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Abstract
The remote delivery of optical reference with highly stable oscillation frequency and carrier phase can eliminate the need of digital signal processing for the estimation of these parameters in optical communication. The distribution distance of the optical reference has been limited, however. In this paper, an optical reference distribution over 12,600 km is achieved while maintaining low-noise characteristics, using an ultra-narrow-linewidth laser as a reference source and a fiber Bragg grating filter for noise removal. The distributed optical reference enables 10 GBaud, 5 wavelength-division-multiplexed dual-polarization 64QAM data transmission without using carrier phase estimation, which significantly reduces off-line signal processing time. In the future, this method can enable all coherent optical signals in the network to be synchronized to a common reference ideally, thereby improving overall energy efficiency and cost.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The remote delivery of optical standards with highly stable frequency and phase over optical fibers and other media has been studied for a variety of purposes in science and engineering. These purposes include, for example, the measurement of variations in the fundamental physical constants [1], radio astronomy [2], geodesy [3], frequency calibration of Terahertz signals [4], and optical clock comparison [5]. More recently, their use in coherent optical communication has also been discussed.
In coherent optical communication, it is essential to mitigate the frequency offset (FO) and phase difference between the carrier lightwave used in the transmitter (Tx) and the local oscillator (LO) lightwave in the receiver (Rx). In a widely deployed digital coherent communication system (schematically shown in the inset of Fig. 1), dedicated digital signal processing (DSP) circuitry is used to estimate and compensate for FO and carrier phase (CP) differences. On the other hand, several approaches have been explored to eliminate the need for such DSP by using optical reference with synchronized frequencies and phases at the Tx and Rx [6–11]. However, other projects appear to be primarily targeted for use in data center networks, where the distribution / transmission distance of optical reference / data signals has been limited to a maximum of 10 km. Also, distribution of reference lightwave from a commodity laser source over 1,200 km between the Tx and Rx has been investigated [12], but it only contributed to the removal of the FO. We have aimed to distribute the optical reference not only for use in data centers but also on a more global scale, and to utilize it for high-order multi-level modulation such as 64 quadrature amplitude modulation (QAM) which is important in the post-400 G communication network [13–16]. The optical reference (or “seed lightwave” in previous studies) was distributed over 150 km in 2015 [13] and over 1,600 km in 2016 [14].
Fig. 1. Conceptual diagram of the proposed system. The reference light source is highly stabilized in frequency and phase. The optical reference is delivered to various nodes, each of which serves as the transmitter (Tx) and/or the receiver (Rx). An optical comb is generated using the optical reference as a seed, to be used for the modulation carriers at the Tx node. Another comb is generated to be used for the local oscillators (LOs) at the Rx node. When QAM signals from the Tx node is coherently received at the Rx node with the LOs, frequency offset (FO) and carrier phase (CP) difference between Tx and Rx can be eliminated, leading to the saving of digital signal processing (DSP) circuits. Frequency locking of the laser source to an absolute frequency reference is optional in the illustrated optical communication system. The inset at the bottom shows the conventional communication system where DSP mitigates FO and CP.
In this paper, we report the successful ultra-long distance optical reference distribution over 12,600 km which corresponds to the lengths of trans-Pacific cables, owing to the drastic improvement of the distribution technology. Since FO and CP estimation DSP can be eliminated, long-distance optical communication can also be an important application of optical standard distribution.
In section 2, we explain the concept and background of coherent optical network which utilizes the optical reference distribution. In section 3, we describe the setup and characterization results of long-distance optical reference distribution system, which is an essential part of the coherent optical transmission system in this study. We describe the experimental setup, DSP, and results of the transmission experiments in section 4, and we present the conclusion in section 5. The Appendix describes the procedure for stability evaluation.
2. Coherent optical network using the optical reference distribution
The conceptual diagram of a coherent optical network using the optical reference distribution is shown in Fig. 1. The optical reference is a coherent lightwave with a frequency stabilization to a high-Q resonator and suffers from very low phase noise. Some applications of optical reference other than telecommunications additionally require frequency locking to an absolute frequency reference, such as an absorption line of an optical lattice clock [17] or a single ion [18]. For use in telecommunications, however, absolute references are not required within an area where the degradation of distributed references is sufficiently small. The optical reference is distributed to various nodes within the area, some of these nodes serving as TXs and others serving as RXs, using only a small portion of the network bandwidth. The remainder of the network bandwidth, not shown in the figure for simplicity, can accommodate data traffic. If optical combs of the same frequency spacing are generated at the Tx and Rx using the distributed optical reference as a seed, the resulting multi-wavelength channel carriers and LOs are approximately frequency- and phase-synchronized with each other, provided that the distributed optical reference and distribution links maintain low phase noise and a long coherence length compared to the difference in distribution path lengths to Tx and Rx. When these carriers are used for wavelength-division-multiplexing (WDM) multi-level modulation signaling and LOs are used for coherent reception, the transmitted signals can be demodulated without FO estimation or feed-forward CP estimation which is computationally expensive at the receiver. A slight CP shift due to imperfect synchronization (for example, FO of 10 kHz) between transmitters and receivers can be implicitly compensated in a polarization-division-demultiplexing process by the multi-input-multi-output (MIMO) DSP. This technique can be also effectively used in a mode division multiplexing high-order QAM system [16], which is more susceptible to carrier phase noise than in a single-mode transmission system because of the equalization-enhancement [19,20] and more constrained in terms of DSP circuit size due to the need of higher-order MIMO. In the general case where Tx and Rx nodes belong to different distribution areas, locking of the optical reference to the absolute frequency reference may also be required to benefit from DSP saving.
