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Abstract
An integrated Stokes vector receiver (SVR) that can retrieve state of polarization of light in the three-dimensional (3D) Stokes space has widespread applications, such as short-reach communication links, polarization-sensitive imaging, and sensing. While various approaches have been demonstrated to date, monolithic integration of polarization components on InP has been a challenging issue. In this paper, we develop a novel 4-port SVR circuit integrated on a compact InP chip to retrieve complete Stokes parameters of incoming light with various intensity and degree-of-polarization. By judiciously designing the lengths and positions of asymmetric waveguide sections, we demonstrate that the SV of signal can be projected onto four vertices of a regular tetrahedron inscribed in the Poincaré sphere. Additionally, we employ this device in decoding 10-Gbaud 4-ary and 8-ary Stokes-vector-modulated signals in the 3D Stokes space.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Polarization manipulation and detection are the key fundamental functions for various optical applications, including telecommunication [1–7], quantum key distribution [8–11], RF photonics [12,13], imaging and sensing [14–16]. In the short-reach optical communication links, for example, there is an increasing interest to extend the signal dimension of the current intensity-modulation direct-detection (IM-DD) formats by introducing the polarization degree of freedom. Since optical field recovery is possible in the three-dimensional (3D) Stokes signal space without using costly coherent transceivers [6], such Stokes-vector modulation direct-detection (SVM-DD) formats are expected as viable solutions in achieving a single-channel capacity beyond 1 Tb/s in low-cost short-reach links [7].
In these applications, a number of discrete optical components were conventionally used for detecting the state of polarization (SOP). On the other hand, photonic integration offers miniaturization, cost reduction, enhanced stability, and added functionality to these systems [4,8–11,14]. In particular, an InP-based photonic integrated circuit (PIC) provides additional capability of monolithically integrating optical amplifiers and high-speed photodiodes (PDs) with minimal insertion losses to achieve highest receiver sensitivity. Among several types of InP-based Stokes vector receiver (SVR) designs [17–22], relatively simple scheme to retrieve SOP using a single-ended PD array was proposed by the authors [19–22]. Unlike the conventional schemes, it offers a unique advantage that neither a polarization-beam-splitter (PBS) nor precisely tuned optical interferometers are required, which are, despite the significant improvements in the recent years [23–26], still challenging to integrate compactly on InP. Up to date, however, we have only demonstrated devices that use three PDs to retrieve three Stokes parameters (S1, S2, S3), leaving out S0 as known a priori. As a result, we could only retrieve SOP of perfectly polarized light with a constant intensity [20–22].
In this paper, we develop a novel 4-port SVR circuit integrated on a compact InP chip and experimentally demonstrate retrieval of SV signals with arbitrary intensity and degree-of-polarization (DOP). By judiciously designing the lengths and positions of asymmetric waveguide sections, we achieve nearly ideal operation to project the SV of incoming signal onto four vertices of a regular tetrahedron inscribed in the Poincaré sphere. As a result, all four Stokes parameters including S0 are retrieved with a high accuracy, enabling us to measure SV and DOP of depolarized light with varying intensity. In addition, we demonstrate the use of this device in decoding 10-Gbaud 4-ary and 8-ary Stokes-vector-modulated (SVM) signals in the 3D Stokes space.
2. Operating principle of 4-port SVR
Schematic of the demonstrated device is depicted in Fig. 1(a). Here, Sin = [S0, S1, S2, S3]T is the 4 × 1 SV of the input light, where S0, S1, S2, S3 are the four Stokes parameters. A 1 × 4 multimode interference (MMI) splitter is used to split the input light equally into four ports. By transmitting through the Stokes vector converter (SVC) sections, which are attached at respective ports as shown in Fig. 1(a), SV of light is converted into four different states depending on the design of SVC. Finally, the light is detected by a polarization-selective PD (PS-PD), which has higher sensitivity for the transverse-electric (TE) mode than the transverse-magnetic (TM) mode, or vice versa. Such PS-PD can be realized by using a strained multiple-quantum-well (MQW) active layer [22]. As we will describe in the following, all four Stokes parameters of Sin can be calculated by using the photocurrent signals at four PS-PDs.
