We use Si3N4 microresonators for generation of DKS frequency combs. These devices lend themselves to co-integration with other photonic devices, using either monolithic approaches on silicon [151] or indium phosphide (InP) [166], hybrid InP-on-silicon approaches [167], or multi-chip concepts [16], [168]. A particularly attractive option is to co-integrate DKS comb generators with advanced multiplexer and demultiplexer circuits [151] and with highly power-efficient IQ modulators [169], [170] to realize chip-scale transceivers that can handle tens of terabit/s of data traffic, as already envisioned in Ref. [16]. For soliton formation, anomalous group velocity dispersion (GVD) is required, necessitating Si3N4 waveguide heights of approximately 800 nm for a width of 1.65 μm. These dimensions are achieved by using the recently developed photonic Damascence process [161], along with a waveguide filtering section to achieve a smooth dispersion profile [162]. A mode-filtering section was incorporated into the microrings in order to suppress higher-order modes [162], see Inset of Fig. 5.1(a). This allows to minimize the number of avoided mode crossings and facilitates soliton comb generation.

Fabrication reproducibility was investigated, leading to a yield of chips enabling DKS generation per batch of approximately 40 %. For resonators taken from the same wafer, we measured an average line spacing of 95.75 GHz with a standard deviation of approximately 70 MHz. We attribute such differences to variations of both the waveguide width and the thickness of the Si3N4 layer between distant micro-resonators within the same wafer. These variations are approximately 20 nm and may be reduced by increasing the uniformity of the fabrication process over the entire wafer. In particular, we expect that the use of highly developed large-scale fabrication equipment such as 193 nm deep-UV lithography and thin-film tools with improved uniformity will overcome these shortcomings in device reproducibility, as already demonstrated in the context of silicon photonics [171]. Note that the line spacing difference between frequency combs can be compensate through thermal tuning, which allows us to adapt the microresonators' FSR over a tuning range of more than 40 MHz, with a precision of approximately 200 kHz. The same technique can be applied to precisely match the line spacing to established ITU grids.

In addition, we measured the differences in power conversion efficiency of the DKS comb generators used in our experiment, leading to values that range from 0.1 % to 0.6 %. These differences in power conversion efficiency are attributed to variations of the quality factors of the pumped resonances, which may be influenced by interactions of the fundamental mode with higher-order modes. Even though mode-filtering sections are used to suppress the propagation of higher order modes within the waveguide, we can still observe slight variations of the spectral envelope with respect to the theoretical sech2 envelope shape. This fact hints to the presence of avoided mode crossings which are characteristic of multimode waveguides. We expect that these limitations can be overcome by optimized device design.

For DKS comb generators with improver power efficiency, high-Q factors are of great importance. Recently, Si3N4 resonators have been demonstrated [172], [173] to reach Q-factors of more than 6 × 106 both in devices with normal [172] and anomalous [173] GVD. Along with tailored optical amplifiers, such devices allow to reduce the electrical power consumption by more than an order of magnitude compared to state-of-the-art ITLA laser arrays, see Section B.6.1.

#### **B.1.2 Soliton comb generation**

The DKS combs are generated by pumping the microresonators with an ECL and a subsequent EDFA, which is operated at an output power of approximately 35 dBm, see Section B.2 and Fig. B1 for a more detailed description of the comb generation setup. A high-power band-pass filter with a 3 dB bandwidth of 0.8 nm is used to suppress the ASE noise originating from the pump amplifier. The soliton state is excited by well-controlled wavelength tuning of the pump ECL from low to high wavelengths across the resonance at a rate of approximately 100 pm/s [75]. Once a multiple-soliton state is obtained, the transition to a single-soliton state is accomplished by fine-tuning of the pump laser towards lower wavelengths [22]. This slow sweep is performed at a rate of approximately 1 pm/s. Light is coupled into and out of the on-chip Si3N4 waveguides by means of lensed fibers, featuring spot sizes of 3.5 µm and coupling losses of 1.4 dB per facet. The pump power in the on-chip waveguide amounts to approximately 32 dBm. The frequency comb used in the single-comb transmission experiment exhibits a line spacing of 95.80 GHz and a 3-dB bandwidth of more than 6 THz. The optical linewidth of individual comb carriers is limited by the optical linewidth of our tunable pump lasers (TLB-6700, New Focus and TSL-220, Santec), which is below 100 kHz. This value is well below that of telecommunication-grade DFB lasers [174] and hence perfectly suited for coherent data transmission [53]. No additional linewidth broadening relative to the pump is measured, i.e., the phase noise of the comb lines is entirely dominated by the pump. Note that an alternative approach to DKS generation has recently been demonstrated [77] where the detuning of the pump laser with respect to the resonance is adjusted by themally shifting the resonance by means of integrated heaters rather than by tuning the wavelength of the pump laser. This technique allows to replace the tunable pump lasers by much more stable CW pump lasers with sub-kHz linewidths. At the output of the microresonator, a tunable fiber Bragg grating (FBG) acts as a notch filter to suppress residual pump light to a power level that matches the other comb carriers. After the FBG, the measured optical power of the entire comb spectrum, see Fig. 5.1(c), amounts to 4 dBm. For the experiments using interleaved transmitter (Tx) frequency combs or a separate receiver (Rx) LO comb, a second DKS comb generator with similar performance is used. The frequency comb from the second device for the interleaved Tx combs (for the Rx LO) features a slightly different line spacing of 95.82 GHz (95.70 GHz) and overall optical power of 0 dBm (8 dBm). For the transmission experiments, an EDFA is used to amplify the combs to an approximate power of 5 dBm per line prior to modulation. The carriers next to the pumped resonance are superimposed by strong amplified stimulated emission (ASE) noise that originates from the optical amplifier. In future implementations, ASE noise can be avoided by extracting the comb light from the microresonator using a drop-port geometry [175]. This would avoid direct transmission of broadband ASE noise through the device and, in addition, would render the notch filter for pump light suppression superfluous.

#### **B.1.3 Dissipative Kerr soliton comb tuning and interleaving**

Precise interleaving of the frequency combs in the second transmission experiment is achieved by adjusting the temperature of each microresonator, thereby changing the refractive index and shifting the resonance frequencies while leaving the FSR essentially unchanged [176]. A detailed sketch of the experimental setup is given in Section B.2. The resonance frequencies of the cavity can be tuned at a rate of approximately – 2.5 GHz/K with an accuracy of approximately 200 MHz, limited by the resolution of the heater of approximately 0.1 K. In addition, as a consequence of intra-pulse Raman scattering [177], the center frequency of the comb can also be tuned by slowly changing the pump frequency during operation at a constant external temperature. The associated tuning range is limited to approximately ± 500 MHz before the comb state is lost; the tuning resolution is given by the pump laser and amounts to approximately 10 MHz for our devices (TLB-6700, New Focus; TSL-220, Santec). These tuning procedures are used both for precise interleaving of DKS combs in the second transmission experiment and for synchronizing the LO comb to the Tx comb in the third transmission experiment.

#### **B.1.4 Data transmission experiments**

For the data transmission experiments [178]–[180], the single or interleaved frequency comb is amplified to 26.5 dBm by a C/L-band EDFA, before the lines are equalized and dis-interleaved into odd and even carriers to emulate WDM. In the laboratory experiment, the de-multiplexer (DEMUX) depicted in Fig. 5.2(a) is implemented by two programmable filters (Finisar WaveShaper, WS) along with C- and L-band filters, that act as dis-interleavers to separate the combs into two sets of "even" and "odd" carriers, see Section B.3 for a more detailed description of the experimental setup. After separation, the carriers are routed to individual dual-polarization in-phase/quadrature modulators (IQmod), which encode independent data streams on each polarization using both the amplitude and the phase of the optical signal as carriers of information. To this end, we use two optical IQ modulators which are driven with pseudo-random bit sequences of length 211 – 1 using QPSK or 16QAM signaling and raised-cosine (RC) pulse shaping with a roll-off factor *ß* = 0.1. The drive signals were generated by arbitrary-waveform generators (AWG). For the transmission experiment using frequency combs as optical source at the Tx, the symbol rate was 40 GBd, and the sampling rate of the AWG was 65 GSa/s (Keysight M8195A). For the experiment with a DKS comb as a multi-wavelength LO, symbol rates of 50 GBd and sampling rates of 92 GSa/s (Keysight M8196A) were used. We refrained from using higher symbol rates since the limited electrical bandwidth of our transmitter and receiver hardware would have led to significantly worse signal quality. In all experiments, polarization division multiplexing (PDM) is emulated by a split-and-combine method, where the data stream of one polarization is delayed by approximately 240 bits with respect to the other to generate uncorrelated data [181]. The data channels are then recombined into a 75 km long standard single-mode fiber (SSMF) fiber using a multiplexer (MUX) and boosted by an erbium-doped fiber amplifier (EDFA), before being transmitted. At the receiver, we select each channel individually by a BPF having a 0.6 nm passband, followed by a C-band or an L-band EDFA, and another BPF with a 1.5 nm passband. The signal is received and processed by means of an optical modulation analyzer (OMA, Keysight N4391A), using either a high-quality ECL line or a tone of another DKS comb as local oscillator. In the latter case, we use an optical band-pass filter to extract the tone of interest from the LO comb, see Section B.5 for details. In all experiments, we perform offline processing including filtering, frequency offset compensation, clock recovery, polarization demultiplexing, dispersion compensation, and equalization.

#### **B.1.5 Transmission impairments and data rates**

In our transmission experiments, performance was impaired by specific limitations of the available laboratory equipment, which can be avoided in real-world transmission systems. For the transmission experiment using a single DKS comb generator as optical source, Fig. 5.2(a), a total of 101 tones were derived from the comb in the C and L band. Out of those, 92 carriers performed better than the BER threshold of 4.5 × 10-3 for widely used second-generation forward-error correction (FEC) with 7 % overhead see Fig. 5.2(e). The pump tone at approximately 192.66 THz and two neighbouring carriers could not be used for data transmission due to strong amplified spontaneous emission (ASE) background from the pump EDFA. Two more directly adjacent channels exceeded the threshold of 4.5 × 10-3, but were still below the BER threshold of 1.5 × 10-2 for soft-decision FEC with 20 % overhead [43]. Another four channels at the low-frequency end of the C-band were lost due to a mismatch on the transmission band of the C-band filters used to realize the demultiplexer, see Section B.3 for a more detailed description. This leads to an overall net data rate (line rate) of 28.0 Tbit/s (30.1 Tbit/s).