As the distribution distance increases, the optical reference deteriorates, leading to the degradation of the system performance. In applications such as optical clock comparison, system performance is mainly affected by low-frequency phase noise due to fiber length variation, which is usually mitigated by phase delay actuators [21]. On the other hand, in the case of communication applications, high-frequency noise caused by amplified spontaneous emission (ASE) in the repeater amplifier and guided acoustic-wave Brillouin scattering (GAWBS) [22,23] in the fiber propagation greatly affects the system performance. In this study, we established a method to suppress the optical reference degradation using a laser source of very narrow linewidth and a narrow bandwidth filter made of a fiber Bragg grating (FBG). The results of this study can be summarized in the following two messages. First, we can distribute an optical reference over more than 12,600 km distance while maintaining a higher source quality than the commercially available Optical Internetworking Forum-compliant Integrated Tunable Laser Assembly (OIF-ITLA). Second, the use of the optical reference distributed by this method enables 10 GBaud, 5 WDM Dual Polarization (DP) 64QAM communications with excellent signal quality without requiring CP estimation. The simplification of DSP has resulted in a 48% reduction in overall off-line signal processing time compared to full DSP. In the future, further improvements in distribution technology could enable all coherent optical signals that flow through backbone networks and data centers around the world to be synchronized to a common optical reference ideally, thereby improving the global energy efficiency and cost.
3. Setup and characterization results of long-distance distribution system
A semiconductor distributed feedback (DFB) laser with an operating wavelength of λ0 = 1558.99 nm, frequency-locked to a high-Q crystalline whispering-gallery mode (WGM) microcavity by self-injection synchronization, was used as an optical reference source. This laser system, similar to the one described in [24], is commercially available and can be an ideal reference source because self-injection locking significantly reduces the linewidth from the free-running state. The instantaneous linewidth of the laser (defined as π × Sν (f) in [24], where Sν (f) represents the frequency-noise power spectral density (FN-PSD) at Fourier frequency f) was precisely characterized by the manufacturer to be about 2 ∼ 20 Hz for f = 103 ∼ 105 Hz, from which a coherence length of 3,000 ∼ 30,000 km was expected. Slow tuning of the oscillation frequency is accomplished by thermal tuning.
The long-distance distribution of the optical reference was evaluated using the recirculation loop shown in Fig. 2(a). Each loop consisted of six combinations of 50 km fiber with a large effective area of 110 µm2 and repeater amplifiers. Polarization scrambling was not needed because polarization multiplexing was not used in this loop. A pair of acousto-optic modulators (AOMs) were used to shape the optical reference into a load pulse with a duration equal to the loop recirculation time. When a load pulse was launched into the loop, a pulse train in which the distribution distance $d = l \times {d_0}$ (d0 = 300 km represents the loop length) increased in proportion to the number of cycles l was generated. The maximum number of cycles was set to 43, and the recirculation gate by AOM2 was closed at the timing of l = 44, so as not to cause interference with the loading of the next optical reference pulse. A manual polarization controller was used in the loop to keep the polarization state of each pulse train constant by monitoring the output waveform of the polarized branch and equalizing the pulse train intensities, for measurement with a single polarization receiver in this section, and for use as a seed for comb generation in the next section. This manual polarization alignment process is particular to the recirculation experiment and would be alleviated in a practical system by using a simpler automatic polarization control after distribution.
Fig. 2. Long-distance optical reference distribution system in this study. (a) Setup of recirculation loop and noise characterization. (b) Transmittance of the FBG filter as a function of the frequency detuning.
To suppress the accumulation of ASE and GAWBS noise, a commercially available, narrow passband FBG filter was inserted into the loop. The FBG filter was stabilized in the temperature so that the transmission center wavelength coarsely agreed with λ0. Figure 2(b) shows the transmittance of the FBG filter measured as described in the Appendix. A suppression ratio of 30 dB and a passband full width at half maximum of ∼70 MHz were observed. The passband width is narrow enough to suppress GAWBS noise from higher order acoustic modes. If only a single AOM was used in the recirculation loop, it would cause a specific carrier frequency shift on every recirculation, and the carrier frequency would shift to the side of the passband of the FBG filter after a few recirculation. Therefore, we used AOM2 + with a frequency shift of +80 MHz and AOM2- with a frequency shift of -80 MHz, to suppress the accumulation of frequency shifts. The FBG filter was partially similar to that described in [25] and had a 55 GHz suppression window around the narrow transmission peak and a flat transmission window outside the suppression window, as shown in the inset of Fig. 2(a). To avoid the accumulation of noise outside the suppression window of the FBG filter, a bandpass filter (BPF) of less than 7 GHz passband is additionally used.
