1. Introduction

With the explosive growth of data rates across all network levels [1], wavelength-division multiplexing (WDM) schemes are becoming increasingly important for short transmission links that connect, e.g., data centers across metropolitan or campus-area networks. In this context, optical frequency combs have emerged as particularly attractive light sources, providing a multitude of narrowband optical carriers at precisely defined frequencies that may replace tens or even hundreds of actively stabilized laser diodes [2–9]. Among the various comb generator concepts, chip-scale devices are of special interest, in particular when it comes to short-distance WDM links, for which compactness and cost-efficient scalability to high channel counts is of utmost importance.

Over the previous years, a variety of chip-scale comb generators have been shown to enable high-speed WDM transmission at Tbit/s data rates. The highest performance was achieved by exploiting Kerr nonlinearities in integrated optical waveguides, either for spectral broadening of initially narrowband frequency combs [8] or for Kerr comb generation in high-Q microresonators [4,6,7]. While these approaches allow to generate hundreds of spectral lines distributed over bandwidths of 10 THz or more, the underlying setups are rather complex, require high pump power levels along with delicate operation procedures, and still comprise discrete components such as fiber amplifiers or external light sources. Other approaches to chip-scale comb generators rely on gain switching of injection-locked DFB lasers [10–12], which may be integrated into chip-scale packages with all peripheral components but suffer from the rather small bandwidth of the overall comb, which typically spans less than 500 GHz [12].

These limitations may be overcome by so-called single-section quantum-dash (QD) mode-locked laser-diodes (MLLD) [13–26]. These devices combine an inhomogeneously broadened gain spectrum of the QD material with passive mode-locking through four-wave mixing and self-induced carrier density modulation [13–15] and allow for generation of broadband flat frequency combs without requiring a saturable absorber. QD-MLLD can be operated by a simple DC current while producing combs that can comprise 50 carriers or more, spaced by tens of GHz and distributed over a spectral range of more than 2 THz. However, the devices suffer from large optical linewidth of the individual tones, which strongly impairs transmission of signals that rely on advanced modulation formats [16–20]. As a consequence, data transmission demonstrations with QD-MLLD have so far relied on intensity modulation of the optical carriers using, e.g., on-off-keying (OOK) [16] or electrical OFDM signals [17], were limited to rather simple modulation phase formats such as quadrature phase-shift keying (QPSK) [18–20], or required dedicated hardware schemes for reducing the optical linewidth of the comb tones [21–24].

In this work, we show that the phase-noise limitations of QD-MLLD-based WDM transmission schemes can be overcome by a continuous feed-forward algorithm based on symbol-wise blind phase search (BPS) [27] without the need for any additional optical hardware. Expanding on our earlier demonstrations [19], our concept allows for data transmission using 16-state quadrature amplitude modulation (16QAM), even in the presence of strong phase noise of the QD-MLLD tones. The viability of our concept is demonstrated in a series of transmission experiments. In a first experiment, we transmit 52 channels over 75 km of standard single-mode fiber (SSMF) using QPSK as a modulation format at a symbol rate of 40 GBd. By exploiting polarization-division-multiplexing (PDM), we achieve an aggregate line rate (net data rate) of 8.32  Tbit/s (7.83 Tbit/s). In a second experiment, we use 38 carriers to transmit PDM-16QAM signals at a symbol rate of 38 GBd over 75 km of SSMF, leading to an aggregate line rate (net data rate) of 11.55 Tbit/s (10.68 Tbit/s). To the best of our knowledge, this is the highest data rate achieved by a DC-driven chip-scale comb generator that does not require any hardware-based phase-noise reduction schemes. Our investigation is supported by an in-depth analysis of the phase-noise characteristics of the QD-MLLD, revealing a strong increase of the FM-noise spectrum at low frequencies as the main problem that has prevented 16QAM transmission so far. Our results combined with the robustness and the ease of operating QD-MLLD show the great potential of such devices as light sources for highly scalable WDM transceivers.

2. Quantum-dash mode-locked laser diodes

The frequency comb sources used in our data transmission experiments consist of InAs/InGaAsP quantum-dash (QD) structures, which are grown by molecular beam epitaxy (MBE) on InP substrates [28]. The active region consists of six stacked layers of InAs QD, embedded into InGaAsP barriers, see Fig. 1(a). The InGaAsP composition is designed to have a bandgap corresponding to a photon energy λ_g= 1.17 µm, and the emission wavelength of the device used in our experiments is approximately 1.55 µm. Details of the dash-in-a-barrier design can be found in [13]. The thickness of the barrier between the QD layers amounts to 40 nm, and the structure is terminated by 80-nm-thick separate confinement heterostructure (SCH) layers of InGaAsP towards the top and bottom InP regions. Electrons are injected into the SCH layer from the n-side, corresponding to the bottom contact in Fig. 1(a), and are then trapped in the QD, emitting photons with a wavelength of approximately 1.55 µm. The photons are guided in a buried ridge waveguide of 1.5 µm width [13]. Cleaved facets act as broadband front and backside mirrors, thereby forming a Fabry-Perot (FP) laser cavity with a total length of 980 µm, corresponding to a free spectral range (FSR) of approximately 42 GHz. Due to the inhomogeneously broadened gain originating from the shape distribution of the QD, multiple longitudinal modes can coexist in the laser cavity. According to [28], mode-locking in QD-MLLD does not require a saturable absorber, but relies on mutual sideband injection due to four-wave mixing and self-induced carrier density modulation at the FSR frequency – similar to actively mode locked laser diodes, but induced by the signal generated from the beating among the laser cavity modes rather than by an external radio frequency (RF) source. This leads to a comb of equally spaced spectral lines with strongly correlated phases [29], thereby forming a periodic output signal with a period corresponding to the cavity round-trip time. The strong phase correlation of neighboring modes leads to a narrow RF beat note measured at the FSR frequency when detecting the periodic output signal with a high-speed photodetector.

 

Fig. 1. Frequency-comb generation in quantum-dash mode-locked laser diodes (QD-MLLD). (a) Top view and cross-section schematic of a QD-MLLD consisting of a ridge waveguide of 1.5 µm width and 980 µm length. The active region comprises six stacked layers of InAs QD separated by 40 nm-thick InGaAsP barriers, see transmission-electron microscope (TEM) image in the Inset [13]. Carriers are injected into the active region through 80-nm-thick separate confinement heterostructure (SCH) layers of InGaAsP, designed to have a bandgap corresponding to a photon energy λ_g= 1.17 µm. The emission wavelength of the devices used in our experiments is approximately 1.55 µm. (b) Setup for frequency comb characterization. The QD-MLLD is driven by a DC current. LF: Lensed fiber. OI: Optical isolator. PD: Photodiode. ESA: Electrical spectrum analyzer. OSA: Optical spectrum analyzer. (c) Number of lines within the 3-dB bandwidth of the comb (blue) and FWHM of the RF beat note (“RF linewidth”, red) at the FSR frequency of 42 GHz as a function of injection current. (d) Optical output power (green) and average OCNR (black) of the comb lines as a function of injection current. Shaded region: Range of favorable operating currents for low RF linewidth, high output power and OCNR, and large number of lines. (e) QD-MLLD frequency comb spectrum for an injection current of 390 mA at a stabilized temperature of 21.2 °C.

