Polarization Splitter-Rotator Based on Multimode Waveguide Grating

: We demonstrate a polarization splitter rotator (PSR) based on multimode waveguide grating (MWG) on a silicon-on-insulator (SOI) platform. Bloch mode hybridization in mini-stopband is exploited to achieve high polarization conversion efﬁciency. The fabricated device yields a high extinction ratio of > 53 dB and > 31 dB, low crosstalk of < − 26.4 dB and < − 40 dB for the injected TE 0 and TM 0 mode, with average insertion loss of 1.2 dB and 1.5 dB in the wavelength regime 1552 nm– 1562 nm. Such a device shows great design ﬂexibility and an easy fabrication process, serving as a good candidate in integrated polarization diversity circuits, especially for applications requiring spectra manipulation. Additionally, the polarization conversion approach provides opportunities to develop novel polarization management devices.


Introduction
Silicon-on-insulator (SOI) has become one of the most promising platforms for photonic integration benefiting from its low cost, high-density integration, and compatibility with CMOS fabrication processes. However, the high index contrast introduces significant polarization dependence, which makes silicon photonic devices incompatible with fiber communication applications where the polarization state in optical fiber is typically random. One efficient solution to eliminate the polarization sensitivity is to use a polarization splitter-rotator (PSR) [1][2][3][4][5], in which the TE 0 mode and TM 0 mode can be separated into two individual waveguides. Meanwhile, one of the polarization states will be converted to the orthogonal one, normally chosen as TE 0 mode considering that most devices are optimized only for TE 0 polarization. Such a polarization handling device is also desired on other material platforms, and has been demonstrated on platforms including InP [6,7], SiN [8] and lithium-niobate-on-insulator (LNOI) [9,10]. Vertical asymmetrical structures are normally required to implement polarization conversion schemes including covering different cladding material [1], fabricating a bi-level taper [11,12], or introducing additional top structures such as gold [13] and SiN [14]. The operation principle of PSRs can be classified into two categories of mode coupling [15] and mode evolution [16,17], according to the energy exchange path when polarization rotation. For mode coupling based PSRs, phase-matching condition should be satisfied. The typical structures adopted are asymmetrical directional coupler (ADC) [18], tapered DC [19], bend DC [20,21], and so on. For mode evolution ones, mode hybridization between TM 0 mode and forward TE 1 mode can occur when light propagates along the adiabatic taper or multimode waveguide [22]. It should be noted that all the reported PSRs are designed for broadband operation, aiming as universal schemes for realizing polarization-transparent photonic integrated circuits (PICs). However, for some critical applications such as polarization insensitive wavelength division (de)multiplexer [23,24], wavelength selective devices such as arrayed waveguide gratings (AWGs) are subsequently required to implement wavelength multiplexing [25], inevitably incurring extra insertion loss and footprint and design complexity to the whole on-chip system. Exploiting novel polarization conversion mechanisms and developing new functional devices are desirable for PICs application.
Mini-stopband (MSB) is derived from the anti-crossing between Bloch modes [26,27]. There have been numerous interesting applications based on MSB, mostly in two dimensional photonic crystal (2D-PhC) such as pulse compression [28], coarse wavelength selection [29], optical filters [30], and selective mirroring in PhC lasers [31,32]. Several functional components based on MSB have also been demonstrated including polarization beam splitter [33] and tunable optical band stop filters [34], in one dimensional photonic crystal (1D-PhC). However, the authors have never considered in particular the coupling between Bloch modes with different polarization, and resultant polarization conversion in multimode waveguide grating (MWG).
In this paper, we demonstrate a novel MWG-based PSR. An anti-crossing of Bloch modes in MSB is exploited to archive highly efficient polarization rotation. The proposed PSR boasts a high extinction ratio, low crosstalk, an easy fabrication process, and great design flexibility. Additionally, such a device can be further cascaded with grating assisted contra-directional couplers (contra-DCs) [35,36], paving the way for critical applications such as polarization insensitive wavelength division (de)multiplexer [23,24] and multichannel polarization-multiplexed differential quadrature phase-shift keying (PM-DQPSK) transceiver [37,38].

Device Structure and Working Principle
The proposed PSR is schematically illustrated in Figure 1, and consists of a linearly tapered multimode waveguide grating (MWG) and adiabatic coupler (AC). The silicon strip waveguides are 220 nm high sitting on a 2 µm buried oxide layer with air cladding, for the demand of vertical symmetry breaking. For the injected TE 0 mode, the light beam keeps propagating along AC, MWG, and linearly tapered waveguide (length L 2 ), then exits at the through (TRU) port. In the case of TM 0 input, the mode is first preserved in the AC region (length L 1 , Gap G), then reversely coupled to be the TE 1 mode by MWG due to the satisfied phase-matching condition and Bloch mode hybridization. In the AC section, the backward TE 1 mode finally evolves into a TE 0 mode of the isolated bottom taper waveguide (width from W 4 to W 3 ) and bends away to the cross (CRO) port.
