1. INTRODUCTION

Rapid spread of cloud computing, high-vision video streaming, and 5G mobile services has led to a steady increase in information traffic in datacenter interconnects and access networks [1]. While intensity-modulation–direct-detection (IMDD) formats such as four-level pulse amplitude modulation (PAM4) are employed in the current short-reach optical links, scaling these IMDD-based transceivers beyond Tb/s is challenging due to the limited spectral efficiency and severe signal distortion caused by the chromatic dispersion of fibers. On the other hand, the digital coherent systems used in metro and long-haul networks can easily expand the capacity by utilizing the full four-dimensional signal space of light and complete compensation of linear impairments through digital signal processing (DSP). However, substantially higher cost, complexity, and power consumption of coherent transceivers have hindered their deployment in short-reach optical interconnects and access networks.

To address these issues, the self-coherent transmission scheme has emerged as a promising approach that bridges the gap between conventional IMDD and coherent systems [2–7]. In this scheme, a continuous-wave (CW) tone is transmitted together with a high-capacity coherent signal, which are mixed at a direct-detection-based receiver to recover the complex optical field of the signal. Unlike fully coherent systems, this scheme eliminates the need for a local oscillator (LO) laser at the receiver side as well as the stringent requirement of using wavelength-tuned narrow-linewidth laser sources, suggesting that substantially lower-cost broad-linewidth uncooled lasers can be used [4]. In addition, since the impacts of laser phase noise and frequency offsets are mitigated, the computational cost of DSP can be reduced significantly [7,8]. Self-coherent systems thus enable low-cost, low-power-consumption, yet high-capacity data transmission, required in future datacenter interconnects and access networks.

 

Fig. 1. Surface-normal SVR based on superimposed meta-atom arrays. (a) Schematic illustration of the receiver module. A single metasurface device implements all the necessary passive optical components of the equivalent circuit as shown in the inset. MS, metasurface; PDA, photodetector array; IC, integrated circuit; HWP, half-wave plate; QWP, quarter-wave plate; PBS, polarization beam splitter. (b) Scalable configuration to receive multiple input channels from a MCF or fiber bundle. (c) Functionality and configuration of the designed metasurface. The incident light from the SMF is split into three paths and focused to six PDs located at different positions according to the input state of polarization. The superimposed meta-atom arrays (MA1, 2, and 3) operate as PBSs and metalenses for $x/y$ linear, $\pm {45}^\circ$ linear, and RHC/LHC polarization bases, respectively.

Download Full Size | PDF

Among several variations of implementing self-coherent systems, the polarimetric scheme using a Stokes-vector receiver (SVR) [9–11] has an advantage in terms of simplicity. In this scheme, the coherent signal is transmitted on a single polarization state, together with a CW tone on the orthogonal polarization state. By retrieving the Stokes parameters ${\bf S} = [{{S_1},{S_2},{S_3}}]$ at the receiver side, the in-phase-and-quadrature (IQ) signal is demodulated through the DSP after compensating for the effects of polarization rotation, chromatic dispersion, and other signal distortions. To date, a number of high-speed polarimetric self-coherent transmission experiments have been reported, employing SVRs implemented with off-the-shelf discrete components [3,10–12]. Toward practical use, integrated waveguide-based SVRs were also realized on Si [13,14] and InP [15–18]. More recently, surface-normal SVRs were demonstrated using nanophotonic circuits [19,20] and liquid crystal gratings [21] with external photodetectors (PDs). Compared to conventional low-cost IMDD receivers, however, these devices still suffer from a large fiber-to-chip coupling loss and/or need for external lenses to focus light to PDs. Thus, it is crucial to develop ultracompact SVRs that can directly couple high-speed optical signals from input fibers to PDs.