For the transmission experiment using interleaved DKS combs as optical source at the transmitter, Fig. 5.2(c), we use a combination of 16QAM and QPSK, depending on the optical signal-to-noise power ratio (OSNR) of the respective carrier, see Fig. 5.2(e). For 16QAM transmission, a total of 126 channels exhibit a BER of less than 4.5 × 10-3, requiring an FEC overhead of 7 %, and 39 additional channels showed a BER below 1.5 × 10-2 , which can be corrected by FEC schemes with 20 % overhead. For the 14 channels at the low-frequency edge of the L band, the modulation format was changed to QPSK due to the low power of these carriers caused by a decrease of amplification of the L-band EDFA in this wavelength range. This leads to an overall net data rate (line rate) of 50.2 Tbit/s (55.0 Tbit/s).

For the transmission experiment using DKS frequency combs both at the transmitter and at the receiver side, Fig. 5.3(a), 99 tones were transmitted and tested. Out of those, a total of 89 channels perform better than the BER threshold for hard-decision FEC with 7 % overhead (4.5 × 10˗3 ), and additional four channels are below the BER limit of 1.5 × 10–2 for soft-decision FEC with 20 % overhead. For the remaining channels, coherent reception was inhibited by low OSNR. This leads to an overall net data rate (line rate) of 34.6 Tbit/s (37.2 Tbit/s). The black circles in Fig. 5.3(d) show the channels with BER above the threshold for 7 % FEC and specify the reasons for low signal quality: low optical carrier-to-noise power ratio (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).

It is further worth noting that field-deployed WDM systems rely on statistically independent data channels rather than on transmitting identical data streams on the "even" and the "odd" channels. As a consequence, real-world signals will suffer much less from coherent addition of nonlinear interference noise than the signals used in our experiments [182]. With respect to nonlinear impairments, our experiments hence represent a bad-case scenario with further room for improvement.

#### **B.1.6 Characterization of the OSNR penalty of frequency comb source**

For comparing the transmission performances of a single comb line to that of a high-quality external cavity laser (Keysight N7714A) reference carrier, we measure the OSNR penalty at a BER of 4.5 × 10-3 , which corresponds to the threshold for FEC with 7 % overhead [43]. For a given BER, the OSNR penalty is given by the dB-value of the ratio of the actually required OSNR to the OSNR that would be theoretically required in an ideal transmission setup [129].

A detailed description of the associated experimental setup is given in Section B.4. The carrier under test is selected by a band-pass filter with a 1.3 nm (160 GHz) wide passband. The carrier is then amplified to 24 dBm by an EDFA (EFDA2 in Fig. B.3 and modulated with a PDM-16QAM signal at 40 GBd. Next, an ASE noise source together with two VOA is used to set the OSNR of the channel while keeping its optical power constant. As an ASE generator, we use a second EDFA (EDFA3 in Fig. B.3(a)). An optical spectrum analyzer (OSA, Ando AQ6317B) is used for measuring the OSNR at the input of the receiver. For each OSNR value, the quality of the channels is determined by measuring the BER using our previously described receiver configuration, see the Section "Data transmission experiments" above in Appendix B.1.4. At a BER of 4.5 × 10-3, a penalty of 2.6 dB with respect to the theoretical OSNR value is observed, see Fig. 5.2(f), which is a common value for technical implementations of optical 16QAM transmitters [139]. For high OSNR, an error floor caused by transmitter nonlinearities and electronic receiver noise is reached. The maximum achievable OSNR of 44 dB at 192.56 THz for transmission with the comb line is dictated by ASE noise of the C/L-band EDFA (EDFA1) right after the FCG, see Fig. B.3. As a reference, the same measurements are repeated using a high-quality ECL (Keysight N7714A) to generate the carrier, which leads to essentially the same OSNR penalty for a given BER as the transmission with the comb line. For a symbol rate of 40 GBd, the results are shown in Fig. 5.2(f), similar results are obtained at other symbol rates such as 28 GBd, 32 GBd and 42.8 GBd. Note that for transmission with the ECL, only one EDFA (EDFA2) is needed to increase the power to 24 dBm before being modulated. As a consequence, a higher maximum OSNR of 58 dB can be achieved with the ECL than with the comb line. Note in addition that for transmission with a single line, the lowest BER reached at 40 GBd is below 10-4, as depicted in Fig. 5.2(f). This value, however, is not reached in the WDM transmission experiment with the full comb, Fig. 5.2(a) and Fig. 5.3(d). For WDM transmission, a larger number of carriers are amplified by the EDFA in front of the modulator, which, together with the limited output power of the EDFA (EDFA 2-5 in Fig. B.2(a)), decreases the optical power per line and hence the OCNR. Moreover, when interleaving two frequency combs, a VOA and a directional coupler are inserted into the setup, thereby introducing additional loss which needs to be compensated by the subsequent EDFA. Using additional EDFA would therefore increase the quality of the received signal.

### **B.2 Kerr soliton frequency comb generation**

Figure B.1(a) shows the detailed setup of the dissipative Kerr-soliton (DKS) frequency comb generators (FCG) used for the data transmission experiments discussed in the main paper. The DKS frequency comb is generated by pumping a silicon nitride (Si3N4) microresonator with an external cavity laser (ECL). A polarization controller (PC) before the microresonator is adjusted for maximum coupling of pump light into the resonance. The pump light generated by the ECL is amplified by an erbium-doped fiber amplifier (EDFA) which is operated at an output power of approximately 35 dBm. After the EDFA, a high-power band-pass filter (BPF) is used to suppress amplified stimulated emission (ASE) noise. Since the passband of the BPF has finite non-zero width, noise near the pump frequency is not fully suppressed, thereby deteriorating the signal quality of the adjacent carriers. A pair of lensed fibers (LF) with a mode field diameter of 3.5 µm are used to couple light into and out of the microresonator, leading to 1.4 dB of insertion loss per facet. The temperature of the microresonator is adjusted and stabilized by a thermoelectric controller (TEC), while an optical

**Figure B.1**: Generation of single and interleaved DKS frequency combs. **(a)** Setup for generation of single and interleaved DKS frequency combs. The frequency comb generator (FCG) for single-comb generation is depicted in black (FCG1); for dual-comb generation and interleaving, a second FCG (FCG2) is used, depicted in brown. The microresonators (M1, M2) are driven by a pair of linearly polarized continuous-wave (CW) external-cavity lasers (ECL) whose output powers are boosted by erbium-doped fiber amplifiers (EDFA). The frequency of each ECL is controlled via an analog signal generated by a function generator (FG) for tuning into a soliton state. Amplified spontaneous emission (ASE) noise from the power booster EDFA is suppressed by two band-pass filters (BPF) with 0.8 nm passbands. Pump light is coupled to and from the resonator chips by lensed fibers (LF) having a mode field diameter of 3.5 µm, which leads to 1.4 dB of losses per facet, measured at the pump wavelength. After the microresonators, optical isolators (ISO) avoid back reflection of light into the chip. Fiber Bragg gratings (FBG), acting as notch filters with a 0.3 nm bandwidth, are used to attenuate the residual pump light to a power level comparable to that of the adjacent carriers. Prior to the interleaving of both frequency combs with a directional coupler, a variable optical attenuator (VOA) with an attenuation of 4 dB adapts the power level of one comb to the other. A real-time oscilloscope connected to a photodiode (PD) and an optical spectrum analyzer (OSA) are used to track the change of transmitted power and to measure the comb spectrum. **(b)** Transmitted optical power measured by the PD as a function of the ECL frequencies, around the center frequency of the cold resonances from M1 (red) and M2 (blue). A width of about 300 MHz is measured for both microresonators, corresponding to a loaded quality factor of approximately 7 × 105 . The different shape of the resonances is attributed to spurious coupling of counter-propagating waves in M2. (Caption continued on next page)

*Figure B.1 continued***: (c)** Temperature-induced frequency shift of the comb carriers from M1 and M2 relative to the frequencies of the comb carriers from M1 at 28 °C. A dependence of – 2.2 GHz/K and – 2.7 GHz/K is measured for M1 and M2, respectively. Temperatures T1 = 25.6°C and T2 = 19.3°C are chosen for M1 and M2 such that the frequency difference of the carriers near the center of the interleaved comb is half the line spacing of the frequency comb from M1.

isolator (ISO) at the output avoids back-reflection of light into the chip. A fiber Bragg grating (FBG) acts as a notch filter with a 0.3 nm bandwidth to suppress the remaining pump laser up to a level comparable to that of the adjacent frequency comb carriers.

DKS frequency combs are generated by operating the microresonator in the effectively red-detuned regime with respect to the cavity resonance, i.e., the pump wavelength is bigger than the wavelength of the thermally shifted resonance. This regime is accessed by fast sweeping of the pump ECL through the cavity resonance from a blue-detuned wavelength to a predefined red-detuned wavelength (forward-tuning), where a multiple-soliton comb state is generated [21], [75], see trace I of Fig. 5.1(b). The transition to a single-soliton state is accomplished in a reliable and deterministic manner by adiabatically reducing the wavelength of the pump laser (backward-tuning) thereby approaching the hotcavity resonance from the red side [22], see trace II of Fig. 5.1(b). In both sweeps, the ECL wavelength is controlled via an analogue voltage signal generated by a function generator (FG). The forward-tuning is performed at a speed of approximately 100 pm/s and is fast enough to avoid excess heating of the microresonator, which would lead to loss of the soliton comb state due to a too strong thermal shift of the cavity resonance. The backward-tuning is performed at a speed of approximately 1 pm/s and is slow enough to adiabatically switch between different multiple-soliton states. A real-time oscilloscope and an optical spectrum analyzer (OSA) are used to track the change of transmitted power and to measure the comb spectrum, respectively, while sweeping the pump wavelength along the resonance.