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To identify favorable parameters for operating the QD-MLLD in transmission experiments, we performed a thorough characterization of the devices using the setup shown in Fig. 1(b). The light emitted by the DC-driven QD-MLLD is collected by a lensed single-mode fiber (LF), which features an anti-reflection coating to avoid distortions by optical back-reflection into the laser cavity. The collected light is sent to an optical spectrum analyzer (OSA) and to a photodiode (PD), which is connected to an electrical spectrum analyzer (ESA) for extracting the RF beat note at the FSR frequency. In our experiment, we swept the pump current and recorded the fiber-coupled output power of the device along with the linewidth of the RF beat note and the optical spectrum, from which we extract the optical carrier-to-noise power ratio (OCNR) and the number of lines within a 3-dB bandwidth of the comb, see Fig. 1(c) – 1(d). Figure 1(c) shows the full width half maximum (FWHM) linewidth of the RF beat note at the FSR frequency and the number of comb lines within the 3-dB bandwidth of the comb as a function of the injection current. The linewidth of the RF beat note decreases with higher injection current and reaches a constant value of approximately 10 kHz at high currents. Note that this decrease of the RF linewidth with injection current has been described in the literature [29,30] and is attributed to the fact that mode-locking in the QD-MLLD relies on nonlinear interaction of the various modes, e.g., through four-wave mixing and carrier density modulation [28]. This interaction increases for higher optical power levels, i.e., higher injection currents, which leads to a decreased RF linewidth. Figure 1(d) shows the fiber-coupled output power and the average OCNR. The OCNR values are first determined individually for each comb line based on the optical spectrum of the frequency comb. As a reference bandwidth for specifying the OCNR, we choose 12.5 GHz, which corresponds to a wavelength span of 0.1 nm at a center wavelength of 1550 nm. Within the 3 dB-bandwidth of the comb, the OCNR of the lines exhibit only small variations of approximately ± 1 dB. The plot in Fig. 1(d) shows the mean OCNR averaged over all lines within the 3-dB bandwidth of the comb. The average OCNR increases with injection current and reaches an essentially constant level of approximately 40 dB above 300 mA.

From Fig. 1(c) and 1(d), we find that the output power, the number of lines and the OCNR monotonically increase with injection current, while the linewidth of the RF beat note decreases. For the transmission experiment, the injection current is hence chosen as high as possible without exceeding the current limit of the diode. As a favorable operation regime, we identify the range between 300 mA and 420 mA, which is shaded in red in Fig. 1(c) and 1(d). We repeated the measurement for other temperatures between 20 and 25 °C, observing a similar trend. Figure 1(e) shows the resulting frequency comb spectrum for an injection current of 390 mA at a stabilized temperature of 21.2 °C. Throughout the subsequent experiments, the injection current and operation temperature of the laser are kept constant to avoid drift of the center frequency of the generated combs. The accuracy of this stabilization amounts to ± 0.1 K for the operating temperature and to ± 0.1 mA for the injection current.

For coherent communications, the carriers used to transmit data need to have high OCNR and narrow optical linewidths, or, equivalently, low phase noise. The recorded OCNR level would in principle safely allow for transmission of 16QAM signals at symbol rates of 50 GBd or more [31]. However, the individual comb tones exhibit strong phase noise, which inhibits the use of advanced modulation formats with high spectral efficiency. In the case of strong phase noise, there is a high probability that the induced phase change causes a wrong recovery of the symbol, thus dramatically increasing the bit-error ratio (BER), even at high OCNR. In the next section, we present a more detailed analysis of the phase noise for individual carriers of the QD-MLLD, whilst Section 4 contains an analysis of the impact of phase noise on the measured BER for QPSK and 16QAM signaling.

3. Phase noise characteristics of QD-MLLD

The optical tones of the QD-MLLD are broadened by several effects [32]. Fundamentally, laser linewidth broadening is caused by the coupling of spontaneous emission into the oscillating mode, leading to spectrally white frequency noise. Other effects such as flicker and random-walk frequency noise contribute to linewidth broadening, too, and occur at longer time scales [33,34], i.e., lower frequencies. Influences of temperature fluctuations and mechanical vibrations happen on an even larger time scale and are disregarded. In the following, we differentiate between short-term and long-term phase noise, leading to a short-term and a long-term linewidth of the comb tone. Short-term phase fluctuations are characterized by a white frequency-noise spectrum and lead to a Lorentzian laser line shape with a FWHM $\Delta {\kern 1pt} {f_\textrm{L}}$, while long-term phase fluctuations lead to a Gaussian spectrum with FWHM $\Delta {\kern 1pt} {f_\textrm{G}}$ [33]. For the devices used in our measurements, the long-term linewidth is observed when considering the frequency fluctuations for observation times ${\tau _0} \gg $ µs, whereas the short-term linewidth is obtained for observation times ${\tau _0} \ll 1$ µs, see Section 3.1 for a more detailed discussion.

For measuring the short-term and long-term optical linewidths of the individual comb lines, we follow two different heterodyne approaches, which are illustrated in Fig. 2(a), Setup I and Setup II. In Setup I, the QD-MLLD output is superimposed with the output of a highly stable tunable local-oscillator laser (LO I) and then sent to a photodetector connected to an ESA for recording the beat-note spectrum and the long-term linewidth. In Setup II, we use a second tunable local oscillator laser (LO II) along with a coherent receiver and high-speed analog-to-digital converter (ADC). The ADC is used to record the RF beat note, from which the intrinsic Lorentzian, i.e., short-term linewidths are extracted by offline processing of the signals [33], see Section 3.2. Both LO I and LO II are external-cavity lasers (ECL, Keysight N7714A) with a specified linewidth below 100 kHz, i.e., the LO linewidths are much smaller than the expected linewidth of the comb lines. This is verified by connecting LO I to Input II (Inp II) of Setup II, and LO II to Input I (Inp I) of Setup I and by observing that in both cases the resulting linewidths of the beat notes are much smaller than those obtained from the QD-MLLD tones, see Fig. 2(b). Note that these measurements can only reveal the relative phase fluctuations of LO II with respect to LO I, which can be considered as an upper boundary of the phase noise of each of the sources. In the following sections, we detail a quantitative phase-noise model, Section 3.1, and use it to extract the QD-MLLD phase-noise characteristics from the measurements obtained from Setup I and Setup II, Sections 3.2 and 3.3.

