Polarization-diversity Stokes-analyzer-based coherent receiver

S. Ishimura; K. Nishimura; Y. Nakano; T. Tanemura

doi:10.1364/OE.27.009071

1. Introduction

Since the early-stage demonstrations of digital coherent optical communication systems [1, 2], numerous studies have shown that the coherent systems can improve the spectral efficiency dramatically by exploiting both polarization multiplexing and high-order modulation formats such as quadrature phase-shift keying (QPSK) and 16-ary quadrature-amplitude modulation (16QAM). As a result, the coherent systems have been put into practical use at a rapid pace, and the 100-Gb/s dual-polarization (DP)-QPSK transceivers are widely deployed in the current commercial systems. Up to date, however, deployment of the coherent receivers has been limited to medium/long-haul applications due to their high cost, and it still seems to be challenging to deploy them in short-reach networks such as intra/inter datacenter networks, where intensity-modulation direct-detection (IMDD) systems are currently dominant. As compared to the DD receiver, the coherent receiver is obviously more complicated because it consists of many optical components such as phase/polarization diversities and eight photodiodes (PDs) or four balanced PDs, while only one PD is necessary in the DD receiver.

Thus far, there are numerous reports aiming to simplify the complicated structure of the coherent receiver while keeping the spectral efficiency higher than the conventional IMDD systems. As one of the solutions, DD-based transmission schemes employing the Stokes analyzer have been actively studied [3–8]. Since multi-dimensional signal space is utilized in these schemes, the spectral efficiency can be improved beyond the conventional one-dimensional IMDD systems. In fact, in [6, 7], signal constellation was designed in the three-dimensional Stokes space. [3–5] also showed that two-dimensional complex signal can be transmitted and detected by a Stokes analyzer. In addition, the receiver structure of the Stokes-analyzer-based scheme has less complexity than that of the coherent receiver because the Stokes receiver can reduce the number of PDs, and remove the local oscillator (LO). However, such DD-based methods either employ only one polarization dimension to transmit signal [3–5], or lack several essential advantages of coherent detection, such as high receiver sensitivity and the ability to compensate for all the linear transmission impairments [6, 7]. On the other hand, there are several studies to simplify the coherent receiver itself. In [9] for example, two 3x3 couplers are used instead of the phase/polarization diversities to reduce the total number of PDs from eight to six. However, the need for either two extra analog-to-digital converters (ADCs) or an analog scaling circuit with specially designed differential amplifiers may be the drawback of this scheme.

As an alternative scheme to realize low-cost coherent transceivers, we have recently proposed a novel polarization-diversity coherent receiver based on the Stokes analyzer [10]. The proposed receiver reduces the number of PDs from eight to six, without the need for extra ADCs or special differential amplifiers. Moreover, splitters and combiners for polarization-multiplexed signals can be replaced by only one polarization beam splitter or combiner (PBS/C) in the proposed architecture. In this paper, we provide the detailed explanations of the proposed receiver and show the results of transmission experiments using the developed prototype of the polarization-diversity Stokes-analyzer-based coherent receiver. We successfully transmit 120-Gb/s DP-QPSK and DP-8QAM signals over a 100-km single-mode fiber (SMF). We believe that the demonstrated architecture could potentially be integrated monolithically on silicon-photonic or InP platforms, to realize compact and low-cost coherent transceivers for short-reach applications.

2. Principle of the Stokes-analyzer-based coherent receiver

2.1. Overview

In this subsection, we describe that a simple coherent receiver can be realized by adding small modifications to the conventional Stokes analyzer. In [7], two types of receiver architectures to detect the Stokes parameters were reported. In particular, the architecture referred to as C-receiver is often used as the Stokes analyzer. Figure 1(a) shows the schematic diagram of the Stokes analyzer, which consists of four branches and four PDs. Note that instead of amplifying the outputs from ports 2, 3, and 4, a 6-dB attenuator is inserted in the S₀ branch. The Stokes parameters obtained from this configuration are given as follows:

