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Abstract
We propose and demonstrate a simple integrated dual-polarization (DP) coherent receiver that does not require a polarization splitter-rotator (PSR). Based on a novel concept, a DP coherent signal is mixed with the local-oscillator (LO) waves inside a single interferometer and detected by five single-ended photodetectors. The signal-signal and LO-LO beat noises are eliminated through differential detection. We design and fabricate a proof-of-concept device on InP and experimentally demonstrate complete retrieval of DP quadrature phase-shift keyed signals. Requiring minimal number of optical components without a PSR, the demonstrated scheme would be attractive particularly for the InP and thick-silicon photonic platforms due to its significantly reduced footprint and ease of fabrication.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Digital coherent technology has revolutionized the optical communication industry in the past decade [1]. By exploiting dual-polarization (DP) high-order modulation formats, such as quadrature phase-shift keying (QPSK) and 16-ary quadrature-amplitude modulation (16QAM), one can achieve high spectral efficiency and receiver sensitivity, as well as the capability of equalizing fiber impairments through digital signal processing (DSP). While DP-QPSK systems are widely deployed in the commercial medium/long-haul networks, there is recently an increasing interest to introduce coherent technology to shorter-reach links, such as intra/inter datacenter networks, where intensity-modulation direct-detection (IM-DD) systems are currently dominant [2,3].
Conventionally, a single-polarization coherent receiver is constructed by using a 90$^\circ$ optical hybrid and four photodiodes (PDs) (or two balanced PDs). For DP operation, therefore, we need two sets of such receivers, together with a polarization beam splitter and a rotator, namely a polarization splitter-rotator (PSR) [1]. This is obviously more complicated than an IM-DD receiver. Thus, photonic integration is inevitable. Indeed, by integrating all these components including PSR on 220-nm-thick silicon-on-insulator (SOI) photonic platforms, compact DP coherent receiver circuits have been demonstrated [4–6]. On the other hand, the use of thicker SOI platforms has been pointed out to attain improved performance in many aspects [7–10]. Moreover, InP-based coherent receivers were demonstrated to show ideal performances, owing to the monolithic integration of high-speed InP-based PDs and amplifiers [11–13]. In such thick-SOI and InP-based photonic platforms, however, on-chip polarization handling remains to be a key technical challenge [8,14–16]. As a result, PSRs are usually not integrated in these coherent receivers [12,13], which have been one of the major obstacles in reducing the cost and size for the short-reach applications.
Here, we propose a novel-concept fully integrated DP coherent receiver, which does not require a PSR. Moreover, it uses only one multimode interference (MMI) coupler (against two optical hybrids in the conventional receiver) to mix DP signals and local oscillator (LO) waves as well as only five single-ended PDs (against eight in the conventional receiver) to retrieve in-phase and quadrature signals in both polarization modes. On the other hand, the required numbers of the transimpedance amplifiers (TIAs) and the analog-digital converters (ADCs) are the same as a conventional DP coherent receiver and would not add extra cost. A proof-of-concept device is fabricated on InP, which is used to experimentally demonstrate complete retrieval of DP-QPSK signals. While a similar PSR-free DP coherent receiver has been proposed previously [17], our scheme is significantly less complicated due to the minimal number of couplers and PDs as well as absence of waveguide crossings. Moreover, the previous work was only demonstrated numerically. To the best of our knowledge, this is the first experimental demonstration of PSR-free DP coherent receiver in any photonic integration platform.
2. PSR-free DP coherent receiver
2.1 Device concept
Figure 1(a) shows a schematic of the proposed fully integrated DP coherent receiver that does not require PSR. In addition, unlike the conventional DP coherent receiver, which uses two optical hybrid couplers to receive both polarization components, we employ only one 3$\times$5 MMI coupler for mixing the DP signal with the LO. The total number of PDs can also be reduced from eight (or equivalently, four balanced PDs) in the conventional scheme to five in the proposed scheme.
Fig. 1. Schematic of the proposed DP coherent receiver without PSR. (a) Entire circuit. (b) SOPs of LO at the input of the device (I), after the delayed MZI (II), and at the outputs of the 3$\times$5 MMI (III). (c) SOPs of LO at (I), (II), and (III), plotted on a Poincaré sphere.