Fig. 1. (a) Schematic top-view (XZ-plane) of the integrated Stokes vector (SV) receiver on InP. (b) Symmetric waveguide (SW) and (c) asymmetric waveguide (ASW) used in the receiver. The birefringence vector b on the Poincaré sphere is solely determined by the waveguide cross-section as depicted in (b) and (c). (d) Illustrations of 4 basis vectors on the Poincaré sphere.
The SVC in each port consists of a symmetric waveguide (SW) and a half-ridge asymmetric waveguide (ASW) as illustrated in Figs. 1(b) and 1(c), respectively. Generally speaking, as the light propagates inside a birefringent waveguide, its SV rotates about a so-called birefringence vector b in the Stokes space [19,20]. The direction of b is determined by the cross-sectional geometry of the waveguide. In a SW that supports TE and TM eigenmodes, b is oriented along the S1 axis as shown in Fig. 1(b). On the other hand, in an ASW as shown in Fig. 1(c), we can engineer the cross-sectional design of the waveguide, so that the electric fields of the eigenmodes are tilted with respect to the x and y axes. If we define φ as the effective angle of this tilt, the orientation of b is expressed as b ∝ [cos(2φ), sin(2φ), 0]T as illustrated in Fig. 1(c). Therefore, we have a freedom to design a customized trajectory of SV conversion by adjusting the length and location of SW and ASW in each SVC. As a result, combination of PS-PD array and four different SVCs is essentially equivalent to projecting the input SV Sin onto four different basis vectors on the Poincare sphere.
If we define a 4 × 1 vector I = [I1, I2, I3, I4]T to represent the photocurrent signals Ii (i = 1, 2, 3, 4) from the four PDs, ${{\textbf S}_{\textrm{in}}}$ and I are related as
Here, A is a 4 × 4 instrument matrix that depends on the SVCs and expressed asFor convenience of explanation, we define a 3 × 1 basis vector ${{\textbf m}^{(i )}}$ as ${{\textbf m}^{(i )}} \equiv {[{m_{11}^{(i )},\; m_{12}^{(i )},\; m_{13}^{(i )}\; } ]^\textrm{T}}$ and a 3 × 1 SV without the S0 component as ${\textbf S}_{\textrm{in}}^{\prime} \equiv {[{{S_1},\; {S_2},{S_3}} ]^\textrm{T}}$. Then, Eq. (1) and Eq. (2) can be expressed alternatively as
From Eq. (3), we can understand that the photocurrent signals from four PS-PDs indeed represent projection of the input SV in the 3D Stokes space onto four basis vectors defined by ${{\textbf m}^{(i )}}$ (i = 1, 2, 3, 4). The condition to have non-singular ${\textbf A}$ is equivalent to have linearly independent basis vectors ${{\textbf m}^{(i )}}$.While there is a great flexibility in designing SVC sections to make ${\textbf A}$ a non-singular matrix, the highest receiver sensitivity is obtained when the condition number of ${\textbf A}$, which is commonly written as $\kappa ({\textbf A} )$, is minimized [27,28]. For the 4-port SVR, we can theoretically prove that this condition is satisfied when the four basis vectors ${{\textbf m}^{(i )}}$ are located at the vertices of a regular tetrahedron inscribed in the Poincare sphere as depicted in Fig. 1(d). In this case, $\kappa ({\textbf A} )= \sqrt 3 $.