In this paper, we demonstrate high-speed polarimetric self-coherent signal detection using a compact surface-normal SVR, composed of a metasurface-based polarization-sorting device and a high-speed two-dimensional PD array (2D-PDA). A metasurface is a 2D array of subwavelength structures that can locally change the intensity, phase, and polarization of input light [22]. Unlike previous works on metasurface-based polarimeters for imaging and sensing applications [23–29], our device is specially tailored for a high-speed SVR that enables direct coupling of self-coherent optical signals from a single-mode fiber (SMF) and lens-less focusing to six high-speed PDs. More specifically, by superimposing three types of meta-atom arrays, it implements the functionalities of all the necessary passive components, namely a ${1} \times {3}$ splitter, three polarization beam splitters (PBSs) with different polarization bases, and six lenses, inside a single ultrathin device. Combined with an InP/InGaAs-based 2D-PDA chip, we demonstrate penalty-free transmission of polarimetric self-coherent signals over a 25-km SMF in various formats such as 20-GBd 16-ary quadrature amplitude modulation (16QAM) and 50-GBd quadrature phase-shift keying (QPSK). Owing to the surface-normal configuration with the embedded focusing functionality, highly efficient lens-free coupling to the 2D-PDA is achieved. The demonstrated SVR, therefore, has comparable complexity as a conventional low-cost IMDD receiver that fits in a compact receiver optical subassembly (ROSA). Moreover, it can readily be extended to receive spatially multiplexed channels from a multicore fiber (MCF) or a fiber bundle, which are expected in future ${\gt}{\text{Tb}}/\text{s}$ highly parallelized optical interconnects [30–33].

2. DEVICE CONCEPT

The schematic of the proposed surface-normal SVR is illustrated in Fig. 1(a). The light from a SMF is incident to a thin metasurface-based polarization-sorting device, which is designed to provide the same functionality as a conventional polarimeter shown in the inset. Namely, it splits the light into three paths, resolves each of them to the orthogonal components in three different polarization bases, and focuses them to six PDs integrated on a 2D-PDA chip. Unlike previously demonstrated metasurface-based polarimeters [23–29], our metasurface implements the ${1} \times {3}$ splitter and six metalenses as well in one region to enable direct coupling from a SMF to a high-speed 2D-PDA. As a result, the entire device can fit inside a compact ROSA module, comparable to the current IMDD receivers. Moreover, owing to the surface-normal configuration, this scheme can easily be scaled to receive multiple spatial channels without increasing the number of components by simply replacing the input SMF to a MCF or a fiber bundle and using a larger-scale PDA [34] as shown in Fig. 1(b).

To enable three operations in parallel using a single metasurface layer, we adopt the spatial multiplexing method [35–37]; three independently designed meta-atom arrays are superimposed as shown by MA1 (red), MA2 (blue), and MA3 (green) in Fig. 1(c). The phase profile $\varphi ({x,y})$ of MA1 is designed to focus the $x$-polarized component of light to ${{\text{PD}}_x}$ and the $y$-polarized component to ${{\text{PD}}_y}$ at the focal plane as shown in the inset. Similarly, MA2 and MA3 function as PBSs with embedded metalenses for the $\pm {45}^\circ$ polarization basis (${a}/{b}$) and the right/left-handed circular (RHC/LHC) polarization basis (${r}/{l}$), respectively, and focus respective components to ${{\text{PD}}_{a,b}}$ and ${{\text{PD}}_{r,l}}$. The Stokes vector ${\bf S} \equiv {({{S_1},{S_2},{S_3}})^T}$ can then be derived by taking the difference of the photocurrent signals as ${S_1} = {I_{x}} - {I_{y}}$, ${S_2} = {I_{a}} - {I_{b}}$, and ${S_3} = {I_{r}} - {I_{l}}$, where ${I_{ p}}$ is the photocurrent at ${{\text{PD}}_p}$. We should note that this scheme with three balanced PDs without polarizers offers the maximum receiver sensitivity among various SVR configurations [38] and is advantageous compared with previous demonstrations that employ a non-optimal polarization basis [19–21].

3. METASURFACE DESIGN AND FABRICATION

As the dielectric metasurface, we employ 1050-nm-high elliptical Si nanoposts on a quartz layer. The phase of the transmitted light and its polarization dependence can be controlled by changing the lengths of two principal axes $({{D_u},\;{D_v}})$ and the in-plane rotation angle $\theta$ of each nanopost (meta-atom) as defined in Fig. 2(a) [22]. Here, in each meta-atom array, MA1-3, we adopt the triangular lattice with a sub-wavelength lattice constant of ${\Lambda} = 700\sqrt 3\;{\text{nm}}$, so that non-zeroth-order diffraction is prohibited. Then, three meta-atom arrays are superimposed by shifting their positions by $a = 700\;{\text{nm}}$ to form the overall metasurface, as shown in Fig. 1(c).