A polarization-multiplexed signal is input to one port of the 3$\times$5 MMI coupler without polarization demultiplexing. On the other hand, a LO wave is incident to the chip with 45$^\circ$ linear polarization [or any other state of polarization (SOP) with $S_1=0$ on the Poincaré sphere]. The LO is first split equally into two ports by a 1$\times$2 MMI coupler and transmits through different waveguides, having a length difference of $\Delta L$, which operates as a delayed Mach-Zehnder interferometer (MZI). In Fig. 1(b), we schematically describe the SOPs of LO waves at the input of the 1$\times$2 MMI coupler (I), after the delayed MZI (II), and at the output of 3$\times$5 MMI coupler (III) for a representative case. These SOPs are also described on the Poincaré sphere in Fig. 1(c).
By adjusting $\Delta L$ to satisfy $\Delta L=\lambda /(2\Delta n_\textrm {eff})$, where $\Delta n_\textrm {eff}$ is the effective refractive index difference between the transverse-electric (TE) and the transverse-magnetic (TM) modes for these waveguides and $\lambda$ is the wavelength, a pair of orthogonally polarized LO waves are generated at the input of the 3$\times$5 MMI coupler as shown in (II) of Figs. 1(b) and 1(c). After propagating through the 3$\times$5 MMI coupler, LO waves with five different SOPs are obtained at the respective output ports. More specifically, we will derive in the subsequent sections that with a proper design of the 3$\times$5 MMI coupler, we can realize an ideal case of generating five LOs with equally spaced SOPs on the Poincaré sphere, as shown in (III) of Fig. 1(c). As the signal is mixed with these LOs and detected by the respective PDs, five different photocurrent signals are generated. We then extract the differential signals from adjacent PDs and process them through DSP to retrieve the dual-polarization complex electric field of the input signal. As we derive in the following section, the signal-signal beat noise is eliminated through this differential detection process.
We should stress that this chip consists of only symmetrical waveguide structures, which can be fabricated by a simple single etching process. On the other hand, the 3$\times$5 MMI coupler should ideally have uniform intensity transmittance to all five output ports from the three input ports, where the signal and two LO waves are launched. This condition can be readily satisfied for an InP device as we will demonstrate experimentally in Section 3.
2.2 Theory
We first define $\textbf {e}_1$ and $\textbf {e}_2$ as the unit complex vectors to describe the polarization states of two LO waves at the input of the 3$\times$5 MMI coupler [plane (II) in Fig. 1]. As explained above, under a proper design of $\Delta L$, these waves can be made orthogonally polarized. For example, $\textbf {e}_1=\frac {1}{\sqrt {2}}\textbf (1, 1)^{\mathrm {T}}$ and $\textbf {e}_2=\frac {1}{\sqrt {2}}\textbf (1, -1)^{\mathrm {T}}$ for $\pm$45$^\circ$ linearly polarized case or $\textbf {e}_1=\frac {1}{\sqrt {2}}\textbf (1, i)^{\mathrm {T}}$ and $\textbf {e}_2=\frac {1}{\sqrt {2}}\textbf (1, -i)^{\mathrm {T}}$ for circularly polarized case, but they could generally be any pair of orthogonal states. The vectors $\textbf (\textbf {e}_1, \textbf {e}_2)$, therefore construct an orthonormal basis: $\textbf {e}^{*}_m\cdot \textbf {e}_{m'}=\delta _{m,m'}$.
We then express the electric field of the signal at the input of the 3$\times$5 MMI coupler as
Here, $A_m$ ($m=$ 1 or 2) denote the complex amplitudes of the signal defined on the $\textbf (\textbf {e}_1, \textbf {e}_2)$ basis. Then, we can write the electric field at the $n$-th output port of the 3$\times$5 MMI coupler as where $P_\textrm {LO}$ is the LO power and $a_{n,m}$ and $b_{n,m}$ represent the complex transfer coefficients to the $n$-th output port for $m$-th polarization component of the signal and LO, respectively. As we explained in the previous section, the 3$\times$5 MMI coupler should ideally have uniform intensity transmission to all five ports such that $|a_{n,m}|^2$ and $|b_{n,m}|^2$ are equal for all $n$ ($n = 1, 2, \ldots , 5$).Using the orthonormal condition, $\textbf {e}^{*}_m\cdot \textbf {e}_{m'}=\delta _{m,m'}$, the photocurrent signal at the $n$-th PD is expressed as
We now extract four differential signals $S_n$ ($n = 1, \ldots , 4$) from the photocurrent of adjacent PDs as shown in Fig. 1(a), so that $S_n = (I_{n} - I_{n+1})/2$. If we define a 5$\times$1 vector $\textbf {I} \equiv (I_1, I_2, I_3, I_4, I_5)^\textrm {T}$, and a 4$\times$1 vector $\textbf {S} \equiv (S_1, S_2, S_3, S_4)^\textrm {T}$, we can write as
where we defineIn practice, the 3$\times$5 MMI coupler shown in Fig. 1 can be realized by employing three input ports of a 5$\times$5 MMI coupler. Assuming that the signal and two LO waves are input to the port 2, 3, and 4 of an ideally polarization-independent 5$\times$5 MMI coupler, $a_{n,m}$ and $b_{n,m}$ are expressed as [18]
2.3 Numerical analysis
We now numerically demonstrate the performance of the proposed receiver for several modulation formats. Since our aim is to compare the theoretical limit of the proposed receiver with respect to the conventional DP coherent receiver configuration, we assume ideal PDs with 100$\%$ quantum efficiency and Nyquist-limited receiver bandwidth. The 3$\times$5 MMI coupler is assumed to have ideal properties described by Eqs. (9)–(11), whereas the optical hybrid couplers used in the conventional scheme are also assumed to have ideal characteristics. We also ignore the thermal noises at the TIAs, which is a valid assumption for sufficiently high LO power, as well as the effects of finite linewidth and relative intensity noise (RIN) of the laser. These factors should influence identically for both the proposed and conventional receiver configurations and therefore can be discussed independently to this work, if necessary.
