Polarization-insensitive silicon intensity modulator with a maximum speed of 224 Gb/s

Zanyun Zhang; Beiju Huang; Qixin Wang; Zilong Chen; Ke Li; Kaixin Zhang; Meixin Li; Hao Jiang; Jiaming Xing; Tianjun Liu; Xiaoqing Lv; Graham T. Reed

doi:10.1364/PRJ.538823

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Abstract

Polarization-insensitive optical modulators allow an external laser to be remotely interconnected by single-mode optical fibers while avoiding polarization controllers, which would be convenient and cost-effective for co-packaged optics, 5G, and future 6G applications. In this article, a polarization-insensitive silicon intensity modulator is proposed and experimentally demonstrated based on two-dimensional centrally symmetric gratings, featuring a low polarization-dependent loss of 0.15 dB in minimum and polarization insensitivity of eye diagrams. The device exhibits a low fiber-to-fiber insertion loss of 9 dB and an electro-optic (EO) bandwidth of 49.8 GHz. A modulation speed of up to 224 Gb/s is also demonstrated.

1. INTRODUCTION

Integrated electro-optic (EO) modulators are crucial in modern communication networks, as they potentially offer higher EO bandwidth and modulation stability than directly modulated lasers. Among devices based on various material platforms [1 –6], silicon-based EO modulators [7] have shown distinct advantages in terms of device footprint, manufacturing cost, and the capability to be integrated with microelectronic circuits. Driven by the constant increase in the data traffic bandwidth, tremendous efforts have been made toward realizing modulators to move data faster and more energy efficiently using the commonly deployed carrier-depletion-based modulation mechanism, in assist of microring cavities [8 –14] or Mach–Zehnder interferometers [15 –17]. Despite the enormous success in the performance evolution of silicon optical modulators, the drawback of polarization sensitivity, originating from the birefringence of silicon submicrometer waveguides, remains the last hurdle to overcome. Polarization-insensitive silicon optical modulators allow optical transceiver chips to be remotely connected to a high-power external laser using only single-mode fibers (SMFs), which would be convenient, reliable, and cost-effective for 5G, future 6G, chip-scale optical interconnect, and microwave photonic applications. Under such circumstances, the external remote laser can be placed in a thermally stable environment to maintain its performance, and the thermal issues for the laser and application-specific integrated circuit (ASIC) or optical transceiver chip become completely separated. Moreover, polarization control or polarization-maintaining fibers can be avoided in the optical link, thus reducing the system’s complexity and cost.

To achieve polarization-insensitive optical modulation, several trial designs have been proposed using different methodologies. By adopting a thick waveguide structure or a specially designed junction shape [18,19], the polarization dependence of optical modulation can be alleviated but at the expense of performance degradation and poor integration compatibility with other devices. Ge/GeSi electroabsorption modulators [20,21] are mature and polarization insensitive; however, they cannot operate in the O-band, which is mainstream for datacom and telecom transceivers. Polarization-insensitive modulators have also been proposed based on the heterogeneous integration of new materials such as polymers [22], graphene [23], gallium [24], indium tin oxide [25], and diffused lithium niobate [26]. However, few of them have been experimentally demonstrated, and high-speed data transmission has not been reported thus far. Another method to achieve this goal is to use a polarization diversity scheme [27 –31]. A polarization-independent silicon reflective MZM [32] and a microring modulator [33] have been demonstrated using a polarization diversity optical interface and a bidirectional transmission scheme based on the silicon-on-insulator (SOI) platform. However, these devices are not intensity modulators, and circulators are necessary in real applications. Notably, many works utilize 2D grating couplers to achieve a dual-polarization transmitter [34,35]. However, they are aiming to realize polarization multiplexing rather than polarization-insensitive operation, as two orthogonal polarizations are modulated independently and polarization combining is not used at the output end. More recently, a polarization-insensitive EO intensity modulator based on thin-film lithium niobate [36] was proposed and experimentally demonstrated. To achieve low polarization-dependent loss (PDL), edge couplers and polarization splitter-rotators (PSRs) are utilized. By driving two MZMs simultaneously with the same signal electrode, a respectable PDL of 0.35 dB is achieved, and very stable PAM4 eye diagrams are obtained for random polarizations. However, such a device is not complementary metal oxide semiconductor (CMOS)-compatible, thus limiting its production, yield, and capability to be integrated with other waveguide devices and electronic circuits.

In this paper, we report for the first time, to our knowledge, the experimental demonstration of a polarization-insensitive silicon optical intensity modulator that can operate at a speed up to 112 Gbaud PAM4, based on an SOI substrate with a 220 nm thick silicon overlayer. The devices exhibit superior static performance, including a fiber-to-fiber insertion loss (IL) of 9 dB, a PDL of 0.15 dB as a minimum, and a modulation efficiency of $1.5 V \cdot cm$ . The EO bandwidth of the modulator reaches 49.8 GHz as the maximum with a bias voltage of 5 V, and up to 224 Gb/s PAM4 modulation is achieved. The polarization insensitivity of the device is also fully investigated for both static and dynamic performance. Despite the nice results obtained, it is more exciting to see there is still much room for improvement in device performance and footprint. We believe this overall integration method of a polarization-insensitive silicon optical intensity modulator can be a good reference for the silicon photonic community. Also, this device concept can be potentially extended to other material platforms, such as thin-film lithium niobate or EO polymers.

