Emerging 6G, cloud computing, and regenerative artificial intelligence applications such as ChatGPT and Sora have led to increasing requirements for large bandwidth and high data transmission rates within and between data centers, which spurs research into utilizing polarization diversity coherent detection in short-reach fiber links.1 To meet the demand for ever-growing internet traffic from next-generation data centers, there has been active research on short-reach coherent optical communication systems.2^–4 The coherent optical communication systems, unlike the current four-level pulse amplitude modulation scheme used in data center interconnects (DCIs), employ not only the dimension of amplitude modulation but also phase and polarization modulation dimensions, thereby enhancing the system capacity and getting advantages of high spectral efficiency, high sensitivity, and flexibility in modulation formats.5 However, coherent detection needs to handle the primary impediments of chromatic dispersion, polarization rotation and laser frequency, and phase offsets. The conventional approach typically resolves the above issues through digital signal processing (DSP) and high-resolution analog-to-digital converter (ADC). Moreover, coherent detection relies on narrow-linewidth and temperature-controlled lasers at both transmitters and receivers.6^–9 As a result, high-speed optical coherent detection is commonly extremely costly and power-hungry.

To resolve the issue of applying coherent detection to short-reach scenarios, energy-efficient coherent detection solutions have attracted increasing attention in recent years, such as simplifying DSP schemes9^,10 and novel coherent detection systems.11^–13 In terms of simplifying coherent DSP, short-reach application scenarios do not require high-level signal processing capability because of the limited linear impairments in DCI.2^–4^,14 Therefore, analog signal processing that utilizes an optical or electrical phase-locked loop (PLL) becomes a promising alternative to replace ADCs and DSP of coherent detection, reducing cost and power consumption.9^–11^,15 Researchers have proposed an analog signal processing method based on a zero-difference coherent detection architecture that uses a PLL structure in the analog domain, avoiding the need for high-speed ADCs and carrier recovery in the digital domain.9^,10 However, the use of high-speed analog circuits is limited by their demanding ability to process high bandwidth and high-speed signals with analog electronic circuits. These schemes are only demonstrated for low-order modulation formats and may be complicated to extend to the higher-order quadrature amplitude modulation (QAM) formats such as DP-16QAM. In addition, the simplification of the multiple-input-multiple-output (MIMO) equalization structure in classical coherent DSPs has been extensively explored by researchers, taking into account the characteristics of the weak dispersion in the short-reach optical links and polarization mode dispersion.16^–20 As for novel coherent detection or coherent-lite systems, researchers have proposed a series of simplified coherent schemes represented by the self-homodyne system.11^,12 The self-homodyne approach utilizes the laser homology to meet the requirement for stable narrow-linewidth lasers in traditional coherent systems, thereby enabling the application of uncooled large-linewidth low-cost lasers in coherent systems. The frequency and phase offsets caused by non-homologous internal difference detection are eliminated in the optical domain, and the complexity of the carrier phase recovery algorithm in high-order modulation format is avoided. This also inherits both the high spectral efficiency of traditional coherent detection and the simple implementation of the DSP parallel structure.

In this paper, we propose a novel pilot-tone-assisted Costas loop (PACL) to compensate for local oscillator (LO) frequency and phase offsets in coherent detection systems based on our previously proposed concept of frequency synchronous optical network (FSON) architecture.21^,22 We also propose the tree-distributed homology FSON architecture and analyze the phase noise based on the number of tree layers. Compared with our previous work using a power monitor module that monitors the minimum of Q-path pilot-tone power to dynamically shift the acoustic optical modulator (AOM) frequency for phase offset compensation in real-time,21 this work proposes the PACL that acquires the phase error more accurately and thus greatly improves the performance of the DSP-free coherent detection. In addition, we only use low-speed circuits to achieve dual-polarization coherent detection without resorting to conventional high-speed DSP application-specific integrated circuits (ASICs). Further, we experimentally demonstrate the DSP-free demultiplexing of 224-Gb/s dual-polarization 16-QAM over a link where the signal and LO paths have a 5-km mismatch with compensation in the optical domain based on the novel FSON architecture. Lastly, we demonstrate the proposed scheme’s capabilities, including a 1-MHz frequency compensation range and a 600-kHz dynamic compensation bandwidth.

