Inverse Design of Ultra-Compact Polarizer for Integrated Silicon Photonics

Abstract

The integrated waveguide polarizer is essential for photonic integrated circuits, and various designs of waveguide polarizers have been developed. As the demand for dense photonic integration increases rapidly, new strategies to minimize the device size are needed. In this paper, we have inversely designed an integrated transverse electric pass (TEpass) polarizer with a footprint of 2.88 µmx 2.88 µm, which is the smallest footprint ever achieved. A direct binary search algorithm is used to inversely design the device for maximizing the transverse electric (TE) transmission while minimizing transverse magnetic (TM) transmission. Finally, the inversedesigned device provides an average insertion loss of 0.99 dB and an average extinction ratio of 33 dB over a wavelength range of 100 nm.

Keywords

inverse design / optical polarization / subwavelength structure

1 Introduction

On-chip silicon photonics has developed into a mainstream technology driven by advances in optical communications [ 1 - 4 ]. Silicon-on-insulator photonic integrated circuits (PICs) represent a powerful platform that is truly compatible with standard complementary metal-oxide-semiconductor (CMOS) processing. The high refractive index of silicon (~3.45) enables a high contrast relative to the surrounding cladding of a silicon waveguide and exhibits strong confinement of the waveguide polarizations. However, any unwanted

fraction of the cross polarization may lead to performance degradation in PICs [ 5 ]. Thus, polarization-diversity technology is extremely important for on-chip silicon photonics \(\left\lbrack {6,7}\right\rbrack\) . Great efforts have been made in realization of integrated polarization handling devices on the silicon-on-insulator (SOI) platform, including polarization splitters [ 8 - 13 ], rotators [ 14 - 16 ] and polarizers [ 17 - 25 ]. Among them, the polarizer is a basic component utilized in PICs to filter out undesired polarization and reduce polarization crosstalk. Polarizers based on silicon hybrid plas-monic waveguides can achieve high extinction ratio (ER) and broadband operation [ 23 - 25 ]. For example, a hybrid plasmonic waveguide by depositing a layer of chromium onto the oxide cladding directly above the \(\mathrm{{Si}}\) waveguide is utilized to attenuate the TM mode [ 24 ]. The major disadvantage for such nanophotonic devices is the high insertion loss (IL) due to the intrinsic loss in the metal, and the metal-involved fabrication process limits their applications. For dielectric polarizers, Xu and Shi [ 19 ] demonstrated a TE-pass polarizer \({29.4\mu }\mathrm{m}\) in length by using an asymmetrical directional coupler (ADC) along with sharp bending and tapered waveguides. At the central wavelength of \({1550}\mathrm{\;{nm}}\) , the measured extinction ratio is \({29.8}\mathrm{\;{dB}}\) . However, the devices are usually wavelength-sensitive, leading to a relatively narrow bandwidth. Additionally, a high-performance polarizer assisted by subwave-length grating is proposed [ 26 ]. The fabricated polarizer demonstrates \(\mathrm{{IL}}< {0.8}\mathrm{\;{dB}}\) and \(\mathrm{{ER}}>\) \({23}\mathrm{\;{dB}}\) in the \({1.26}- {1.36\mu }\mathrm{m}\) and \({1.52}- {1.58\mu }\mathrm{m}\) wavelength range. However, such structure is difficult to fabricate and occupies relatively large footprint.

As the demand for dense photonic integration increases rapidly, it is essential to minimize device size. Photonic inverse design provides an effective solution, with its well-known capability to boost degrees of design freedom [ 27 ]. In this way, inverse-designed devices can achieve flexible manipulation of polarization in an extremely small footprint. By engineering the dielectric permittivity profile using inverse design algorithms, these structures offer ultra-compact and remarkable performance [ 28 ]. To date, various inverse-designed optical devices such as polarization beam splitters [ 29 ], 3 dB power splitters [ 29 - 31 ], and wavelength multiplexers [ 32 ] have been reported. Bing Shen et al.[ 29 ] demonstrated an integrated polarization beamsplitter with a footprint of \({2.4\mu }\mathrm{m}\times {2.4\mu }\mathrm{m}\) , achieving an ER greater than \({10}\mathrm{\;{dB}}\) within a bandwidth of \({32}\mathrm{\;{nm}}\) .

In this paper, we propose an ultra-compact PhC-like [ 30 ] subwavelength (SW) TE-pass polarizer using direct-binary-search (DBS) algorithm. The device occupies an area of \({2.88\mu }\mathrm{m}\times\) \({2.88\mu }\mathrm{m}\) and can be fabricated with a single lithography step. The simulation results show that the average IL and average ER are \({0.99}\mathrm{\;{dB}}\) and \({33}\mathrm{\;{dB}}\) over a wavelength range of \({100}\mathrm{\;{nm}}\) , respectively. The inverse-designed ultra-compact polarizer holds great potential for ultra-dense photonic integrated circuits.