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2. DEVICE CONCEPT AND PRINCIPLE

For the design of polarization-insensitive silicon-based optical modulators, polarization-insensitive optical coupling and optical modulation have to be achieved simultaneously. The tricky problem lies in how to make the total device structure be seen as identical optically for two orthogonal polarizations in fiber, considering the unavoidable birefringence of silicon submicrometer waveguides. Here, we present a device concept using an integrated design of optical coupling and optical modulation with a symmetric structure for two orthogonal polarizations. The proposed polarization-insensitive silicon optical intensity modulator is schematically shown in Fig. 1(a). The key component of this device is a four-port 2D grating coupler designed for perfectly vertical coupling. When the fiber is perfectly aligned in the grating center, the 2D gratings function as a PSR, as well as a 3 dB power splitter for two orthogonal polarization components ( $p$ polarization and $s$ polarization) due to the structural symmetry. Thus, two parallel MZ interferometers (MZIs) are formed with the back-to-back configuration of the 2D gratings. With the assistance of two waveguide crossings, single-drive push–pull phase shifters can be embedded in the two MZIs and connected in parallel with GSG-pattern electrodes [Fig. 1(c)]. Thus, the two MZI modulators can be driven by the same electrical signal, and the modulated optical signal can be coupled by the 2D gratings after optical interference and polarization combination. Compared to the conventional MZMs, our device is capable of operating with two orthogonal polarizations simultaneously and the overall optical transmission and modulation are independent of the input polarization state in theory.

$Polarization-insensitive silicon optical modulator based on two-dimensional gratings. (a) Schematic diagram of the polarization-insensitive silicon optical modulator. (b) Schematic diagram of the 2D grating coupler. (c) Schematic diagram of the cross-sectional view of the phase shifter. (d) Simulated near-field optical intensity profile of the grating diffraction mode with light incident from the four access waveguides. (e) Simulated far-field optical intensity profile of the grating diffraction mode. (f) Simulated microwave mode profile of the CPW electrodes for a frequency of 40 GHz. (g) Calculated coupling efficiency (CE), upward backreflection (Rub), and waveguide backreflection (Rwb) of the optimized grating coupler design. (h) Calculated EO S21 of the modulator as a function of frequency and applied bias voltage.$

Figure 1.Polarization-insensitive silicon optical modulator based on two-dimensional gratings. (a) Schematic diagram of the polarization-insensitive silicon optical modulator. (b) Schematic diagram of the 2D grating coupler. (c) Schematic diagram of the cross-sectional view of the phase shifter. (d) Simulated near-field optical intensity profile of the grating diffraction mode with light incident from the four access waveguides. (e) Simulated far-field optical intensity profile of the grating diffraction mode. (f) Simulated microwave mode profile of the CPW electrodes for a frequency of 40 GHz. (g) Calculated coupling efficiency (CE), upward backreflection ( $R_{u b}$ ), and waveguide backreflection ( $R_{w b}$ ) of the optimized grating coupler design. (h) Calculated EO $S_{21}$ of the modulator as a function of frequency and applied bias voltage.

The polarization-independent operation of this device can be theoretically proven based on a transfer matrix approach. An arbitrary input polarization state in the SMF can be denoted with the following normalized Jones vector: ${\vec{α}}_{pol_I} = (\begin{matrix} a_{1} e^{j φ_{1}} \\ a_{2} e^{j φ_{2}} \end{matrix}) = (\begin{matrix} \sqrt{a} \\ \sqrt{1 - a} e^{j Δ φ} \end{matrix}); Δ φ = φ_{1} - φ_{2},$ (1)where the power splitting ratio between the $p$ polarization and $s$ polarization is assumed as $a$ and $1 - a$ , respectively. $Δ φ$ is the phase difference between the two polarization modes. Thus, an arbitrary polarization state can be only determined by the two parameters of $a$ and $Δ φ$ .

The 2D grating coupler couples the input light and converts it into the TE mode of four access waveguides. If the four waveguides are labeled as port1, port2, port3, and port4 from top to bottom, the state vector after grating diffraction can be expressed as follows: ${\vec{α}}_{grat_I} = (\begin{matrix} \begin{matrix} \sqrt{\frac{η (1 - a)}{2}} e^{j (Δ φ + φ^{'})} \\ \sqrt{\frac{η \cdot a}{2}} e^{j φ^{'}} \end{matrix} \\ \begin{matrix} \sqrt{\frac{η (1 - a)}{2}} e^{j (Δ φ + φ^{'})} \\ \sqrt{\frac{η \cdot a}{2}} e^{j φ^{'}} \end{matrix} \end{matrix}) = \sqrt{η} e^{j φ^{'}} (\begin{matrix} \begin{matrix} \sqrt{\frac{1 - a}{2}} e^{j Δ φ} \\ \sqrt{\frac{a}{2}} \end{matrix} \\ \begin{matrix} \sqrt{\frac{1 - a}{2}} e^{j Δ φ} \\ \sqrt{\frac{a}{2}} \end{matrix} \end{matrix}),$ (2)where $η$ is the coupling efficiency (CE) of the grating coupler, which should be the same for two polarizations due to the structure symmetry and perfectly vertical coupling scheme of the 2D grating couplers (GCs). The scaling factor of 1/2 in the square root represents the perfect 3 dB splitting ratio of the grating when the fiber is placed right in the middle of the GC. $φ^{'}$ is the common phase shift introduced by the grating coupler. Due to the central symmetry of the grating, $φ^{'}$ should be the same for all the waveguide ports. By extracting the terms with global parameters of $η$ and $φ^{'}$ , the optical state vector can be expressed as the right of the equation.

