Stokes vector receivers (SVR) bridge the 4-D (i.e. dual-polarization complex signals) coherent detection and the conventional intensity-only 1-D direct detection (DD). By multi-dimensional polarization modulation in Stokes space, SVR maximizes the electrical spectral efficiency (ESE) of DD receivers by recovering at most 3-D signals. However, most 3-D schemes lack the capability of optical field recovery, an essential requirement for digital post-compensation of fiber dispersion that elongates the achievable distance. We propose a 3-D Stokes-space field modulation to enable 3-D signal field recovery, verified by a 3-D 32-Gbaud per dimension probabilistic-constellation-shaped 64-QAM transmission over 260-km fiber at C-band. This sets an ESE record of 16.5 (net ESE of 13.9) bit/s/Hz for DD receivers.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
24 January 2019: A typographical correction was made to the title.
Direct detection (DD) is traditionally regarded as a simple detection method that recovers the optical intensity. Compared with coherent detection, DD reduces the receiver hardware cost including the local laser, and more crucially, realizes an uncooled transceiver that avoids the sophisticated wavelength alignment between the transmitter and the receiver. Further, DSP is simplified without digital carrier recovery; and in consequence, the laser linewidth requirement is relaxed at transmitter, which allows the usage of low-cost lasers. However, the conventional intensity modulation (IM) DD lacks a critical capability of field recovery (FR) that enables both the multi-dimension modulation and the digital compensation of fiber impairments linear with the optical field. There emerged some proposals combining self-coherent DD with polarization division multiplexing (PDM) to achieve the multi-dimensional FR [1,2]. However, these systems normally add optical filters to realize signal-carrier separation before O/E detection, which should reserve a frequency gap between signal and carrier. A filter with sharp roll-off factor significantly increases the receiver expense and loses the unique advantage of DD – the uncooled transceiver. The revival of Stokes vector receiver (SVR) [3–10] utilizes the intrinsic polarization diversity in Stokes space, and bridges the gap between the 4-D (i.e. dual-polarization IQ signals) coherent detection and the 1-D intensity-only DD. Various Stokes-space modulations (SSM) have extended the modulation degree of freedom to either 2-D [3–6] or 3-D [7–10]. Furthermore, several 2-D SSMs [3,5,6] realize the FR that enables digital chromatic dispersion (CD) compensation to elongate the achievable distance to hundreds of kilometers. Unfortunately, although maximizing the electrical spectral efficiency (ESE) of SVR, most 3-D SSMs cannot perform 3-D FR, limiting their achievable distance below 1 km [7,9] at C-band without CD pre-compensation .
Recently, Kramers-Kronig detection (KKD) [11–13] revives single-sideband (SSB) modulation [14,15] as a simple 1-D FR method via DD. Despite its superior performance of combating the 2nd-order signal-to-signal beat noise (SSBN) , KKD inherits the intrinsic drawback of SSB: (i) it requires high carrier-to-signal power ratio (CSPR) to guarantee an accurate FR, which degrades the system OSNR sensitivity; (ii) it doubles the required receiver bandwidth to recover an IQ signal from the 1-D intensity, which reduces the achievable ESE by half. In this paper, we combine SSM with SSB-FR, and propose a 3-D Stokes-space field modulation (SS-FM) that empowers SVR to recover the 3-D optical field. SS-FM places an SSB signal at one polarization, and a double-sideband (DSB) signal at the other. Compared with previous 3-D SSM, SS-FM dramatically extends the achievable distance from several hundred meters to several hundred kilometers by CD post-compensation; while compared with SSB, it decreases the overall CSPR due to the extra DSB signal at the orthogonal polarization, and maximizes the ESE for DD receivers. An early attempt uses block-wise phase switching (BPS) at one polarization to realize 3-D FR in Stokes space , but BPS wastes the transmitter bandwidth, and its FR suffers from SSBN at receiver. By the novel SS-FM, we demonstrate a 3-D SSM (32-Gbaud per dimension) 64-QAM transmission over 260-km standard single mode fiber (SSMF). To push the system to its capacity limit, we apply the probabilistic constellation shaping (PCS)  using 64-QAM with an entropy of 5.5-bit/symbol, leading to a total raw data rate of 528 Gb/s. PCS not only provides continuous rate adaption to approach the system capacity, but also achieves a shaping gain due to the Gaussian-like constellations .