Without both filters, the optical signal-to-noise ratio (OSNR) of the optical reference (measured by an optical spectrum analyzer with a nominal resolution bandwidth of 0.02 nm and a noise integration bandwidth of 0.1 nm) degrades to ∼39 dB after the first recirculation and to ∼23 dB after 42 times recirculation. On the other hand, if both filters are used and the noise is filtered according to the profile of Fig. 2 (b), it is estimated that the OSNR after the first recirculation can be improved to ∼59 dB. As the optical reference iterates recirculation and the noise is filtered multiple times, the ratio of the signal to noise from initial recirculation will converge to approximately 70 dB or more, resulting in an aggregate OSNR of approximately 52 dB after 42 cycles.
The 24-hour stability (standard deviation) of the laser oscillation frequency relative to the filter peak frequency was estimated to be ∼6 MHz when no manual tuning was used. To maintain best noise filtering performance, we occasionally performed thermal tuning of the laser oscillation frequency to the filter peak, rather than tuning the filter peak frequency to the laser.
The optical reference after l-times recirculation was down-converted to in-phase (I) and quadrature-phase (Q) components through delayed self-homodyning and sampled to perform noise analysis, using a 90° hybrid, balanced photodiodes (BPDs), 2-channel 160 GSample/s analog-to-digital converters (ADCs) and a trigger signal synchronized with the l-th recirculating pulse. The FN-PSD Sν (f) was then deduced based on the method explained in [26,27].
Figure 3(a) shows the FN-PSD measured at various distribution distances as a function of offset frequency f. As the distribution distance increased, FN-PSD at f = 106 Hz increased from 0.5 Hz2/Hz (corresponding to total instantaneous linewidth of π × Sν (f) = 1.6 Hz) to 50 Hz2/Hz (160 Hz), while the increase in FN-PSD was suppressed at f > 2 × 107 Hz presumably owing to the FBG filtering. Figure 3(a) also plots the FN-PSD of the OIF-ITLA pair obtained by heterodyne measurements for comparison. At f = 106 Hz, the FN-PSD of these lasers was 20 kHz2/Hz (instantaneous linewidths of 31 kHz each), indicating that the optical reference had much lower frequency noise in this region even after a distribution of 12,600 km (l = 42). On the other hand, the noise of the optical reference was slightly higher compared to the noise of OIF-ITLAs in the range of f = 108 to 109 Hz. However, this slight difference is difficult to recognize unless low background measurements are used and does not pose a significant problem in practical use. If necessary, this excess noise would be further suppressed by using additional FBG filters for the LO. Figure 3(b) shows the result of the optical reference distribution when the FBG filter is removed. A remarkably large distribution distance dependent increase of FN-PSD was observed in the range of f = 108 to 109 Hz. The incremental component proportional to f2 was presumably due to ASE and the components with discrete peaks were presumably due to GAWBS. A noise cut-off at around 109 Hz was observed and attributed to the BPF filtering, presumably with a slight frequency detuning from the carrier frequency.
Fig. 3. Frequency-noise power spectral density (FN-PSD) of the distributed optical reference as a function of offset frequency. (a) with and (b) without FBG filtering. The FN-PSD of OIF-ITLAs is also shown for comparison. The measurement background is estimated by extrapolating the traces in the high offset frequency region.
The increase of FN-PSD can also be represented by the integrated phase errors [26], as
Fig. 4. Root-mean-square phase error of the distributed optical reference, calculated from FN-PSD in Fig. 3, as a function of the distribution distance.
4. Coherent optical communication system
The measurement in the previous section revealed the excellent noise characteristics of the distributed optical reference. Next, we experimentally evaluate the performance of the coherent communication system employing such distributed optical reference.
4.1 Experimental setup
Figure 5(a) shows a demonstration setup of coherent optical communication. A Tx node and a Rx node were added to the system shown in Fig. 2 (a), and the nodes and source were connected by large effective area fibers of 50 km with each other. Figure 5(b) shows a configuration diagram of the Tx node. After polarization adjustment, the distributed optical reference was modulated into a comb-like spectrum at the frequency f1 = 25 GHz. This comb generation was based on an asymmetric Mach-Zehnder interferometer [28], and approximately 10 optical multi-carriers were obtained, as shown in the optical spectrum of Fig. 6(a). These carriers were wavelength-division-demultiplexed, and only one wavelength channel out of the five central wavelength channels (λ = λ+2, λ+1, λ0, λ-1, λ-2) was extracted for the measurement. The measurement channel was IQ modulated to 64 QAM signal of 10 GBaud and pattern length of 215-1 by a LiNbO3 modulator. The measurement channel was wavelength-multiplexed with another 4-channel, 10 GBaud 64 QAM signal on the 25 GHz frequency grid around the measurement channel to be served as a dummy. Polarization multiplexing was achieved by combining a 521-symbol delayed signal in a Y-polarization to the X-polarized signal. The resulting WDM-DP-64QAM signals, represented by the optical spectrum in Fig. 6(b), were transmitted to the Rx node.
Fig. 5. Coherent transmission setup. (a) Overview. The optical reference from the laser source is distributed to the Tx node via the recirculation loop and to the Rx node via a 50 km fiber span. WDM-DP-QAM signals are transmitted over 50 km from Tx to Rx. (b) Tx and (c) Rx node.
