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Abstract
We propose an ultra-broadband and ultra-compact polarization rotator (PR) structure on the silicon-on-insulator platform. The subwavelength gratings (SWGs) are introduced at the waveguide corner in order to excite the hybridized modes and realize the polarization rotation. The dispersion-engineered SWG can dramatically reduce the polarization conversion length deviation. High polarization extinction ratio > 20 dB and low excess loss < 1 dB can be achieved over 1.26-1.675 μm wavelength range, which covers O-, E-, S-, C-, L-, and U-bands. The total device size is as small as 4.8 × 0.34 μm2. To the best of our knowledge, the proposed structure is the first silicon PR that could cover all of the optical communication bands.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Over the recent years, the silicon nanowire waveguides have been used to develop various photonic integrated devices [1]. The high refractive index contrast between Si (nSi ≈3.46) and SiO2 (nSiO2 ≈1.45) provides strong light confinement and enhanced light-matter interaction, but also gives rise to the waveguide birefringence. Almost all the silicon nano-photonic devices are polarization-sensitive and the polarization-insensitive devices are usually difficult to realize [2–4] due to the distinct difference between TM0 and TE0 modes [5]. The birefringence problem can be addressed by utilizing the polarization diversity circuit (PDC) [6]. The input TM0/TE0 modes are firstly separated by the polarization beam splitter (PBS) [7–10]. After that, one polarization is rotated to the orthogonal one by utilizing the polarization rotator (PR), so that all the functional devices can work at a single polarization state. Finally, the divided polarizations are combined by using the PBS and PR reversely.
In the PDC, the PR is one of the basic components enabling the conversion between TM0 and TE0 modes. A series of PRs have been reported, including the ones based on adiabatic tapers [11–14], asymmetrical directional couplers (ADCs) [15–18] and cut-cornered structures [19–24]. For the taper-based PRs, the incident TM0 mode can convert to TE1 mode by utilizing the polarization hybridization process [11–14]. However, the taper length has to be long enough to satisfy the adiabatic condition, and an additional TE1-TE0 converter is required, which leads to a large device size. The ADC-based PRs can also obtain the polarization conversion by matching the effective indices of TM0 and TE0 modes in the adjacent waveguides [15–18]. However, the ADC-based PRs always require air cladding to break the symmetry, which limits the applications. For the cut-cornered PRs, the incident single polarization can be decomposed to be a couple of hybridized modes (HP1 and HP2) in the cut-cornered waveguide, and the orthogonal polarization can be formed after half a beat length [19–24]. The cut-cornered structures are commonly used in the PDC due to the small device size as well as high polarization extinction ratio [25–27]. However, these different types of PRs all suffer from a relatively narrow working bandwidth, since the polarization conversion length always varies with the wavelength.
In this paper, we propose an ultra-broadband and ultra-compact PR structure that could work over all the optical communication bands. The proposed PR is based on the cut-cornered structure, but the corner region is replaced by the subwavelength gratings (SWGs) to increase the working bandwidth [28–33], as shown in Fig. 1. By engineering the dispersion of the SWG, a high polarization extinction ratio PER > 20 dB and a low excess loss EL < 1 dB can be achieved over a record broadband from 1.26 to 1.675 μm.
Fig. 1 The configuration of the proposed PR. The inset shows SWG region with some key parameters labeled.
2. Design and analysis
In this paper, the device is designed based on the silicon-on-insulator (SOI) platform with a 340-nm thick Si core layer and a 2-μm thick SiO2 buffer layer. We choose the 340-nm SOI platform to ensure the strong light confinement over all the optical communication bands, especially at longer wavelengths. The cladding is chosen to be SiO2. In the following calculations, we consider the TM0-TE0 conversion process, but one should note that the PR is reciprocal and the TE0-TM0 conversion process should be almost the same. To simplify the calculation, we substitute the SWG region with the effective medium [34]:
where nxx/nyy/nzz are the effective medium refractive indices in x-/y-/z-directions, no/ne are the ordinary/extraordinary indices, and f is the SWG duty cycle. We then calculate the polarization rotation angle θpol in the SWG-assisted cut-cornered waveguide. Here, the SWG duty cycle is set to be f = 0.5 as an example. The θpol is defined as [19]: where ηTM0-HPi is the power coupling ratio between TM0 mode and HPi mode, TM0 is the fundamental transverse magnetic mode in the channel waveguide, HPi is the i-th hybridized mode in the SWG-assisted cut-cornered waveguide. The mode profiles for TM0 and HPi are obtained using the finite element method (FEM). Figure 2 shows calculated polarization rotation angle θpol with varied waveguide width wwg, etching depth hetch and etching width wetch at three different wavelengths (λ = 1.26 μm, 1.55 μm and 1.675 μm). To ensure a complete polarization conversion, the TM0-HP1 and TM0-HP2 power coupling ratios should satisfy ηTM0-HP1:ηTM0-HP2 = 50:50, leading to θpol = 45°. It can be observed that the wavelength-independent θpol = 45° can be obtained as long as the waveguide geometry is mirror-symmetric (hwg = wwg, hetch = wetch). Further simulations show that such property can also be found with different f. Thus, by utilizing a mirror-symmetric waveguide geometry, the only factor that limits the PR working bandwidth is the conversion length variation at different wavelengths.Fig. 2 The calculated polarization rotation angle θpol with varied wwg, hetch and wetch at three different wavelengths (λ = 1.26 μm, 1.55 μm and 1.675 μm).