2. 3-D Stokes-space field modulation and recovery
Different from long-haul transmissions which pursue high optical spectral efficiency (OSE) to maximize the fiber capacity, electrical spectral efficiency (ESE) is a primary consideration over OSE for short-reach applications, because the optical spectrum resource is normally abundant in commercially-deployed short-reach networks. High ESE maximizes the capacity per laser for a band-limited transceiver, and thus decreases the transceiver cost per bit. For example, we compare the 3-channel WDM IM-DD and the single-channel 3-D SVR system with the same transceiver bandwidth, consequently, the same achievable rate. Both systems require 3 digital modulations and detections, while the 3-channel WDM needs 2 more lasers. This not only increases the laser cost itself, but more critically, brings about a more sophisticated wavelength management issue. As a result, we analyze the modulation/detection dimension with reference to ESE instead of OSE. For example, using a -Hz coherent receiver, the 4-D polarization-multiplexed (POL-MUX) system can deliver -baud complex signal in total with ideal Nyquist shaping to the signal. The self-coherent SSM  shown by Fig. 1(b) places a pure carrier on X-POL to be detected self-coherently with the DSB signal on Y-POL, and sacrifices the 2-D degrees of freedom of X-POL. Proposed most recently, the POL-MUX SSB  recovers the dual-polarization optical field from and after SVR using SSB-FR. This format maximizes the optical spectral efficiency (OSE); nevertheless, it sacrifices the ESE of SVR: a -Hz receiver can only recover -baud signal in Fig. 1(c). It is desirable to design an SSM to maximize the ESE meanwhile realize a complete 3-D FR. In Fig. 1(d), we assign an SSB signal on X-POL and a DSB signal on Y-POL. The SSB/DSB is defined with reference to a strong carrier inserted on X-POL, whose power should be sufficiently large to guarantee an effective SSB-FR [11,15]. After SVR, the Stokes-space polarization recovery (PR) retrieves and , where and stands for the dual-polarization field and is the Stokes parameter. The X-POL field can be recovered by SSB-FR methods like KKD  or SSBN cancellation . Given , can be recovered from by division. In particular, the -POL signal (i.e. the denominator) never crosses zero due to the sufficient CSPR, also interpreted as the minimum phase condition in KKD . This 3-D Stokes-space FR (SS-FR) is illustrated by Fig. 1(e).
SS-FM is well distinguished from previous 3-D SSMs, because it can be regarded as three independent -baud IQ signals: (i) the 3-D SS-FR is detached from the signal processing of individual IQ signals (i.e. SS-FR is modulation independent), and consequently, the FR of Y-POL is independent from the digital demodulation of X-POL; (ii) both the transmitter and receiver DSP blocks can be parallelized, a welcoming feature for real-time DSP chips. There is an extra bonus for 3-D SS-FM due to the strong carrier on X-POL: its PR can be performed by analog polarization identification (API) without digital clock recovery . In Jones space, SS-FM signal behaves like a polarized light; and in Stokes space, only the time average is positive while both and are zero. Therefore, the orientation of axis is straightforward distinguished at receiver. Fixed the , - plane is perpendicular to , and the rotation within the plane is simply a constant phase shift of Y-POL that can be easily estimated. A similar concept has been applied to the POL-MUX SSB system .