 

Fig. 2. Linewidth measurement and phase-noise characterization for selected comb lines of the QD-MLLD. (a) Experimental setups: In Setup I, the QD-MLLD output is superimposed with the output of a narrowband local oscillator laser (LO I) and detected by a single photodiode (PD) and an electrical spectrum analyzer (ESA) to extract the long-term linewidth $\Delta {f_\textrm{G}}$. In Setup II, a second LO laser (LO II) is used along with a coherent receiver and a high-speed analog-to-digital converter (ADC) for measuring the temporal phase-noise characteristics, from which we extract the FM-noise spectrum that reveals the intrinsic Lorentzian linewidth $\Delta {f_\textrm{L}}.$ LF: Lensed fiber. OI: Optical isolator. PC: Polarization controller. LO I, LO II: Tunable external cavity lasers (ECL). OH: Optical hybrid. BPD: Balanced photodiodes. Inp I, Inp II: Auxiliary inputs for verification of the LO laser linewidths. (b) Long-term and short-term optical linewidths of the different comb lines. The long-term linewidths were recorded with an effective ESA observation time of ${\tau _{0,\textrm{ESA}}} \approx 150$ µs. (c) Power spectra ${S_{{f_{\textrm{inst}}}}}$ of instantaneous frequency fluctuations (FM noise) along with model fits according to Eq. (1). The length of the recorded time-domain beat signal is 125 µs. The data were obtained by testing a QD-MLLD tone with Setup II (QD-MLLD, blue) or by connecting LO I to Inp II of Setup II (LO I/II, red). In both cases, the wavelength of the tested tone was 1547.3 nm. Note that the second measurement can only reveal the relative phase fluctuations of LO II with respect to LO I, which can be considered as an upper boundary of the phase noise of each of the sources. Since the linewidth of LO I is much smaller than that of the QD-MLLD tone, the phase fluctuations in the first measurement can be attributed to the QD-MLLD tone. (d) Phase-noise variance $\sigma _\phi ^2$ as a function of measurement time τ, both for LO I and for the QD-MLLD tone. (e) Power spectra as a function of the frequency offset from the carrier for LO I and for the QD-MLLD tone (resolution bandwidth $\delta f = 400\,\textrm{kHz}\textrm{)}\,\textrm{.}$

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3.1. Phase-noise and linewidth model

In the following, we give a short overview on the model used for quantitatively describing the phase noise of the MLLD tones. More details of the underlying theoretical background and a derivation of the mathematical relationships can be found in [35]. The complete statistical characteristics of the phase noise or, equivalently, the frequency noise of a laser oscillator can be obtained from the so-called FM-noise spectrum ${S_{{f_{\textrm{inst}}}}}$, i.e., the power-spectral-density function of the instantaneous optical frequency fluctuations ${f_{\textrm{inst}}}(t )$, which can be modeled by [36,37]

The FM-noise spectrum can be separated into two areas that influence the measured line shape in distinctively different ways, depending on the observation time. For long observation times, the measured linewidth will be dictated by FM-noise components at low Fourier frequencies, where flicker and random-walk frequency noise dominates. Specifically, the resulting line can be approximated by a Gaussian if the line shape is dominated by frequency noise at Fourier frequencies f smaller than a frequency ${f_{\textrm{high}}}$ defined by [35]

In contrast to that, the observed line shape is Lorentzian if the observation time is chosen short enough, i.e., if the lower frequency limit ${f_{\textrm{low}}}$ is high enough to exclude the impact of flicker and random-walk frequency noise. The relevant part of the FM- noise spectrum can then be considered white, and the intrinsic Lorentzian linewidth $\Delta {\kern 1pt} {f_\textrm{L}}$ is directly proportional to the constant spectral power density ${S_\textrm{L}}$ of the frequency noise [33],

These considerations allow us to give a more precise definition of the terms “long-term linewidth” and “short-term linewidth” introduced earlier. The long-term linewidth $\Delta {\kern 1pt} {f_\textrm{G}}$ is observed for observation times ${\tau _0} \gg {\tau _{\textrm{low}}} = {1 / {{f_{\textrm{high}}}}}$ (usually ${\tau _0} > 5{\tau _{\textrm{low}}}$), where ${f_{\textrm{high}}}$ is obtained from Eq. (2). For ${\tau _0} \ll {\tau _{\textrm{low}}}$, the short-term linewidth, i.e., the intrinsic Lorentzian linewidth $\Delta {\kern 1pt} {f_\textrm{L}}$ is found. Measuring the FM-noise spectrum of the QD-MLLD tones and fitting Eq. (1) to the measurement allows us to obtain both the intrinsic linewidth $\Delta {\kern 1pt} {f_\textrm{L}}$, see Section 3.2, the long-term linewidth $\Delta {\kern 1pt} {f_\textrm{G}}$, see Section 3.3, and the parameter ${\tau _{\textrm{low}}} \approx 1$ µs, which corresponds to the observation time that roughly marks the transition between the two regimes. Alternatively, the long-term linewidth $\Delta {\kern 1pt} {f_\textrm{G}}$ can be extracted by means of an ESA that records the beat-note spectrum of the comb tone with the tone emitted by LO I, see Section 3.3.

The results of the linewidth measurements are shown in Fig. 2(b) with short-term linewidths $\Delta {\kern 1pt} {f_\textrm{L}}$ ranging from approximately 1.5 MHz at the center of the frequency comb to 4 MHz at the edges, and long-term linewidths $\Delta {\kern 1pt} {f_\textrm{G}}$ ranging from 7 MHz at the center to 12 MHz at the edges. The increase of the linewidths towards the edges of the comb spectrum is related to the timing jitter of the periodic signal generated by the QD-MLLD [14]. The long-term linewidths in the comb center are in good agreement with the values found in [14].