To further break the shackles of coherent optical communication in short reaches, it is a very effective and feasible scheme to use the FSON to obtain the light sources in coherent transponders.22 An FSON architecture contains relatively small and stable frequency offsets among different light sources, which can meet the high requirements of short-reach coherent optical communication systems on narrow-linewidth and frequency-stability lasers. Figure 1(a) shows the proposed FSON architecture concept for DCI, which is designed to align the frequencies of the transmitter and receiver lasers within a data center. It is assumed that all the transmitter and receiver lasers within a data center come from the same ultra-stable narrow-linewidth laser source. The frequency of the transmitter laser in each server node can be expressed as fS, and the frequency of the receiver laser is expressed as fL. The laser frequency difference Δf between the transmitter and receiver can be expressed as Δf=|fS−fL|. It is set that this frequency difference must not exceed a relatively small value such as a few kilohertz within a data center, which would be compatible with the bandwidth of the optical phase lock loop afterward.22 For system stability and scalability reasons, another ultra-stable narrow-linewidth laser as a backup is needed for redundancy like a spine-leaf architecture to prevent the sudden breakdown of the sole light source. The ultra-low linewidth laser in the FSON architecture serves as a stable laser source that can be shared by all transponders within the data center. This eliminates the path length matches for all the signals and LOs, which is required for self-homodyne systems.

The proposed FSON architecture is the foundation of DSP-free coherent detection system’s viability. On this basis, it is important to further discuss the FSON architecture. Here, we propose the tree-distributed homology FSON architecture as shown in Fig. 1(b) (detailed tree-distributed homology nodes with the number of tree layers and branches per layer are shown in Fig. S1 in the Supplementary Material). According to ITU-T Rec G.692, if we assume that the total output power [including accumulated amplified spontaneous emission (ASE) power] is equal after each amplifier and that the gain G≫1, and then the optical signal-to-noise ratio is given approximately by OSNR=Pout−L−NF−10LogN−10Log[hνΔν0],(1)where Pout is the output power in dBm, L is the span loss among amplifiers in dB, NF is the external noise figure in dB, Δν0 is the optical bandwidth, N is the number of spans in fiber links, and we have assumed that all the span losses are equal. In the 1550-nm band, 10Log[hνΔν0]=−58dBm at 0.1-nm optical bandwidth. Assume that the output power of the erbium-doped optical fiber amplifier (EDFA) Pout is 24 dBm. The loss among cascaded EDFAs is ∼27dB (including ∼6-dB span and optical device connection loss and 21-dB splitter loss). The noise figure (at −3dBm input signal) of the AEDFA-CL-23 optical amplifier is ∼6dB. In general, the optical signal-to-noise ratio (OSNR) of LO would preferably be large, such as greater than 40 dB for high-order modulation formats.23 Therefore, N can be approximated from Eq. (1) which is around 7. This means that in the case of a loss of 27 dB per layer, the tree network can be distributed to about seven layers, and the OSNR of LO can still be maintained at 40 dB. The number of branches per layer is 27, which is 128 in total. The estimated maximum supportable transceivers with ultra-stable narrow-linewidth laser source are 1287>1014 in theory, which is large enough to encompass the optical transceivers for the entire data center. Thanks to the benefits of the tree-like homodyne network architecture, we can share the ultra-stable narrow-linewidth laser within the data center, theoretically supporting 128 distributions of one layer, as shown in Fig. S1 in the Supplementary Material. As the number of layers in the tree-like homodyne network expands, the cost of EDFAs will decrease exponentially (for example, with each additional EDFA, it is possible to expand by 128 virtual laser sources). Of course, practically, it needs more detailed optimization in the number of layers and branches per layer mentioned above in the future for reliability purposes. As long as the OSNR of the LO after passing through multiple EDFAs is higher than 40 dB, it can be readily shown that the system penalty is negligible.