The structure parameters of width, period, grating number, and corrugation width in the uniform MWG region are denoted by W 2 , Λ, N, and δw, respectively, as labeled in Figure 1b. As a potential application scenario, we also propose an easy architecture of a polarization insensitive wavelength duplexer, simply by cascading MWG-based PSR and grating assisted contra-directional coupler. As depicted in Figure 1c, the injected TM 0 mode will be backward converted to TE 0 by PSR and dropped at different ports because of the different grating period Λ. Meanwhile, the injected TE 0 mode propagates through the whole PSRs region, is then dropped to different ports by contra-DCs. Note that the longitudinal-apodization design is normally requires suppressing the sidelobe of the spectra and reducing channel crosstalk. The structure parameters of width, period, grating number, and corrugation width in the uniform MWG region are denoted by W2, ᴧ, N, and δw, respectively, as labeled in Figure 1b. As a potential application scenario, we also propose an easy architecture of a polarization insensitive wavelength duplexer, simply by cascading MWG-based PSR and grating assisted contra-directional coupler. As depicted in Figure 1c, the injected TM0 mode will be backward converted to TE0 by PSR and dropped at different ports because of the different grating period ᴧ. Meanwhile, the injected TE0 mode propagates through the whole PSRs region, is then dropped to different ports by contra-DCs. Note that the longitudinal-apodization design is normally requires suppressing the sidelobe of the spectra and reducing channel crosstalk.
To illustrate the working principle of the proposed PSR, we calculated the photonic band structure of uniform MWG using the three-dimensional finite-difference time-domain (3D-FDTD) method, with structure parameters: ᴧ = 414 nm, W2 = 900 nm, δw = 100 nm, fill factor ff = 0.5. For the unit cell, non-uniform meshing is utilized with minimum mesh sizes Δxmin = Δymin = 10 nm, and Δzmin = 20 nm. Bloch periodic boundary conditions are imposed on the two surfaces perpendicular to the x-axis, and perfectly matched layer (PML) boundary conditions are applied on the other surfaces. Figure 2a shows the band structure of TE0, TE1, and TM0 Bloch mode. The photonic band gaps (PBGs) are located at 187.8 THz-190.2 THz, 200.07 THz-201.2 THz, respectively, which means that there is no allowed mode in uniform MWG. Anti-crossing between TM0 and TE1 modes can also be observed, giving rise to a MSB at frequencies ranging from 194.0 THz to 195.3 THz (or wavelengths from 1.536 μm to 1.547 μm). Hence, the input TM0 mode located in MSB can be converted to backward TE1 Bloch mode, and vice-versa. Note that the conversion between the TM0 and TE1 Bloch modes in the uniform MWG should satisfy the phase matching condition: λc/ᴧ = (Neff1 + Neff2), where Neff1 and Neff2 represent the effective refractive indices of the two coupled Bloch modes, and λc is central wavelength. The group indices NgTE1 and NgTM0 of both modes can be extracted from the slope of their dispersion relation, taken far from the coupling region [27]. The value of coupling coefficient can be derived by the following expression [39]: To illustrate the working principle of the proposed PSR, we calculated the photonic band structure of uniform MWG using the three-dimensional finite-difference time-domain (3D-FDTD) method, with structure parameters: Λ = 414 nm, W 2 = 900 nm, δw = 100 nm, fill factor ff = 0.5. For the unit cell, non-uniform meshing is utilized with minimum mesh sizes ∆x min = ∆y min = 10 nm, and ∆z min = 20 nm. Bloch periodic boundary conditions are imposed on the two surfaces perpendicular to the x-axis, and perfectly matched layer (PML) boundary conditions are applied on the other surfaces. Figure 2a shows the band structure of TE 0 , TE 1 , and TM 0 Bloch mode. The photonic band gaps (PBGs) are located at 187.8 THz-190.2 THz, 200.07 THz-201.2 THz, respectively, which means that there is no allowed mode in uniform MWG. Anti-crossing between TM 0 and TE 1 modes can also be observed, giving rise to a MSB at frequencies ranging from 194.0 THz to 195.3 THz (or wavelengths from 1.536 µm to 1.547 µm). Hence, the input TM 0 mode located in MSB can be converted to backward TE 1 Bloch mode, and vice-versa. Note that the conversion between the TM 0 and TE 1 Bloch modes in the uniform MWG should satisfy the phase matching