In the cut-cornered PR, the polarization conversion length Lc can be obtained using the following equation [19]:
where λ is the working wavelength, neff,HP1/neff,HP2 are the effective indices for the HP1/HP2 modes. From Eq. (6), one has to optimize the dispersion of neff,HP1-neff,HP2 to reduce the wavelength dependence of Lc. We firstly calculate the normalized mode dispersion coefficients DHP1,norm and DHP2,norm for the HP1 and HP2 modes with varied wetch and f using FEM and effective medium substitution [see Fig. 3(a)]. The etching depth and etching width are set to be hetch = wetch to ensure θpol = 45°. Here, the DHP1,norm and DHP2,norm are defined as:where n0,HPi is the effective index for HPi mode at 1.55 μm wavelength, dneff,HPi/ dλ is the mode dispersion slope for HPi. It can be found that the mode dispersion can be engineered by changing wetch and f. Moreover, the variation range for DHP2,norm is much larger than the one for DHP1,norm, thus, one could engineer the dispersion of neff,HP1-neff,HP2 by changing the SWG parameters. The normalized conversion dispersion coefficient Dκ,norm is then calculated for the SWG-assisted PR with varied wetch and f at 1.55 μm wavelength, as shown in Fig. 3(a). The Dκ,norm is defined as:where κ0 is the polarization conversion coefficient at 1.55 μm wavelength, dκ/dλ is the conversion dispersion slope. Here, the κ is defined as the reciprocal of the Lc:It can be found that the zero-dispersion can be obtained in the SWG-assisted PR at 1.55 μm wavelength with various (f, wetch) combinations. The SWG duty cycle is chosen as f = 0.5 to ensure a large feature size. The etching width is then determined to be wetch = 150 nm to obtain the zero-dispersion. We calculate the HP1/HP2 mode profiles in the cut-cornered waveguide with the optimized parameters using FEM and effective medium substitution. Figure 3(b) shows the calculated electric field profiles where strong polarization hybridization can be observed. The Lc dispersion curve is then calculated with hetch = wetch = 150 nm and f = 0.5, shown in Fig. 3(c). We also calculate the Lc dispersion for the conventional cut-cornered PR in Ref [19]. For the conventional structure, the Lc significantly varies with wavelength, leading to a relatively limited bandwidth [5,19]. For the SWG-assisted PR, a dramatically flattened Lc dispersion curve can be observed, where the Lc variation range is only < 0.6 μm over the 1.26-1.675 μm wavelength span.Fig. 3 (a) The calculated dispersion coefficients DHP1,norm, DHP2,norm and Dκ,norm with varied hetch = wetch and f at 1.55 μm wavelength. (b) The calculated electric field profiles for HP1 and HP2 modes. (c) The calculated Lc dispersion curves for the SWG-assisted and conventional PRs.
In the above analyses, the SWG structure is considered as a homogeneous effective medium, whose performance is independent with the SWG pitch Λ. However, for the actual SWG formed by the periodic dielectric segments, the dispersion can be anomalous when the Bragg wavelength is approached λB = 2Λ·neff,HPi, which could help to flatten the dispersion further [28,29]. Figure 4(a) shows the calculated band diagrams for the HP1 and HP2 modes with different Λ using 3D finite-difference time-domain (FDTD) method and Fourier transform. The mesh grid size and simulation time step are set to be dx = dy = dz = 5 nm and dt = 0.01 fs to satisfy the simulation accuracy requirement for the subwavelength structures [31]. The calculated wavelength range is chosen as 1.26-1.675 μm to cover all the optical communication bands. Here, the normalized propagation constant βnorm,HPi is defined as:
where neff,HPi is the effective index for HPi mode, Λ is the SWG pitch, and λ is the working wavelength. The Bragg reflection occurs when βnorm,HPi = 0.5. From the calculated diagrams, the threshold SWG pitch is Λ ≈240 nm. We then calculate the Lc dispersion curves with varied Λ < 240 nm using the calculated band diagrams. From the results shown in Fig. 4(b), one could find an additional zero-dispersion point around the O-band when the pitch is chosen as Λ > 228 nm.Fig. 4 (a) The calculated band diagrams for HP1 and HP2 modes. (b) The calculated Lc dispersion curves with varied Λ.