Figure 2 shows the calculated bit-error rate (BER) characteristics of 1550-nm 100-GBd DP coherent signals, received at the shot-noise-limited case [Fig. 2(a)] and the optical-noise-limited case [Fig. 2(b)]. Note that the former corresponds to a case without optical amplifier, whereas the latter corresponds to a case with optical amplifier(s) in the link, whose amplified spontaneous emission (ASE) dominates the receiver sensitivity. In all cases, analytically calculated BER values (solid lines) are confirmed excellently by the Monte-Carlo numerical simulations (circles), where randomly generated noises with Gaussian distribution are added to the signal to derive BER. We can therefore confirm that a DP coherent signal with arbitrary modulation format can be retrieved by the proposed receiver configuration.
Fig. 2. BER of 100-GBd DP signals with different modulation formats received by the proposed (solid lines and circles) and conventional (broken lines) coherent receivers, calculated under (a) the shot-noise-limited case and (b) the ASE-noise-limited case.
From Fig. 2(a), we see that in a shot-noise-limited case, the receiver sensitivity of the proposed scheme is degraded by 3 dB with respect to the conventional coherent receiver. This penalty is attributed to the fundamental nature of the proposed receiver, where a DP signal and LO waves are mixed inside a single interferometer without polarization demultiplexing. Since there is 50$\%$ probability that the signal is orthogonally polarized with respect to the LO wave at each output port of the 3$\times$5 MMI coupler, 1/2 of the received signal power in average is lost without contributing to the signal-LO beat term in Eq. (3), which corresponds indeed to the 3-dB penalty. Nevertheless, since the signal does not need to transmit through a polarization beam splitter and rotator (which would introduce additional insertion losses in practice) before detection, the proposed scheme can still offer an advantage owing to its overall simplicity and compactness. In contrast, for the case of optically amplified link, there is no sensitivity penalty as shown in Fig. 2(b). This is obvious since the 3-dB equivalent loss in our proposed receiver would not degrade the optical signal-to-noise ratio (OSNR) of an optically amplified signal with ASE noise.
3. Experimental demonstration on InP platform
For experimental proof-of-concept demonstration, the passive section of the circuit without the PD array is designed and fabricated on InP. As noted in the previous section, the 3$\times$5 MMI section needs to be designed properly, such that it functions as a uniform coupler for both the TE and TM modes. This condition can be satisfied relatively easily for an InP-based MMI, which generally has a weak polarization dependence [19].
3.1 Device design and fabrication
As shown in Figs. 3(a) and 3(b), we employ a 3$\times$5 MMI coupler based on ridge InP waveguide with a 500-nm-thick InGaAsP core layer, whose bandgap wavelength is 1.37 µm. The MMI width is set to be 20 µm, while the width of the input/output waveguides are tapered to 3 µm before connected to the MMI section with 4-µm pitch. Note that the center three ports (Ports 2, 3, and 4) are used at the input side.
Fig. 3. Designed 3$\times$5 MMI on InP. (a) Top view. (b) Cross-sectional structure. (c) Optimal MMI length for TE and TM modes as a function of the etching depth. (d) Transmission and phase errors from all input ports to all output ports.
Figure 3(c) shows the optimal length $L$ of MMI to achieve ideal 3$\times$5 coupler for the TE and TM modes as a function of the etching depth $h$, derived by the eigenmode expansion (EME) method. We can see that by setting $h = 200$ $\textrm {nm}$ and $L = 701$ µm, polarization-independent coupling is obtained. For this optimized design, Fig. 3(d) shows the transmission and phase error properties from all three input ports to all five output ports for both the TE and TM modes. We can confirm that the excess loss in addition to the inherent -7 dB transmission is below 0.8 dB, whereas the phase error is suppressed within $\pm$2.8 deg over the 1530-1570 nm wavelength range.