We built the cascaded EDFAs laser signal phase noise measurement setup as shown in Fig. 1(c). The 1550.12-nm laser signal output from the ultra-narrow linewidth laser NKT-X15 is split into two paths by a 1 × 2 coupler, one of which is used for the LO with the AOM frequency shift and the other passes through attenuators and EDFAs to simulate a tree-distributed homology FSON architecture. Then, the cascaded EDFAs output optical signal and LO beats. The beat signal is detected by the balanced photodetector to reduce the common-mode noise interference. The AOM (upshift mode, +1 order) is operated at the driving frequency of 78.125 MHz. The direct digital synthesizer is used for clock synchronization of the AOM drive frequency and phase noise analyzer. The optical signal power input to the EDFA is attenuated to −3dBm, and the optical power of the EDFA output signal is 20 dBm. The phase noise of the beat signal is shown in Fig. 1(c). The area of the phase noise curve enclosed by the horizontal and vertical axes indicates the time jitter of the measured frequency signal. Thus, it can be used to determine the quality of the optical signal. Between 0.1 and 5 Hz, the phase noise curves change with the introduction of EDFA, and between 1 and 5 Hz, the phase noise curves change with the increasing number of EDFA. The laser phase noise from the cascaded EDFA still maintains a reduction in signal power of 40 dB compared with the center frequency at 2-kHz frequency offsets. The result demonstrates that the laser phase stability is not significantly degraded after passing through five EDFAs. It should be noted that, thanks to the homodyne architecture of the FSON, the external-cavity laser (ECL) with a linewidth of 100 kHz can also be used as the master laser because coherent detection can eliminate the common-mode noise between the signal light and the local oscillator.

Figure 2(a) shows the experimental setup for the dual-polarization 224-Gb/s 16-QAM DSP-free carrier phase recovery based on FSON with PACL module via a 5-km transmission, which also means the signal and LO paths will have such a large length mismatch. In detail, the PACL module is that we add a low-frequency pilot tone in the I-path of the data signal, and the Costas loop is used to obtain and compensate for the frequency and phase offsets at the receiver, which can allow the carrier phase recovery in the optical domain with low-speed circuits. The NKT-X15 narrow-linewidth laser is used to generate a 1550.12-nm optical carrier with 14-dBm output power, which is split into two branches respectively for the signal and receiver LO. For the signal branch, the optical signal is fed into a dual-polarization modulator driven by an arbitrary waveform generator (AWG, Keysight 8195A) to generate four 28-Gbaud 16-QAM modulated signals. To extract the phase offset between the signal and receiver LO, we add a pilot tone of 9.155 MHz on the I-path to assist phase offset capture and adjust the pilot-tone power to 1.03% data signal power to reduce the impact on the data signal. In fact, the choice of pilot-tone power directly affects the ability of PACL to capture the frequency and phase offsets. The higher the pilot-tone power, the more easily PACL can capture the frequency and phase offsets and compensate for those accurately. However, a higher pilot-tone power can affect the demodulation performance of the X-polarization signal. We adjust the pilot-tone power to 0.51%, 1.03%, 3.02%, and 5.00% data signal power and measure the impact of different pilot-tone powers in the modulation signal on the receiver optical power penalty as shown in Fig. S2 in the Supplementary Material. Compared with other pilot-tone powers, we adjust the pilot-tone power to 1.03% data signal power, and the bit error rate (BER) curve shows the best performance, that is, the signal can be recovered below 7% forward error correction (FEC) threshold at the −20-dBm receiver power. The pilot tone with 0.51%, 3.02%, and 5.00% data signal power causes approximately a 2-, 2-, and 6-dB receiver optical power penalty, respectively. The modulated optical signal is transmitted to the receiver with −17.1dBm output optical power via 5-km fiber links (1.3-dB loss). The EDFA is used to compensate for fiber links and other optical component losses. On the other branch, the LO is transmitted to the receiver with ∼9-dBm optical power.