We demonstrate the transmission of 3-D SS-FM signals over 260-km SSMF, using the setup in Fig. 2. The three 32-Gbaud baseband signals are generated by the DSP below the setup with 80-GSa/s transmitter sampling rate. We use the constant composition distribution matcher  to shape the 64-QAM symbol with an entropy of 5.5 bits. Two 32-Gbaud signals are digitally combined to a 64-Gbaud DSB signal with 1-GHz gap between the two sidebands. The 1550-nm laser output is split into three paths. Path 1 is the pure carrier; path 2 contains a 16.5-GHz optical frequency shifter and an IQ modulator driven by a 32-Gbaud signal (i.e. around 0.5-GHz gap between the signal and the main carrier). Their polarizations are aligned to a polarizer to form an SSB signal on X-POL. Path 3 generates the Y-POL signal using an IQ modulator driven by the 64-Gbaud signal. Except for the carrier, the signal power spectrum densities (PSD) of the two polarizations are kept as the same. The CSPR of X-POL is 11 dB, leading to an overall CSPR of 6.3 dB. Inset (iii) shows the optical spectrum. The power density of the left sideband is higher than the right one, because it overlaps two SSB signals. The optical spectrum analyser reads both signal and carrier power for OSNR measurement. The light is launched into 260-km SSMF consisting of two 80-km spans and one 100-km span, with the optimum power of 7 dBm. We use a simplified SVR based on 4 intensity detections, whose outputs are sampled by a 33-GHz oscilloscope at 80 GSa/s. We use KKD for SSB-FR at X-POL. CD compensation is applied to avoid the redundant OFDM guard interval. Carrier recovery compensates the fiber length mismatch among the 3 paths at transmitter. We apply generalized mutual information (GMI) to evaluate the performance of this PCS signal, which takes into account the bit-interleaved coded modulation (BICM) and bit-metric decoding (BMD) for a practical estimation of the achievable rate [16, Sec. III; 19, Sec. II; 20].
Figure 3(a) shows the received Stokes vector distribution in Poincare sphere. Despite the chaotic Stokes vectors due to the high peak-to-average power ratio (PAPR) of OFDM signals, the distribution is biased towards one hemisphere (i.e. polarized). Its average point indicates the axis orientation at transmitter. API simply aligns the axes between transmitter (the red line) and receiver (the blue line) by a 3 × 3 rotation matrix and reaches Fig. 3(b).
Figure 4(a) presents the OSNR sensitivity of the back-to-back (B2B) system for individual SSB signals. While the two SSB signals at Y-POL presents similar performance, the X-POL signal suffers from faster performance degradation. Such phenomenon is caused by the noise folding effect of SSB detection, namely, the optical noise at the vacant sideband would be folded to the signal sideband after the square-law detection, which brings 3-dB OSNR penalty, like the OSNR difference at 4-bit MI level. In contrast, the OSNR of 44 dB (without loading optical noise) results in little performance difference. The performance imbalance can be adjusted by the PSD ratio between the two polarizations in practical 3-D SS-FM transmission systems. In this experiment, we keep the signal PSD of the two polarizations as the same, which corresponds to 4.7-dB CSPR decrement with reference to the SSB polarization; while at most the SSB polarization should increase its PSD 3-dB higher than the DSB polarization to balance the performance at low OSNR range, and the CSPR decrement becomes 3 dB. Figure 4(b) shows the OSNR sensitivity for various transmission distance. The achievable rate (i.e. GMI) is 486 Gb/s for B2B system with the normalized GMI (NGMI) of 0.9264, and 446 Gb/s after 260-km SSMF transmission with the NGMI of 0.8586. The inset shows an aggregated 64-QAM constellation of all the 3 SSB signals after 260-km fiber.
We demonstrate a 3-D Stokes-space field recovery (SSFR) with 528-Gb/s single-channel raw information rate and 446-Gb/s achievable rate after 260-km SSMF transmission using 32-GHz receiver bandwidth. This sets an electrical spectral efficiency (ESE) record of 16.5 (net ESE of 13.9) bits/s/Hz for direct detection, and a distance record among high-baud-rate 3-D Stokes-space modulations without dispersion pre-compensation. The 3-D SSFR paves a promising pathway towards high-capacity short-reach applications by maximizing the bandwidth utilization of direct detection receivers while extending the transmission distance with digital dispersion compensation.
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