On the other hand, to generate orthogonally polarized LO waves by the delayed MZI section as shown in Fig. 1, we employ 2-µm-wide single-mode ridge waveguide with a uniform etching depth of $h = 200$ $\textrm {nm}$. Using the effective refractive index difference between the TE and TM modes, the length difference $\Delta L$ is derived to be 75 µm. We should note that unlike the effective refractive index itself, its polarization dependence $\Delta n_\textrm {eff}$ is far less sensitive to various fabrication errors and environmental changes since the TE and TM modes exhibit nearly parallel dispersion curves against various parameter changes. For example, even if the wavelength width has a large deviation from 1.8 to 2.2 µm, the error in phase difference between the TE and TM modes after propagating 75 µm is calculated to be smaller than $\pm$5 deg.
The designed device was fabricated by the electron-beam lithography, followed by the lift-off of 20-nm-thick Cr hard mask. The Cr pattern was then transferred to an SiO$_2$ layer through CHF$_3$/Ar-based reactive-ion etching (RIE). Using the SiO$_2$ layer as a hard mask, the InP and InGaAsP layers were etched by inductively coupled plasma reactive-ion etching (ICP-RIE) based on CH$_4$/H$_2$ gas mixture, combined with the cyclic O$_2$ ashing process. Figure 4 shows the micrograph and the scanning-electron microscope (SEM) images of the fabricated device.
Fig. 4. (a) Top photograph of the fabricated device and SEM images at (b) the input waveguide cross-section and (c) at the 3$\times$5 MMI output.
3.2 Static characterization
First, we characterize the 3$\times$5 MMI coupler and the delayed MZI section by sending a broadband TE- or TM-polarized light from an erbium-doped fiber amplifier (EDFA) to the input LO port of the chip and observing the output spectrum by using an optical spectrum analyzer. Following the procedure demonstrated in [20], we can characterize phase properties at each output port of the 3$\times$5 MMI.
Figure 5(a) shows the measured transmission spectra at the five output ports when a TE or TM mode light is input to the LO port. For both polarization modes, uniform transmission with a constant 2$\pi$/5 phase offset is obtained among the five ports, in agreement with the ideal case described by Eqs. (9)–(11). In addition, we can see that the TE and TM modes are out of phase. This result indicates that the phase difference between the two LO waves at the 3$\times$5 MMI input is offset by $\pi$ for the TE and TM modes after propagating $\Delta L$, in agreement with the design.
Fig. 5. Static characterization of the fabricated device on InP. (a) Measured transmission spectra at each output port when a TE or TM mode light is input to the LO port. (b) Measured SOPs on the Poincaré sphere at each output port when a lightwave with $S_1=0$ at 1550-nm wavelength is input to the LO port. Note that the rotation around the $S_1$ axis at the output waveguides are calibrated.
Next, we input a lightwave with $S_1=0$ at 1550-nm wavelength to the LO port and observe its SOP at the outputs from the 3$\times$5 MMI. Figure 5(b) shows the measured SOP at the five ports. As we can expect from the results in Fig. 5(a), the SOPs are uniformly distributed to form a regular pentagon on a Poincaré sphere, which corresponds to the ideal case discussed in Section 2. By using these LO waves for the homodyne detection, therefore, we can project the input DP coherent signal to five different states, so that complete information of the signal can be retrieved.
3.3 DP-QPSK experiment
Finally, we investigate the feasibility of receiving DP coherent signal using the experimental setup shown in Fig. 6. Due to the limitation of the equipment as well as large coupling losses between the InP chip and the fiber arrays, the baudrate was limited to 2 GBd in this experiment. Higher-speed operation should be possible in future by inserting spot-size converters (SSCs) and integrating PDs on the same chip to minimize the insertion loss. We should also note that while a single laser source was used in this experiment due to the lack of equipment, an independent narrow-linewidth laser could be used for LO at the receiver side in practice, as in standard coherent systems.
Fig. 6. Experiment of 2-GBd DP-QPSK signal detection using the fabricated device. (a) Setup. (b) Retrieved signals. Note that the signals from five PDs are measured independently in this experiment for convenience, but in practice, four TIAs and ADCs could be used as shown in Fig. 1(a).