2 Design and Simulations

Generally, the inverse-designed device is divided into \(M \times N\) unit shapes, called “pixels”. Each pixel can be completely occupied by silicon or air, representing the logical ” 1 ” or ” 0 ” state, respectively. The binary pattern can be simulated by finite-difference time domain (FDTD), during the inverse design process. In Fig. 1 (a), the proposed PhC-like subwavelength TE-pass polarizer is designed on a standard SOI platform with a \({220}\mathrm{\;{nm}}\) -thick top silicon \(\left({n \approx {3.45}}\right)\) layer over a \({3\mu }\mathrm{m}\) -thick buried oxide \(\left({n \approx {1.45}}\right)\) layer. Here, as demonstrated in our previous work [ 27 ], we use a novel partial-air-filling, instead of full-air-filling, feature shape to represent the ” 0 ” pixel in the pattern shown in Fig. 1 (b). Specifically, for ease of fabrication, a silicon square with a central circular air hole is adopted as the configuration for the partial air-filling unit. The inverse design region, consisting of \({24}\times {24}\) discrete pixels, covers a compact footprint of only \({2.88\mu }\mathrm{m}\times\) \({2.88\mu }\mathrm{m}\) . Each pixel is a square of \({120}\mathrm{\;{nm}}\times\) \({120}\mathrm{\;{nm}}\) with a circular hole. The hole has a diameter of \({110}\mathrm{\;{nm}}\) and a depth of \({220}\mathrm{\;{nm}}\) .

Each hole has a binary state of the dielectric property: silicon or air. Hence, the refractive index could be engineered at every location of the device in a deep subwavelength scale. The widths of the input and output waveguides are \({450}\mathrm{\;{nm}}\) . To guarantee that the inverse-designed TE-pass polarizer can filter out undesired TM-polarized light, the input waveguide is positioned along the \(x\) -axis and the output waveguide is positioned along the \(y\) -axis, ensuring that the TE- and TM-polarized light propagate through a \({90}^{\circ }\) bend. Specifically, the TM-polarized light suffers significantly larger radiation losses, when TE- and TM-polarized light propagate through a \({90}^{\circ }\) bend [ 18 ]. In this way, the working mechanism of the inverse-designed TE-pass polarizer is equivalent to bent waveguides. To ensure that the TE-pass polarizer can achieve bidirectional operation, we set the pixels to be symmetric along the diagonal in the inverse design process. As shown in Fig. 1 (c), the bidirectional operation indicates that regardless of whether the light is injected from Port1 or Port2, TE-polarized light passes through, while TM-polarized light is filtered out. Due to the diagonal symmetry of pixels, the light injected from Port1 and Port2 will propagate through the same dielectric constant distribution, thereby achieving the same transmission characteristics. In this way, the TE-pass polarizer can achieve bidirectional operation when the inverse design is finished.

The DBS algorithm is employed to determine the material of each hole to be silicon or air one by one during the inverse design process. For the design of a polarizer, the ER should be maximized while the IL should be minimized. Specifically, the figure-of-merit (FOM) is introduced to evaluate the effectiveness of the optimization, which is defined as

(1) \[\mathrm{{FOM}}= \alpha \left({1 -{t}_{\mathrm{{TE}}}}\right)+ \left({1 -\alpha }\right){t}_{\mathrm{{TM}}}\]

where \({t}_{\mathrm{{TE}}}\) and \({t}_{\mathrm{{TM}}}\) are the transmittances of TE and TM modes, respectively. \(\alpha\) is a weighted coefficient to control the weight of two terms in Eq.(1). In this design, we set \(\alpha\) to 0.5 . For an ideal TE-pass polarizer, the FOM is 0 .

The 3D FDTD simulations via a commercial software (lumerical FDTD solutions) are performed to calculate the FOM, and a DBS optimization algorithm is employed to inversely design the device pattern. Fig. 1 (d) illustrates the iterative procedure in DBS algorithm. We choose one pixel to modify its occupied material (silicon or air), and then compute the FOM. If the FOM improves, the new pixel state is maintained. If not, the last state reverts to original. Then, one iteration ends when all the pixel states are inspected and the final pattern becomes the starting point for the next iteration. The optimization terminates when FOM exhibits no improvement compared with that of last iteration. The entire inverse design process requires approximately \({96}\mathrm{\;h}\) to be completed.