The output light from the input grating coupler is injected into four tapered waveguides and then single-mode waveguides for low-loss transmission. Slightly different, the light in port1 and port4 enters the phase shifter area (PSA) directly after a length of single-mode transmission while the light in port2 and port3 will pass through an additional waveguide crossing before entering the PSA. Assuming the effective optical length between the grating and the PSA is $L$ for port1 and port4, and $L^{'}$ for port2 and port3, the state vector of the four waveguide ports at the entrance of the PSA can be described as follows: ${\vec{α}}_{w g_I} = \sqrt{η} e^{j φ^{'}} (\begin{matrix} \begin{matrix} \sqrt{\frac{1 - a}{2}} e^{j (Δ φ + ω \frac{L}{c})} \\ \sqrt{\frac{1 - a}{2}} e^{j (Δ φ + ω \frac{L^{'}}{c})} \end{matrix} \\ \begin{matrix} \sqrt{\frac{a}{2}} e^{j ω \frac{L^{'}}{c}} \\ \sqrt{\frac{a}{2}} e^{j ω \frac{L}{c}} \end{matrix} \end{matrix}),$ (3)where $ω$ is the angular frequency of the injected light, and $c$ is the light speed in vacuum. The components of port2 and port3 exchange due to the existence of waveguide crossing. As the phase shifters are in single-drive push–pull scheme, the transfer matrix of the PSA can be expressed as $\bar{T_{PS}} = (\begin{matrix} e^{j φ_{a}} & 0 & 0 & 0 \\ 0 & e^{j φ_{b}} & 0 & 0 \\ 0 & 0 & e^{j φ_{b}} & 0 \\ 0 & 0 & 0 & e^{j φ_{a}} \end{matrix}),$ (4)where $φ_{a}$ and $φ_{b}$ correspond to the phase change in two waveguides introduced by the modulation signal respectively. Here, the optical loss due to free carrier absorption is disregarded. Consequently, the state vector following modulation is expressed as ${\vec{α}}_{w g_O} = \bar{T_{PS}} \cdot {\vec{α}}_{w g_I} = \sqrt{η} e^{j φ^{'}} (\begin{matrix} \sqrt{\frac{1 - a}{2}} e^{j (Δ φ + ω \frac{L}{c} + φ_{a})} \\ \sqrt{\frac{1 - a}{2}} e^{j (Δ φ + ω \frac{L^{'}}{c} + φ_{b})} \\ \sqrt{\frac{a}{2}} e^{j (ω \frac{L^{'}}{c} + φ_{b})} \\ \sqrt{\frac{a}{2}} e^{j (ω \frac{L}{c} + φ_{a})} \end{matrix}) .$ (5)

The state vector arriving at the output grating interface can be expressed as ${\vec{α}}_{grat_O} = \sqrt{η} e^{j φ^{'}} (\begin{matrix} \sqrt{\frac{1 - a}{2}} e^{j (Δ φ + ω \frac{2 L}{c} + φ_{a})} \\ \sqrt{\frac{a}{2}} e^{j (ω \frac{2 L^{'}}{c} + φ_{b})} \\ \sqrt{\frac{1 - a}{2}} e^{j (Δ φ + ω \frac{2 L^{'}}{c} + φ_{b})} \\ \sqrt{\frac{a}{2}} e^{j (ω \frac{2 L}{c} + φ_{a})} \end{matrix}) .$ (6)

After the grating diffraction process, the light in four access waveguides is converted into an arbitrary polarized light by the optical interference and polarization combination. Considering the global phase shift $φ^{'}$ and coupling efficiency $η$ introduced by the output gratings, the Jones vector of the out-of-plane coupled light can be expressed as ${\vec{α}}_{pol_O} = η e^{2 j φ^{'}} (\begin{matrix} \sqrt{\frac{1 - a}{2}} e^{j Δ φ} (e^{j (ω \frac{2 L}{c} + φ_{a})} + e^{j (ω \frac{2 L^{'}}{c} + φ_{b})}) \\ \sqrt{\frac{a}{2}} (e^{j (ω \frac{2 L^{'}}{c} + φ_{b})} + e^{j (ω \frac{2 L}{c} + φ_{a})}) \end{matrix}),$ (7)which can be further simplified as ${\vec{α}}_{pol_O} = η \sqrt{(1 + \cos Δ φ^{'})} e^{2 j φ^{'} + φ_{0}} (\begin{matrix} \sqrt{1 - a} \cdot e^{j Δ φ} \\ \sqrt{a} \end{matrix}),$ (8)where $Δ φ^{'} = \frac{2 ω}{c} (L - L^{'}) + (φ_{a} - φ_{b}) a n d φ_{0} = \frac{ω}{c} (L + L^{'}) + \frac{(φ_{a} + φ_{b})}{2}$ .