For the interleaved-comb experiment, Fig. 5.2(c), two DKS comb sources, namely M1 and M2, with comparable free spectral ranges (FSR) are used in parallel. The equipment required for the second FCG (FCG2) and for interleaving the soliton Kerr combs of the two microresonators is marked in brown in Fig. B.1(a). FCG2 is setup similar to FCG1 as discussed above. For interleaving, the two DKS frequency combs from FCG1 and FCG2 are superimposed by a directional coupler. Note that for the microresonator M2, a lower conversion efficiency of optical pump power to soliton power is observed as compared to that of microresonator M1. This can be attributed to spurious coupling of counter-propagating waves in M2, which also explains the difference in the shape of the resonances from M1 and M2 depicted in Fig. B.1(b). Therefore, the power level of the frequency comb from M1 is adapted to that of M2 by a variable optical attenuator (VOA) before interleaving with the directional coupler. This results in a uniform power spectral envelope of the interleaved frequency comb. To obtain an interleaved comb with evenly spaced carriers, the working temperatures of the microresonators are set such that one of the frequency combs is offset by half the line spacing with respect to the other. Figure B.1(c) shows the frequency shift of the carriers of M1 (red) and M2 (blue), relative to the frequency of the carriers from M1 at 28 °C, as a function of the microresonator temperature. Both frequency combs follow a linear trend with a shift of -2.2 GHz/K and –2.7 GHz/K for M1 and M2, respectively [176]. At the temperature T1 (T2) for microresonator M1 (M2) the frequency difference between the central carriers of both combs is half the line spacing. The pump frequency for the microresonator M1 (M2) is set to 192.61 THz (192.66 THz) for the chosen chip temperature of T1 = 25.6 °C (T2 = 19.3 °C). At such temperatures, the measured line spacing is 95.80 GHz (95.82 GHz) for M1 (M2), leading to a difference of approximately 20 MHz, or 0.02% of the line spacing. Such a difference would lead to a variation of the line spacing by ± 1 GHz at the edges of the interleaved frequency comb as compared to the line spacing near the center of the comb. This mismatch can be avoided by carefully matching the line spacing of the two combs, e.g., by improving the uniformity of the fabrication process, see Appendix B.1.1 for details. In the transmission experiment, the variation of line spacing did not have any significant influence on the quality of the received signal.

## **B.3 Data transmission experiments using Kerrsoliton frequency combs in the transmitter**

The setup used for massively parallel wavelength-division multiplexing (WDM) data transmission is depicted in Fig. B.2(a). The single (interleaved) frequency comb generated by FCG1 (FCG1 and FCG2) is amplified by a C/L-band EDFA (EDFA 1) to a level of approximately 5 dBm (2 dBm) per carrier. For a realistic emulation of massively parallel WDM transmission, neighboring carriers need to be encoded with independent data streams [183], [184]. To this end, the comb is divided into even and odd carriers by a de-interleaver (DI) stage. The DI stage contains a directional coupler (CPL1) that divides the optical power into two parts, which are fed to a C-band and an L-band programmable filter (Finisar WaveShaper; WS). The WS splits even and odd carriers within the respective band. After the C- and the L-band WS, each set of carriers is amplified by EDFA 2-5 to compensate for optical losses caused during de-interleaving. Next, the Cand L-band odd carriers are recombined by the use of a C/L-band multiplexer (C/L MUX) before being coupled into an optical in-phase/quadrature (IQ) modulator (IQ1). The even carriers are also recombined and sent through IQ2. The WS are adjusted to compensate for the power differences of the comb carriers and for the spectral variations of the EDFA gain profile, thereby producing an overall flat spectrum at the inputs of IQ1 and IQ2. Both modulators are driven by either 16QAM or QPSK drive signals generated by a high-speed arbitrary waveform generator (AWG, Keysight M8195A 65 GS/s) using pseudo-random bit sequence (PRBS) of length 211 – 1, to encode data on each frequency comb carrier at a symbol rate of 40 GBd. Raised-cosine pulse shaping at a roll-off factor of *β* = 0.1 is used for improved spectral efficiency. After modulation, odd and even channels are combined by a directional coupler (CPL2). Polarization-division multiplexing (PDM) is emulated by splitting the data stream into two paths and recombining them on orthogonal polarizations with a decorrelating delay of approximately 1.5 ns (60 symbols) in one path and an attenuator in the other one for maintaining the same power levels. Hence, even if both polarizations contain the same PRBS sequence, they are detected as uncorrelated data streams at the coherent receiver. The signal is then amplified and transmitted through 75 km of standard

**Figure B.2**: Data transmission with single and interleaved DKS frequency combs as WDM carriers at the transmitter. **(a)** Data transmission setup: The single (interleaved) frequency comb generated by FCG1 (FCG1 and FCG2) from Fig. B.1(a) is amplified by EDFA 1 to a level of approximately 5 dBm (2 dBm) per carrier. Afterwards, WDM is emulated by encoding independent data into neighboring carriers. To this end, the comb is divided into even and odd carriers by a de-interleaver (DI) stage. The DI stage contains a directional coupler (CPL1) that divides the optical power into two parts, which are fed to a C-band and an L-band programmable filters (WS). The WS split the input comb lines into even and odd carriers within their respective bands. Each set of carriers is amplified by an EDFA to compensate for the optical losses caused by the de-interleaving. Next, C- and L-band carriers from each set are recombined by the use of a Cand L-band multiplexer (C/L MUX) and coupled into two optical IQ modulators (IQ1, IQ2), driven by 16QAM or QPSK drive signals generated by a high-speed AWG. We use a symbol rate of 50 GBd. After combining the modulated signals by a directional coupler (CPL2), PDM is emulated by splitting the data stream into two paths and recombining them on orthogonal polarizations using a polarization beam combiner (PBC) with a delay line (DL) in one path and a variable optical attenuator (VOA) in the other one to decorrelate the data while maintaining the same power levels. The signal is amplified and transmitted through a 75 km long standard single mode fiber (SSMF). At the receiver, a tunable BPF with a 0.6 nm passband selects the channel under test, which is amplified by a C- or L-band EDFA (EDFA 7), depending on which channels are being investigated. A second BPF (1.5 nm passband) suppresses the ASE noise from the EDFA. The modulated channels are received on a dual-polarization coherent receiver using a conventional external-cavity laser as optical local oscillators (LO). (Caption continued on next page)

*Figure B.2 continued*: An optical modulation analyzer (OMA) comprising two real-time oscilloscopes is used to record and process the data signals. Labels MP1 and MP2 represent monitor ports where the spectra shown in b and c, respectively, were recorded. These spectra show impairments of the OCNR which limit the signal quality. **(b)** Frequency comb spectrum in the vicinity of both pump frequencies showing the ASE noise coming from the pump EDFA, see Fig. D.1. **(c)** Frequency comb spectrum of the carriers at the gap between the C- and L- band WS. The low optical power of the carriers at the low-frequency edge of the C-band is caused by a mismatch between the C-passbands of the C/L MUX and the WS. **(d)** Transmission profiles of the C- and L-band WS (red) and of the C- and L-band C/L MUX (blue). For decreasing frequency, the C-band of the C/L MUX shows a decreasing transmission already from 191.7 THz, whereas the transmission band of the C-band WS reaches to 191.2 THz. This mismatch causes strong attenuation of the carriers within this region.

single mode fiber (SSMF). At the receiver, a tunable BPF with a 0.6 nm passband selects the channel under test. The signal is then amplified by a C- or Lband EDFA (EDFA 7), depending on which frequency band is being investigated, and is passed through a second 1.5 nm passband BPF to suppress the ASE noise from the EDFA. Afterwards, the channel is received on a dual-polarization coherent receiver which uses a conventional continuous-wave laser as an optical local oscillator (LO). An optical modulation analyzer (OMA, Keysight N4391A) comprising two real-time oscilloscopes (Keysight DSO-X 93204A, 80 GSa/s) is used to record and process the data signals. The constellation diagram for each channel is obtained after performing signal processing consisting of digital low-pass filtering, polarization demultiplexing, chromatic dispersion compensation, frequency offset estimation, carrier phase estimation, and adaptive equalization. The block length for performing the signal processing is chosen to be 1024 symbols, which is optimized to effectively track the changes of carrier phase and polarization of the received signal. The extracted bit error ratio (BER) is used as a metric to quantify the signal quality of each channel and it is shown in Fig. 5.2(e) of the main paper. Note that for the interleaved-comb experiment, we chose the approach of first recombining the unmodulated combs by means of a directional coupler, Fig. B.1(a), and then de-interleaving them again by means of the DI stage, Fig. B.2(a), to perform spectral flattening on the unmodulated carriers rather than on the densely packed spectrum of the data signals. Equalizing the data signals would unavoidably have led to distortions due to spectral variations of the attenuation within individual WDM channels.

Limitations of the transmission capacity of our experiments were identified by investigating the spectrum of the interleaved frequency comb at the monitor ports MP1 and MP2 in Fig. B.2(a). A fraction of the spectrum, measured at MP1 around the frequency of the pump lasers is shown in Fig. B.2(b). The spectrum exhibits strong residual ASE noise coming from the pump EDFA of FCG1 and FCG2, which passes the relatively wide 0.8 nm BPF centered at the pump frequencies of approximately 192.6 THz. This ASE noise directly deteriorates the optical carrier-to-noise power ratio (OCNR) of the tones adjacent to the pump frequencies, rendering these carriers unusable in the data transmission experiments. Figure B.2(c) depicts a fraction of the spectrum measured at MP2 and centered at the frequency gap between the C and the L bands near 191.4 THz. The gap originates from the limited bandwidth of the C- and the L-band WS. As can be seen in Fig. B.2(c), there is a strong attenuation of the carriers at the low-frequency edge of the C-band. This is caused by a mismatch between the passbands of the C/L MUX and the passbands of the WS, see Fig. B.2(d). For decreasing frequency, the C-band output of the C/L MUX shows a decreasing transmission starting already at 191.7 THz whereas the C-band WS features a flat transmission band that goes down to 191.2 THz. For the high-frequency edge of the L-band, the passband mismatch does not have any influence because the C/L MUX shows perfect transmission for all frequencies that can pass the L-band WS. All these impairments are not related to the comb sources and can be avoided by using optimized devices and filters with matched passbands. We hence believe that there is considerable room for improving signal quality and further increasing the overall transmission capacity.

Another constraint in the data transmission experiments was the limited saturation output power of EDFA 2-5. To quantify the influence of the power per tone on the BER, an extra experiment is performed with less channels but the same spectral efficiency (SE). To this end, we reduce the number of L-band channels from 97 to 48. These channels were located in the center of the L band, and the number of C-band channels were not changed. In this situation, an average BER of 2.3 × 10-3 was obtained for the L-band channels, corresponding to approximately half the averaged BER of 4.7 × 10-3 obtained when all L-band carriers were used for transmission. This proves that the current tranmission capacity is not limited by the comb source, but by the components of the

tranmission systems. Note, in addition, that for the interleaved-comb experiment the power per carrier at the input of EDFA 1 is reduced compared to the single Kerr soliton comb experiment due to an additional directional coupler for interleaving the combs and due to a variable optical attenuator (VOA) used to adapt the power levels of the two combs, see Fig. B.1(a). This explains the slightly worse performance in signal quality of the received channels using interleaved frequency combs at the transmitter as compared to the signal quality of the received channels when using a single Kerr soliton comb at the transmitter.