3. Device design and fabrication
In order to locate ${{\textbf m}^{(i )}}$ at the vertices of a regular tetrahedron inscribed in the Poincaré sphere, we propose to employ an identical ASW having φ and a length LASW in ports 2, 3, and 4 as shown in Fig. 1. We set φ to be 27.37°, so that $\cos 4\varphi ={-} 1/3$, and LASW to the half-beat length. Under a such condition, the SV rotates by 180° about b ∝ [cos(2φ), sin(2φ), 0]T inside the AWG as shown in Fig. 1(c), so that the SV component along a vector $({{S_1},\;{S_2},\;{S_3}} )= \left( { - 1/3,\;2\sqrt 2 /3,\;0} \right)$ is converted to a state on the S1 axis through ASW and detected by PS-PD2 at port 2. At port 3 and port 4, the location of ASW is offset by lengths Loff and 2Loff, respectively, where Loff is set to rotate the SV by 120o around the S1-axis on the Poincare sphere. As a result, we can convert three SV components lying on the same plane of ${S_1} ={-} 1/3$, separated by 120o from each other, to (S1, S2, S3) = (1, 0, 0) at port 2, 3, and 4, and subsequently detected by PS-PD2, PS-PD3, and PS-PD4, respectively. Combined with the photocurrent signal from PS-PD1, which detects the S1 component of input light, we can retrieve projection to all four basis vectors on the tetrahedron as shown in Fig. 1(d).
In this work, a passive SVR circuit without PS-PD array was fabricated for proof-of-principle demonstration. In the SVC section, we employed 2-µm-wide ridge waveguide for the SW and 1-µm-wide half-ridge waveguide for the ASW with 500-nm-thick InGaAsP core layer. From a full-vectorial eigenmode analysis, the residual core thickness in the ASW was set to be 280 nm to achieve φ = 27.37°, while LASW and Loff were determined to be 150 µm and 58 µm, respectively, to satisfy the aforementioned conditions. To facilitate the smooth transition of optical mode between SW and ASW, a 15-µm-long tapered waveguide was inserted at their interface. A self-aligned process [29] was adopted to fabricate the ASW sections. Figure 2 shows the micrograph of the entire device as well as cross-sectional scanning-electron microscope (SEM) images at the SW and the ASW sections. The total device footprint is 0.3 × 1.5 mm2.
Fig. 2. (a) Top photograph of the fabricated device and cross-sectional SEM images at (b) SW and (c) ASW sections.
From the results of eigenmode analysis, we numerically estimate that the allowable fabrication errors in the waveguide width and the etching depth at the AWG sections to be 100 nm and 40 nm, respectively, to keep the receiver power penalty below 1 dB from the ideal case. We should note that this relatively small fabrication tolerance results from the fact that we have fixed LASW to the half-beat length for design simplicity in this work, although there are actually numerous choices of LASW and φ to construct a regular tetrahedron. Indeed, we have recently found that it is possible to select LASW and φ to maximize the tolerance, in which case the allowable fabrication errors expand to as large as 220 nm and 120 nm for the waveguide width and etching depth, respectively [27].
4. Experiments
4.1 Setup
The experimental setup is depicted in Fig. 3. We employed two different transmitter configurations to generate input light to the device. For the static measurement (see inset I in Fig. 3), combination of a polarizer (POL), a half-wave plate (HWP), and a quarter-wave plate (QWP) was used to set the SV of input light to a specific state. To investigate the applicability of the device to partially depolarized light, a variable optical attenuator (VOA-1) was inserted before an erbium-doped fiber amplifier (EDFA), so that the degree-of-polarization (DOP) could be varied. Another VOA (VOA-2) was used to adjust the input power to the device. When VOA-1 and VOA-2 are both set to 0 dB, the input signal power to the chip was 6 dBm and the optical signal-to-noise ratio (OSNR) was 29 dB.
Fig. 3. Schematic of the experimental setup. The transmitter for the static and high-speed measurements are shown in inset-I and inset-II, respectively. The resultant constellations of SVM signal at different points (marked as a, b and c) of the high-speed transmitter are shown on the Poincare sphere.