 

Fig. 2. Meta-atom design. (a) Schematic of a periodic array of Si nanoposts placed at the vertices of a triangular lattice with a lattice constant $a$ of 700 nm. The transmission of $x$- and $y$-polarized light is simulated for various axis lengths $({{D_u},\;{D_v}})$ of the elliptical posts. (b) Required $({{D_u},\;{D_v}})$ to obtain phase shifts $({{\varphi _u},\;{\varphi _v}})$ for $x$- and $y$-polarized light. For ease of fabrication, the ranges of ${D_u}$ and ${D_v}$ are limited from 100 to 650 nm. (c) Amplitude of transmittance for each case in (b) as a function of $({{\varphi _u},\;{\varphi _v}})$.

Download Full Size | PDF

First, we set $\theta$ to 0 and simulate the transmission characteristics of a uniform nanopost array for $x$- and $y$-polarized light at a wavelength of 1550 nm by the rigorous coupled-wave analysis (RCWA) method [39]. From the simulated results, we first derive ${t_u}({{D_u},\;{D_v}})$ and ${t_v}({{D_u},\;{D_v}})$, which denote the complex transmittance for $x$- and $y$-polarized light as a function of ${D_u}$ and ${D_v}$, respectively. Then, we derive the required $({{D_u},\;{D_v}})$ that provides a phase shift of (${\varphi _u},\;{\varphi _v}$) for each polarization component. The results are plotted in Fig. 2(b) (see Section S1 of Supplement 1 for details). The amplitude of transmittance for each case is also shown in Fig. 2(c). We can confirm that by setting the dimensions of the ellipse appropriately, arbitrary phase shifts for $x$- and $y$-polarized components can be achieved with high transmittance.

By rotating the elliptical nanoposts by $\theta$ as shown in Fig. 2(a), such birefringence can be applied to any linear polarization basis oriented at an arbitrary angle [40]. We should note that the phase shifts and amplitudes of transmission are nearly insensitive to $\theta$ [22], and similar results as shown in Figs. 2(b) and 2(c) are obtained for all $\theta$ (see Section S2 of Supplement 1 for investigations about insensitivity to $\theta$). This is because the light is strongly confined inside each Si nanopost, so that the optical coupling among neighboring meta-atoms has only a minor influence on the transmission.

We can also provide arbitrary phase shifts to orthogonal circular-polarization states by using the geometric phase shift of meta-atoms [41]. First, we judiciously select ${D_u}$ and ${D_v}$ to satisfy ${\varphi _v} = {\varphi _u} + \pi$, so that each nanopost operates as a half-wave plate (HWP). In this case, input RHC and LHC states are converted to LHC and RHC, respectively. In addition, their phases after transmission are written as $({{\varphi _r},\;{\varphi _l}}) = ({{\varphi _u} + 2\theta ,{\varphi _u} - 2\theta})$ (see Section S3 of Supplement 1 for the derivation). Therefore, ${D_u}$ and ${D_v}$ of each nanopost are selected to obtain desired ${\varphi _u}$ ($=({{\varphi _r} + {\varphi _l}})/2$) while satisfying the condition ${\varphi _{v}} = {\varphi _u} + \pi$. The angle $\theta$ is also determined to be $({{\varphi _r} - {\varphi _l}})/4$.

To realize the function of a metalens, each meta-atom array needs to impart a spatially dependent phase profile given as [42]

 

Fig. 3. Metasurface design and fabrication. (a) Required phase profiles for MA1, 2, and 3. (b) Two-dimensional histograms of meta-atom dimensions ${D_u}$ and ${D_v}$ for MA1, 2, and 3 used in our designed metasurface. (c) Optical microscope image and (d), (e) SEM images of the fabricated device. In (e), the image is false-colored to distinguish MA1, 2, and 3.