S_{1} = I_{x} - \frac{1}{2} S_{0} = \frac{1}{2} (| E_{x} |^{2} - | E_{y} |^{2}),

S_{2} = I_{45^{\circ}} - \frac{1}{2} S_{0} = Re [E_{x} E_{y}^{*}],

S_{3} = I_{R} - \frac{1}{2} S_{0} = Im [E_{x} E_{y}^{*}],

We can see from Eqs. (2) and (3) that a coherent cross term between E_x and E_y is retrieved through $S_{2} + i S_{3}$ . Therefore, if we first assume that the incoming complex signal has only the x-polarization component, we can retrieve the linear complex signal $E_{x, s i g}$ as $S_{2} + i S_{3} = Re [E_{x, s i g} E_{y, L O}^{*}] + i Im [E_{x, s i g} E_{y, L O}^{*}]$ by adding the LO light on the y-polarization before sending to the Stokes analyzer as shown in Fig. 1(b). In addition, the S₁ parameter, which denotes the power difference between $E_{x, s i g}$ and $E_{y, L O}$ is unnecessary, so that we can discard the S₁ branch as shown in Fig. 1(c). Here, the process of subtracting 6dB-attenuated S₀ from S₂ and S₃ is realized by one resistive divider and two differential amplifiers. Finally, the polarization-diversity configuration for the Stokes-vector coherent receiver can be implemented in a greatly simplified scheme as shown in Fig. 1(d). We should note that one PBS(C) can play the role of both splitting two polarization components of the signal, and combining LO at the same time. Compared with the conventional dual-polarization coherent receiver, the number of the PDs is reduced from eight to six, without the need for any special differential amplifiers or extra ADCs.

Fig. 1 Receiver structures of (a) the Stokes analyzer; (b) the Stokes analyzer with LO provided at the receiver side; (c) the Stokes-analyzer-based coherent receiver; (d) the polarization-diversity Stoke-analyzer-based coherent receiver.

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2.2. Quantitative explanation

In this subsection, the aforementioned concept is explained quantitatively using mathematical expressions. Let ${(E_{x, s i g}, E_{y, s i g})}^{T}$ and ${(E_{x, L O}, E_{y, L O})}^{T}$ be the Jones vectors of an incoming signal and LO, respectively. After passing through PBS, the Jones vector from the upper output port is written as ${(E_{x, s i g}, E_{y, L O})}^{T}$ , while that from the lower port is ${(E_{x, L O}, E_{y, s i g})}^{T}$ as shown in Fig. 1(d). We first consider the upper output port from the PBS, which is split into three branches. The light in the first branch, labeled as (i), is guided to a 45-degree polarizer, followed by a PD. The Jones vector just before PD, $E_{(i)}$ can be represented as

E_{(i)} = \frac{1}{2} (\begin{matrix} 1 & 1 \\ 1 & 1 \end{matrix}) \frac{1}{\sqrt{3}} (\begin{matrix} E_{x, sig} \\ E_{y, LO} \end{matrix}) = \frac{1}{2 \sqrt{3}} (\begin{matrix} E_{x, sig} + E_{y, LO} \\ E_{x, sig} + E_{y, LO} \end{matrix}) .

Note that the first matrix in Eq. (4) denotes the Jones matrix of the 45-degree polarizer. After PD detection, the output current from the PD, $I_{(i)}$ is given as

I_{(i)} \propto | E_{(i)} |^{2} = \frac{1}{6} [| E_{x, s i g} |^{2} + 2 Re [E_{x, s i g} E_{y, L O}^{*}] + | E_{y, L O} |^{2}] .

On the other hand, the light at the second branch (ii) is directly guided to PD, so that the output current from the PD, $I_{(ii)}$ is given as

I_{(ii)} \propto | E_{(ii)} |^{2} = \frac{1}{3} [| E_{x, s i g} |^{2} + | E_{y, L O} |^{2}],

where

E_{(ii)}

denotes the Jones vector at the branch labeled as (ii) just before PD. Meanwhile, the light at the branch labeled as (iii) is guided to PD after passing through a quarter-wave plate (QWP) and a 45-degree polarizer. Therefore, the Jones vector just before PD,

E_{(iii)}

is given as

E_{(iii)} = \frac{1}{2} (\begin{matrix} 1 & 1 \\ 1 & 1 \end{matrix}) (\begin{matrix} 1 & 0 \\ 0 & i \end{matrix}) \frac{1}{\sqrt{3}} (\begin{matrix} E_{x, sig} \\ E_{y, LO} \end{matrix}) = \frac{1}{2 \sqrt{3}} (\begin{matrix} E_{x, sig} + {iE}_{y, LO} \\ E_{x, sig} + {iE}_{y, LO} \end{matrix}) .

Note that the second matrix denotes the Jones matrix of QWP. The output current from PD is given as

I_{(iii)} \propto | E_{(iii)} |^{2} = \frac{1}{6} [| E_{x, s i g} |^{2} + 2 Im [E_{x, s i g} E_{y, L O}^{*}] + | E_{y, L O} |^{2}] .