For the dynamic experiment (see inset II in Fig. 3), two polarizer-free lithium niobate phase modulators (LN-PM1 and LN-PM2) were cascaded to generate a high-speed SVM signal [30]. First, continuous-wave (CW) light at 1549-nm wavelength from a laser was incident to LN-PM1 with the polarization state aligned at 45o with respect to the crystal axes of LN-PM1. By driving LN-PM1 using a binary non-return-to-zero (NRZ) signal, two constellations are generated on the S2-S3 plane as shown in Fig. 3 inset II-a. The second polarization controller (PC2) was then used to transform these two polarization states into linearly polarization states on the S1-S2 plane (see inset II-b). Finally, LN-PM2 was driven by a PAM-4 signal to create eight constellations on Poincare sphere (see inset II-b). A dual-polarization coherent receiver (CR) was used to confirm the generated 8-ary SVM signal and to tune two PCs as well as amplitudes and relative skews of NRZ and PAM-4 signals. We should note that such SVM transmitter can potentially be realized on a compact InP chip [19].
In this work, we employed off-chip POLs and PDs, which were coupled to four ports of the device via a fiber array to emulate the integrated PS-PD array. Polarization variations inside the fiber pigtails were carefully calibrated before the measurements. For the high-speed experiment, an EDFA and optical bandpass filter (OBPF) were inserted before each PD. A real-time digital storage oscilloscope (DSO) was employed to capture the waveforms from four PDs, which were then processed off-line to retrieve Sin.
4.2 Static characterizations
First, the matrix ${\textbf A}$ of the actual device was derived by sending light with several known SOPs and measuring the optical power at each port for respective cases. VOA-1 and VOA-2 were set to 0 dB in these measurements. Figure 4(a) shows the measured power at each PD as we rotate the input SV on the S1-S3 plane around S2 axis (ϕ = 0). Similarly, Fig. 4(b) shows the results when the SV is rotated on the S2-S3 plane around S1 axis (ϕ = 90°). The definitions of θ and ϕ are shown in Fig. 4(c). In both cases, we see that the photocurrent is maximized at a different angle for each port, which represents the projection of input SV onto four different basis vectors in the 3D Stokes space. From these results, ${\textbf A}$ and the basis vectors ${{\textbf m}^{(i )}}$ can be calculated. Figure 4(d) shows the derived basis vectors ${{\textbf m}^{(i )}}$ of the actual fabricated device. As designed, we see that ${{\textbf m}^{(i )}}$ constitute four vertices of a nearly perfect tetrahedron in the Stokes space. To quantitate the performance of our device, the condition number of ${\textbf A}$ is calculated to be $\kappa ({\textbf A} )= 1.94$. Compared with the ideal case of perfect tetrahedron, where $\kappa ({\textbf A} )= \sqrt 3 $, our fabricated device exhibits a receiver power penalty of 0.5 dB.
Fig. 4. (a,b) Measured optical power at four ports as the input SV is rotated on S1-S3 plane (ϕ = 0) around S2 axis (a) and on S2-S3 plane (ϕ = 90°) around S1 axis (b). (c) Definitions of θ and ϕ. (d) Basis vectors ${{\textbf m}^{(i )}}$ of the actual fabricated device. We see that ${{\textbf m}^{(i )}}$ constitute vertices of a nearly perfect tetrahedron, as designed.
By using the derived ${\textbf A}$, we can measure SOP of input light with arbitrary power and DOP. Figure 5(a) shows the SV of perfectly polarized light (DOP = 100%) measured as we rotate the input SV around the S1 (blue dots) and S2 (red dots) axes. The inner trajectories represent the results when the input light is attenuated by 3 dB through VOA-2. For clarity, we plot in Fig. 5(b) the input (lines) and retrieved (circles) Stokes parameters for the 3-dB-attenuated case as the input SV is rotated around the S2 axis. We can confirm an excellent agreement between the input and measured Stokes parameters.