### **B.4 OSNR measurements**

In this section we introduce the formalism used to calculate the theoretical BER obtained in a data transmission experiment as a function of the optical signalto-noise power ratio measured at the reference bandwidth of 0.1 nm (OSNRref), see Fig. 5.2(f) of the main paper. We estimate the required theoretical OSNRref per channel as a function of the target BER for different symbol rates. Furthermore, we also examine our experimental measurement results.

#### **B.4.1 Theoretical required OSNR for error free transmission with FEC**

The BER of quadratic *K*-ary QAM signals with *r* bits per symbol can be analytically calculated from the OSNRref (measured for instance with an optical spectrum analyzer, OSA) [44], [129]. The basic assumptions are that optical additive white Gaussian noise (AWGN) is the dominant source of errors, thus neglecting nonlinear effects and electronic noise, and that reception is data-aided, which is required to measure directly the experimental BER. The relation for 16QAM, where *K* = 2*r* = 16, is given by

$$\text{BER} = \frac{3}{8} \text{erfc} \sqrt{\frac{\text{OSNR}}{10}} \,, \tag{\text{B.I}}$$

where OSNRis the signal-to-noise power ratio, where the noise power is measured within the signal bandwidth *B*s for the same polarization as the signal. The signal bandwidth *B*s corresponds to the effective bandwidth of a receiver filter that is matched to the received pulse shape. For raised-cosine pulses as used in our experiments, this bandwidth corresponds to the symbol rate and does not depend on the roll-off-factor β. The OSNR is related to the commonly used signal-to-noise power ratio OSNRref, where the signal and noise powers are measured in both polarizations in a reference bandwidth *B*ref.

$$\text{OSNR} = \frac{\text{2B}\_{\text{ref}}}{p \cdot B\_s} \text{OSNR}\_{\text{ref}} \text{ \textsuperscript{},} \tag{\text{B.2}}$$

with *p* = 1 for a single-polarization signal and *p* = 2 for a polarization-multiplexed signal [32]. The reference bandwidth *B*ref is taken to be 12.5 GHz, which corresponds to 0.1 nm resolution bandwidth of an OSA at 1550 nm carrier wavelength. If redundancy is included in the coding of the bit stream to reduce the BER, Eq. (B.2) is modified by the coding overhead, *Oc*, to:

$$\text{OSNR} = (\text{l} + O\_c) \frac{\text{2}B\_{\text{ref}}}{p \cdot B\_s} \text{OSNR}\_{\text{ref}} \text{ \,. \,\tag{\text{B.3}}}$$

Combining Eqs. (B.1) and (B.3), we can derive the required OSNRref for a given symbol rate and coding overhead. Figure B.3 shows the theoretical required OS-NRref per channel for a targeted raw BER of 4.5 × 10-3 with *Oc* = 7 % coding overhead as a function of the net symbol rate. In this context, raw BER means the uncorrected BER obtained before applying forward-error correction (FEC) based on the 7 % of redundancy. For example, at a symbol rate of 40 GBd, an OSNRref higher than 20 dB is required theoretically to achieve a raw BER below the targeted threshold BER of 4.5 × 10-3 , and FEC will allow to bring the BER further down to values below 10-15. Note that the OSNRref values provided in Fig. B3 refer to the input of the coherent receiver, and hence must be considered as a minimum requirement for the OSNRref at the output of the transmitter discussed in Section B.6 and specified in Table B.1. Note that in field deployed systems, impairments such as electronic noise or nonlinear effects will increase the required OS-NRref by the so-called OSNR penalty. The OSNR penalty has been experimentally measured for our system at different symbol rates, see Section B.4.2.

**Figure B.3**: Theoretical required OSNRref at the input of the coherent receiver as a function of the net symbol rate for a targeted raw BER of 4.5 × 10-3. The plot refers to 16QAM signaling, dual-polarization transmission, and a 7 % coding overhead. Raw BER means the BER before applying FEC, which can bring the final BER down to values below 10-15.

#### **B.4.2 OSNR measurements**

In an extra set of experiments, we compare the 16QAM transmission performance of individual comb lines of our Kerr soliton frequency comb, featuring optical linewidths below 100 kHz, to that of a high-quality ECL reference carrier (Keysight N7714A) with an optical linewidth of approximately 10 kHz. As a metric for the comparison we use the OSNR penalty. For a given BER, the OSNR penalty is given by the dB-value of the ratio of the actually required OSNR to the OSNR that would be theoretically required in an ideal transmission setup, see Section B.4.1 and Fig. B.3. The corresponding setup for OSNR penalty measurements is depicted in Fig. B.4(a). We use the frequency comb from FCG1, Fig. B.1(a), tap it directly after the FBG, and amplify it by a C/Lband EDFA (EDFA 1) to bring the comb to a level of approximately 5 dBm per carrier – just like in the transmission experiment. The carrier under test is then selected by operating the C-band WS as a band-pass filter with a 1.3 nm (160 GHz) wide passband and coupled to a C-band EDFA (EDFA 2). The bandwidth of the WS is chosen to effectively suppress all the neighboring comb lines. For the reference transmission experiments, an ECL with an output power of 16 dBm is directly connected to EDFA 2. In both cases, the carrier under test is amplified to 24 dBm by EDFA 2 before being modulated in IQ 1 using 40 GBd PDM-16QAM. To quantify the signal quality, we investigated the BER

of the received channel for different OSNRref values. The OSNRref of the signal is adjusted by using a noise-loading system, consisting of an ASE noise generator (EDFA 3) and two VOA. The VOA are used to modify the ASE noise power while feeding the preamplifier (EDFA 4) of the receiver with a constant optical input power. This assures that the same receiver sensitivity is maintained for all OSNRref values investigated. An optical spectrum analyzer (OSA, Ando AQ6317B) is used to measure the OSNRref at the input of the receiver. For each OSNRref level, signal quality is determined by using the OMA to measure the BER after EDFA4 and after an additional BPF.

A section of the comb spectrum recorded at MP3 and showing four carriers of the unmodulated frequency comb is depicted in Fig. B4(b). Here, the carriers still exhibit an OCNRref of approximately 50 dB, measured at a reference bandwidth of 0.1nm (12.5 GHz). This value, however, cannot be maintained throughout the setup and is reduced by the noise of the subsequent amplifiers. After filtering by the 1.3 nm BPF, the carrier under test features an optical power of approximately 0 dBm. Note that this is a much lower power level than the 16 dBm of output power generated by the ECL. To enable a fair comparison that also accounts for the superior per-carrier power levels of the ECL, we decided to use the ECL at its full output power rather than attenuating it to the 0 dBm provided by the comb source. As a consequence, we find an OCNRref of 58 dB of the ECL carrier after EDFA 2, which is higher than the 42 dB achieved for the amplified comb line at 193.56 THz, see spectra in Fig. B4(c), measured at MP4. Note that two noise floor levels can be identified for the comb carrier. The high-power spectral shoulder around the carrier, which is used to calculate the OCNRref, is caused by the noise of EDFA 1 and is suppressed further away from the carrier by the 1.3 nm BPF, whereas the low-power background arises from the noise of EDFA 2. Hence, the maximum achievable OSNRref for transmission with the comb line is dictated by ASE noise of the C/L-band EDFA (EDFA 1) right after the FCG. Using comb sources with higher output levels can help to further increase the signal quality. An exemplary data signal spectrum for the ECL (red) and comb (blue) carriers before entering the coherent receiver is shown in Fig. B.4(d) as measured at MP5. Both signals are set to the same power and the same OSNRref using the VOA.

**Figure B.4**: Comparison of isolated frequency comb carriers with ECL carriers for data transmission. **(a)** Setup for OSNR penalty measurements: The frequency comb is generated by FCG1, see Fig. B.1(a), and amplified by a C/L-band EDFA (EDFA 1). A single carrier is either generated by an ECL or selected from the comb by operating the C-band programmable filter (WS) as a band-pass filter (BPF) with a 1.3 nm (160 GHz) passband. The carrier under test further amplified to 24 dBm by EDFA 2 before being modulated with PDM-16QAM at 40 GBd. To adjust the optical signal-to-noise ratio (OSNR) of the signal, a noise-loading system is used, consisting of an ASE noise generator (EDFA 3) and two VOA to modify the ASE noise power while feeding EDFA 4 with a constant optical input power. The signal is sent to the receiver where it is further amplified and analyzed by an OMA. Labels MP3, MP4 and MP5 represent monitor ports where the spectra shown in b, c and d, respectively, were recorded. These spectra have been corrected to take into account the tapping ratios of the respective power splitters. **(b)** Section of the frequency comb spectrum (resolution bandwidth RBW = 0.01 nm) as obtained from the output of FCG1. The carriers show an OCNR of approximately 50 dB at a reference bandwidth of 0.1 nm. **(c)** Frequency comb (blue) and ECL (red) carriers after EDFA 2. The frequency comb carrier shows two noise floor levels: The high-power spectral shoulder around the carrier is caused by ASE from the C/ L band EDFA (EDFA 1), which is suppressed further away from the carrier by the 1.3 nm-wide BPF, whereas the low-power ASE noise background arises from EDFA 2. The OCNR of the ECL carrier amounts to 58 dB, whereas an OCNR of 42 dB is achieved for the comb line at 193.56 THz, both measured at a reference bandwidth of 0.1 nm. **(d)** Spectrum of the received modulated data for both the frequency comb and ECL carriers with 40 GBd PDM-16QAM modulation.

Results of the OSNR penalty measurements are depicted in Fig. 5.2(f) of the main paper. The carriers derived from the frequency comb source do not exhibit any additional implementation penalty in comparison to those generated by the reference ECL. However, the higher achievable OCNR provided by the ECL may translate into longer transmission link, which makes DKS frequency comb sources more suitable for rather short metro and regional distances. Similar results were also obtained when comparing ECL and comb carriers at symbol rates of 28 GBd, 32 GBd and 42.8 GBd.