Thus, the normalized output power of a photodiode detecting this signal is $T_{out} = ⟨ {\vec{α}}_{pol_O}^{*} \cdot {\vec{α}}_{pol_O} ⟩ = \frac{1}{2} η^{2} (1 + \cos Δ φ^{'}) .$ (9)

It can be seen that the modulated optical power is independent of the input polarization state, $a$ and $Δ φ$ .

3. DEVICE DESIGN AND FABRICATION

The devices were fabricated on a 200 mm SOI wafer with a 220 nm top silicon layer using commercially available silicon photonic active device technology with a feature size of 130 nm and copper interconnects. The chip manufacturing followed a standard process flow that included DUV-193 nm scanner lithography, inductively coupled plasma etching, ion implantation, plasma-enhanced chemical vapor deposition, and metallization. Figure 2(a) shows a microscope image of the fabricated optical modulator chip, consisting of two 2D GCs functioning as input and output optical interfaces and a 2.5 mm long phase shifter along with GSG-pattern traveling wave electrodes. Figures 2(b) and 2(c) show scanning electron microscopy (SEM) images of the optical interface before and after removal of the oxide cladding, respectively. For efficient fiber–chip coupling, dielectric material stack thinning was utilized to open GCs, shown as a circular hole with a depth of approximately 5 μm and a diameter of 125 μm. To reduce the device footprint, parabolic adiabatic tapers were designed and utilized, with an IL of 0.09 dB at the optimized length of only 110 μm. Figure 2(d) shows an SEM image of the 2D GCs, which are crucial components of the device. To achieve polarization-independent optical coupling, rectangular scatters are designed as centrally symmetric and well fit for perfectly vertical coupling conditions at a central wavelength of 1310 nm. As the optical reflection at the fiber–grating interface contributes to the return loss, which affects the optical power stability, the GCs must be optimized for high efficiency and low backreflection. Thus, grating apodization for near-perfect mode matching efficiency [37,38] is key in the design procedure. Figures 1(d) and 1(e) show the simulated near-field and far-field optical intensity profiles of the grating diffraction mode of the optimized grating for waveguide incidence, which show a similar pattern to the mode profile of the single-mode fiber. The performance of the optimized design is shown in Fig. 1(g). The simulated CE is $- 1.49 dB$ (71%) at peak wavelength and the minimum upward backreflection ( $R_{u b}$ ) and waveguide backreflection ( $R_{w b}$ ) obtained from mode expansion monitors are about $- 22$ and $- 17.5 dB$ , respectively. Two waveguide crossings [Fig. 2(e)] are employed to make two pairs of “coherent” waveguide arms neighboring each other [Fig. 2(f)] to form single-drive push–pull phase shifters [39 –42]. To ensure power balance in the MZMs, the waveguide crossings should feature low loss and low crosstalk. Additionally, the optical phase change induced by the waveguide crossings needs to be calculated and compensated for considering phase matching. Our design utilizes a spline interpolation function to define the shape of the waveguide crossings. The optimized device, with a footprint of $9 μm \times 9 μm$ , features a measured IL of 0.08 dB in average and a crosstalk of approximately $- 50 dB$ . The EO phase shifter [Fig. 2(g)], consisting of two single-drive push–pull phase shifters connected in parallel by sharing the same GSG-pattern traveling wave electrodes, is another critical part of the modulator. Figure 2(h) shows an SEM image of the cross-section of the rib waveguide in the phase shifter, designed with a width of 380 nm and a 70 nm thick partially etched rib area for carrier doping and metal contact. The P-type and N-type doping concentrations are $3.7 \times 10^{17} {cm}^{- 3}$ and $6 \times 10^{17} {cm}^{- 3}$ , respectively. The doping concentration of the medium doped region ( $P +, N +$ ) and the heavily doped region ( $P + +, N + +$ ) are $4 \times 10^{18} {cm}^{- 3}$ and $1 \times 10^{20} {cm}^{- 3}$ , respectively. This integration architecture offers two distinct advantages. First, the load capacitance can be effectively reduced compared to that of a conventional phase shifter design. This is a very important issue for this type of modulator because the total capacitance would be doubled due to the parallel connection of two identical phase shifters. The simulation results indicate that the capacitance per unit length is reduced by 0.1 fF/μm (approximately 30%) compared to a conventional phase shifter with the same doping design. The reduction in capacitance leads to a lower microwave loss and a higher EO bandwidth. Second, the characteristic impedance of the traveling wave electrode can be designed close to $50 Ω$ , which is a standard value for commercially available RF probes, cables, and microwave amplifiers. Figure 1(f) shows the simulation results of the microwave mode profile of the CPW electrodes for a frequency of 40 GHz. To achieve a large EO bandwidth, the capacitance-loaded traveling wave electrodes were optimized to fulfill impedance matching, as well as velocity matching between the microwave and optical signals. With a given thickness of 500 nm, the signal electrode width and the gap between the signal and ground electrodes were designed as 30 μm and 14 μm, respectively. On-chip resistors (N-type heavily doped silicon region) are integrated at the end of the CPW electrode to form a terminator of $50 Ω$ . By modeling the device at the circuit-level, the EO bandwidth of the modulator can be predicted. Figure 1(h) shows the calculated EO $S_{21}$ parameter of the optimized modulator design as a function of frequency, applied voltage, and terminator resistance. The EO bandwidth increases drastically with the applied voltage due to reduced P-N capacitance and increased characteristic impedance. The calculated EO bandwidth reaches 46 GHz under a bias voltage of 5 V and terminator resistance of $50 Ω$ . By introducing an impedance mismatch at the CPW termination, the bandwidth can be further improved to 52 and 61 GHz with a terminator resistance of 40 and $30 Ω$ , respectively. However, this will lead to a larger microwave reflection and power consumption [43]. Also, pursuing the bandwidth limit is not the main focus of our proof-of-concept device.