At the receiver, an automatic polarization controller (APC, General Photonics PSY-201, Chino, California, United States) with a 3-dB insertion loss is used to ensure that the modulated optical signal fed into the AOM maintains constant polarization. This helps to mitigate any potential impact of AOM polarization sensitivity. The AOM (upshift mode, +1 order) is operated at the driving frequency of 78.125 MHz with a 2.5-dB insertion loss, and it is used as a feedback actuator to compensate for phase offset in the coherent system. To eliminate the effects of the AOM frequency shift, the AWG output data signal spectrum is shifted down the same frequency. The signal and LO are input to a coherent receiver which outputs four tributaries of the dual-polarization 16-QAM signal, where the I- and Q-path signal outputs are split by a power divider and fed into the PACL module for controlling the AOM and compensating the frequency and phase offsets. Finally, the four tributaries are picked up by the digital storage oscilloscope (DSO) with 40 GSa/s. The offline signal processing of the sampled data is to emulate the clock-data recovery module in a conventional PAM system. There is neither frequency/phase recovery nor MIMO in the offline signal processing.

The schematic of optical signal spectra at both the transmitter and receiver and the proposed PACL module architecture are shown in Figs. 2(b) and 2(c). For convenience, we ignore the proportional constants. The pilot tone modulated at the I-path can be expressed as k(eiΩt−e−iΩt),(2)where the k and Ω represent the proportional factor and the angular frequency of the pilot tone, respectively. When the signal is transmitted to the receiver, the phase offset introduced by the link can be expressed as eiΔθ. The Δθ represents the optical phase offset. At the receiver, the pilot tone obtained by the coherent receiver can be expressed as S=k(eiΩt−e−iΩt)eiΔθ,(3)where the real part can be expressed as S1=k1cos(Δθ)cos(Ωt).(4)

The imaginary part can be expressed as S2=k2sin(Δθ)cos(Ωt).(5)

As the pilot tone is a low-frequency signal compared with the data signal, we input the I- and Q-path signals from the coherent receiver into a low-pass filter (LPF) to filter out the high-frequency component. The LPF is 50 MHz in the experimental setup. They are then mixed and can be expressed as S1×S2=14k1k2sin(2Δθ)[1+cos(2Ωt)].(6)

Then, it is passed through an LPF to give a phase error signal 14k1k2sin(2Δθ). There are also low-frequency components from the actual data. However, these appear as background noise because they are uncorrelated with the pilot tone. Finally, the phase error is fed into the proportion integration differentiation (PID) to control the AOM frequency shift and compensate for the frequency and phase offsets between the signal and the receiver LO. As the PACL is essentially a phase-locked loop as well, this requires that the PACL module has a phase margin of 45 deg to ensure the stability of phase locking, namely, when the fiber link introduced frequency fluctuation beyond 12τ, where τ represents the loop delay of the PLL, the PLL begins to become unstable. In addition, the pilot-tone frequency has a limited impact on the residual phase noise because the phase error signal is 14k1k2sin(2Δθ) received by an LPF that is independent of frequency. However, the amplitude of the pilot tone impacts the PACL module’s capability of capturing the phase error signal. The low pilot-tone power will reduce the compensation capability of the PACL module, which causes an increase in residual phase noise.

It is noted that the proposed method resembles a classical Costas loop. The difference is that the classical Costas loop is used for carrier frequency recovery from suppressed-carrier modulation signals, which relies on high-speed analog circuits while our pilot-tone assisted approach uses low-speed circuits.24 In doing so, we achieve a record dual-polarization 224-Gb/s 16-QAM 5-km transmission with reset-free carrier phase recovery in the optical domain. In addition, the above operations are the same for both X- and Y-polarization tributaries because they are independent. Compared with our previous approach22 by monitoring and minimizing the intensity of the Q-path signal, PACL can retrieve the sign of the phase error θ directly, enabling much robust recovery of the PLL.