These three output currents are fed into differential amplifiers. Note that the current $I_{(ii)}$ is split as

I_{(ii)}^{'} \propto \frac{1}{6} [| E_{x, s i g} |^{2} + | E_{y, L O} |^{2}],

by a resistive divider. From the upper differential amplifier, the in-phase component,

I_{I, X}

is obtained as

I_{I, X} = I_{(i)} - I_{(ii)}^{'} \propto Re [E_{x, s i g} E_{y, L O}^{*}] .

From the lower differential amplifier, on the other hand, the quadrature component, $I_{Q, X}$ is obtained as

I_{Q, X} = I_{(iii)} - I_{(ii)}^{'} \propto Im [E_{x, s i g} E_{y, L O}^{*}] .

Using Eqs. (10) and (11), the complex amplitude of the optical signal, $E_{x, s i g}$ can be retrieved.

In the same manner, the IQ components of $E_{y, s i g}$ are also obtained from the lower output port from the PBS as

I_{I, Y} \propto Re [E_{y, s i g} E_{x, L O}^{*}],

I_{Q, Y} \propto Im [E_{y, s i g} E_{x, L O}^{*}] .

Therefore, dual-polarization IQ signals can be detected using the polarization-diversity Stokes-analyzer-based coherent receiver architecture proposed in Fig. 1(d) In terms of the receiver sensitivity, the Stokes-analyzer-based coherent receiver suffers from a degradation of 4.77 dB compared to the phase-diversity homodyne receiver in the thermal-noise-limited case. This is due to the intrinsic loss caused by the 1x3 splitter and the polarizer. However, such degradation may be acceptable in short-reach applications, such as intra-datacenter networks, where link margin is relatively large. On the other hand, in a system where an optical pre-amplification is employed, namely, the ASE-noise-limited case, the sensitivity of the Stokes-analyzer-based coherent receiver would be almost unchanged from that of the phase-diversity homodyne receiver, because the ASE noise overwhelms the vacuum fluctuation noise.

Fig. 2 Prototype of the polarization-diversity Stokes-analyzer-based coherent receiver. (a) Optical circuit in the receiver. (b) External appearance of the prototype.

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3. Experiment

3.1. Prototype development

To evaluate the Proof-of-Concept (PoC) of the aforementioned concept, a prototype of the polarization-diversity Stokes-analyzer-based coherent receiver was developed. We implemented the receiver using free-space optical components as shown in Fig. 2(a). The external appearance of the developed prototype module is shown in Fig. 2(b). In the optical circuit, the 1x3 splitter shown in Fig. 1(d) was replaced by two types of beam splitters: the first one has the splitting ratio of 0.33:0.66, while the second one has that of 1:1. A light coming from PBS was firstly divided by the ratio of 0.33:0.66. Subsequently, the light split by the ratio of 0.66 was split in half again by the second splitter so that all three branches had identical optical power. One of the two was collected at the collimator after passing through a 45-deg polarizer (A-1/B-1), while the other path was guided directly to the collimator (A-2/B-2). On the other hand, the light split by the first splitter with the ratio of 0.33 was transmitted through both QWP and a 45-deg polarizer before collected at the collimator (A-3/B-3). Note that the role of the QWP is to rotate the relative phase of LO on the x (or y) polarization by $π / 2$ with respect to that of the signal component on the y (or x) polarization. Therefore, the fast axes of the two QWPs in the upper and lower branches in Fig. 2(a) were aligned to y and x directions, respectively.

Since this prototype was developed based on free-space optical components, its size is rather large as shown in Fig. 2(b). However, this novel architecture could potentially be integrated on silicon or InP to realize compact and low-cost coherent transceivers. On the silicon photonic platform, for example, various types of polarization splitters and rotators have already been realized by the mature fabrication technologies [11]. Even on InP, monolithic polarization rotators and splitters have recently been available by the generic foundry services [12, 13]. Furthermore, by integrating polarization-sensitive strained quantum-well PDs, we have recently demonstrated a fully integrated InP Stokes vector receiver [14], which is actually similar to the coherent receiver presented in this work.

Fig. 3 Experimental setup of the transmission experiment.