Figure 2.(a) Microscope image of the fabricated polarization-insensitive silicon optical modulator. (b) SEM image of the optical fiber interface with an oxide cladding showing the opening for grating couplers. (c) SEM image of the optical fiber interface after oxide cladding removal showing the grating coupler, taper waveguides, and waveguide crossing. (d) Zoomed-in SEM image of the O-band 2D grating coupler. (e) SEM image of the optical waveguide crossing. (f) SEM image of the transition between channel waveguides and rib waveguides of the phase shifter. (g) SEM image of the cross-section of the whole phase shifter. (h) Zoomed-in SEM image of the rib waveguides in the phase shifter.

4. STATIC PERFORMANCE CHARACTERIZATION

The static performance of the fabricated device was first investigated using the experimental setup built with an O-band tunable laser (Keysight N7776C), a polarization synthesizer (Keysight N7786C), and an optical multiport power meter (Keysight N7745C). The grating coupling loss and PDL were first characterized using a back-to-back configuration of the 2D gratings with balanced waveguide arms. Figure 3(a) shows the measured fiber-to-fiber IL and PDL of the test device, depicted in the inset microscope image. Given perfect phase matching, the fiber-to-fiber IL should be the sum of twice the grating coupling loss and waveguide transmission loss. By normalizing the waveguide transmission loss and taper waveguide loss, the grating coupling loss is estimated to be no more than 3.6 dB/facet. The measured Fabry–Perot (FP) ripple [shown in the inset of Fig. 3(a)] is approximately 0.4 dB on average, which corresponds to a backreflection of approximately $- 16 dB$ . The PDL is as low as 0.15 dB at the peak coupling wavelength of 1298 nm and is below 1 dB across the wavelength range from 1280 to 1320 nm, showing the superior polarization-insensitive behavior of optical coupling. Figure 3(b) shows the measured fiber-to-fiber IL and PDL of the proposed optical modulator. The total IL of the device is 9 dB in the static condition, including 3 dB for the phase shifter, 0.38 dB contributed by the tapered waveguides and waveguide crossings, and the remaining 5.62 dB corresponding to the grating coupling loss of the two facets. This result indicates an overestimation of the grating coupling loss previously, which is possibly due to the incomplete constructive interference in a “balance-arm-designed” MZI. As an arm’s length difference of 93.66 μm is introduced, an interference pattern with a free spectral range (FSR) of approximately 4.3 nm is clearly shown, and the notch depth around the coupling central wavelength exceeds 20 dB at maximum, indicating nearly perfect 3 dB power splitting/combining by the 2D GCs. The static extinction ratio (ER) can be further improved using a finer lithography process and thermal control for phase error compensation. The measured PDL is more sensitive to wavelength variations when compared to a balanced-arm device, showing a maximum PDL around the notch wavelengths and minimum PDL around peak transmission wavelengths. Considering the optical power is very low at the dip wavelengths, a relatively sensitive behavior to polarization variations is not hard to understand. However, it is exciting to see that the floor of the PDL curve is quite low and flat, which means a polarization-insensitive optical transmission of the device. As the working wavelength for modulation will be chosen far away from the notch wavelengths, a very low PDL can be maintained for the proposed modulator. The zoomed-in PDL curve of a single FSR in Fig. 3(b) shows that the PDL near the peak wavelengths closely aligns with a mean value of 0.15 dB, matching the minimum PDL of the balanced-arm device. To highlight the performance advantage of the proposed device, a standard Mach–Zehnder modulator, fabricated in the same chip with identical doping design, phase shifter length, and arm length difference, was also measured in terms of fiber-to-fiber IL and PDL for comparison. As shown in Fig. 3(c), the fiber-to-fiber IL is about 13 dB including the coupling loss of two focusing grating couplers provided as a foundry PDK device, while the PDL is larger than 30 dB at all wavelengths. One may see some strange spikes in the measured PDL, which may be due to sampling errors in the measurement and should be neglected. Figure 3(d) shows the measured optical spectral response of the proposed optical modulator with an applied voltage from 0 V to a half-wave voltage $V_{π}$ of 6 V, corresponding to a modulation efficiency of $1.5 V \cdot cm$ . The fluctuation of the spectra is mainly contributed by the FP resonance in the device and random phase errors induced by the fabrication imperfections of the grating scatters and waveguides. The polarization dependence of EO modulation is a very important issue for the proposed modulator. Figures 3(e) and 3(f) show the measured static ER of the modulator for different input states of polarization (SOPs) under a bias voltage of 4 V and zoomed-in view at the short span of central coupling wavelengths. Using the polarization synthesizer, two orthogonal linear polarizations and two circular SOPs, defined by Stokes parameters, were chosen for static ER comparison. The ER spectra corresponding to different SOPs almost overlap with each other, indicating superior polarization insensitivity of the static EO modulation. This also agrees well with the circuit-level simulation results of the EO modulator, which is obtained using Interconnect in the Ansys Lumerical software package.