Download Full Size | PDF

Figure 3(b) shows the 2D histograms illustrating the distributions of the meta-atom dimensions (${D_u}$, ${D_v}$) employed for MA1, 2, and 3 in our designed metasurface. We can confirm that MA1 and MA2 exhibit nearly identical distributions across the entire range. On the other hand, only a limited range of meta-atom dimensions are employed in MA3 because each meta-atom must satisfy the HWP condition (${\varphi _v} = {\varphi _u} + \pi$). The average transmittance for the selected meta-atoms is calculated to be more than 92% from the RCWA results shown in Fig. 2(c).

Note that a rather large (2 mm) metasurface is used in this work due to the limitation in reducing the focal length $f$ in the current optical setup. In a fully packaged module as shown in Fig. 1(a), we can readily shrink the entire area of the metasurface to a few tens of micrometers by reducing $f$ and designing the geometrical parameters of each nanopost to satisfy the required phase profiles given by Eq. (1). Hence, unlike other surface-normal high-speed SVRs in the literature that require additional lenses [19–21], our receiver can be fit inside compact dimensions in a few millimeters or less.

The designed metasurface was fabricated using a silicon-on-quartz (SOQ) substrate with a 1050-nm-thick Si layer. The nanopost patterns were defined by electron-beam lithography with ZEP520A resist. Then, the patterns were transferred to the Si layer by inductively coupled plasma reactive-ion etching (ICP-RIE) using ${\text{SF}_6},\;{\text{C}_4}{\text{F}_8}$, and ${\text{O}_2}$. An optical microscope image and scanning electron microscopy (SEM) images of the fabricated metasurface are shown in Figs. 3(c)–3(e).

4. STATIC CHARACTERIZATION OF THE FABRICATED METASURFACE

We first characterized the fabricated metasurface by observing the intensity distribution at the focal plane for various input states of polarization (SOPs). The experimental setup is shown in Fig. 4(a). A CW light with a wavelength of 1550 nm was incident to the metasurface. The SOP was modified by rotating a HWP and quarter-wave plate (QWP). The image at the focal plane was magnified at 50 times by a 4-f lens system and captured by an InGaAs camera. From the detected intensity values at the six focal positions, the Stokes vector was retrieved as described in Section 2. To enable quantitative measurement of the focused power, we inserted a flip mirror and detected the total power by a bucket PD after spatially filtering the focused beam at each target position using an iris.

 

Fig. 4. Experimental characterization of the fabricated metasurface at 1550-nm wavelength. (a) Schematic of the optical setup. The flip mirror is used to switch between capturing the intensity distribution at the focal plane and measuring the power of each focused beam. TLS, tunable laser source; PC, polarization controller; VOA, variable optical attenuator; FC, fiber collimator; Pol., polarizer; HWP, half-wave plate; QWP, quarter-wave plate; MS, metasurface; M, flip mirror; PD, photodetector. (b) Measured intensity distributions at the focal plane (top) and optical power at the six focused spots normalized to each polarization basis (bottom) for different input SOPs. (c) Retrieved and input Stokes vectors on the Poincaré sphere. (d) Measured (bars) and simulated (stars) focusing efficiencies to respective PDs. The intrinsic loss due to splitting into three paths is shown by a green line. The input polarization is labeled on the top of each bar.

Download Full Size | PDF

Figure 4(b) shows the observed intensity distributions when the input Stokes vector is set to ($\pm 1$, 0, 0), (0, $\pm 1$, 0), and (${0},\;{0},\;\pm {1}$). We can confirm that the incident light is focused to the six well-defined points by transmitting through the metasurface. Moreover, its intensity distribution changes with the SOP; $x/y$ linear, ${\pm}{45}\deg$ linear, and RHC/LHC components of light are focused to the designed positions. The full-width-at-half-maximum (FWHM) of each focused spot is measured to be around 9.5 µm. For clarity, we also plot in Fig. 4(b) the measured power at the six focused spots normalized to the respective polarization basis in each case. As expected theoretically, the highest power is observed at the correct PD position, whereas that at the orthogonal polarization PD position is suppressed, and those at the other four PDs are exactly half of the peak power. We can therefore retrieve the Stokes vector by taking the power difference between the paired spots as described in Fig. 1(c).