Fig. 6. Comb generation and QAM signals. (a) Optical spectrum of Tx-node comb output. (b) Optical spectrum of transmitted signal. (c) Optical spectrum of Rx-node comb output. Five wavelength channels (λ+2, λ+1, λ0, λ-1, λ-2) are used for transmission. (d) Dependence of the QAM transmission performance on the launch power.
Figure 5(c) shows the configuration of the Rx node. After polarization adjustment, a single-drive intensity modulator was used to modulate the optical reference into a comb-like spectrum at a frequency f2 = 25 GHz (equal to f1 at least down to 4 × 10−9). In this case, as shown in the optical spectrum of Fig. 6(c), the higher order harmonics were considerably weak, and therefore the number of wavelength channels had to be limited to 5. The comb component corresponding to the measurement channel was separated by wavelength-division-demultiplexing, to be used as the LO of the DP coherent receiver. The QAM signal after the wavelength-division-demultiplexing was also launched into the receiver, and I and Q components of both polarized waves (X, Y) were sampled as a data stream of 2 M symbols by 4-channel, 80 GSample/s ADCs. Eight shots of data stream on each wavelength channel and distribution distance were used for the analysis. For comparison, we also evaluated a conventional intradyne coherent system by reconnecting the *-marked parts in Fig. 5(b) and Fig. 5(c) to the OIF-ITLAs.
Figure 6(d) shows the test results on the bit error rate (BER) of the DP-64QAM signal transmission, obtained by using the full DSP (to be explained in the next subsection) at the receiver, as a function of the launch power to the transmission fiber. The optimum launch power was around 0 dBm. The BER was almost flat when the launch power was about -4 to + 2 dBm, suggesting that nonlinear signal distortion begins to appear in this region. In subsequent measurements, the launch power was fixed at -4 dBm per wavelength channel for both optical reference and OIF-ITLA to exclude the impact of nonlinear signal distortion.
4.2 Digital signal processing
Two sets of off-line DSP shown in Fig. 7 were compared. The left-hand set named “full DSP” consisted of following sub-processes: The front-end correction and Gram–Schmidt orthogonalization of the receiver were performed first. Then, the slight frequency shift due to the difference between the frequencies of AOM2 + and AOM2- in the distribution loop was externally monitored and corrected. This part is unnecessary in an actual telecommunications system where no recirculation exists. After down-sampling to two samples per symbol, FO estimation based on the fourth power algorithm was performed periodically. After root-raised-cosine (RRC) filtering and direct current (DC) offset correction, adaptive 2 × 2 MIMO equalization with 61 taps including feed-forward CP estimation [29] was performed to solve the polarization mixing and to mitigate other static linear impairments. In the MIMO processing, the first 163,835 symbols were regarded as known training sequences and were equalized by the Data Aided (DA) Least Mean Square (LMS) algorithm and the remaining symbols were blindly equalized by the Decision Directed (DD) LMS algorithm. The feed-forward CP estimation was characterized by two parameters: Parameter B determines the resolution of the phase estimation and B = 64 was chosen in this study. Parameter N is the half-width of the filter and N = 36 was chosen. After equalization, each symbol was decoded by hard decision, and BER was calculated from blindly equalized 1.4 M symbols. On the other hand, the right-hand DSP set named “simplified DSP” does not employ periodic FO estimation and feed-forward CP estimation in MIMO equalization.
Throughout the full DSP, the periodic FO estimation and MIMO equalization accounted for 3% and 64% of the total off-line processing time, respectively. MIMO equalization in simplified DSP was accomplished in a 63%-shorter processing time compared to the case of MIMO equalization in full DSP, resulting in an overall processing time reduction of 48%.
When the laser sources are OIF-ITLAs, a large FO occurs. Figure 8(a) shows FO profiles extracted from 8-shot received data using full DSP. The FO drifted on the order of 100 MHz due to dithering of the laser oscillation frequency around the targeted value. Signal demodulation was not possible unless this offset was removed, and therefore FO estimation was required periodically. As can be seen from the profiles of the residual CP differences (extracted using the DSP) in Fig. 8(b), rapid drifts of the CP remained after the FO removal. Unless such CP drifts were simultaneously compensated, adaptive MIMO equalization cannot achieve adequate convergence.
Fig. 8. Time profiles. (a) FO and (b) CP when OIF-ITLAs are used. (c) FO and (d) CP when 0 km-distributed optical reference is used. (e) FO and (f) CP when 12,600 km-distributed optical reference is used. Each of (a)-(f) contains eight profiles, each profile being deduced from one shot of the transmission data stream.
These problems could be avoided by using optical references instead. First, Fig. 8(c) and Fig. 8(d) show the profiles of the FO and the CP difference when the distribution distance is 0 km, respectively. In this case, since the optical path length of the signal from the light source through the Tx to the Rx is substantially the same as the optical path length of the LO lightwave, the FO and the CP difference became very small. Also, Fig. 8(e) and Fig. 8(f) show the FO and the CP profiles when the distribution distance is 12,600 km, respectively. It is remarkable that even though the optical path lengths were quite different, only slow CP drift was observed. This was because the optical reference source had extremely high coherence. Such slow CP drifts could be eliminated by adaptive MIMO equalization alone.