Figure 3.Static performance characterization results. (a) Measured fiber-to-fiber IL and PDL of a back-to-back configuration of the O-band 2D GCs with balanced waveguide arms. (b) Measured fiber-to-fiber IL and PDL of the proposed modulator. (c) Measured fiber-to-fiber IL and PDL of a standard Mach–Zehnder modulator. (d) Measured fiber-to-fiber optical transmission spectra of the proposed modulator with different applied voltages ranging from 0 to 6 V. (e) Static ER with respect to wavelength under different incident SOPs. (f) Zoomed-in view of the static ER under different incident SOPs at the short span of central coupling wavelengths.

5. DYNAMIC PERFORMANCE CHARACTERIZATION

The dynamic performance of the proposed device was investigated using the experimental setup shown in Fig. 4(a), where the test branches for EO bandwidth, eye diagrams, and bit error rate (BER) are combined. The small-signal EO bandwidth ( $S_{21}$ parameter) of the fabricated device was first characterized. With externally applied voltages as DC bias, a 67 GHz VNA (Keysight N4373E) coordinating with an LCA (Keysight N5247B) is used for small-signal performance characterization. The high-frequency small electrical signal is fed into the modulator with a 67 GHz bandwidth RF probe of GSG pattern. The modulated optical signal is pre-amplified by an optical fiber amplifier (OFA) and fed into the LCA for high-frequency electrical-optical conversion. Figure 4(b) shows the measured EO $S_{21}$ of the modulator under different bias voltages, with the incident polarization setting as 45° linear. The EO bandwidth drastically increases with the bias voltage due to the reduction in the junction capacitance and the impedance mismatch-induced peaking effect. With a DC bias voltage of 5 V, the measured EO bandwidth at the quadrature point reaches 47.8 GHz. The shallow ripples on the EO $S_{21}$ curve may be attributed to microwave reflections and optical intensity fluctuations during the measurement. To investigate the polarization insensitivity, the EO $S_{21}$ under different incident polarizations was measured for comparison, as shown in Fig. 4(c). With a bias voltage of 5 V, the measured EO bandwidths are 47.8, 49.8, 46, and 42.5 GHz for 45° linear, 135° linear, left-handed circular, and right-handed circular polarizations, respectively. The differences may be attributed to polarization variation-induced spectral shifts, fabrication imperfections, and random measurement errors, which are all inevitable in the measurement. Overall, the device shows superior polarization insensitivity of the EO bandwidth. In addition, the microwave reflection ( $S_{11}$ parameter) is below $- 12 dB$ at all frequencies, and the extracted characteristic impedances along the device show good impedance matching between the electrode and the microwave source.

Figure 4.Dynamic performance characterization. (a) Experimental setup of the dynamic performance measurement. TL, tunable laser; PC, polarization controller; AWG, arbitrary waveform generator; OFA, optical fiber amplifier; LCA, lightwave component analyzer; VNA, vector network analyzer; DCA, digital communication analyzer. (b) EO bandwidth ( $S_{21}$ parameter) of the optical modulator under different bias voltages for an incident polarization of 45° linear. (c) EO bandwidth ( $S_{21}$ parameter) of the optical modulator under different incident polarizations with a bias voltage of 5 V.