3.2. Short-term linewidth from measured FM-noise spectrum

The intrinsic Lorentzian linewidth $\Delta {\kern 1pt} {f_\textrm{L}}$ for each line of the frequency comb is obtained from the FM-noise spectrum ${S_{{f_{\textrm{inst}}}}}$ using Eqs. (1) and (5). To measure ${S_{{f_{\textrm{inst}}}}}$, we first recover the in-phase (I) and quadrature (Q) component of the electric field of individual comb carriers with a coherent receiver [33,38,39] using Setup II of Fig. 2(a). In these measurements, LO II is tuned to generate an I and a Q beat signal with the respective comb line at an intermediate frequency of approximately 1 GHz. This choice of intermediate frequency guarantees that the beat note with an FWHM of the order of a few tens of MHz does not extend to negative frequencies, thereby avoiding impairment by spectral foldback. The time-dependent phase differences between the LO tone and the comb tone are derived from the I and the Q signals, and the frequency offset is removed by fitting the time-dependent increase of the phase with a linear function. The time-dependent random phase fluctuations $\phi (t )$ are then obtained from the difference of the measurement data and the linear fit. To extract the associated instantaneous frequency fluctuation ${f_{\textrm{inst}}}(t )$, we compute the time-derivative of the measured phases,

To extract the model parameters ${S_\textrm{L}}$, ${S_\textrm{1}}$ and ${S_2}$ of Eq. (1) from our measurements, we perform a parameter fit of the model prediction to the measured data. The fitting procedure comprises several steps: For smoothing the measured FM- noise spectrum, we used a moving-average filter for which the length increases with frequency. We start from a filter length of 1 tap, i.e., no averaging, at Fourier frequencies of up to 70 kHz and then increase the filter length exponentially to 800 taps at a Fourier frequency of 100 MHz. This approach was necessary to maintain the strong increase of the FM-noise spectrum towards low frequencies (< 100 kHz) while effectively reducing the uncertainties at higher frequencies (> 1 MHz). Prior to fitting the smoothed data, we re-sample it to obtain points that are equidistant with respect to the logarithm of the Fourier frequency. This avoids a situation where the least-squares errors of the fit are dominated by the noisy high-frequency part of the spectrum while the physically relevant low-frequency part does not play a role. The results of the fit are robust with respected to the choice of initial fitting parameters and of the tap number that the averaging filter uses towards high frequencies. For the MLLD tone, we obtain ${S_\textrm{L}} = 5.9 \times {10^5} \;\textrm{Hz} \textrm{,} \,{S_1} = 9.4 \times {10^{11}}\;\textrm{H}{\textrm{z}^2} \;\textrm{and} \;{S_2} = 2.3 \times {10^{17}}\;\textrm{H}{\textrm{z}^3}$, leading to an intrinsic Lorentzian linewidth $\Delta {\kern 1pt} {f_\textrm{L}}$ = 1.9 MHz. We repeat the measurement for different QD-MLLD lines, see Fig. 2(b). For the beat of LO I with LO II, we find ${S_\textrm{L}} = 4.0 \times {10^3}\;\textrm{Hz} \;\textrm{,} \,{S_1} = 3.2 \times {10^9}\;\textrm{H}{\textrm{z}^2},$ and ${S_2} = 2.2 \times {10^{15}}\;\textrm{H}{\textrm{z}^3}$, leading to an intrinsic linewidth of the measured beat note of 12 kHz.

Note that the intrinsic linewidth $\Delta {\kern 1pt} {f_\textrm{L}}$ can also be inferred from the delay-dependent phase differences $\Delta {\phi _\tau }(t )= \phi ({t + \tau } )- \phi (t )$ and the associated phase-noise variance [33]

3.3. Long-term linewidth measurement

The long-term linewidth $\Delta {\kern 1pt} {f_\textrm{G}}$ is measured using the heterodyne setup shown in Fig. 2(a), Setup I. To this end, we tune LO I close to a comb line of the QD-MLLD and detect the superposition of both on a PD. The spectrum of the resulting photocurrent is centered about the difference frequencies of the comb line and the tone emitted by LO I and is measured using an electrical spectrum analyzer (ESA).

For better comparison of the results obtained from the ESA measurement to the long-term FWHM linewidths extracted from Eq. (3), we estimate the effective observation time ${\tau _{0,\textrm{ESA}}}$ that has to be assigned to the ESA measurement. For a given frequency span $\Delta {\kern 1pt} f$, the effective observation time ${\tau _{\textrm{0,ESA}}}$ that is needed to record this span using the ESA is dictated by the resolution bandwidth $\delta f$ [41] ,

In our measurements, we select different comb lines by tuning LO I, see Fig. 2(b). In these measurements, two important requirements need to be fulfilled: First, the resulting intermediate frequency must be much larger than the expected spectral half width of the investigated comb line. This is ensured by choosing an intermediate frequency of approximately 1 GHz. Second, the phase fluctuations of the LO must be much smaller than those expected for the investigated comb line. The validity of this assumption was already assured when recording the frequency noise spectrum, see Section 3.2.

The long-term linewidth is extracted by evaluating the FWHM of a model function that is fit to the measured spectra. In general, the line-shape is described by a Voigt function, i.e., a convolution of a Lorentzian and a Gaussian [34,40]. This function, however, may be approximated by a Gaussian near the line center [34]. In our analysis we have investigated the impact of fitting both types of curves to the measured data. Both fits lead to virtually the same results for $\Delta {f_\textrm{G}}$ with deviations of less than 5%. The long-term linewidths indicated in Fig. 2(b) are obtained from the Voigt function. For a QD-MLLD tone close to 1547.3 nm, we obtain a long-term linewidth $\Delta {f_\textrm{G}}$ of approximately 8 MHz, Fig. 2(e), blue curve.

As a check, we also re-confirm that the linewidth of LO I can be neglected by measuring the long-term optical linewidth of the beat note between LO I and LO II using Setup I, leading to $\Delta {f_\textrm{G}} = 0.6\;\textrm{MHz}$ for an ESA resolution bandwidth of $\delta f = 400\,\textrm{kHz}$, see Fig. 2(e), red curve. We further compare the long-term linewidth obtained from the ESA measurement to that extracted from the fitted FM-noise spectrum. To this end, we use Eqs. (3) and (4) which, for ${S_\textrm{L}} = 4.0 \times {10^3}\;\textrm{Hz}\,\textrm{,}$ ${S_1} = 3.2 \times {10^9}\;\textrm{H}{\textrm{z}^2},$ ${S_2} = 5.0 \times {10^{17}}\;\textrm{H}{\textrm{z}^3},$ ${f_{\textrm{low}}} = {1 \mathord{\left/ {\vphantom {1 {{\tau_{0,\textrm{ESA}}}}}} \right.} {{\tau _{0,\textrm{ESA}}}}} = 8\,\textrm{kHz}$, and ${f_{\textrm{high}}} = {1 \mathord{\left/ {\vphantom {1 {{\tau_{\textrm{low}}}}}} \right.} {{\tau _{\textrm{low}}}}} = 2\,\textrm{MHz}{\kern 1pt}$ lead to a long-term linewidth $\Delta {\kern 1pt} {f_\textrm{G}}$ of approximately 14 MHz. This is in good agreement with the width obtained from the directly measured line shape.