4.3 Bit error rate analysis
Figure 9(a) shows the results of the BER calculation as a function of distribution distance when simplified DSP was used for each wavelength channel. Each marker represents the BER for each shot, and a dashed line connects the average of the eight shots. The results of BER by OIF-ITLAs as well as those by the optical reference distribution method without FBG filter were also plotted for comparison. As described above, when the OIF-ITLAs were used, the demodulation by the simplified DSP failed, and the BER was 0.5. Without the use of the FBG filter, the BER increased rapidly with increasing distribution distance, reaching a threshold of 20% overhead forward error correction (FEC) [30] (BER = 2.7 × 10−2, Q-factor = 5.7 dB) at a distribution distance of 3,000 km. In contrast, when the FBG filter was used, the BER for all five wavelength channels remains below the threshold of 7% overhead FEC [31] (BER = 3.8 × 10−3, Q-factor = 8.53 dB) up to a distribution distance of 12,600 km. The BERs for λ = λ+2 and λ-2 (average 2.2 × 10−3 and 2.3 × 10−3) were higher than those of the three center channels (average 7.1 × 10−4, 1.4 × 10−3, and 8.8 × 10−4), presumably due to the lower optical signal-to-noise ratio (about 9 dB, as shown in Fig. 6(c)) of LOs in these channels after Rx node comb generation. Considering that the FBG filter could remove the accumulated noise of the optical reference accompanied by the distribution, this problem would be alleviated in the future by using the narrowband filter also after the comb.
Fig. 9. 64 QAM transmission results. (a) Bit error rate (BER) of each wavelength channel λ as a function of the distribution distance d of the optical reference, demodulated using the simplified DSP. (b) BER of each wavelength channel demodulated using the full DSP. The X and * symbols represent the BER values for each data shot. The dashed lines connect the averaged BER values. The forward error correction (FEC) thresholds of 20% and 7% overheads correspond to BER = 2.7 × 10−2 and 3.8 × 10−3, respectively. Q-factors are indicated by the right-side vertical scale. (c) Constellations of the demodulated signals under the conditions indicated by the Greek letters in (a) and (b). α, d = 0 km, λ = λ0. β, d = 12,600 km, λ = λ0. γ, d = 12,600 km, λ = λ-2. δ, d = 3,000 km, λ = λ0, without FBG filtering. ɛ, with OIF-ITLA lasers and full DSP. α to δ are calculated using the simplified DSP.
Figure 9(b) shows the calculation result of BER when full DSP was used. In this case, the signals using the OIF-ITLAs could be demodulated with an average BER of 4.9 × 10−4. However, the BERs of the three central channels (2.3 × 10−4, 2.2 × 10−4 and 1.8 × 10−4 on average) were even lower when the optical reference after the 12,600 km distribution was used. The BERs of the center channel obtained by simplified DSP were comparable to those obtained by OIF-ITLAs and full DSP.
Figure 9(c) shows examples of constellations of demodulated signals under some conditions indicated by Greek letters in Fig. 9(a) and Fig. 9(b). We observe that the error was almost uniformly distributed among each constellation point, except for the example (δ) in which no FBG filter was used.
5. Discussion
In this study, by using an ultra-narrow-linewidth laser with frequency stabilization to a high-Q resonator as a source and a narrow-band FBG filter for ASE and GAWBS noise removal, optical reference distribution over an extremely long distance (12,600 km) comparable to the trans-Pacific distance was carried out. We verified that the distributed optical reference showed better source quality than OIF-ITLA outputs for use with 10 GBaud, 5 WDM DP-64QAM coherent communication, and that DSP for frequency offset estimation and carrier phase estimation could be eliminated. In comparison with the previous experiment [14] (distribution distance of 1,600 km), the distribution distance has been drastically extended by 7.8 times. The reduction of off-line digital signal processing time reached 48%. The filtering technique in this study is expected to be applicable not only to simple extension of the distribution distance, but also to insertion of large loss elements and circuits. With further improvements in filter performance, we expect that it will be possible in the future to synchronize all coherent signals flowing anywhere in the world ideally to a common optical reference, or more likely to mutually synchronized international optical references. In this study, FBG narrow band filter was used because of its passive property and low power consumption. Other filtering techniques, such as Brillouin amplification [32], may also be applicable.
Now we discuss some of the remaining technical issues below. First, the number of wavelength channels in this study was limited to five due to comb generation based on the intensity modulator. When different techniques are used, such as a dispersion-engineered nonlinear fiber mixer after modulation [33], more carriers are generated from a single optical reference. However, it is also known that the phase-noise property deteriorates as the comb-band expands [34–36]. We expect that narrowband filtering for the generated carriers is able to mitigate carrier degradation as well, to be demonstrated in the next step. A high finesse resonator filter with a matched free spectral range may efficiently filter multiple carriers at a time.