In our setup we observe an OSNR penalty of 2.6 dB with respect to the theoretical required OSNRref. This value compares well with similar transmission experiments [139], [185], [186]. In Ref. [185], an OSNRref penalty of approximately 2.5 dB is observe with respect the theoretical required OSNRref when transmitting DP-16QAM at 43 GBd. It is reasonable therefore to consider a penalty of 2.5 dB, meaning that an OSNRref per channel of approximately 22.5 dB is required for error free transmission using FEC with 7% overhead [43] at 40 GBd and approximately 23 dB at 50 GBd. In our transmission experiment, described in Fig. 5.3 of the main paper, the minimum measured channel OSNRref amounts to 23 dB, measured at a reference bandwidth of 0.1 nm. The corresponding channel is at the high-frequency edge of the C-band. The measured raw BER for this channel corresponds to approximately 4.5 × 10-3, which fits the expected required OSNRref derived in the previous section.

## **B.5 Coherent reception using a Kerr-soliton frequency comb LO**

Figure B.5(a) shows the WDM data transmission setup with a DKS frequency comb generator (FCG) as a multi-wavelength source at the transmitter (signal) and as a multi-wavelength local oscillator at the receiver (LO). The microresonator used at the transmitter side (Tx) corresponds to M1 from Fig. B.1(a). To provide the multi-wavelength LO, an additional microresonator (M3) with similar line spacing is used at the receiver side. Both combs are matched in absolute frequency position by adjusting the microresonators' temperature. The pump frequency for the signal (LO) comb is 193.56 THz (192.89 THz), the on chip pump power is 32.5 dBm (32 dBm) and the temperature is set to 16.4 °C (23.4 °C). We chose to pump the aforementioned resonances as they present the highest power conversion efficiency. The frequency comb obtained from M3 features a slightly lower line spacing of approximately 95.70 GHz as compared to that of M1, 95.80 GHz, due to fabrication inaccuracies. When using the carriers from M3 as LO for coherent intradyne detection, such difference in line spacing translates into a non-zero intermediate frequency (IF). The IF can be brought down to values below 100 MHz near the center of the frequency combs at around 191.5 THz but it reaches relatively high frequencies of approximately 4 GHz when coherently demodulating the signals at the low frequency edge of the L band and at the high frequency edge of the C band. The high IF, however, does not prohibit data transmission as it can be removed using digital signal processing after detection of the transmitted signal with our coherent receiver. However, for high IF, the received signal is slightly affected by the limited electrical bandwidth (BW = 33 GHz) of the analog-to-digital convertor (ADC) of our coherent receiver. This leads to a reduction of the electrical power, and thus of the electrical signal-to-noise ratio, of our baseband signal. The high IF, nonetheless, can be avoided by carefully matching the line spacing of the two Kerr soliton frequency comb sources during fabrication.

As in the previous experiments, WDM transmission is emulated by encoding independent data streams on adjacent channels, see Fig. B.2(a). To this end, the transmitter frequency comb (signal) is de-interleaved into even and odd carriers using two programmable filters (WS) for the C band and the L band. After amplifying the respective carriers by EDFA 2-5 operated at 24 dBm of output power, the C-band and L-band portions of the odd (even) carriers are combined by directional couplers and sent through optical IQ-modulators IQ1 (IQ2).

**Figure B.5**: All-soliton data transmission setup using a dissipative Kerr-soliton (DKS) frequency comb as a multi-wavelength local oscillator for coherent detection. **(a)** Data transmission setup: Two independent DKS frequency comb generators provide both the carriers for WDM coherent data transmission (signal) and for parallel intradyne detection (LO). At the transmitter side (Tx), WDM is emulated by encoding independent data into neighboring carriers. To this end, the comb is divided into even and odd carriers by a de-interleaver (DI) stage. As in the previous experiments, the DI stage contains a directional coupler (CPL1) that divides the optical power into two parts, which are fed to a C-band and an L-band programmable filter (WS) to select even and odd set of carriers within the respective band. Each set of carriers is amplified by an additional EDFA to compensate for the optical losses caused by the de-interleaving. Next, the C- and L-band carriers from each set are recombined by a directional coupler and sent through two different optical IQmodulators (IQ1, IQ2). Both modulators are driven by 16QAM drive signals generated by a highspeed arbitrary waveform generator (AWG) using pseudo-random bit sequences (PRBS) of length 211 – 1. The symbol rate amounts to 50 GBd, and we use raised-cosine pulse shaping with a rolloff factor *β* = 0.1. After combining the signals by a directional coupler (CPL2), polarization division multiplexing (PDM) is emulated by splitting the data stream into two paths and recombining them on orthogonal polarizations with a decorrelating delay in one path and an attenuator in the other for maintaining the same power levels. The PDM signal is amplified and transmitted through a 75 km long standard single mode fiber (SSMF). (Caption continued on next page)

*Figure B.5 continued***:** At the receiver side (Rx), the LO tones and the transmitted channels are filtered and amplified before being coupled to a dual-polarization coherent receiver which performs digital signal processing (DSP) to decode the data and to determine the BER. A polarization controller (PC) and polarizer are used to adjust the LO-line to the pre-defined input polarization of the coherent receiver. The spectra recorded at monitor ports (MP) 6 and 7 are shown in panels b and c. **(b)** Spectrum of the combined odd and even carriers prior to modulation. The flat spectrum is achieved by adjusting the WS to compensate for the power differences of the frequency comb carriers and the spectral variations of the EDFA gain profiles. **(c)** Spectrum of the data channels prior to fiber transmission. The spectrum was taken in eight segments with individually optimized bias points of the modulators to compensate for the wavelength dependence of the devices.

Note that the C/L MUX of the de-interleaver (DI) stage from Fig. B.2(a) has been replaced by a directional coupler to avoid the power attenuation of the carriers at the low-frequency edge of the C-band, which was described in Section B.3. The WS are also used to compensate the power differences of the carriers and the spectral variations of the EDFA gain profile, thereby producing an overall flat spectrum at the input of IQ1 and IQ2, which is to be seen in Fig. B.5(b), measured at monitor port MP6. The modulators are driven by 16QAM drive signals generated by a high-speed arbitrary waveform generator (AWG, Keysight M8196A) using pseudo-random bit sequences (PRBS) of length 211–1. We use a symbol rate of 50 GBd with raised-cosine pulse shaping at a roll-off factor of *β* = 0.1. The larger analog bandwidth of this AWG (32 GHz) allowed us to use higher symbol rates as compared to the experiments described in Section B.3. Polarization-division multiplexing (PDM) is again emulated by temporally delaying one of the polarizations using a delay line (DL) and combining on orthogonal polarizations in a polarization beam combiner (PBC). The signal spectrum is shown in Fig. B.5(c), measured at monitor port MP7. The WDM data stream is amplified and transmitted over 75 km of standard single-mode fiber (SSMF). At the receiver (Rx), each transmitted channel is selected individually by an optical tunable band-pass filter (BPF), followed by an EDFA (EDFA 7) and a second BPF to suppress ASE noise. The selected channel is then sent to a dual-polarization coherent receiver which, in contrast to the data transmission experiment described in Section B.3, uses a spectral line from the Kerr soliton comb at the receiver side as a local oscillator

(LO). The portion of the setup that is related to generation and selection of the LO carrier is depicted in green in Fig. B.5(a). For detection of channels in the C-band, a wavelength-selective switch (WSS) is used to select the LO tone. For the L-band, the WSS could not be used for selecting LO tones due to its limited optical bandwidth, and we deploy a BPF instead. The selected LO tone is then amplified by EDFA 8, filtered by a second BPF to suppress the ASE from the EDFA, and fed to the dual-polarization coherent receiver which consists of an optical modulation analyzer (OMA, Keysight N4391A) together with two realtime oscilloscopes (Keysight DSO-X 93204A 80 GSa/s). The detected signal undergoes a number of digital post processing stages comprising digital lowpass filtering, polarization demultiplexing, chromatic dispersion compensation, frequency offset estimation, carrier phase estimation and adaptive equalization. The block length for performing signal processing is chosen to be 1024 symbols, which is optimized to track the varying physical quantities of the received signal, such as carrier phase and polarization. The measured BER (averaged from different recordings with a length of 106 bit) for all transmitted channels is given in Fig. 5.3(d) of the main paper.

### **B.6 Energy consumption analysis**

In this section, we investigate the electrical power consumption of DKS-based frequency comb sources and compare our results with state-of-the-art integrated tunable laser assemblies (ITLA). In the proof-of-concept experiments presented in the main paper, the comb generator relies on general-purpose benchtop-type research equipment, for which the sum of all power ratings is approximately 1.3 kW. This number is of course not representative for an industrial implementation of the comb source in a real communication system, where components can be chosen to exactly match the specific requirements of the comb generation scheme. For a meaningful analysis of the power consumption, we hence consider dedicated components that correspond to the commercially available state of the art, and combine them with specifically designed Si3N4 microresonators which are optimized to achieve maximum power of the outermost comb lines that are still within the C- and L-band. This leads to an improved optical signalto-noise power ratio (OSNR) after amplification and modulation of the generated comb carriers. We conclude Section B.6 with the investigation and the comparison of the achievable OSNR for both DKS- and ITLA-based sources of carriers for WDM data transmission.

#### **B.6.1 Electrical power consumption of comb generators and ITLA array**

Our experiments described in the previous sections and in the main paper demonstrate that chip-scale DKS comb generators are well suited for massively parallel coherent WDM transmission, both as a multi-wavelength source at the transmitter and as multi-wavelength LO at the receiver. In particular, the concept allows the generation of hundreds of inherently equidistant highly stable optical tones, thereby eliminating the need for individual wavelength control of each carrier. In addition, DKS can dramatically reduce electrical power consumption as compared to a bank of individual laser modules despite the rather low power conversion efficiency of the nonlinear comb generation process. In the following section, we investigate the power consumption of different DKS comb generation schemes with resonators of different *Q*-factors in combination with either off-the-shelf optical amplifiers or tailored optical amplifiers that feature optimized power consumption. As a model system, we choose a comb source that can generate 114 discrete tones with a spacing of 100 GHz corresponding to the full number of ITU-channels in the C band (1530 nm to 1565 nm) and the L band (1565 nm to 1625 nm) [187]. We design the coupling and the dispersion of the microresonator to find an optimum trade-off between high comb power and large bandwidth. It turns out that DKS comb sources have the potential to reduce the power consumption by up to an order of magnitude in comparison to an array of state-of-the-art integrated tunable laser assemblies (ITLA).