Figure 4(c) shows the retrieved Stokes vectors on the Poincaré sphere. The average error $| {{\Delta}{\bf S}} |$ is as small as 0.028. Figure 4(d) shows the absolute focusing efficiencies to all six spots measured under the corresponding input SOP. Similar efficiencies are obtained over a broad wavelength range from 1500 to 1600 nm by the 3D full-wave simulation (see Section S4 of Supplement 1 for details). Subtracting the 4.8-dB (i.e., 33%) intrinsic loss due to the ${1} \times {3}$ splitter [see Fig. 1(a)], the measured excess loss is around 6.1 dB (i.e., efficiency of around 25%), whereas the measured cross talk to the orthogonal PD position is suppressed by 13–20 dB. While this excess loss is already comparable to the coupling and propagation losses of the previously reported waveguide-based SVRs [13–18], it is slightly larger than those of other metasurfaces demonstrated for different applications [22]. One possible reason for this degradation is the imperfect design scheme employed in our work, where three different meta-atom arrays are simply superimposed without considering the complex interactions among each other. This issue should be mitigated by adopting more advanced algorithms that take into account nonzero interactions between adjacent meta-atoms [43,44]. In addition, further improvement in performance is expected by applying anti-reflection coating at the silica surface and optimizing the fabrication processes to minimize errors.

5. SELF-COHERENT SIGNAL TRANSMISSION EXPERIMENT

We then performed a polarimetric self-coherent signal transmission experiment using the fabricated metasurface. The experimental setup is shown in Fig. 5. We employed a 19-pixel 2D-PDA with InP/InGaAs-based p–i–n structure [45], from which six PDs were used as shown in Fig. 5(b). Each PD had a diameter of 30 µm, measured bandwidth above 10 GHz, and responsivity of 0.3 A/W. Since the detection areas of PDs as well as their separation (60 µm) were sufficiently larger than the measured FWHM of the focused spot (9.5 µm), the aperture loss and cross talk were negligible. The 2D-PDA chip was packaged with the radio-frequency (RF) coaxial connectors connected to each PD. The 2D-PDA was placed at the focal distance of 10 mm from the metasurface as shown in Fig. 5(c). This distance was merely limited by the current setup and should be reduced to a sub-millimeter scale in a practical fully packaged module, which can be comparable to current IMDD receiver modules.

 

Fig. 5. Self-coherent transmission experiment using the fabricated metasurface and 2D-PDA. (a) Experimental setup. AWG, arbitrary waveform generator; PBC, polarization beam combiner; EDFA, erbium-doped fiber amplifier; OBPF, optical bandpass filter; Osc, oscilloscope. In the insets, three-B-PD and four-S-PD configurations are depicted. (b) Optical microscope image of the fabricated 19-pixel 2D-PDA. The six circled PDs were used in this experiment. (c) Photograph of the receiver.

Download Full Size | PDF

 

Fig. 6. Experimental results of self-coherent signal transmission at a wavelength of 1550 nm. (a)–(c) Measured BER curves and constellation diagrams of 15-GBd 16QAM signals before (back-to-back) and after 25-km transmission using the three-B-PD configuration. (d)–(f) Measured BER curves and constellation diagrams of 20-GBd 16QAM and 50-GBd QPSK signals after 25-km transmission using the four-S-PD configuration.