We test the performance of the system in the dual-polarization 224-Gb/s 16-QAM 5-km transmission case. The BER performance for the four-tributary dual-polarization 16-QAM signal (XI, XQ, YI, and YQ) is shown in Fig. 3(a) (detailed BER performance for the X- and Y-polarization of four-tributary dual-polarization 16-QAM signals can be seen from Fig. S3 in the Supplementary Material). The imbalance in I/Q performance may be attributed to the addition of a 9.155-MHz pilot tone on the I-path to assist in phase offset capture. We have simulated the impact of different pilot-tone powers on the signal-to-noise ratio (SNR) of the received data signal, shown in Fig. S4 in the Supplementary Material. In our experiment, a pilot tone with 1% data signal power has a limited impact on the detection and demodulation of received DP-16QAM signals. The X-polarization 16-QAM signal can be recovered below the 7% FEC threshold at the −17dBm receiver power, whereas the Y-polarization 16-QAM signal can be recovered at the −20dBm receiver power. The DSP-free coherent optical detection scheme based on the FSON architecture has been demonstrated to meet the requirements of short-reach optical interconnection applications, especially intra-data center. It should be noted that there is an ∼3-dB receiver optical penalty between X- and Y-polarization signals. We consider that the diffraction efficiency of light with different polarizations passing through the AOM is not the same, and we will conduct in-depth research on this work in the future. We can rotate the constant polarization light through different waveguides to align with the same polarization direction before it enters the AOM. Figure 3(b) shows the BER performance for X- and Y-polarization SNRs. It should be noted that we proposed PACL as an active frequency and phase offset compensation module. The frequency and phase offsets caused by non-homologous internal difference detection can be eliminated in the optical domain. The eye diagrams and constellation diagrams of the 224-Gb/s DP-16QAM signal are shown in Figs. 3(c) and 3(d). It can be observed that when the PACL module is on, the eye diagram of the four-tributary DP-16QAM signal remains open. This shows that the frequency and phase offsets between signal and LO are compensated without DSP. In addition, we compare the power consumption of the proposed DP-16QAM demultiplexing system with traditional coherent detection systems and other DSP-free systems. The detailed information is in Note 1, Fig. S5 in the Supplementary Material.9^,25^,26

The PACL module can compensate for the frequency and phase offsets between the receiver LO and the signal, whereas the power of the pilot tone in the I- and Q-path signals shows a maximum and a minimum, respectively. We add the pilot tone of 9.155 MHz at the transmitter and measure the pilot tone amplitudes of the I- and Q-path tributaries to characterize the phase lock. Figures 4(a) and 4(b) show the pilot tone amplitudes of the I- and Q-path tributaries. When the PACL module is on, the amplitudes of the pilot tone are more than 23 dB lower in the Q-path compared with the power in the I-path. It also shows that the pilot tone is added to the I-path at the transmitter and can be stabilized in the I-path at the receiver by the above method, even with phase fluctuations from the fiber link, which indicates that the phase locking between the signal and the receiver LO is successful.

To systematically verify the frequency compensation range and dynamic compensation bandwidth of the above PACL module, we modulated the frequency offset and the variable phase to simulate the laser frequency and phase fluctuations between the signal and the LO as shown in Fig. 2(d). The maximum range of frequency offsets that the proposed PACL module can compensate for is 1 MHz, limited by the voltage range of PID outputs. The frequency difference between the signal and the LO is shown in Fig. 4(d). When the PACL module is turned on, the frequency and the phase offsets are compensated and shown as a stable single frequency on the spectrum. Thus, the demultiplexing of the dual-polarization 16-QAM signal can still be achieved with the 1-MHz frequency compensation range. Furthermore, we use a phase modulator (PM) to incorporate additional controllable phase changes and measure the results of the received signals for different phase variations to verify the PACL module dynamic compensation bandwidth. The Vπ voltage of this PM is ∼7V. We use a sine wave signal to drive PM with 10 dBm output power (∼2Vpeak-to-peak), thus introducing a maximum phase shift of ∼50deg. The back-to-back BER performance with different dynamic compensation bandwidths for the four-tributary dual-polarization 16-QAM signals (XI, XQ, YI, and YQ) is shown in Fig. 4(c). It can be seen that the 16-QAM signals can be recovered below the 7% FEC threshold with the 600-kHz phase fluctuation speed. This meets almost all intra-DCI application scenarios, especially demonstrating the stability of the proposed solution in the case of the FSON architecture.