In our analysis, we investigate the electrical power consumption, *P*el, of three different implementations of DKS comb generators (DKS-1, DKS-2, DKS-3) and compare it to the power consumption of an array of state-of-the-art ITLA, see Table B.1. DKS-1, DKS-2, and DKS-3 are based on a power-optimized scheme depicted in Fig. B.6. The scheme is designed to feature low electrical power consumption while providing an optical output power per carrier of 13 dBm, which is comparable to the power levels provided by high-quality ITLA sources [188]. The DKS comb generator comprises a Si3N4-based microresonator chip, which is driven by a CW laser and a subsequent pump amplifier [189], [190]. The wavelength of the pump laser is adjusted by a controller [191], and the temperature of operation of the microresonator is kept stable with the use of a thermoelectric controller (TEC) [192]. For DKS-1, we assume a microresonator that has the same characteristics, with respect to *Q*-factor and dispersion, as the devices used in our experiments and is pumped at the same power level. The frequency comb output from the microresonator is next split into C and L bands and amplified by the first comb amplifiers [190] (AMP 1 and 2). Tailored gain-equalizing filters are used to correct the power variations between the amplified carriers, leading to a flat spectrum.

**Table B.1:** Electrical power required for the generation of 114 carriers on the C and L bands having an optical power of approximately 13 dBm per carrier. DKS-based configurations are shown in columns 2-4, and the associated comb generation scheme is depicted in Fig. B.6(a) a. DKS-1: off-the-shelf equipment; DKS-2: Off-the-shelf equipment and optimized microresonators; DKS-3: Tailored amplifiers with optimized power consumption and optimized microresonators. The last column considers the use of 108 ITLA as source of WDM carriers. For each configuration, the last two rows show the minimum and maximum OCNRref (OS-NRref) that occurs for any channel in the C- or L-band. OCNRref refers to the optical carrierto-noise power ratio at the output of the comb generator, i.e., after the DEMUX depicted in Fig. B.6 OSNRref refers to the optical signal-to-noise power ratio measured after modulation, recombination and re-amplification of the WDM channels, i.e., after AMP 5 and AMP 6 in Figure B.9. Both parameters are measured for a reference bandwidth of 0.1 nm.

These filters can be realized, e.g., by concatenating fiber Bragg gratings with different periodicities [193] or by using an acousto-optic tunable filter with multi-frequency acoustic signals generated by a single transducer [194]. To obtain the target power level of 13 dBm/carrier, high-power optical amplifiers (AMP 3 and 4) are used before separating the carriers by a wavelength demultiplexer (DEMUX) for independent modulation. The DEMUX [195] features a channel spacing of 100 GHz and supports 44 channels in the C-band and 70 channels in the L-band.

For the DKS-1 scheme, we assume a microresonator with the same *Q*-factor and under the same operation conditions as the LO comb of the transmission experiment depicted in Fig. 5.3 of the main paper. For estimating the OCNRref and OSNRref values, we use a comb spectral shape that mirrors the one measured during our experiment. To estimate the electrical power dissipation *P*el associated with DKS-1, we assume state-of-the-art off-the-shelf amplifiers that match the requirements of gain and optical output power while featuring low electrical power consumption, see the corresponding references in first column of Table B.1. This leads to a total power consumption of approximately 110 W for generation of 114 carriers – less than one third of the power consumption obtained for 114 independent ITLA.

For the DKS-2 and DKS-3 scheme, we assume Si3N4 microresonators having intrinsic *Q*-factors of 6 × 106 with dispersion and coupling parameters that were optimized for maximizing the power of the outermost comb lines that are still within the C- and L-band, see Section 5.2 and Refs. [90], [173], [196]for details. The assumption of a *Q*-factor of 6 × 106 is based on recent reports about Si3N4 microresonators resonators, where optimized fabrication processes have led to *Q*-factors even exceeding 6 × 106 , both in devices with normal [172] and anomalous [173] GVD. While DKS-2 is still based on state-of-the-art off-theshelf amplifiers, DKS-3 assumes tailored optical amplifiers that have the highest electrical-to-optical power conversion efficiency [197]. This results in DKS-3 having a total power consumption of approximately 42 W for generation of 114 carriers – more than an order of magnitude below the power consumption of the considered ITLA array.

**Figure B.6**: Power-optimized setup for DKS frequency comb generation and amplification for data transmission. A tunable CW laser followed by a pump amplifier are used to drive the microresonator. The operation temperature of the microresonator is kept stable by a TEC. After separating the C and L band tones by a C/L-band DEMUX, the tones of each band are amplified by the comb amplifiers AMP 1 and 2. Optical filters compensate the spectral power variations among the carriers of the frequency comb in each band. High-power optical amplifiers AMP 3 and 4 are used before the wavelength demultiplexer (DEMUX) to obtain the target power level of ~ 13dBm per carrier.

Naturally, the amplifiers used to boost the optical power of the comb lines reduce the optical carrier-to-noise power ratio (OCNR) with respect to the carriers from an ITLA, which do not need to be amplified prior to modulation. This reduction of the OCNR was investigated analytically, as discussed in Section B.6.3, and the results were verified by simulations using the commercial tool OptSim [198]. The last two rows of Table B.1 give the results of the investigation. The Max/Min OCNRref values of Table B.1correspond to the maximum and minimum values of the OCNR for the DKS frequency comb carriers and for the ITLA carriers within the C- and L-band prior to modulation, measured at a reference bandwidth of 0.1 nm. For the DKS frequency comb carriers, OCNRref was measured at the output of the DEMUX, see Fig. B.6, whereas it was taken from the datasheet of a commercial device for the case of the ITLA carriers [188]. Using DKS sources leads to optical carriers with OCNRref values that range from 35.0 dB to 38.5 dB. The difference between the maximum and the minimum OCNRref values is due to the difference in power between the comb carriers over the whole C and L band and due to the difference in noise figure between the C and L band amplifiers. The Max/Min OSNRref values of Table B.1 give the maximum and minimum values of the OSNR, measured at a reference bandwidth of 0.1 nm, for the DKS frequency comb and ITLA tones after modulation, multiplexing and re-amplification, prior to transmission through the single-mode fiber. Due to the amplified spontaneous emission (ASE) noise added during re-amplification of the DKS-based channels, the OS-NRref of the DKS comb generator and the ITLA differ much less than the associated OCNRref. Furthermore, the DKS-based channels exhibit OSNRref values above 34.5 dB, which would correspond to theoretically achievable BER of less than 10-34 for 50 GBd 16QAM transmission assuming impairments only by additive white Gaussian noise, without inter-symbol interference [129]. This is a purely virtual value, much smaller than any BER relevant to real-world 16QAM systems which are deteriorated by noise and are typically operating at BER values of more than 10-6. This analysis shows that DKS comb tones will not exhibit any practically relevant impairment of transmission performance in comparison to much more power hungry arrays of individually stabilized ITLA. For details on the analytical OSNR calculation, refer to Section B.6.3.

It is further worth noting that DKS comb generators are particularly advantageous when large numbers of carriers are to be generated. Fig. B.7 shows the dependence of the electrical power consumption per carrier on the total number of carriers for the implemented three DKS comb generation configurations. The power consumption per line for DKS comb sources decreases considerably with the number of lines. With only 20 lines, the DKS-3 scheme already exhibits a power consumption per line which is half of that required by ITLA sources. Note that Fig. B.7 is based on the assumption that the amplifiers used for DKS frequency comb generation consume constant electrical power. This may lead to an overestimation of the power consumption since the electrical pump power of the EDFA can be reduced if only a few comb lines are to be utilized. Moreover, we did not consider that the design of the microresonator can be adapted for power-efficient generation of narrowband combs, see Section B.2 below. In addition, the power consumption per carrier when using an ITLA array is considered constant. This may not be the case if techniques to synchronize all optical sources, e.g. through frequency locking, are employed. Fig. B.7 hence represents a rather conservative estimation of the performance that can be achieved with DKS comb sources.

**Figure B.7:** Electrical power consumption per carrier as a function of the number of carriers. We compare the power consumption of the DKS comb generation schemes detailed in Table B.1 and Fig. B.6 (DKS-1, DKS-2, DKS-3) to that of an array of integrated tunable laser assemblies (ITLA).

#### **B.6.2 Dispersion and coupling parameters of SiN microresonators**

In this section, we explain the optimization of the microresonator carried out to maximize the achievable OSNR of a DKS frequency comb. For a given input power, such optimization is done by maximizing the optical power of the outermost lines of the C and L band of the frequency comb, which have the lowest power and hence limit the achievable OSNR. It turns out that for a moderate input power of *P*in = 400 mW or 26 dBm, which allows the use of a pump amplifier with low power consumption, we obtain OSNRref values higher than 35 dB, which are more than sufficient for real-world communication systems, see discussion in Section B.6.1. In addition, we investigate the power conversion efficiency of the DKS comb source, and the bandwidth of the frequency comb.

To maximize the power of the weakest lines at the edges of the C and L band, the group velocity dispersion (GVD) and the coupling rate of the microresonator to the external waveguide, κ ex , are varied within values that can be engineered by varying the Si3N4 waveguide dimensions as well as the resonator-to-waveguide distance in combination with specially designed coupling regions [173], [196]. The analytical expression for the line power, in Watts, of the DKS frequency comb at the output of the microresonator, solved in the limit of low resonator loss, is given by [21]:

$$P(\mu) = \frac{\kappa\_{\rm ex} D\_2 \hbar \alpha\_0}{4g} \text{sech}^2 \left(\frac{\kappa \mu}{2} \sqrt{\frac{D\_2 \hbar \alpha}{\kappa\_{\rm ex} g P\_{\rm in}}}\right),\tag{B.4}$$

where µ ωω = − ( 0 1 ) *D* is the comb mode index relative to the pumped mode, 1 *D* 2π is the free spectral range, 2 *D* 2π is the per-resonance frequency shift due to GVD, *g/2*π is the nonlinear coupling constant or Kerr frequency shift per photon, *P*in is the input pump power, and κκ κ = +0 ex is the total cavity lossrate including the internal loss rate, κ 0 , and the coupling rate to the external waveguide, κ ex . In our model, we set a realistic value of internal loss rate to *κ*0 = 2π × 30 MHz (which corresponds to the intrinsic *Q* ~ 6 × 106 ) [173] and the nonlinear coefficient is assumed to amount to *g* = 2π × 0.27 Hz. In addition, we assume that the soliton operates at the maximum pump-cavity resonance detuning, which corresponds to the maximum output power and the broadest comb spectrum available for the given pump power [21], [177]. Note that Eq. (B.4) is based on the assumption of high resonator finesse [199] and is hence not valid any more as the loss of the resonator κ is increased to large values. For a comprehensive study over a broader range of values, we therefore perform simulations using the Lugiato-Lefever equation to retrieve the spectral envelope of the DKS frequency comb [155]. Figure B.8a shows the optical power of the weakest line within the C and L-band attained through these simulations when the dispersion parameter 2⁄2 and the ratio between the external coupling and the intrinsic loss ⁄0 are varied from 0.2 to 2.0 MHz and from 1 to 25, respectively. We find that there exists an optimal value for *κ* and 2 *D* 2π where the weakest line of the frequency comb within the C and L band is maximized. We find that for ex κ π2 525 = MHz and 2 *D* 2 0.4 π = MHz the outermost line reaches a maximum power of 46 µW or -13.4 dB, which allows OCNRref values above 35 dB for the comb carriers obtained from DKS-2 and DKS-3 comb generation and amplification schemes. The power consumption, OCNRref and OSNRref values of Table B.1, for DKS-2 and DKS-3 configurations, have been derived considering such optimized microresonators. Figure B.8(b) depicts the values of the ratio, in dB, between the power of the strongest and the weakest comb line within the C and L band. For the optimum values of κ ex and 2 *D* 2π a ratio of 5 dB is obtained, which is comparable to the approximately 6 dB of power ratio observed in our measurements.

