boldsymbol{E}}\_s \underline{\boldsymbol{n}}\_{\text{LO}}^\* \right|^2 + \quad \left| \underline{\boldsymbol{E}}\_{\text{LO}}^\* \underline{\boldsymbol{n}}\_s \right|^2 \end{aligned} \tag{A.4}$$

Eq. (B.4) can be modified by using the OCNR relation for the LO

$$\text{OCNR} = \frac{\left| \underline{E}\_{\text{LO}} \right|^2}{\left| \underline{n}\_{\text{LO}} \right|^2},\tag{A.5}$$

and the OSNR relation for the signal

$$\text{OSNR} = \frac{\left| \underline{E}\_s \right|^2}{\left| \underline{n}\_s \right|^2}. \tag{A.6}$$

Introducing Eqs. (A.5) and (A.6) into Eq. (A.4),

$$\left| \boldsymbol{u}\_{\rm noise}^{2} = \left| \underline{E}\_{s} \right|^{2} \left| \underline{E}\_{\rm LO} \right|^{2} \left( \frac{1}{\rm OCNR} + \frac{1}{\rm OSNR} \right). \tag{A.7}$$

Defining the OSNR for OCNR → ∞ as

$$\text{OSNR}\_{\text{os}} = \frac{\left| \underline{E}\_{s} \right|^{2} \left| \underline{E}\_{\text{LO}} \right|^{2}}{i\_{\text{noise}}^{2}},\tag{A.8}$$

the OSNR can be extracted from Eq. (A.7) leading to

$$\text{OSNR} = \left(\frac{1}{\text{OSNR}\_{\text{-}\phi}} - \frac{1}{\text{OSNR}\_{\text{line}}}\right)^{-1}.\tag{A.9}$$

For simplification, in Section 3 it is assumed that the OCNR of the carrier is the same as the OCNR of the LO. This assumption is reasonable when the same type of frequency comb source is used both at the transmitter side and at the receiver side.

### **A.2 Omission of modulated noise**

The noise power given by Eq. (3.3) in Chapter 3 is modulated. The simple analysis in Chapter 3, however, does not take this effect into account. Considering modulated noise would make the analysis data dependent. This section justifies why a modulated noise is not considered in the analysis of Chapter 3.

In the case of amplitude modulation, the noise will be modulated and is therefore not stationary. For PSK formats, the model in Chapter 3 works fine and the results would not change. If comparing different QAM formats, the noise modulation will have a certain impact, which is related to the peak-to-average-power ratio. Also, the shape of MUX and DEMUX filters will have an impact. In the typically used link-limited regime, the effect of modulated noise can be disregarded since the dominating ASE noise is added after modulation. In the sourcelimited regime, neglecting the amplitude modulation of the noise might lead to a slight overestimation of the performance. A quantitative analysis of this effect, however, would depend on the modulation format and the associated modulation loss and would require exact knowledge of the spectral transmission characteristics WDM DEMUX and MUX used for separating and combining the comb lines. Although it is an interesting and important aspect, a detailed analysis of this effect would go beyond the main focus of this thesis.

In addition, format-dependent modulation losses are not considered in the analysis, but an overall insertion loss of the modulator of 25 dB both for 16QAM and 64 QAM is assumed. This loss includes both the optical insertion loss of the device and the modulation loss.

Equation Chapter (Next) Section 1

# **B. Microresonator-based solitons for WDM communications (Tx, Rx)**

The content of this section has been published in the Methods and Supplementary Information of the journal publication [J1] that was published with equal contribution from the author of this thesis and Juned N. Kemal. The contributions of the various co-authors are explained in the introduction of Chapter 5 on page 97. To fit the structure and layout of this document, it was adapted accordingly.

*[start of Methods and Supplementary Information of paper [J1]]*

#### **Microresonator solitons for massively parallel coherent optical communications**

*Nature, Volume 546, Issue 7657, pp. 274-279, 2017 DOI: 10.1038/nature22387*

Pablo Marin-Palomo1,† , Juned N. Kemal1, † , Maxim Karpov2,† , Arne Kordts2 , Joerg Pfeifle1 , Martin H. P. Pfeiffer2 , Philipp Trocha1 , Stefan Wolf 1 , Victor Brasch2 , Miles H. Anderson2 , Ralf Rosenberger1 , Kovendhan Vijayan1 , Wolfgang Freude1,3, Tobias J. Kippenberg2 , Christian Koos1,3

### **B.1 Methods**

#### **B.1.1 Fabrication of high-***Q* **Si3N4 microresonator**