4. Coherent transmission using QD-MLLD

In this section, we first investigate the effect of the inherent phase noise of QD-MLLD carriers on coherent data transmission for different modulation formats and symbol rates, see Section 4.1. We show that symbol-wise blind phase search (BPS) [27], relying on continuous feed-forward estimation and correction of the instantaneous phase difference between the LO tone and the carrier, substantially improves the transmission performance of the QD-MLLD and finally enables the use of 16QAM signaling, see Fig. 3. Details of the phase tracking algorithm are described in Section 4.2.

 

Fig. 3. Influence of phase noise on coherent transmission at different symbol rates, modulation formats, and OSNR values. The analysis relies on using a single comb line with an intrinsic linewidth of 1.9 MHz as a carrier at a wavelength of 1540.4 nm. As a reference, we use a narrowband optical carrier provided by an ECL with an intrinsic linewidth of ∼ 10 kHz. The transmission performance of the ECL tone is compared to that of the QD-MLLD tone using either block-wise CPR (MLLD/block-wise CPR) or symbol-wise BPS (MLLD/symbol-wise BPS). (a) Experimental setup. EDFA: Erbium-doped fiber amplifier. POF: Programmable optical filter. IQ-mod: In-phase/quadrature (IQ) modulator. AWG: Arbitrary waveform generator. PDM: Polarization division multiplexing. VOA: Variable optical attenuator. OSNR meas.: Optical signal-to-noise-ratio measurement unit. DL: Delay line. PBC: polarization beam combiner. ASE: Amplified spontaneous emission. BPF: Band-pass filter. LO: Local oscillator. (b) Error-vector magnitude (EVM) measured for PDM-QPSK signaling at different symbol rates. For QPSK, we did not find a sufficient number of errors within our limited recording lengths and can hence only provide the EVM. We find that symbol-wise BPS algorithm can essentially overcome the phase-noise-related limitations observed for block-wise CPR and bring the transmission performance of the MLLD tone close to that of a narrowband ECL tone. (c) BER results for PDM-16QAM signaling for different symbol rates. In these measurements, the OSNR was around 35 dB. For practically relevant symbol rates beyond 30 GBd, symbol-wise BPS can essentially overcome the phase-noise-related impairments. The measured BER values fit well to the simulation results (dashed lines) labelled “Sim. MLLD” and “Sim. ECL”. (d) BER results for PDM-16QAM signaling at 38 GBd for different OSNR values. The OSNR values are measured after EDFA 4, see Subfigure (a). For OSNR values of 25 dB or less, symbol-wise BPS allows the QD-MLLD tone to perform nearly as good as a narrowband ECL carrier with OSNR penalties of approximately 0.5 dB.

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As a reference, we use the transmission performance obtained by block-wise carrier phase recovery (CPR) which is part of the Vector Signal Analyzer (VSA) software offered by Keysight Technologies (89600 series VSA software) [42]. In this approach, received symbols are processed in blocks, within which a certain frequency offset and an otherwise constant phase difference between the LO tone and the carrier are corrected. To this end, the phases of symbols in a block are extracted and unwrapped. The frequency offset is then extracted from a linear regression of the time dependence of the unwrapped phases. Details can be found in [42]. Note that this block-wise CPR does not allow for dynamic phase tracking. We further benchmark the results obtained from the MLLD by replacing the comb tone by an ECL carrier with an intrinsic linewidth of approximately 10 kHz. For optical signal-to-noise power ratios (OSNR) of 25 dB or less that are typically found at the receivers of 16QAM transmission links [43], the transmission performance achieved with QD-MLLD tones in combination with BPS is comparable to that offered by high-quality ECL carriers.

In Sections 4.3 and 4.4, we present a series of transmission experiments demonstrating the ability of the symbol-wise BPS scheme to compensate for the phase noise of the QD-MLLD tones. In a first experiment, we transmit 52 channels spaced by 42 GHz over 75 km of standard single-mode fiber (SSMF) using QPSK as a modulation format, see Section 4.3. Using polarization-division-multiplexing (PDM), we achieve an aggregate line rate of 8.32 Tbit/s, which reduces to a net data rate of 7.83 Tbit/s when considering a 6.25% overhead necessary for hard-decision forward error correction (FEC) of BER values below 4.7  × 10⁻³ [44]. In a second experiment, we use 38 carriers to transmit PDM-16QAM signals over 75 km of SSMF at an aggregate line rate of 11.55 Tbit/s, which corresponds to a net data rate of 10.68 Tbit/s when accounting for a FEC overhead of 6.25% for 32 channels and of 20% for the remaining six channels [44], see Section 4.4. This corresponds to the highest data rate achieved by a DC-driven chip-scale comb generator without any additional hardware-based phase-noise reduction [21–24].

4.1 Influence of comb carrier linewidth and OSNR on coherent communications

To quantify the influence of the linewidth of the QD-MLLD comb lines on coherent transmission, we measure the BER at different symbol rates for both QPSK and 16QAM. The experimental setup is depicted in Fig. 3(a). After amplification of the frequency comb by EDFA1 to an output power of 17 dBm, we filter the comb line of interest using a programmable optical filter (POF). A 3dB-bandwidth of approximately 10 GHz of the POF is chosen to effectively suppress all neighboring comb lines. The filtered carrier, centered at a wavelength of 1540.4 nm, is amplified to a power of 24 dBm and sent through an IQ modulator. The phase-noise properties of this carrier are essentially the same as those of the carrier at 1547.3 nm, which is analyzed in detail in Figs. 2(c) – 2(e). The modulator drive signal is synthesized by an arbitrary-waveform generator (AWG) based on a pseudo-random bit sequence (PRBS) of length 2¹¹ − 1. The bit sequence is mapped to either QPSK or 16QAM symbols with pulses having a raised-cosine (RC) spectrum with a 5% roll-off for QPSK and 10% for 16QAM. PDM is emulated by splitting the data signal and decorrelating the split signals in time by approximately 5.3 ns using a delay line (DL) [4]. Finally, both signals are combined in orthogonal polarization states using a polarization beam combiner (PBC). To adjust the OSNR of the signal, a noise-loading stage (ASE source) is used. The signal is then sent to the receiver, where it is further amplified by EDFA3 and EDFA4. Bandpass filters (BPF) are used to suppress out-of-band noise after each amplifier. The signal is finally detected by an optical modulation analyzer (OMA, Keysight N4391A) acting as a dual-polarization coherent receiver (DP-CR) with built-in local oscillator (LO) laser. The intrinsic linewidth of the LO is approximately 10 kHz. The output of the DP-CR is digitized by a 4-channel 80 GSa/s real-time oscilloscope (two synchronized Keysight DSO-X 93204A) and recorded for offline digital signal processing (DSP). The digitized signal undergoes a number of DSP steps, comprising timing recovery, MIMO equalization, frequency offset compensation, carrier phase compensation, and decoding, see Section 4.2 for details.