A LiNbO$_3$ IQ modulator was driven by two tributaries from a 2-channel arbitrary waveform generator (AWG) to generate an optical QPSK signal. To perform polarization multiplexing, the signal was split into two branches, decorrelated by a fiber delay line, and combined by a polarization beam combiner (PBC). After amplified by an EDFA, the signal was launched to the fabricated device under test (DUT). On the other hand, the SOP of the LO was aligned to $S_1=0$ at the DUT input by using a polarization controller (PC). Fiber arrays were employed to couple the signal and LO to the DUT, and also to couple light out from all five ports of the DUT simultaneously. The launched powers to the DUT were 11 dBm and 7 dBm for LO and signal, respectively. Due to the lack of SSCs on the InP chip and residual fluctuation ($\sim$ 1 µm) of the waveguide position at the fiber arrays, the fiber-to-chip coupling loss was as large as 15 dB/facet. Including the 7 dB intrinsic loss (due to 3$\times$5 MMI coupler) and 3-dB excess on-chip loss, the total fiber-to-fiber loss was around 40 dB.
The output lightwaves from the five ports were amplified by EDFAs and detected by off-chip single-ended PDs, which were independently connected to two real-time oscilloscopes, running synchronously at 5 GS/s. Through offline DSP, we first compensated for the optical delays caused by the different length of EDFAs, down-sampled the signals at 4 GS/s, and then equalized them using real-valued 5$\times$4 multi-input multi-output (MIMO) half-symbol-spaced adaptive finite-impulse-response (FIR) filters. As the adaptive algorithm, we employed the decision-driven least-mean-square (DD-LMS) algorithm, which was modified based on [21,22] to remove phase noise and simultaneously apply the 5$\times$4 matrix multiplication described in Eq. (8). Therefore, the effects of laser phase drift and various linear impairments, such as the polarization mixing and group velocity dispersion inside the transmission fiber, could be automatically calibrated, similar to the conventional coherent systems.
Figure 6(b) shows the retrieved 2-GBd DP QPSK signal using the fabricated device. The error vector magnitudes (EVM) are 20.4$\%$ and 19.5$\%$ for the $x$ and $y$ polarization components, respectively. We can confirm that both polarization components are indeed retrieved by using the proposed receiver with only single interferometer. Due to the large fiber-to-fiber loss of the device, the output powers from the DUT are as low as -29 dBm and -33 dBm for the LO and signal, respectively. As a result, the sensitivity in this case is severely limited by the thermal noise of the oscilloscopes. In addition, due to a port-to-port variation ($\sim$ 3 dB) of the coupling losses at the output fiber array, the signal powers detected at the five PDs are not perfectly balanced, which should be the major cause of the residual skew observed in the signal constellation [Fig. 6(b)]. Therefore, by integrating the PDs and reducing the fiber-to-chip input coupling loss via spot-size converters, we expect to have better sensitivity with less skew and achieve higher-speed operation.
We should also note that we have employed five independent signals as the DSP input in this work to ensure flexibility in the experiment. In practice, we could use four differential TIAs and ADCs as shown in Fig. 1(a), so that the numbers of TIAs and ADCs are the same and the complexity of DSP should also be similar to those of a conventional DP coherent receiver.
4. Conclusion
We have proposed and demonstrated an integrated PSR-free DP coherent receiver circuit for low-cost short-reach applications. Based on a novel concept of using a single MMI coupler to mix DP signals with LO waves at five different SOPs, in-phase and quadrature signals on the both polarization modes can be retrieved through DSP without polarization demultiplexing in the optical domain. Compared with the conventional DP coherent receiver, the total number of PDs is also reduced from eight to five in the proposed scheme, while the numbers of TIAs and ADCs are unchanged. The signal-signal and LO-LO beat noises are eliminated through differential detection.
From a rigorous analysis, we demonstrated error-free detection of 100-GBd DP QPSK, 16QAM, and 64QAM signals. A proof-of-concept device was then designed and fabricated on InP, which was used to experimentally demonstrate complete retrieval of DP-QPSK signals. Although the baudrate was limited to 2 GBd in this work due to the large coupling losses and limitation of experimental equipment, the device should operate at higher speed by reducing the overall losses with SSCs and integrated PDs. To the best of our knowledge, this is the first experimental demonstration of PSR-free DP coherent receiver in any photonic integration platform. While the proposed device is especially attractive for the InP-based coherent receivers due to its compact footprint with a minimal number of optical components and ease of fabrication requiring only a single-etching step, the concept should also be applicable to other platforms as well, such as thick SOI platforms, where the integration of high-performance PSR is challenging.
Funding
New Energy and Industrial Technology Development Organization.
Disclosures
The authors declare no conflicts of interest.
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