**Figure B.8:** Optimization of minimum comb line power by varying the cavity GVD parameter D2 and the coupling rate κex. **(a)** Heat map for minimum comb line power as a function of D2 and κex The crosses mark the comb spectra depicted in c. with 'D' indicating the ideal point where a global maximum of the power of the weakest comb line within the C and L band is achieved. **(b)** Map of the comb line power variation as maximum/minimum comb power in dB as a function of D2 and κex, with the same highlighted points as in a. **(c)** Frequency comb spectrum corresponding to the data points A to D from panels a. and b. The plotted frequency range corresponds to C and L-band. Comb D exhibits an optimal balance between a high total output power as well as the broadest bandwidth, allowing for an increased OCNR and OSNR per carrier.

Figure B.8(c) contains four comb spectra taken from the points marked as crosses on Fig. B.8(a),(b). The interplay between spectral broadening and overall power increase is well demonstrated. In general, decreasing the dispersion *D*2 tends to increase the bandwidth while reducing the total comb power. Conversely, increasing the resonator coupling κ ex leads to an increase in total comb power but a reduction in the soliton bandwidth. This is due to more light escaping the cavity, and consequently reducing the conversion efficiency from the pump to the comb lines. Hence, for a given value of dispersion *D*2 there exists an optimum value of κ ex that maximizes the power of the weakest line at the edge of the C and L-band. In Fig. B.8(a), these values are indicated by points A to D for four values of *D*2. Point D corresponds to the overall maximum that can be achieved by optimization of both parameters.

In addition, we have analyzed the power conversion efficiency, Γ, of the DKS comb sources for the same range of values for κ ex and 2 *D* 2π . The general expression can be calculated as [156], [200]

$$\Gamma = \frac{P\_{\rm out}^{\rm sol}}{P\_{\rm in}} = \frac{\pi \kappa\_{\rm ex}}{\kappa} \sqrt{\frac{\kappa\_{\rm ex} D\_2 \hbar o\_0}{\varepsilon P\_{\rm in}}} \ , \tag{B.5}$$

where sol *P*out is the total soliton power exiting the microresonator. For the optimum values κ ex and 2 *D* 2π , the power conversion efficiency amounts to 2.5 %, greatly improving the maximum value of 0.6 % observed in the experimental setup.

#### **B.6.3 OSNR for DKS and ITLA WDM sources**

The OCNRref and OSNRref values shown in Table B.1 have been obtained through an analytic study of the amplified stimulated emission (ASE) noise power generated after amplifying the initially low-noise frequency comb carriers using a chain of amplifiers. To verify the results of our analysis, the DKS frequency comb generation setup shown in Fig. B.6 has also been simulated. In both the analytical calculations and simulations, the gain of the optical amplifiers is assumed to be constant across the bandwidth occupied by the frequency comb. This assumption can be justified by the amplifier specifications of different EDFA manufacturers which assure variations of gain to be lower than 1 dB [201]. ASE noise was quantified by the noise figure of the comb amplifiers. Optical amplifiers for the L band are assumed to feature a 1 dB higher noise figure with respect to their counterparts in the C band [201], [202]. In our model, we consider a noise figure of 4 dB (5 dB) for the C band (L band) comb amplifier AMP 1 and a noise figure of 6 dB (7 dB) for the C band (L band) comb amplifier AMP 2, which are the maximum noise figure values specified for the corresponding amplifiers and should hence lead to a

**Figure B.9:** Communication setup assumed for estimating the OSNR levels that can be achieved with the various DKS-based comb generation schemes discussed in Table B.1. The DKS frequency comb generator is described in more detail in Fig. B.6. The carriers are modulated by dual polarization coherent transmitters (DP Tx). The C- and L-band signals are re-amplified by separate booster amplifiers AMP 5 and AMP 6, combined by a C/L-band MUX, and transmitted through 75 km of single-mode fiber (SMF). At the receiver, the channels are demultiplexed and sent through a pre-amplifier before detection by a dual-polarization coherent receiver (DP Rx).

conservative estimate of the OSNR. The noise figure of the amplifiers is also assumed to be flat within the bandwidth occupied by the frequency comb. Moreover, insertion loss values of all the passive components were also taken into account. The C/L-band DEMUX feature a 0.5 dB insertion loss, the gain-equalizing filters, which compensate for the power difference between comb carriers, present an insertion loss of approximately 5 dB in addition to the wavelengthdependent attenuation profile required for gain flattening [203], and the wavelength DEMUX is considered to have 3 dB insertion loss [195]. For the calculation of the OSNRref obtained after modulation and re-amplification by booster amplifiers AMP 5 and 6 and prior to transmission through the single-mode fiber, we further need to quantify the optical losses associated with modulating data signals onto the carriers and with recombining these carriers into the transmission fiber, see Fig. B.9. To this end, we assume state-of-the-art dual-polarization IQ modulators with 13 dB of insertion loss for each polarization [110], [204] along with a modulation loss of 2.55 dB, corresponding to the peak-toaverage symbol power ratio of 16QAM signals [205]. To recombine the channels into the single-mode transmission fiber, an optical multiplexer (MUX) and a C/L-band MUX with 3 dB and 0.5 dB of insertion loss, respectively, are considered. For re-amplification of the modulated signal by AMP 5 (6), we assume an amplifier with a noise figure of 5.5 dB (6.5 dB) for the C (L) band. The output power is set such that the power per channel is 0 dBm, which is the typical launch power per channel into standard single mode fibers (SSMF) to reduce the nonlinear impairments while optimizing the channel OSNR [107], [108].

Note that the comb amplifiers AMP 1 … AMP 4 in Fig. B.9 are deliberately placed between the comb generator and the respective DEMUX. In fully integrated schemes, it would be desirable to avoid amplifiers before the modulators. However, due to the low comb line powers directly after the resonator and the generally high insertion loss of the IQ modulators, such schemes would lead to low power levels at the input of the transmitter booster amplifiers AMP 5 and AMP 6 and the OSNRref of the transmitted signal would drop to values below 23 dB. For this reason, placing of an EDFA prior to modulation is a common approach in most comb-based transmission schemes [97].

Figure B.10 shows the spectrum obtained from our simulation using the commercial tool OptSim [198]. The spectrum exhibits a maximum OCNRref of 39 dB for the leftmost comb line in the C-band and a minimum OCNRref of 35 dB for the leftmost comb line in the L-band. These values are in accordance with the OCNRref values measured in our experiments, which amount to 35 … 39 dB for the single comb, and to 30 … 37 dB for the interleaved combs. In contrast to that, the experimentally measured OSNRref values of the data signal typically amount to 20 … 24 dB (23 … 27 dB) for the case of the interleavedcomb (single-comb) experiment. This is significantly below the values of more 34 dB that can be expected when using optimized equipment, see Table B.1. The low OSNRref in the experiment is caused by a rather high insertion loss of the electro-optic modulators that we used in our experiment, which lead to low power levels coupled into the subsequent EDFA (EDFA 6 in Fig. B.2).

The simulations are confirmed by an analytical estimation. To this end, we start from the input signal power *P*0 to Comb Amplifiers #1 & #2 and derive the OSNR from the noise figure of the system.

**Figure B.10:** Merged plot of the amplified frequency comb spectra, at the output of amplifiers AMP 3 and AMP 4, in Fig. B.9, after accounting for the subsequent DEMUX insertion loss. The spectra are obtained from our simulation using the commercial tool OptSim [198]. RBW: resolution bandwidth.

For an output signal power *P*s and ASE noise power *P*ASE, the OSNR is given by the equation:

$$\text{OSNR} = \frac{P\_{\text{s}}}{P\_{\text{ASE}}} \tag{\text{B.6}}$$

with *P*s and *P*ASE given by [206]

$$P\_{\mathbf{s}} = G \, P\_0 \,, \tag{\text{B.7}}$$

$$P\_{\rm ASE} = h\nu \, B\_{\rm ref} \, F \left( G - \mathbf{l} \right) \,, \tag{\text{B.8}}$$

where *G* is the EDFA gain, *h* is the Planck constant, *v* is the input signal's center frequency, *B*ref is the noise reference bandwidth (centered at *v*) and *F* is the noise figure of the EDFA. For a chain of amplifiers connected by passive components with power transmission factor *α*, 0 1 < ≤ α , the total gain *G*t and the noise figure *F*t of the system are given by

$$G\_{\mathbf{t}} = \prod\_{n=1}^{N} G\_n \alpha\_n \tag{\text{B.9}}$$

$$F\_{\mathbf{t}} = \frac{1}{G\_{\mathbf{t}}} + \left(F\_{\mathbf{t}} + \frac{F\_{2}}{G\_{\mathbf{t}}\alpha\_{1}} + \frac{F\_{3}}{G\_{\mathbf{t}}\alpha\_{1}G\_{2}\alpha\_{2}} + ... + \frac{F\_{n}}{\prod\_{n=1}^{N-1}G\_{n}\alpha\_{n}}\right). \tag{B.10}$$

Using Eqs. (B.6) to (B.10), the maximum and minimum OCNRref and OSNRref values of the DKS frequency comb generation and amplification configurations given in Table B.1 are calculated analytically. These values are also found to be in accordance with the simulations results. Note that the DKS frequency comb generation setup assumed in Table B.1 already contains the booster EDFA (AMP 5 and AMP 6 in Fig. B.9) after the modulator. For transmission over a distance of 75 km, the OSNRref measured after a state-of-the-art preamplifier [207] (Pre-Amp. In Fig. B.9) would be 2 dB below the OSNRref values at the transmitter that are specified in Table B.1.