The measured signal quality parameters are summarized in Fig. 3(b) and 3(c) for QPSK and 16QAM signals. In these plots, green traces represent the results obtained from using block-wise CPR (‘MLLD/block-wise CPR’) as implemented in Keysight’s VSA software [42]. In this analysis, the block length was varied between 100 and 200 symbols, depending on the symbol rate. The blue traces are obtained using continuous feed-forward symbol-wise BPS algorithm (‘MLLD/symbol-wise BPS’) [27], see Section 4.2 for details. The red traces (‘ECL’) are obtained by repeating the experiment using a narrowband ECL as an optical source. The ECL is tuned to the same wavelength as the comb tone and has an intrinsic linewidth of approximately 10 kHz, and we can hence assume that the transmission performance is not impaired by phase noise. This is confirmed by observing that block-wise CPR and symbol-wise BPS lead to the same result for the ECL-based transmission. For QPSK, Fig. 3(b), the limited recording length did not contain enough errors for a statistically reliable measurement of the BER. We therefore use the error vector magnitude (EVM) rather than the BER as a performance metric [31]. Assuming that the signals are impaired by additive white Gaussian noise only, the measured EVM would correspond to BER values below 10⁻¹⁰ [31]. Note that the EVM can be defined in two different ways depending on the normalization, which either refers to the maximum field in the constellation, or to the average field resulting from summing the power of all possible symbols [45]. Here, we refer to the second definition, i.e., we normalize the EVM to the average field. For 16QAM, we measure the BER directly.

Generally, the impact of phase noise increases with decreasing symbol rates, i.e., longer optical symbol periods, which leads to an increase of the EVM or the BER at low symbol rates for the QD-MLLD experiments with block-wise CPR, see green traces in Fig. 3(b) and 3(c). At high symbol rates, the signal quality is impaired by the decreasing SNR and by the bandwidth limitations of our AWG, leading to higher EVM and BER. Using the symbol-wise feed-forward BPS, the impact of phase noise can be greatly reduced, both for QPSK and 16QAM, see blue traces. For QPSK, the transmission performance comes close to that of the narrowband ECL, illustrated by the red trace. 16QAM is generally more sensitive to phase noise than QPSK, since more phases need to be discriminated. In this case, at low symbol rates, even the symbol-wise BPS is not capable of compensating the complete impact of phase noise. Still, the performance of the QD-MLLD experiments with symbol-wise BPS does not show any substantial penalty compared to that of the ECL-based transmission at practically relevant symbol rates of 30 GBd or more.

To quantitatively confirm the results depicted in Fig. 3(c), we have performed simulations of 16QAM transmission at different symbol rates. In these simulations, we neglect low-frequency FM noise and only consider the spectrally white part of the FM-noise spectrum. To this end, we model the underlying phase fluctuations as a Wiener process where the variance of the stochastic phase increments is chosen to produce an intrinsic linewidth of 1.9 MHz for the QD-MLLD carrier and of 10 kHz for the ECL carrier. We further consider additive white Gaussian noise (AWGN), modeling the noise contributions of the optical amplifiers and the receiver electronics. The AWGN level used in each simulation is obtained from the signal-to-noise ratio (SNR) of the measured data signals. The dashed lines in Fig. 3(c) show the simulation results, which are in good agreement with their measured counterparts.

Finally, we measure the BER as a function of the OSNR, see Fig. 3(d), for 16QAM and a symbol rate of 38 GBd, which is used for the high capacity WDM transmission experiment, see Section 4.4. In this measurement, we again compare the QD-MLLD with block-wise phase recovery (green trace) and symbol-wise phase tracking (blue trace) as well as the ECL reference (red trace). For a BER of 4.7 × 10⁻³, corresponding to the threshold for hard-decision FEC with 6.25% overhead [44], the implementation penalty amounts to approximately 0.9 dB for ECL-based transmission and to approximately 1.4 dB for the MLLD tone. The penalty of the MLLD tone with respect to the ECL carrier hence amounts to approximately 0.5 dB. This value is not only found at the FEC threshold, but more generally for all OSNR values of less than 25 dB. Thus, under realistic transmission conditions [43], the carriers of the QD-MLLD comb source perform similarly as a high-quality individual ECL carrier. The slightly lower performance of the MLLD tone observed at high OSNR beyond 25 dB, see Fig. 3(d), is attributed to residual phase noise that is still left after phase tracking [27]. This is confirmed by the simulation results shown in Fig. 3(c), which reproduce the measured BER performance both for the MLLD and the LO carrier by accounting for the measured linewidth of the respective carrier and by assuming OSNR levels between 20 dB and 25 dB. For the simulation, the OSNR level of each channel is derived from the SNR of the measured data signal.

4.2 Data recovery using feed-forward symbol-wise blind phase search

The continuous feed-forward algorithm for symbol-wise phase tracking was implemented in Matlab following the scheme introduced by Pfau et al. [27]. It is part of a multi-step DSP procedure, see Inset of Fig. 3(a). First, the signal is resampled to two samples per symbol followed by timing recovery [46,47]. A 30-tap MIMO equalizer based on the constant-modulus algorithm (CMA) is then used to demultiplex the two orthogonal polarizations of the signal and to compensate for linear transmission impairments [48]. The received symbols from the MIMO equalizer then undergo frequency-offset correction [49]. For QPSK, the 4^th-power of the received symbols is calculated to remove the information of the modulated phase. This leaves only the rapidly increasing phase caused by the frequency offset between signal carrier and LO. The frequency offset is then corrected by fitting a linear curve to the unwrapped phase as a function of time and by subtracting the fitted curve from the measured phase offset. For the case of 16QAM signaling, the 4^th-power scheme can be adapted by QPSK-partitioning [50]. Once the carrier frequency offset is compensated, carrier phase noise compensation is carried out based on a “symbol-wise” BPS algorithm [27].

The BPS algorithm starts with selecting a group of $N$ complex symbols which are centered around the symbol of interest. The phases of these complex symbols are then modified by adding identical test phases ${\phi _{{\kern 1pt} \textrm{t}}}$. The test phases are varied, and the sum of the squares of the N Euclidean distances of the measured symbols to their closest constellation points in the complex plane is measured. The optimum phase is determined by searching the minimum value of this sum [27]. Note that for symbol-wise BPS, the group of symbols used for phase estimation is slid along with the symbol of interest such that an individual phase correction term is computed for each symbol. This is in contrast to “block-wise” phase recovery, where all symbols within a block are treated with the same phase-correction parameter. For evaluating our measurements, we apply 45 equidistant test phases for covering an unambiguity range of $\pm 45^\circ $ for an M-QAM signal with a quadratic constellation.