Download Full Size | PDF

A CW light at a wavelength of 1550 nm was generated from a tunable laser source (TLS) and split into two ports, which served as the signal and the pilot tone ports. At the signal port, a ${{\text{LiNbO}}_3}$ IQ modulator was used to generate a high-speed coherent optical signal. The Nyquist filter was applied to the driving electrical signals from an arbitrary waveform generator (AWG). The modulated optical signal was then combined with the pilot tone by a polarization beam combiner (PBC). The optical power of the pilot tone was adjusted by a variable optical attenuator (VOA), so that their powers were nearly balanced. The self-coherent signal was then transmitted over a 25-km SMF. Evaluations for the back-to-back case (without 25-km SMF) were also performed for comparison. At the receiver side, the optical signal-to-noise ratio (OSNR) was controlled using another VOA, followed by an erbium-doped fiber amplifier (EDFA) and an optical bandpass filter (OBPF). The six light waves focused by the metasurface were detected by the six PDs on the 2D-PDA simultaneously. The electrical signals from the six PDs of the PDA were amplified by differential RF amplifiers and then captured by a real-time oscilloscope (OSC). At a baudrate beyond 20 GBd, we could not use the balanced PD (B-PD) configuration due to the residual skew inside the PDA module. In these cases, we employed four single-ended PDs (S-PDs), where the electrical signals from ${{\text{PD}}_x},\;{{\text{PD}}_y},\;{{\text{PD}}_a}$, and ${{\text{PD}}_l}$ were independently captured by a four-channel real-time OSC, so that the skew could be calibrated during DSP. In this configuration, all four Stokes parameters can be retrieved by a simple matrix multiplication process (see Section S5 of Supplement 1 for details). By comparing the results using two configurations, the use of four S-PDs was validated (see Section S6 of Supplement 1 for details). To equalize and reconstruct the original IQ signal, we employed offline DSP with the ${2} \times {3}$ and ${2} \times {4}$ real-valued multi-input–multi-output (MIMO) equalizers [46,47] for three-B-PD and four-S-PD configurations, respectively.

 

Fig. 7. Experimental results of self-coherent signal transmission at wavelengths of (a) 1540 nm and (b) 1565 nm. (a), (b) Measured BER curves of 15-GBd 16QAM signals before (back-to-back) and after 25-km transmission using the three-B-PD configuration. The insets represent the retrieved constellation diagrams.

Download Full Size | PDF

Figures 6(a)–6(c) show the bit-error rate (BER) curves and the constellations for 15-GBd 16QAM signals, measured using the three-B-PD configuration. Figures 6(d)–6(f) show the results for 20-GBd 16QAM and 50-GBd QPSK signals, measured by the four-S-PD configuration. We can confirm that BERs well below the hard-decision forward error correction (HD-FEC) threshold are obtained in all cases. Since the self-coherent system allows retrieval of a fully complex optical field, all linear impairments caused by chromatic and polarization-mode dispersions are removed perfectly through DSP [3], resulting in negligible penalty even after 25-km SMF transmission. Finally, Fig. 7 shows the measured BER curves and constellation diagrams of 15-GBd 16QAM signal at 1540-nm and 1565-nm wavelengths, demonstrating the wideband operation of our designed metasurface. Although the metasurface has sufficiently broadband characteristics over the entire $C$ band (see Section S4 of Supplement 1 for the simulated wavelength dependence of our metasurface), the baudrate in this work was limited by the bandwidth of the 2D-PDA. Therefore, beyond-100-GBd transmission should be possible by using higher-speed surface-normal PDs with 3-dB bandwidth exceeding 50 GHz [48,49].

6. CONCLUSION

We have proposed and demonstrated a surface-normal SVR using a dielectric metasurface and 2D-PDA for high-speed polarimetric self-coherent systems. Three independently designed meta-atom arrays based on Si nanoposts were superimposed onto a single thin metasurface layer to implement both the polarization-sorting and focusing functions simultaneously. Using a compact metasurface chip fabricated on a SOQ substrate, we demonstrated 25-km transmission of 20-GBd 16QAM and 50-GBd QPSK self-coherent signals. The operating baudrate was merely limited by the 2D-PDA, so that higher-capacity transmission should be possible by using a PDA with a broader bandwidth. Owing to the unique surface-normal configuration with the embedded lens array functionality, a compact receiver module with size and complexity comparable to conventional IMDD receivers can be realized. Moreover, it can easily be extended to receive spatially multiplexed channels by simply replacing input SMF to MCF and employing larger-scale integrated PDA technology [34]. This work would, therefore, pave the way toward realizing cost-effective receivers for ${\text{future}}\; \gt \!{\text{Tb}}/\text{s}$ spatially multiplexed optical interconnects.