Fig. 5. Static measurement of SV for perfectly polarized light (DOP = 100%). (a) Measured SVs plotted in the Stokes space with (inner trajectories) and without (outer trajectories) 3-dB attenuation. (b) Measured Stokes parameters for the 3-dB-attenuated case. The lines and dots represent the input SOP and the SOP retrieved by the device, respectively.
Since all four Stokes parameters including S0 are retrieved, we can measure the DOP and SOP of depolarized light as well. Figures 6(a) and 6(b) show the measured results for a depolarized light with DOP of 70% and 40%, respectively. Here, DOP (pink circles) was calculated from the detected Stokes parameters as $\textrm{DOP} = \sqrt {S_1^2 + S_2^2 + S_3^2} /{S_0}$, while that of the input light (pink solid lines) was derived from the OSNR measured by an optical spectrum analyzer. The DOP was controlled by adjusting VOA-1. From Figs. 6(a) and 6(b), we can confirm excellent agreement between the actual input and retrieved SOPs and DOPs for all cases. These results indicate that all four Stokes parameters including S0 are successfully retrieved.
Fig. 6. Measured Stokes parameters for (a) 70% and (b) 40% DOP. The lines and dots represent the input SOP and the SOP retrieved by the device, respectively.
4.3 High-speed experiments
Finally, we investigated the feasibility of the device to retrieve SV of high-speed 4-ary and 8-ary SVM signals by employing the transmitter configuration described in inset II of Fig. 3. To generate a 4-ary SVM signal, only LN-PM2 was driven by a PAM-4 signal.
Figure 7 shows the results of detecting 20-Gb/s 4-ary SVM signal and 30-Gb/s 8-ary SVM signal, both driven at 10-Gbaud symbol rate. Retrieved SV data for both cases are plotted in Fig. 7(a) and Fig. 7(b). We can observe single and double circular trajectories for the 4-ary and 8-ary signals, respectively, as expected from our transmitter scheme based on the cascaded phase modulators. Figures 7(c) and 7(d) shows the SV data after removing the transient data points, where we see clear distinct constellations on the Poincare sphere. The device should therefore be applicable in detecting high-speed SVM signals in the 3D Stokes space for the future short-reach optical communication links [1–7].
Fig. 7. Retrieved SV for (a) 20-Gbps 4-ary SVM and (b) 30-Gbps 8-ary SVM signals. SV after removing transient points for (c) 20-Gbps 4-ary SVM and (d) 30-Gbps 8-ary SVM signals.
5. Conclusions
We have designed and fabricated an integrated 4-port SVR circuit on InP and demonstrated retrieval of SV in the 3D Stokes space. By judiciously designing the lengths and positions of asymmetric waveguide sections, we achieved nearly ideal arrangement of the basis vectors to project input SV onto the four vertices of a regular tetrahedron inscribed in Poincaré sphere. As a result, all four Stokes parameters including S0 were retrieved, which enabled measurement of SV and DOP of depolarized light as well. Finally, we demonstrated the use of this device in decoding 10-Gbaud 4-ary and 8-ary SVM signals in the 3D Stokes space. With monolithic integration of MQW-based PD array [22], this device can be substantially simpler and more compact than a dual-polarization coherent receiver that requires eight PDs, two optical hybrids, and a number of polarization optics. It should therefore be useful in the future low-cost short-reach optical communication links, as well as other applications, such as sensing, RF photonics, and integrated quantum optics, where on-chip polarization detection is appreciated.
Funding
Japan Society for the Promotion of Science (15H03985, 26000010).
Acknowledgments
Portions of this work were presented at the Optical Fiber Communications Conference in 2019, “4-port integrated Stokes vector receiver circuit for multi-level 3D signal detection and OSNR monitoring,” (paper W3B.6).
Disclosures
The authors declare no conflicts of interest.
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