Second, as the number of carriers increases, more precise control of comb spacing becomes necessary. For example, frequencies of carriers out of a C- and L-band comb source may be maximum 5 THz away from the seed carrier frequency. Difference of comb spacings for Tx and Rx at 2 × 10−9 can lead to maximum FO of 10 kHz, which is close to the tolerance limit. We hope that chip-scale atomic clocks [37] will provide an efficient solution to this problem.
Third, comb generation at each node requires automatic polarization control of the optical reference, which introduces a certain power consumption in the system. In this experiment, we used hand-made polarization control units with three-stage polarization controller based on specialty fiber [38], each stage driven at a maximum voltage of 5 V and a current of 80 mA, and feed-back controllers with a power consumption of 2 W based on field-programmable gate array system-on-chip (FPGA-SoC) [39]. As a result, the total power consumption per unit was 3.2 W at the maximum. Since this power consumption is shared by all wavelength channels, increasing the number of carriers will significantly alleviates this drawback.
Forth, automated stabilization of FBG filters distributed around the network. To employ dynamic stabilization as in [25], slight dithering may need to be introduced to the seed laser.
Fifth, frequency stability may be compromised to some degree in practical systems. Field-deployed fibers generally suffer from environmental phase noises, due to either slow drift in length caused by temperature changes or mechanical vibrations in the frequency range of typically 10 to 20 Hz [40,41]. The acoustic phase noise caused by latter leads to increased frequency instability for the integration time of about 10−2 s. According to [42], frequency instability (Allan deviation) of 1,840 km deployed fiber link in the free-running condition reached about 10−11. Assuming that the Allan variance increases linearly with the link length, the frequency instability for 12,600 km deployed fiber link is expected to reach 2.6 × 10−11 (i.e. frequency offset of ∼5 kHz). We expect that frequency instability to this degree is within the tolerance of MIMO DSP in this study. The instability would be further reduced if the distribution to Tx and Rx shares part of the fiber links. The power level of acoustic noise in a deployed fiber link is significantly case-dependent, however, and hence further study will be needed to widely realize successful deployments.
Finally, it would be a great challenge to incorporate the proposed distribution scheme into the system for metrological and other applications, where optical reference needs to be distributed in a bidirectional manner.
Appendix – Measurement of FBG filter profile
The transmission spectrum of the FBG filter shown in Fig. 2(b) was measured by scanning the laser oscillation frequency while stabilizing the FBG transmission peak frequency at around f0 = 192.299 THz and monitoring the input / output optical power. Since it is difficult to accurately measure the laser oscillation frequency with a standard wavelength meter, the frequency value on the horizontal axis was obtained by converting from the temperature control voltage V of the laser. A coarse-tuning measurement using a wavelength meter showed that the oscillation frequency fc changes linearly by about 5.4 GHz for the change of the control voltage by 1.5 V. Since the setting resolution of the control voltage is 0.1 mV, it is possible to scan the frequency in the step of 0.36 MHz minimum. The frequency detuning from the transmission peak of the FBG filter was determined by the following equation
where V0 represents the control voltage at the transmission peak and R = 3.6 MHz/mV. We scanned V in a short time to obtain the transmittance of the FBG filter $T({{f_\Delta }} )$ as a function of ${f_\Delta }.$The relative stability of the frequencies between independently controlled FBG filter and laser was estimated as follows. First, we adjust the laser oscillation frequency near the transmission peak of the filter. Then we fixed the laser control voltage and periodically measured the time series of the transmittance of the filter ${T_i}.$ The time series of the corresponding frequency detuning ${f_{\Delta i}}$ was calculated by ${f_{\Delta i}} = {T^{ - 1}}({{T_i}} ).$ The standard deviation of the frequency detuning for 24-hour measurement was about 6 MHz. The frequency drift of several-MHz has significant impact on the recirculation loop experiment. Therefore, in the main experiment, we occasionally tuned the laser oscillation frequency to track the transmission peak frequency of the filter.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. B. M. Roberts, P. Delva, A. Al-Masoudi, et al., “Search for transient variations of the fine structure constant and dark matter using fiber-linked optical atomic clocks,” New J. Phys. 22(9), 093010 (2020). [CrossRef]
2. C. Clivati, R. Ambrosini, T. Artz, A. Bertarini, C. Bortolotti, M. Frittelli, F. Levi, A. Mura, G. Maccaferri, M. Nanni, M. Negusini, F. Perini, M. Roma, M. Stagni, M. Zucco, and D. Calonico, “A VLBI experiment using a remote atomic clock via a coherent fibre link,” Sci. Rep. 7(1), 40992 (2017). [CrossRef]
3. J. Grotti, S. Koller, S. Vogt, et al., “Geodesy and metrology with a transportable optical clock,” Nat. Phys. 14(5), 437–441 (2018). [CrossRef]
4. S. Nagano, M. Kumagai, H. Ito, M. Kajita, and Y. Hanado, “Phase-coherent transfer and retrieval of terahertz frequency standard over 20 km optical fiber with 4 ×10−18 accuracy,” Appl. Phys. Express 10(1), 012502 (2017). [CrossRef]
5. C. Lisdat, G. Grosche, N. Quintin, et al., “A clock network for geodesy and fundamental science,” Nat. Commun. 7(1), 12443 (2016). [CrossRef]
6. G. M. Brodnik, M. W. Harrington, J. H. Dallyn, D. Bose, W. Zhang, L. Stern, P. A. Morton, R. O. Behunin, S. B. Papp, and D. J. Blumenthal, “Optically synchronized fibre links using spectrally pure chip-scale lasers,” Nat. Photonics 15(8), 588–593 (2021). [CrossRef]
7. M. Morsy-Osman, M. Sowailem, E. Elfiky, T. Goodwill, T. Hoang, S. Lessard, and D. V. Plant, “DSP-free ‘coherent-lite’ transceiver for next generation single wavelength optical intra-datacenter interconnects,” Opt. Express 26(7), 8890–8903 (2018). [CrossRef]
8. J. K. Perin, A. Shastri, and J. M. Kahn, “Design of Low-Power DSP-Free Coherent Receivers for Data Center Links,” J. Lightwave Technol. 35(21), 4650–4662 (2017). [CrossRef]
9. R. Zhang, Y.-W. Chen, K. Kuzmin, and W. I. Way, “Intra-Data Center 120Gbaud/DP-16QAM Self-Homodyne Coherent Links with Simplified Coherent DSP,” in Optical Fiber Communication Conference (OPG, 2022), paper W1G.1.