As a rough estimate, a symbol-wise phase tracking technique relying on averaging of measured phases over a moving group of N symbols can effectively suppress frequency noise components occurring at Fourier frequencies up to $f = {1 \mathord{\left/ {\vphantom {1 {N{T_\textrm{S}}}}} \right.} {N{T_\textrm{S}}}}$, where ${T_\textrm{S}}$ corresponds to the symbol duration. This is confirmed by simulating 16QAM transmission at a symbol rate of 38 GBd, an intrinsic linewidth of the carrier of $\Delta {\kern 1pt} {f_\textrm{L}} = 1.9\;\textrm{MHz}$, and an OSNR of 35 dB, see Fig. 4. In this simulation, we perform BPS with different averaging lengths N and then extract the residual phase error of the various symbols with respect to the respective ideal constellation point. The residual instantaneous frequency fluctuations ${f_{\textrm{inst}}}(t )$ are then extracted from this time series of phase errors using the relation given in Eq. (6), and the FM-noise spectrum is derived by taking the Fourier transform of the autocorrelation function of ${f_{\textrm{inst}}}(t )$. The FM-noise spectra for different averaging lengths are then compared to the FM-noise spectrum of the carrier prior to modulation, indicated by a blue trace in Fig. 4. For N = 10 (red trace) we find that the frequency noise is effectively suppressed for Fourier frequencies smaller than approximately 4 GHz, whereas for N = 100 symbols (green trace), the suppression is only effective up to approximately 400 MHz, thus confirming the above-mentioned rule. Note that for N = 10, we observe a slight increase of the frequency noise level towards higher Fourier frequency. We attribute this to the impact of additive white Gaussian noise which may distort the phase recovery for small N. Note that flicker and random-walk frequency would occur at Fourier frequencies below 1 MHz, see Fig. 2(c), and would hence also be effectively suppressed by BPS.

 

Fig. 4. FM- noise compensation by blind-phase search (BPS) for different averaging lengths N: In the simulation, we assume 16QAM transmission at a symbol rate of 38 GBd, an intrinsic linewidth of the carrier of $\Delta {f_\textrm{L}} = 1.9\;\textrm{MHz,}$ and an OSNR of 35 dB. The traces show the residual FM-noise spectrum of the received signal after blind phase search, relying on averaging of measured phases over a moving group of N = 10 (red trace) and N = 100 (green trace) symbols. The blue trace indicates the spectrally white FM-noise spectrum of the carrier prior to modulation. As a rough estimate, BPS relying on a moving group of N symbols can effectively suppress frequency noise components occurring at Fourier frequencies up to $f = {1 \mathord{\left/ {\vphantom {1 {N{T_\textrm{S}}}}} \right.} {N{T_\textrm{S}}}}$, where ${T_\textrm{S}} \approx 26\,\textrm{ps}$ corresponds to the symbol duration. Flicker and random-walk frequency would occur at Fourier frequencies below 10⁶ Hz and would hence also be effectively suppressed by BPS.

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For a carrier with given phase noise and a fixed OSNR, an optimum number N of symbols within a group exists that provides an ideal trade-off between strong resilience to noise when averaging over many symbols for large N and the ability to track fast phase fluctuations, which requires small N. For a symbol rate of 38 GBd, an intrinsic linewidth of the QD-MLLD tone of 1.9 MHz, and OSNR levels of approximately 25 dB, best values of N are typically between 20 and 40. For N = 40 and symbol rates of 2 GBd or more, the overall averaging time of the phase-tracking scheme amounts to at most 20 ns. This is much shorter than the limit ${\tau _{\textrm{low}}} \approx 1$ µs of the observation time, beyond which flicker and random-walk frequency noise start to become noticeable, see Section 3.1. We may hence conclude that the phase-noise-related impairments that remain after symbol-wise phase tracking are solely dictated by the intrinsic (short-term) linewidth of the device related to the spectrally white component of the FM-noise.

Note that there is a residual probability that cycle slips occur in the BPS algorithm. To check this aspect, we have investigated our 16QAM recordings with OSNR values of 19.8 dB, 20.6 dB and 21.3 dB and with lengths of 6 × 10⁵ symbols without finding any cycle slips. We hence conclude that the BPS phase recovery is able to reliably track the phase over long symbol sequences. In a real system, this might have to be backed up by advanced FEC schemes [51] or pilot symbols [52].

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

Note that BPS is not the only phase tracking technique that allows to compensate impairments introduced by optical carriers with strong phase noise. Comparative study of other phase-tracking techniques such as digital phase-locked loops, Viterbi & Viterbi phase estimation, or algorithms based on Kalman filtering can, e.g., be found in Refs. [53–55]. In these studies, one conclusion is that feed-forward techniques such as BPS are more phase-noise tolerant and better suited for high symbol rates than feedback phase tracking such as digital phase-locked loops or algorithms based on Kalman filtering. Regarding feedforward methods, it has also been shown that BPS outperforms other algorithms such as Viterbi & Viterbi phase estimation in terms of phase-noise tolerance, and previous studies indicate that the Viterbi & Viterbi algorithm is not well suited for compensating the phase noise of QD-MLLD carriers at rather low symbol rates of 12.5 GBd [18].

It should also be noted that the performance advantages of symbol-wise BPS come at the price of increased computational complexity when compared to block-wise phase recovery. A more detailed discussion of the trade-off between the computational effort and the performance of BPS can, e.g., be found in [55]. Despite this complexity increase of the phase-tracking algorithm, the overall DSP complexity at the receiver does not change to a substantial degree, since the computational effort is mainly dominated by chromatic-dispersion (CD) compensation and FEC decoding [56].

4.3 52 × PDM-QPSK 7.83 Tbit/s data transmission

To demonstrate the viability of QD-MLLD in WDM transmission, we perform an experiment at a symbol rate of 40 GBd using QPSK as modulation format. The experimental setup is shown in Fig. 5(a). The total QD-MLLD output power is boosted by EDFA1 to 17 dBm. Using a programmable optical filter (POF), we select 52 tones from the frequency comb, marked in blue in Fig. 5(b), and separate them into odd and even carriers. The two sets of carriers are later encoded with independent data streams to emulate a realistic WDM signal [2,4]. The POF additionally flattens the power spectrum of the carriers. After amplification and flattening, the OCNR of the comb lines amounts to approximately 35 dB. The even and odd carriers are amplified by subsequent EDFA2 and EDFA3 and sent through a pair of IQ modulators. Both modulators are driven by QPSK signals with RC spectrum pulses with a 5% roll-off, generated by an AWG using a PRBS of length 2¹¹−1 at a symbol rate of 40 GBd. After combining the signals, PDM is emulated by a split-and-combine method, described in Section 4.1. The data stream is amplified and transmitted over 75 km of SSMF, see Fig. 5(c) for the power spectrum before and after modulation. At the receiver, we amplify the signal and select each channel using a 0.6 nm tunable BPF followed by EDFA6 and a second tunable 1.5 nm BPF to suppress out-of-band ASE noise. The signal is detected with a DP-CR and undergoes a number of DSP steps, as described in Sections 4.1 and 4.2. To undo the dispersive effect of the 75 km-long fiber link, we additionally perform CD compensation.