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3.2. Transmission experiment

Using the developed prototype, we demonstrated 120-Gb/s DP-QPSK (30 Gbaud) and DP-8QAM (20 Gbaud) transmission over a 100-km SMF. The experimental setup is shown in Fig. 3. A CW light was injected to an LiNbO₃ IQ modulator (IQM). The half-wave voltage and the bandwidth of the IQM was 3.5 V and 25 GHz, respectively. The IQM was driven by Nyquist-filtered 30-Gbaud QPSK signals or 20-Gbaud 8QAM signals generated from an arbitrary waveform generator (AWG) having two RF ports. The sampling rate andthe bandwidth of the AWG was 65 Gs/s and 25 GHz, respectively. To perform polarization multiplexing, the signal was split into two branches and a fiber delay was inserted in one of the two branches for decorrelation before combined by PBC. The optical signal was transmitted over a 100-km SMF with the launched power of -1.5 dBm. After the transmission, optical signal-to-noise ratio (OSNR) was controlled by a variable optical attenuator (VOA). Before injected to the prototype, the signal was pre-amplified with an erbium-doped fiber amplifier (EDFA) and OSNR was monitored by an optical spectrum analyzer (OSA). Each optical output from the prototype was detected by PD. The injected power to each PD was set at around 2 dBm, and the bandwidth of each PD was 50 GHz. Two resistive dividers were employed to split the RF outputs of the branches labeled as (A-2) and (B-2) with 6-dB attenuation. As a consequence, we have eight RF branches just before four differential amplifiers. Finally, we obtained four outputs from the four amplifiers, and they were captured by a 4-channel digital oscilloscope (DSO) running at 80 Gs/s. It should be noted that all the lengths of both optical and electrical paths were equally adjusted. The DSP block diagram is also shown in Fig. 3. When the 30-Gbaud QPSK was transmitted, the four captured signals were down-sampled by 3/4, while when the 20-Gbaud 8QAM was transmitted, they were down-sampled by 1/2. Subsequently, the signal was equalized with half-symbol-spaced adaptive finite-impulse-response (FIR) filters. As the adaptive algorithm, we employed the decision-driven least-mean-square (DD-LMS) algorithm, which was modified based on [15, 16] to remove phase noise, frequency offset, and IQ imbalance simultaneously. Finally, the BER values were calculated by comparing with the original bits.

Fig. 4 Results of the transmission experiment. Measured BERs as a function of OSNR in the case of (a) 30-Gbaud DP-QPSK and (b) 20-Gbaud DP-8QAM. Constellation diagrams (c) for the 30-Gbaud DP-QPSK (OSNR = 21 dB) and (d) for the 20-Gbaud DP-8QAM (OSNR = 25 dB).

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Figures 4(a) and 4(b) show the measured BERs of 30-Gbaud DP-QPSK and 20-Gbaud DP-8QAM signals, respectively, transmitted over the 100-km SMF. Theoretical and back-to-back BERs are also shown in the figures. Figures 4(c) and 4(d) show the constellation diagrams for the 30-Gbaud DP-QPSK (OSNR = 21 dB) and the 20-Gbaud DP-8QAM (OSNR = 25 dB) respectively after the 100-km transmission. No significant difference between BERs in the back-to-back case and after the 100-km transmission is observed. Compared to the theoretical limit, we see penalties of about 5 dB for the DP-QPSK and 6 dB for the DP-8QAM, respectively, at BER of $3.8 \times 10^{- 3}$ , which is the threshold of the 7% hard-decision (HD) forward error correcting (FEC) code. These penalties may stem from imperfection of the developed prototype such as power imbalances in the optical and RF circuits. Nevertheless, we can confirm that the BER below the FEC threshold can be achieved with the received OSNR greater than 18 dB in the case of DP-QPSK and 22 dBin the case of DP-8QAM.

4. Conclusions

We have proposed a polarization-diversity Stokes-analyzer-based coherent receiver based on the Stokes analyzer. Since the number of the PDs are reduced from eight to six with simple analog circuits to detect IQ components, the receiver has less complexity than conventional coherent receivers. In addition, splitters and combiners for DP signals can be replaced by only one PBS in the proposed receiver, which can greatly simplify the receiver structure. For evaluation of PoC, we developed a prototype receiver module using free-space optical components. Using the prototype, we have successfully transmitted 120-Gb/s DP-QPSK and DP-8QAM signals over a 100-km SMF with the BERs below the 7%-HD FEC threshold. We believe that the demonstrated architecture could potentially be integrated monolithically on silicon-photonic or InP platforms, to realize compact and low-cost coherent transceivers for short-reach applications.

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Polarization-diversity Stokes-analyzer-based coherent receiver

Abstract

1. Introduction

2. Principle of the Stokes-analyzer-based coherent receiver

2.1. Overview

2.2. Quantitative explanation

3. Experiment

3.1. Prototype development

3.2. Transmission experiment

4. Conclusions

References

Cited By

Figures (4)

Equations (13)

Optics Express