10. X. Liang, J. D. Downie, J. E. Hurley, H. Su, D. Butler, S. Johnson, and W. Hurley, “Study of Self-Homodyne Coherent System Using Multicore Fiber for Data Center,” IEEE Photonics J. 14(4), 7234306 (2022). [CrossRef]
11. L. Wang, Y. Zeng, X. Wang, T. Jiang, Y. Xiang, H. He, Z. Hu, H. Jiang, and M. Tang, “Bi-Directional Self-Homodyne Transmission With MIMO-Free DSP for Next-Generation Data Center Interconnects,” J. Lightwave Technol. 40(18), 6179–6189 (2022). [CrossRef]
12. M. Mazur, J. Schröder, A. Lorences-Riesgo, M. Karlsson, and P. A. Andrekson, “Experimental Investigation of Link Impairments in Pilot Tone Aided Superchannel Transmission,” IEEE Photonics Technol. Lett. 31(6), 459–462 (2019). [CrossRef]
13. J. Sakaguchi, M. Kumagai, Y. Li, T. Ido, Y. Awaji, and N. Wada, “DSP-complexity Reduction of QAM-based Coherent Optical Networks Enabled by Seed Lightwave Distribution,” in Conference on Lasers and Electro-Optics (OPG, 2015), paper SW1M.7.
14. J. Sakaguchi, Y. Awaji, and N. Wada, “Seed Lightwave Distribution over 1600 km for 64QAM-based Coherent WDM Optical Networks with Low DSP-complexity,” in European Conference on Optical Communications (IEEE, 2016), paper W.4.P1.SC5.57.
15. J. Sakaguchi, S. Xu, M. Shiraiwa, T. Miyazawa, Y. Awaji, and N. Wada, “Dynamic Restoration of Seed Lightwave Distribution System for Low-DSP-complexity Coherent Optical Networks,” in Opto-Electronics and Communications Conference (IEEE, 2017), paper 3-2K-3.
16. J. Sakaguchi, W. Klaus, B. J. Puttnam, J. M. Delgado-Mendinueta, Y. Awaji, and N. Wada, “Spectrally-Efficient Seed-Lightwave-Distribution System using Space-Division-Multiplexed Distribution Channel for Multi-core 3-Mode-Multiplexed DP-64QAM Transmission,” in European Conference on Optical Communications (IEEE, 2017), paper M.1.E4.
17. H. Katori, “Optical lattice clocks and quantum metrology,” Nat. Photonics 5(4), 203–210 (2011). [CrossRef]
18. N. Huntemann, C. Sanner, B. Lipphardt, C. Tamm, and E. Peik, “Single-Ion Atomic Clock with 3×10−18 Systematic Uncertainty,” Phys. Rev. Lett. 116(6), 063001 (2016). [CrossRef]
19. W. Shieh, “Interaction of laser phase noise with differential-mode-delay in few-mode fiber based MIMO systems,” in Optical Fiber Communication Conference (OPG, 2012), paper OTu2C.6.