We have proposed an FSON-based tree-distributed homology architecture and analyzed the architecture in terms of the number of tree layers and the number of branches per layer. We find that the FSON architecture-supported server node number is large enough for all the optical transceivers within a data center, and it is scalable and compatible. Then, we experimentally demonstrate DSP-free coherent detection of 224-Gb/s dual-polarization 16-QAM signals over 5-km mismatch fiber links with the PACL module. When the PACL module is on, the power of the pilot tone signal is more than 23 dB lower in the Q-path compared with the power in the I-path. The proposed method has a 1-MHz frequency compensation range and 600-kHz dynamic compensation bandwidth. It demonstrates that the proposed scheme can meet the requirements of short-reach optical interconnection applications, especially intra-data centers, and demonstrates the proposed scheme’s capability to extend to 16-QAM or even higher-order modulation formats.

In conclusion, the FSON architecture and proposed FSON-based tree-distributed homology architecture have demonstrated their feasibility and superiority for data center optical interconnections. It indicates that our scheme holds great potential for future upgrades to higher-order modulation formats and more efficient data transmission with data centers. Moreover, the integration of discrete optical components onto a silicon photonics platform promises significant advancements in reducing cost and power consumption, enhancing system robustness, and addressing the challenges of real-world deployment. The proposed scheme provides an attractive solution for the evolution of traditional PAM-4-based data centers toward more advanced coherent interconnects.

We carried out the experiments with an ultra-low noise erbium fiber laser NKT-X15, having a central wavelength of 1550.12 nm, a linewidth of less than 100 Hz, and an output power of 14 dBm. The AWG (Keysight 8195A) was employed to modulate data signals with output amplitudes of 500, 470, 430, and 500 mv and output delays of 0, 1, 0, and 4 ps for four channels, respectively. This is to compensate for the signal amplitude and phase imbalance on the transmitter. The same operation was used for the ICR at the receiver with output amplitude setting parameters of 3, 2.7, 3, and 2, and output delays of 0, 0, 0, and 1 ps for four channels, respectively. The EDFA (AEDFA-CL-23) was employed to compensate for the fiber link and optical component loss that was operated in APC mode for the tree-distributed homology FSON architecture system and in ACC mode for an optical communication system. The automatic polarization controller (General Photonics PSY-201) used Stokes vector parameters to measure and optimize the polarization control of the laser and ensured that the optical signal fed into the AOM maintained a constant polarization. The AOM used in our setup, while employing discrete optical components, operated with an RF driving power of 2 W. However, we also know the commercial low-power AOMs that require only up to 0.4 W of RF driving power, such as the G&H T-M080-0.5C8J model, which can reduce significant power consumption. The PACL module operated with a control voltage range of 0 to 2V and a maximum driving current of less than 10 mA. The voltage-controlled oscillator (VCO) we have chosen is the DRFA10Y, which requires a driving voltage of 24 V and a current of 0.15 A. The optical fiber link is G625D with 0.2 dB/km loss. We utilized the Rohde & Schwarz FSPN-26 phase noise analyzer, which was configured with an input beat frequency signal of 78.125 MHz. The XCORR factor employed in our analysis is 1.

For simplicity, we describe only the optical signal modulation process of the X-polarization I/Q data signal. A modulated optical signal with a pilot tone can be expressed as X=Axei(wt+φx)+k(eiΩt+e−iΩt), where X is the X-polarization modulated optical signals, Ax is the amplitude of X-polarization modulated optical signals, w is the carrier frequency, and φx is the X-polarization modulated phase. As we add AOM to the conventional coherent optical communication system, all modulated optical signals are frequency-shifted by the AOM, which also results in a frequency shift of the received signal. Therefore, we need to shift the spectrum of the AWG output signal at the transmitter. The modulated optical signal can be expressed as X=[Axei(wt+φx)+k(eiΩt+e−iΩt)]×e−iΩAOMt, where ΩAOM is the drive frequency of the AOM.

Biographies of the authors are not available.