A large-signal data transmission experiment was carried out to test the modulation speed limit of the modulator. An arbitrary waveform generator (AWG, Keysight M8199B) with a maximum baud rate of 224 Gbaud was used to generate high-speed pseudorandom binary sequence (PRBS) electrical signals. A 55 GHz broadband microwave amplifier (SHF807) was employed to boost the driving swing to about $3.5 V_{pp}$ . Then, the amplified driving signal was fed into a 67 GHz RF probe with a GSG pattern to drive the modulator. To compensate for the on-chip optical loss, an O-band OFA is used for post-chip amplification with an output power of 5 dBm. Finally, the amplified modulated optical signal is sent to a digital communication analyzer (DCA, Keysight N1000A) with an optical head of 120 GHz bandwidth for the eye diagram test. For the best eye diagram quality, the working wavelength and DC bias condition were carefully chosen. Figures 5(a)–5(d) show the selected eye diagrams measured at baud rates of 72, 90, 100, and 112 Gbaud for OOK modulations, where both the original eyes without any equalization and eye diagrams enabled by five-tap FFE are shown with the measured results of average optical power, ER, and signal-to-noise ratio (SNR). For improved eye quality, averaging was used to counter the random noise introduced by the internal-chip reflections and from the OFA. As can be seen, the originally obtained extinction ratios for 72, 90, 100, and 112 Gbaud OOK modulations are 3.719, 3.102, 2.873, and 2.325 dB, respectively, showing a clear roll-off of frequency response at the bandwidth limit. Despite that the high baud rate eyes are clearly open, the ERs obtained at the above baud rates can be further increased to 6.405, 4.901, 4.806, and 4.006 dB with five-tap FFE enabled, and open eye diagrams up to 150 Gbaud OOK can be achieved. We then further explore the speed limit of the device using the PAM4 modulation scheme with a baud rate scanned from 56 to 112 Gbaud. At a low baud rate, the open eye diagrams can be obtained with FFE disabled in the DCA. When the baud rate is approaching 90 Gbaud, the original eyes are almost closed due to the rapid deterioration of SNR. Thus, FFE with a higher tap count of 32 is utilized for clear open eyes at 100 and 112 Gbaud, which is shown in Figs. 5(e) and 5(f). Under the symbol error rate (SER) level of $1 \times 10^{- 3}$ , the TDECQs obtained are 1.66 and 3.1 dB for 100 and 112 Gbaud PAM4 eye diagrams, respectively. The back-to-back (B2B) BER was also estimated using the jitter mode analysis in the DCA with a PRBS pattern length of $2^{11} - 1$ . The BERs calculated are at a level of $1 \times 10^{- 2}$ and $5 \times 10^{- 2}$ for 100 and 112 Gbaud PAM4 signals, respectively, which are better than or quite close to the soft-decision forward error correction limit (SD-FEC: $2 \times 10^{- 2}$ ). Such device performance is quite promising for 200 Gb/s-per-lane applications with high-performance DSP closely integrated.

Figure 5.(a)–(d) Selected eye diagrams for OOK modulation at 72, 90, 100, and 112 Gbaud, with the original eyes and eyes enabled by five-tap FFE shown for comparison. (e), (f) Selected eye diagrams for 100 and 112 Gbaud PAM4 modulation enabled by 32-tap FFE.

The polarization insensitivity of dynamic eye diagrams was also analyzed and demonstrated using this proposed device. In assist of the polarization synthesizer, the input polarization state can be tuned, and eye diagram changes can be observed. As a sample of the experiment, eight different states of polarization (SOPs) are selected for eye diagram tests and polarization sensitivity analyses. Figure 6(a) shows the eight SOPs examined on the Poincaré sphere and the corresponding ellipse representations, including six fixed polarizations (0°, 45°, 90°, and 135° linear, left-handed circular, and right-handed circular) and two random polarizations defined by Stokes parameters [SOP1: (0.57, $- 0.54$ , 0.62) and SOP2: (0.34, 0.52, 0.78)]. To show the polarization insensitivity of high-speed modulation, 100 Gbaud OOK modulation is utilized for the experiment. To avoid the effect of the random noise, we choose to observe the eye diagrams with five-tap equalization enabled. Figure 6(b) shows the average optical power, ER, and SNR recorded for the eye diagrams with the eight input SOPs. The average power with a variation of only 0.59 dBm shows the superior PDL of the device during high-speed operation, while the slightly changed ER and SNR enable the eyes to open with high quality for all the input SOPs. This experimental demonstration coincides with the simulation results and the measured static performance and EO bandwidth results. The dynamic ER variations can be attributed to the device structure asymmetry induced by fabrication imperfections of the gratings, waveguides, p-n doping regions, and metal electrodes and the measurement uncertainty induced by fiber vibration and optical intensity fluctuations. Due to the unbalanced-arm design, it is observed that the working point chosen for the modulator would be important for both eye quality and polarization insensitivity. This can be mainly attributed to two factors. First, it is found that the change of input SOP may lead to a slight spectral shift of the modulator, due to fabrication imperfections and phase mismatch between the waveguide arms. Although the shift is quite limited, the effect cannot be ignored and should be wavelength dependent as the measured PDL. Second, although the static ERs obtained are quite stable for different SOPs, the frequency response difference for two push–pull phase shifters, due to the fabrication uniformity of PN dopings and electrodes, can affect the modulation depth in high-speed modulation. This also contributes to the uncertainty of polarization sensitivity at different working wavelengths. Improving the polarization insensitivity further can be achieved by introducing the thermal heaters to all the waveguide arms for phase error correction. A broadband device with a balanced-arm design may also be helpful to decrease the sensitivity to operation point drift. Overall, the device shows a clear advantage of polarization insensitivity over the standard modulator designs while the dynamic performance is at the same level as the state-of-the-art silicon EO modulators.

Figure 6.(a) Eight different input SOPs of 0° linear (L0°), 45° linear (L45°), 90° linear (L90°), 135° linear (L135°), left-handed circular (LCP), right-handed circular (RCP), and two random SOP1 and SOP2 shown on the Poincaré sphere. (b) Average power, ER, and SNR of the 100 Gbaud OOK modulation eye diagrams as a function of input polarization states.