The polarization extinction ratio (PER) and excess loss (EL) spectra are then calculated with different Λ using 3D FDTD method, as shown in Fig. 5. The eigen-mode expansion (EME) is utilized to obtain the TM0/TE0 transmittance at the output port. The number of SWG periods N is also optimized to obtain the largest bandwidth. Here, the PER and EL are defined as:
where TTM-TE/TTM-TM are the TE/TM transmittance when TM-polarized light is launched. From Fig. 5(a), the polarization extinction ratio can be PER > 25 dB over a BW25dB > 415 nm bandwidth when the SWG pitch and the period number are chosen as Λ = 232 nm and N = 21. Moreover, one could find three peaks in the PER spectra, indicating that there are two zero-dispersion points and the conversion length is perfectly matched at three different wavelengths, which agree well with the results shown in Fig. 4(b). We also calculate the EL spectra with different Λ and N, as shown in Fig. 5(b). From the spectra, the EL is a little bit higher than 1 dB at the 1.26 μm wavelength when Λ = 232 nm and N = 21 due to the Bragg reflection. The SWG pitch is then modified to be Λ = 228 nm to obtain a low EL < 1 dB over the whole optical communication bands. One should note that the polarization extinction ratio can still be PER > 20 dB over the wavelength range from 1.26 to 1.675 μm (BW20dB > 415 nm) with the modified parameters.The optimized parameters are summarized as following: hwg = 340 nm, wwg = 340 nm, hetch = 150 nm, wetch = 150 nm, f = 0.5, Λ = 228 nm, N = 21. The light propagation profiles and transmission responses for the optimized PR are calculated using 3D FDTD method. From the light propagation profiles shown in Fig. 6(a), the incident TM0 mode (see Hy field) can completely convert to TE0 mode (see Ey field) with low loss. Moreover, the residual TM0 power is negligible, indicating a high PER. Furthermore, such complete conversion can be observed at different wavelengths, indicating the flattened dispersion. Figure 6(b) shows the calculated transmittance spectra for the optimized PR. From the spectra, a high PER > 20 dB and a low EL < 1 dB can be achieved over 1.26-1.675 μm wavelength span, which covers O-, E-, S-, C-, L- and U-bands. The excess loss and polarization extinction ratio are calculated to be EL ≈0.34 dB and PER ≈25 dB at 1.55 μm wavelength. Further simulations show that the transition loss at the junction between the input channel waveguide and the cut-cornered waveguide can be as low as ≈0.15 dB at 1.55 μm wavelength for the optimized structure.
Fig. 6 (a) The calculated light propagation profiles for the optimized PR. (b) The calculated transmittance spectra for the SWG-assisted and conventional PRs.
One could find that the total excess loss is roughly double the transition loss (there are two junctions), indicating that the polarization conversion is complete and the transition scattering is only source of loss in the PR. We also calculate the transmittance spectra for the conventional cut-cornered PR in Ref [19] for comparison, as shown in Fig. 6(b). For the conventional structure, the PER > 20 dB bandwidth is only < 60 nm. We also investigate the fabrication tolerance for the SWG-assisted PR. The transmittance spectra with deviated structural parameters are calculated using 3D FDTD method. The commercial SOI platform always suffers from the silicon thickness variation, which could lead to the performance non-uniformity for the wafer scale fabrication. We calculate the transmittance spectra for the PR with varied δhwg, as shown in Fig. 7. It can be found that the low EL < 1 dB and high PER > 16 dB can still be obtained with δhwg = ± 10 nm, showing great potential for the large scale fabrication. The line-width variation can also affect the device performance. We calculate the transmittance spectra for the PR with deviated waveguide width (δwwg), non-etched block width (Λ·δf) and SWG pitch (δΛ) over a ± 10 nm range (see Fig. 7). From the results, the EL < 1.5 dB and PER > 14 dB can be still obtained over 400-nm bandwidth even if the parameters are deviated over ± 10 nm range. In the overlay etching process, the etching depth deviation (δhetch) and overlay misalignment (δwetch) can also influence the device performance. We also calculate the transmittance spectra with δhetch = ± 10 nm and δwetch = ± 10 nm, as shown in Fig. 7. One could find that the broadband property (EL < 1 dB, PER > 15 dB over 400-nm bandwidth) can still be maintained with the deviated hetch and wetch. Overall, the SWG-assisted PR shows large fabrication tolerance, and is compatible with the standard silicon photonic fabrication processes (i.g., 193-nm DUV lithography and dry etching) [35,36].
3. Conclusion
In conclusion, we have theoretically investigated an ultra-broadband and ultra-compact PR using the SWG structures. By engineering the SWG dispersion, the working bandwidth can be dramatically enhanced. For the optimized PR, the polarization extinction ratio and excess loss can be PER > 20 dB and EL < 1 dB over the 1.26-1.675 μm wavelength range. The device size is as small as 4.8 × 0.34 μm2. We have compared the performances of the reported silicon PRs in Table 1. From the table, one could find that our proposed PR could achieve small device size, low EL, high PER and especially a record bandwidth BW20dB > 415 nm. To the best of our knowledge, the proposed SWG-based structure is the first silicon PR that could cover all the optical communication bands [5]. Our design is based on the 340-nm SOI platform, however, one could use the bi-level taper to integrate the proposed PR with the SOI waveguides with other thicknesses [37]. We believe that the proposed SWG-assisted PR could find its application in the high-performance polarization diversity circuit.
Table 1. Comparison of several silicon polarization rotators
Funding
National Key Research and Development Program (2016YFB0402502); National Natural Science Foundation of China (1171101320, 61675178).
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