The corresponding optimized pattern is shown in Fig. 2 (a). The total number of iteration steps was 5 , and the evolution of FOM is shown in Fig. 2 (b). It can be observed that the final FOM converges to 0.19 . The non-zero FOM could be attributed to intrinsic insertion losses present in the optimized pattern. Predictably, there is still room for improvement in the optimized results. This is attributed to the local optima property of the DBS algorithm [ 24 ]. The magnitude of the electric fields \(\left|\mathrm{E}\right|\) for the input TE and TM polarizations injected from Port1 are plotted in Fig. 2 (c) and Fig. 2 (d), respectively. From the simulations, we can clearly see that the incident light generates mode superpositions within the device. Specifically, these guided modes interact in the inverse-designed region, allowing only the TE mode to pass through the output waveguides, while the TM mode quickly scatters within the pattern. As a result, the TE-pass polarizer is achieved. Furthermore, the electric fields \(\left|\mathrm{E}\right|\) for the TE and TM polarization injected from Port2 are plotted in Fig. 2 (e) and Fig. 2 (f), respectively. The polarized light inputs from Port1 and Port2 have the same transmission characteristic (the TE mode passes through the output waveguide while the TM mode quickly scatters). This shows the bidirectional operation of the inverse-designed TE- pass polarizer.

To evaluate the performance of the polarizer, the ER and IL are defined as follows

(2) \[\mathrm{{ER}}= {10}\lg \left({{P}_{\mathrm{{TE}}}/{\mathrm{P}}_{\mathrm{{TM}}}}\right)\]

(3) \[\mathrm{{IL}}= -{10}\lg \left({P}_{\mathrm{{TE}}}\right)\]

where \({P}_{\mathrm{{TE}}}\) and \({P}_{\mathrm{{TM}}}\) are the normalized output power for the TE mode and the TM mode. Specifically, the simulated transmission spectrum and the corresponding IL and ER of optimized device are shown in Fig. 3 . The output power of the TE mode is significantly higher than that of the TM mode, with a peak difference of \({37}\mathrm{\;{dB}}\) . The transmission curve is uniformly flat, indicating that this structure exhibits good broadband performance. Specifically, the inverse-designed device provides an average insertion loss of \({0.99}\mathrm{\;{dB}}\) and an average extinction ratio of \({33}\mathrm{\;{dB}}\) over a wavelength range of \({100}\mathrm{\;{nm}}\) . Tab. 1 summarizes the performance of various configurations of TE-pass polarizers in recent years, which employ materials such as \(\mathrm{{Cr}}\) , Au, and phase changes materials (PCM). When comparing the performance of our proposed PhC-like subwavelength polarizers with previously reported ones, our work exhibits ultra-compact footprint of \({2.88\mu }\mathrm{m}\times {2.88\mu }\mathrm{m}\) . Furthermore, the device provides an average insertion loss of \({0.99}\mathrm{\;{dB}}\) and an average extinction ratio of \({33}\mathrm{\;{dB}}\) over a wavelength range of \({100}\mathrm{\;{nm}}\) .

To investigate the fabrication tolerance, we have simulated the performance of the device under hole diameter variations. For the PhC-like subwavelength structure, the device performance will significantly deteriorate under hole diameter variation. Specifically, we calculate the transmittance spectra with diameter deviations from \(-{10}\mathrm{\;{nm}}\) to \(+{10}\mathrm{\;{nm}}\) . As shown in Fig. 4 (a-b), when the diameter deviation is \(\pm {10}\mathrm{\;{nm}}\) , the average IL increases about \({2.2}\mathrm{\;{dB}}\) and the average ER decreases about \({10}\mathrm{\;{dB}}\) . Additionally, the average IL increases about \({0.9}\mathrm{\;{dB}}\) and the average ER decrease about \(4\mathrm{\;{dB}}\) for \(+ 5\mathrm{\;{nm}}\) diameter variation, respectively. This means that the PhC-like subwavelength structure-based polarizer is robust to fabrication errors of \(+ 5\mathrm{\;{nm}}\) diameter deviations. Fortunately, the PhC-like subwave-length structure can eliminate the random changes of etching holes with the lag-effect-insensitive feature by the single step etching processes, compared with other inverse designed structures with random feature sizes. For the future fabrication of these devices, we may estimate the etching velocity before etching the device and avoid under etching by setting an appropriate etching time.

3 Conclusion

In conclusion, we have designed an ultra-compact integrated nanophotonic TE-pass polarizer using inverse design based on direct-binary-search algorithms. The device provides an average insertion loss of \({0.99}\mathrm{\;{dB}}\) and an average extinction ratio of \({33}\mathrm{\;{dB}}\) over a wavelength range of \({100}\mathrm{\;{nm}}\) . Notably, the device achieves ultra-compact footprint of \({2.88\mu }\mathrm{m}\times {2.88\mu }\mathrm{m}\) , which is the smallest footprint to date. The inverse-designed ultra-compact polarizer holds great potential for ultradense photonic integrated circuits.

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Funding

National Natural Science Foundation of China(62175076)

National Natural Science Foundation of China(62105028)

National Natural Science Foundation of China(62475085)

Natural Science Foundation of Hubei Province of China(2024AFA016)

Natural Science Foundation of Hubei Province of China(2024AFB612)

Open Project Program of Hubei Optical Fundamental Research Center ()