 

Fig. 5. PDM-QPSK data transmission with QD-MLLD. (a) Experimental setup used to emulate the WDM transmission experiment. EDFA: Erbium-doped fiber amplifier. POF: Programmable optical filter. AWG: Arbitrary-waveform generator. PDM: Polarization division multiplexing. VOA: Variable optical attenuator. DL: Delay line. PBC: Polarization beam combiner. SSMF: Standard single-mode fiber. BPF: Band-pass filter. LO: Local oscillator. (b) Optical spectrum of the QD-MLLD frequency comb. The 52 lines selected for WDM experiment are colored in blue. (c) Top: Superimposed spectra of odd and even carriers before modulation. Bottom: Spectrum of 52 modulated carriers. (d) EVM of the transmitted WDM channels. The maximum recording length of 2 × 10⁶ bit leads to a minimum BER of 6.5 × 10⁻⁶ that can be measured in a statistically reliable way. This corresponds to an EVM of 22.9%. Below this value, the expected BER is smaller and cannot be measured within our recordings of 10⁶ symbols – the associated range of EVM values is shaded in green. Importantly, all 52 channels fall below an EVM of 38.5%, which corresponds to a BER of 4.7 × 10⁻³, representing the threshold for hard-decision FEC with 6.25% overhead [44].

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The measured EVM values are shown in Fig. 5(d). For evaluating the recorded signals, the averaging length N used for BPS is optimized individually for each channel, and amounts to approximately 30 symbols. For QPSK transmission, the signal quality is comparatively high with EVM levels down to 16%, which would correspond to a BER of 2 × 10⁻¹⁰ assuming that the signals are impaired by additive white Gaussian noise (AWGN) only. To measure a statically reliable BER reaching a confidence level of 99% within a confidence interval of 100%, at least 13 erroneous bits have to be found in each recording [45]. This would lead to recording lengths of more than 6 × 10¹⁰bit, which is far beyond the storage capabilities of our oscilloscope. We hence limited our recordings to a practically well manageable length of approximately 2 × 10⁶ bit and rely on the EVM as a quality metric. For this length, the smallest BER that can be measured with the above-mentioned confidence amounts to 6.5 × 10⁻⁶, which would correspond to an EVM of approximately 22.9%. Recordings with EVM values below this value are not accessible to direct BER measurements and fall into the green shaded area in Fig. 5(d). A statistically reliable measurement of the BER was hence only possible for the two channels at the lowest carrier frequency – the measured BER values are indicated in Fig. 5(d) and are in good agreement with the BER estimated from the EVM assuming that the signals are impaired by AWGN only. Importantly, all 52 channels fall below an EVM of 38.5%, which corresponds to a BER of 4.7 x 10⁻³ [45], representing the threshold for hard-decision FEC with 6.25% overhead [44]. This leads to an aggregate line rate of 8.32 Tbit/s and a net data rate of 7.83 Tbit/s, transmitted over 75 km of SSMF with a net spectral efficiency of 3.8 bit/s/Hz.

4.4 38 × PDM-16QAM 10.68 Tbit/s data transmission

We also perform a 16QAM transmission demonstration to prove the viability of symbol-wise blind phase search (BPS) for more complex modulation formats. We use the same setup as for the QPSK experiments, see Fig. 5(a). The symbol rate amounts to 38 GBd, and we use 38 carriers from our QD-MLLD frequency comb for WDM transmission, see Fig. 6(a) for the flattened power spectrum before and after modulation. We use pulses with RC spectrum having a 10% roll-off. The WDM transmission experiments relies on the central 38 comb lines, which offer a spectral flatness of better than 3 dB. The measured BER for each of the transmitted WDM channels is depicted in Fig. 6(b). For each channel, five signal sequences were recorded, each containing 10⁶ bit. This recording length is sufficient to provide more than 100 erroneous bits in each of our measurements, hence allowing for a statistically reliable BER estimation, see Section 4.3. Also here, the averaging length N used for BPS is optimized for each channel, see Section 4.2. Out of the 38 channels, 32 fall below the BER threshold of 4.7 × 10⁻³ for hard-decision FEC with 6.25% overhead, while the remaining six channels fall below the BER threshold of 1.44 × 10⁻² for FEC with 20% overhead [44]. This leads to an aggregate line rate of 11.55 Tbit/s and a net data rate of 10.68 Tbit/s with a net spectral efficiency of 6.7 bit/s/Hz. To the best of our knowledge, our experiments represent the first demonstration of optical 16QAM signal transmission using multiple carriers from a DC-driven chip-scale comb generator without any hardware-based phase-noise reduction schemes, leading to the highest data rate achieved in such an experiment. From Fig. 6(b) one can observe that channels at higher frequencies have a better signal quality. This is due to the fact that our preamplifiers EDFA5 and EDFA6 have a higher noise figure for decreasing optical frequency. Exemplary constellation diagrams for dual polarization channels at carrier frequencies 195.46 THz and 194.64 THz are shown in Fig. 6(c).

 

Fig. 6. Data transmission results of 38 channels carrying PDM-16QAM signals at 38 GBd. (a) Top: Combined odd and even carriers prior to modulation. Bottom: 38 modulated carriers prior to transmission. The line rate amounts to 304 Gbit/s per channel. (b) Measured BER of the transmitted channels. The BER increase towards lower carrier frequencies is attributed to an increase of the noise figures of EDFA5 and EDFA6 with decreasing optical frequency. (c) Exemplary constellation diagrams recorded at different optical carrier frequencies.

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Note that the FSR of 42 GHz of the MLLD comb generator was deliberately chosen for our experiments to enable transmission at maximum spectral efficiency with the available transmitter equipment. Specifically, the AWG (Keysight M8195) used for driving the I/Q modulators was limited to a bandwidth of approximately 20 GHz, which led to high penalties when utilizing 16QAM at symbol rates beyond 40 GBd, see Fig. 3(c). Other FSR can be obtained by cleaving the devices at a different length to achieve line spacings of, e.g., 25 GHz [20] or 50 GHz that comply to ITU standards.

5. Summary

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