Last, Table 1 compares the performance of this work with the published results in similar topics. This table summarizes only experimentally demonstrated polarization-insensitive EO modulators for fair comparison. It should be highlighted that this is the first demonstration of a polarization-insensitive optical intensity modulator with a modulation speed up to 224 Gb/s PAM4. Thanks to the centrally symmetric 2D grating and perfectly vertical coupling scheme, our device exhibits the smallest PDL while maintaining clear advantages in most performance metrics compared to previously demonstrated polarization-insensitive silicon-based EO modulators. Compared to the thin-film lithium niobate device, our device achieves a similar EO bandwidth but with a significantly smaller footprint, superior modulation efficiency, and a higher maximum bitrate.Table 1.

Comparison of Key Performance Metrics for Experimentally Demonstrated Polarization-Insensitive EO Modulators^a

Reference	Platform and Type	$V_{π} L_{π} (V \cdot cm)$	PDL (dB)	IL (dB)	Speed (Gb/s)	BW at $V_{b}$	Footprint^b
[19]	SOI (MZM)	11	2.3	15^c	40 (OOK)	27 GHz at –3 V	1.35 mm
[20]	Ge/SiGe (MQW)	N.A.	3.5	37.5^c	N.A.	8.8 GHz	900 μm
[33]	SOI (MRM)	N.A.	N.A.	5.5^c	22.8 (QPSK)	$< 10$ GHz at –2 V	$\sim 200 μm$
[36]	TFLN (MZM)	6.2	0.35	2^c	100 (PAM4)	50 GHz	20 mm
This work	SOI (MZM)	1.5	0.15	3.38^c	224 (PAM4)	49.8 GHz at –5 V	2.5 mm
This work	SOI (MZM)	1.5	0.15	9^d	224 (PAM4)	49.8 GHz at –5 V	2.5 mm

BW, 3 dB EO bandwidth; PDL, polarization-dependent loss; IL, insertion loss.

Defined as the modulation length for MZM-type and EAM-type devices, and the maximum length in two dimensions of the device for MRM-based device.

On-chip insertion loss excluding the fiber-chip coupling loss.

Fiber-to-fiber insertion loss.

6. DISCUSSION

As presented above, the fabricated modulator exhibits superior polarization insensitivity of EO modulation in both static and dynamic measurements while maintaining a performance (IL, $V_{π} L_{π}$ , EO bandwidth, modulation speed) comparable to that of state-of-the-art conventional silicon Mach–Zehnder modulators [15,44 –46]. This shows great promise for the application of such devices in future optical interconnects or optical modules. As a proof-of-concept, it is important to note that the device’s performance can be enhanced in various ways. Given that the fabrication imperfections can be minimized, the polarization insensitivity can be further improved both in terms of the PDL and eye diagram sensitivity to polarization variations. The optical reflections at the grating interfaces may be problematic. These can be alleviated by using a polysilicon grating overlay [47 –49] structure or an optimized grating scatter shape obtained by an inverse-design methodology [50] while utilizing an index matching oil in the coupling or packaging process. Additionally, thermal tuning is not applied or used in our device, which can compensate for the random phase errors induced by fabrication imperfections and is thus beneficial to the dynamic range for optical interference. If a thermal tuning function is added to the device, then the optical phase balancing in different arms and the modulation efficiency can be improved. This type of EO modulator may be slightly bulky for intra-chip or inter-chip applications. However, microcavities [51,52] or slow-light waveguides [53,54] can be incorporated into the structure to reduce the device footprint to tens or hundreds of micrometers, and a higher EO bandwidth can be expected. Although polarization-insensitive operation can also be realized by using the edge couplers and on-chip polarization splitter and rotators following a similar design concept, it should be highlighted that the proposed modulator, benefitting from its surface-normal optical interfaces, can be very suitable for interfacing with multicore fibers (MCFs) [55]. By utilizing highly compact mode converters [56,57], the length of tapered waveguides can be effectively cut to 5 or 10 μm while maintaining an acceptable transmission efficiency, which may enable a two-dimensional array integration of the optical interfaces with a standard seven-core MCF of 35 μm pitch. Thus, a terabit polarization-insensitive optical transmitter may be possible by using a single optical cable, which would be very promising for the application of next-generation optical modules, active optical cables, etc.

Acknowledgment

Acknowledgment. The authors would like to thank Dr. Huan Zhang and Dr. Fenghe Yang for the help during the chip sample preparation for SEM measurement. We would like to thank the Analytical and Testing Centre of Tiangong University for SEM measurement.

Author Contributions.Z. Z. contributed to the conceptualization, guidance of the overall project, and manuscript preparation; B. H. contributed to the funding acquisition, fruitful discussions, and manuscript revision; Q. W., Z. C., and K. Z. contributed to the device design, simulation, and device measurement; K. L. contributed to the technical guidance and fruitful discussions during the device measurement and manuscript preparation; M. L., H. J., J. X., and T. L. contributed to the device layout design and device performance characterization; X. L. contributed to the device characterization and fruitful discussions; and G. T. R. contributed to the supervision of the initial work at University of Southampton, valuable comments, and fruitful discussions of this follow-up work.

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