20. J. M. Delgado-Mendinueta, W. Klaus, J. Sakaguchi, S. Shinada, H. Furukawa, Y. Awaji, and N. Wada, “Numerical Investigation of the Equalization Enhanced Phase Noise Penalty for M-Quadrature Amplitude Modulation Formats in Short-Haul Few-Mode Fiber Transmission Systems with Time-Domain Equalization,” Appl. Sci. 8(11), 2182 (2018). [CrossRef]
21. N. R. Newbury, P. A. Williams, and W. C. Swann, “Coherent transfer of an optical carrier over 251 km,” Opt. Lett. 32(21), 3056–3058 (2007). [CrossRef]
22. R. M. Shelby, M. D. Levenson, and P. W. Bayer, “Guided acoustic-wave Brillouin scattering,” Phys. Rev. B 31(8), 5244–5252 (1985). [CrossRef]
23. M. Nakazawa, M. Yoshida, M. Terayama, S. Okamoto, K. Kasai, and T. Hirooka, “Observation of guided acoustic-wave Brillouin scattering noise and its compensation in digital coherent optical fiber transmission,” Opt. Express 26(7), 9165–9181 (2018). [CrossRef]
24. W. Liang, V. S. Ilchenko, D. Eliyahu, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, “Ultralow noise miniature external cavity semiconductor laser,” Nat. Commun. 6(1), 7371 (2015). [CrossRef]
25. W.-C. Ng, A. T. Nguyen, S. Ayotte, C. S. Park, and L. A. Rusch, “Overcoming phase sensitivity in real-time parallel DSP for optical coherent communications: Optically filtered lasers,” J. Lightwave Technol. 32(3), 411–420 (2014). [CrossRef]
26. T. N. Huynh, L. Nguyen, and L. P. Barry, “Phase noise characterization of SGDBR lasers using phase modulation detection method with delayed self-heterodyne measurements,” J. Lightwave Technol. 31(8), 1300–1308 (2013). [CrossRef]
27. M. Al-Qadi, M. O’Sullivan, C. Xie, and R. Hui, “Phase noise measurements and performance of lasers with non-white FM noise for use in digital coherent optical systems,” J. Lightwave Technol. 38(6), 1157–1167 (2020). [CrossRef]
28. T. Sakamoto, T. Kawanishi, and M. Izutsu, “Asymptotic formalism for ultraflat optical frequency comb generation using a Mach-Zehnder modulator,” Opt. Lett. 32(11), 1515–1517 (2007). [CrossRef]
29. T. Pfau, S. Hoffmann, and R. Noé, “Hardware-Efficient Coherent Digital Receiver Concept With Feedforward Carrier Recovery for M-QAM Constellations,” J. Lightwave Technol. 27(8), 989–999 (2009). [CrossRef]
30. D. Chang, F. Yu, Z. Xiao, N. Stojanovic, F. N. Hauske, Y. Cai, C. Xie, L. Li, X. Xu, and Q. Xiong, “LDPC convolutional codes using layered decoding algorithm for high speed coherent optical transmission,” in Optical Fiber Communication Conference (OPG, 2012), paper OW1H.4.
31. International Telecommunication Union, Telecommunication Standardization Sector (ITU-T), document Rec. G.975.1, (2004).
32. M. Perusi, A. Choudhary, T. Inoue, D. Marpaung, B. J. Eggleton, K. Solis-Trapala, H. N. Tan, and S. Namiki, “Low noise frequency comb carriers for 64-QAM via a Brillouin comb amplifier,” Opt. Express 25(15), 17847–17863 (2017). [CrossRef]
33. B. P.-P. Kuo, E. Myslivets, V. Ataie, E. G. Temprana, N. Alic, and S. Radic, “Wideband parametric frequency comb as coherent optical carrier,” J. Lightwave Technol. 31(21), 3414–3419 (2013). [CrossRef]
34. A. H. Gnauck, B. P.-P. Kuo, E. Myslivets, R. M. Jopson, M. Dinu, J. E. Simsarian, P. J. Winzer, and S. Radic, “Comb-based 16-QAM transmitter spanning the C and L bands,” IEEE Photonics Technol. Lett. 26(8), 821–824 (2014). [CrossRef]
35. E. Temprana, V. Ataie, B. P.-P. Kuo, E. Myslivets, N. Alic, and S. Radic, “Low-noise parametric frequency comb for continuous C-plus-L-band 16-QAM channels generation,” Opt. Express 22(6), 6822–6828 (2014). [CrossRef]
36. J. Sakaguchi, Y. Awaji, and N. Wada, “Optimal Pilot-Tone-Aided Multi-Core Fiber Transmission Using a Wideband Comb Transmitter,” IEEE Photonics Technol. Lett. 29(15), 1245–1248 (2017). [CrossRef]
37. M. Hara, Y. Yano, M. Kajita, H. Nishino, Y. Ibata, M. Toda, S. Hara, A. Kasamatsu, H. Ito, T. Ono, and T. Ido, “Microwave oscillator using piezoelectric thin-film resonator aiming for ultraminiaturization of atomic clock,” Rev. Sci. Instrum. 89(10), 105002 (2018). [CrossRef]
38. Electronically Addressed Polarization controller, https://www.fiberlogix.com/product/electronically-addressed-polarization-controller/.
39. Zybo, https://digilent.com/reference/programmable-logic/zybo/.
40. S. M. F. Raupach, A. Koczwara, and G. Grosche, “Optical frequency transfer via a 660 km underground fiber link using a remote Brillouin amplifier,” Opt. Express 22(22), 26537–26547 (2014). [CrossRef]
41. Ł. Śliwczyński and P. Krehlik, “Measurement of acoustic noise in field-deployed fiber optic cables,” in European Frequency and Time Forum (IEEE, 2014), pp. 339–342.
42. S. Droste, F. Ozimek, T. Udem, K. Predehl, T. W. Hänsch, H. Schnatz, G. Grosche, and R. Holzwarth, “Optical-Frequency Transfer over a Single-Span 1840km Fiber Link,” Phys. Rev. Lett. 111(11), 110801 (2013). [CrossRef]