In addition to the ASE noise introduced by the various amplifiers, nonlinear interference noise will also influence the OSNR at the receiver. For a quantitative analysis, we consider the 50 GBd PDM-16QAM transmission experiment in which we use a DKS comb generator as a source of LO tones, see Fig. 5.3 of the main paper. We assume typical parameters for the transmission fiber such as a nonlinearity coefficient of γ = 2 W-1 km-1, a dispersion coefficient of *β*2 = 20 ps2 /km, and a fiber loss coefficient of *a* = 0.2 dB/km. The average input power to the transmission fiber was assumed to be 0 dBm per channel, which matches our laboratory experiment. For the estimation, we use the model described in Ref. [30]. After the first 75 km transmission link, we estimate an effective OS-NRNL of approximately 32.5 dB, which would correspond to an OSNRref,NL of 38.5 dB, taking into account nonlinear interference noise from self-phase modulation, cross-phase modulation, and four-wave maxing, but no ASE noise from any EDFA deployed in the system. After an additional 75 km link, the OSNRNL (OSNRref,NL) reduces to 29 dB (35 dB). These OSNRref numbers are comparable to the values estimated at the output of the transmitter when taking into account only the ASE noise of the various EDFA, but no fiber nonlinearities. We hence conclude that in optimized systems, fiber nonlinearities may have significant impact even for transmission over rather short distances that are typically found in metro and regional networks. These impairments can be compensated by exploiting the strong correlation of frequency variations of the comb carriers [34] – another key advantage of comb-based transmission schemes, leading to better signal quality and allowing higher capacity and reach. Note that the OSNRref,NL values estimated for nonlinear impairments are much higher than the OSNRref of approximately 23 dB that we actually measured in our current experiment.

We hence conclude that nonlinearities of the transmission fiber did not significantly impact signal quality of our experiment

*[End of Methods and Supplementary Information of journal publication [J1]]*

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# **D. Glossary**

## **D.1 List of Abbreviations**

180

182

### **D.2 List of mathematical symbols**

#### **Greek symbols**

# **Acknowledgments**

This dissertation was written during my doctoral studies at the Institute of Photonics and Quantum Electronics (IPQ) at the Karlsruhe Institute of Technology (KIT). This work was integrated into the Erasmus Mundus doctorate program Europhotonics (grant number 159224-1-2009-1-FR-ERA MUNDUS-EMJD).  I hereby acknowledge their contributions to the achievements of this work.

First, I would like to express my gratitude to my main advisor Prof. Christian Koos for granting me the opportunity to join his team at IPQ as a PhD student and be part of such a motivating and knowledgeable team. I thank Prof. Koos for guiding me through the different projects in which I participated. The success of this work would not have been possible without his extraordinary dedication and his ability to confront any challenge in a pragmatic way. Those lateevening paper discussion did pay off.

I would like to express my sincere appreciation to Prof. Wolfgang Freude for his effort and patience in supporting me through my PhD. Especially for his encouraging advice to improve my writing and presentation skills. Even at the end of my PhD, I still feel deeply impressed by his extraordinary linguistic skills.

I thank Prof. Randel for his guidance on the last stage of my PhD. In particular, his exceptional knowledge of signal processing has had a noticeable impact on the success of this work.

I would like to also thank Prof. Jens Biegert, who warmly welcomed me to his team at ICFO and made my short stay there pleasant and productive.

From a humble standpoint, I feel grateful for the supervision from such top-tier Professors and I hope to have taken hold of some of their knowledge throughout these years.

I would like to thank all IPQ colleagues who have made my stay at IPQ more enjoyable. I am honestly grateful to Jörg Pfeifle and Juned N. Kemal, who supervised me during my first months at IPQ and taught me all I needed to know regarding, e.g., optical communications and characterization of mode-locked lasers. Thanks to them, I could become quickly independent and take the lead in transmission experiments. Similarly, I would like to thank Stefan Wolf, who helped me numerous times to tackle unexpected issues with system lab equipment, and was always accessible for discussing measurement results. I also thank Philipp Trocha, not only for his assistance during tough experiments and for his discussions on soliton dynamics - which allowed me to understand some of the curious behavior of these states in the lab - but also for helping me many times deal with work-related and personal paperwork. I also thank Dengyang Fang for sharing exciting moments in the lab for the last year and a half, and making the last part of my PhD memorable.

I would like to thank all the colleagues with whom I had the pleasure to share the office and most part of my PhD. I this regard, I thank again Jörg Pfeifle, for the long discussion about soliton generation, and phase noise properties of MLLD, and Juned N. Kemal, for the uncountable discussions we had of every peculiar phenomenon we observed in the lab. Their experience and assistance were undoubtedly crucial for the success of this work. I also thank Alban Sherifaj, Tilahun Gutema, Sentayehu Wondimu, Jonas Krimmer, and Patrick Matalla for making the tea/coffee breaks interesting by sharing thoughts from politics and history to movies and videogames.

I would like to thank my PhD colleagues Aleksandar Nesic, Denis Ganin, Adib Hossain, Muhammad Rodlin Billah (aka, Oding), Yilin Xu, Stefan Singer, Philipp Dietrich, Heiner Zwickel, Simon Schneider, Claudius Weimann, Yasar Kutuvantavida, Matthias Lauermann, Carsten Eschenbaum, Mareike Trappen, and Pascal Maier for a great time we spent together at IPQ. I particularly thank Tobias Harter, not only for his advice and help during my PhD but also for the great moments we shared at the institute and especially at the memorable 2016 CLEO conference. I also thank my colleagues Christop Füllner, Clemens Kieninger, and Alexander Kotz for those late-afternoons table tennis games. I want to also thank my former Master students Vincent Lauinger, Yizhao Jia, Raquib Ehsan, Alban Sherifaj, Daniel Drayss, and Erdem Cil, that I had the privilege to supervise during my PhD and with whom I shared important moments and allowed me to obtain supervision knowledge, quite important for academia.

I would like to thank my colleagues at ICFO, Daniel Rivas, Nicola di Palo, Ugaitz Elu, Aurelien Sanchez, and especially Tobias Steinle, who introduced me to CEP techniques and taught me valuable electronic knowledge. They made my stay at ICFO really valuable and enjoyable.

I would like to especially thank the group of Prof. Tobias Kippenberg at EPFL, whose collaboration made a great part of this Thesis possible. I want to especially thank Maxim Karpov, for teaching me how to generate solitons in the lab and for the countless discussions we had regarding the properties of their microresonators. I want to also thank Prof. Abderrahim Ramdane and his group for their valuable collaboration in this work.

I would like to thank Andrea Riemensperger, Marie-Luise Koch, Tatiana Gassmann, and Bernadette Lehmann, for providing such great administrative support and for making IPQ atmosphere more pleasant. I would also like to thank my Mentor, Dr. Martin Lauer, and the coordinators from the Erasmus program Sophie Brasselet, Crina Cojocaru, Jordi Mompart and Hugues Giovannini. I would like to thank David Guder, Oswald Speck, and Martin Winkeler, and Marco Hummel for always being available to help with spontaneous IT, mechanical or electro-optical needs.

This work would not have been possible if it wasn't for the unconditional support of my family and friends. I thank my siblings Laura and Carlos and I especially thank my parents Melchor and Ascensión which have made uncountable sacrifices to make my life cheerful and easier and to provide me with an excellent education. I especially want to thank my fiancée Öncü, which has spent all these years by my side and has enjoyed and suffered with me the good and bad moments of my PhD. Her joyful character, able to make me laugh and cheer me up, and our little adventures through Germany made this PhD easier to handle.

# **List of Publications**

### **Book Chapter**

[B1] J. N. Kemal, **P. Marin-Palomo**, M. Karpov, M. H. Anderson, W. Freude, T. J. Kippenberg, and C. Koos, "Chip-Based Frequency Combs for Wavelength-Division Multiplexing Applications," In: Willner A. E. (Ed): *Optical Fiber Telecommunications VII*, 7th ed. Elsevier (Imprint: Academic Press), Chapter 2, pp. 51–102, 2020.

### **Journal Publications**

### **Conference Publications**

### **Karlsruhe Series in Photonics & Communications, Vol. 33 Edited by Profs. C. Koos, W. Freude and S. Randel**

Karlsruhe Institute of Technology (KIT) Institute of Photonics and Quantum Electronics (IPQ) Germany

The number of devices connected to the internet and the required data transmission speeds are increasing exponentially. To keep up with this trend, data center interconnects should scale up to provide multi-Tbit/s connectivity. With typical distances from a few kilometers to 100 km, these links require the use of a high number of WDM channels. The associated transceivers should have low cost and footprint. The scalability of the number of channels, however, is still limited by the lack of adequate optical sources.

In this book, we investigate novel chip-scale frequency comb generators as multi-wavelength light sources in WDM links. With a holistic model we estimate the performance of comb-based WDM links, and we compare the transmission performance of different comb generator types, namely a quantum-dash mode-locked laser diode and a microresonator-based Kerr comb generator. We characterize their potential for massively-parallel WDM transmission with various transmission experiments. Combined with photonic integrated circuits, these comb sources offer a path towards highly scalable, compact, and energy-efficient Tbit/s transceivers.

#### **About the Author**

Pablo Marin-Palomo was born in 1990 in Tossa de Mar, Spain. In 2014, he received the Master degree in Optics and Photonics from Karlsruhe Institute of Technology (KIT), which awarded him the Dr.-Ing. (Ph.D) degree in 2021. He is now a postdoc researcher at the Vrije Universiteit Brussel (VUB), where he focuses on novel integrated light sources for THz and optical communications.

ISSN 1865-1100 ISBN 978-3-7315-1129-8

Gedruckt auf FSC-zertifiziertem Papier

Pablo Marin-Palomo

**33**

Chip-scale optical frequency comb sources for Tbit communications