condition: λ c /Λ = (Neff 1 + Neff 2 ), where Neff 1 and Neff 2 represent the effective refractive indices of the two coupled Bloch modes, and λ c is central wavelength. The group indices Ng TE1 and Ng TM0 of both modes can be extracted from the slope of their dispersion relation, taken far from the coupling region [27]. The value of coupling coefficient κ can be derived by the following expression [39]: where ∆λ is bandwidth of MSB, and N g = N gTE0 + N gTM1 /2. For the uniform MWG considered above, the parameters extracted from the dispersion diagram of Figure 2a are Ng TE1 = 5.05, Ng TM0 = 4.11, and ∆λ/λ 2 c = 0.463 × 10 3 m −1 , leading to κ = 6.66 × 10 3 m −1 . This value is lower than the one of common waveguide Bragg gratings without polarization conversion, typically > 50 × 10 3 m −1 [40]. Additionally, we can effectively tune κ by using lateral phase delay modulation [41], for the purpose of apodization design. Figure 2b shows the local picture of MSB associated to the coupling between TM 0 and TE 1 Bloch modes. The electric field patterns are represented in Figure 2c,d. This value is lower than the one of common waveguide Bragg gratings without polarization conversion, typically > 50 10 [40]. Additionally, we can effectively tune by using lateral phase delay modulation [41], for the purpose of apodization design. Figure  2b shows the local picture of MSB associated to the coupling between TM0 and TE1 Bloch modes. The electric field patterns are represented in Figure 2c,d.  Figure 3a shows the transmission and reflection spectra of uniform MWG with N = 100 when TE0 and TM0 mode are injected. The results are calculated using uniform meshing with Δxmin = Δymin = Δzmin = 20 nm, which ensure accuracy and calculation efficiency. One MSB ranging from 1.541 μm to 1.551 μm is observed; the reflection of the TM0 mode is about 96%. We note that the transmission of input TE0 mode is near 96% in MSB, while the major component of backward fields is TM1 mode. However, this crosstalk is negligible due to the weak reflection and large propagation loss of TM1 mode for the proposed device.  Figure 3a shows the transmission and reflection spectra of uniform MWG with N = 100 when TE 0 and TM 0 mode are injected. The results are calculated using uniform meshing with ∆x min = ∆y min = ∆z min = 20 nm, which ensure accuracy and calculation efficiency. One MSB ranging from 1.541 µm to 1.551 µm is observed; the reflection of the TM 0 mode is about 96%. We note that the transmission of input TE 0 mode is near 96% in MSB, while the major component of backward fields is TM 1 mode. However, this crosstalk is negligible due to the weak reflection and large propagation loss of TM 1 mode for the proposed device.  We further simulate light propagation profiles in uniform MWG using 3D-FDTD, at typical wavelengths of 1.546 μm, 1.509 μm, and 1.496 μm, which are presented in Figure  3b-f. As predicted in the band structure, the launched TE0 mode can maintain its polarization and propagate through uniform MWG (Figure 3b), at a wavelength of 1.546 μm. Meanwhile, the TE0 mode will be gradually attenuated as a radiation mode being located above the light line (Figure 3c), at a wavelength of 1.509 μm (198.8 THz), with a transmission of 83%. For the launched TM0 mode at 1.546 μm, the major component of backward field is TE1 mode, as shown in Figure 3d. TM0 mode is gradually attenuated at a wavelength of 1.496 μm due to being located in the PBG (Figure 3f), while freely propagating at a wavelength of 1.509 μm as a purely Bragg-guided mode (Figure 3e).
To reduce insertion loss and suppress back-reflection incurred by mode mismatch between strip waveguide and uniform MWG, two linearly tapered gratings are utilized at both ends of the uniform MWG with minimum sidewall corrugation δwmin, minimum We further simulate light propagation profiles in uniform MWG using 3D-FDTD, at typical wavelengths of 1.546 µm, 1.509 µm, and 1.496 µm, which are presented in Figure 3b-f. As predicted in the band structure, the launched TE 0 mode can maintain its polarization and propagate through uniform MWG (Figure 3b), at a wavelength of 1.546 µm. Meanwhile, the TE 0 mode will be gradually attenuated as a radiation mode being located above the light line (Figure 3c), at a wavelength of 1.509 µm (198.8 THz), with a transmission of 83%. For the launched TM 0 mode at 1.546 µm, the major component of backward field is TE 1 mode, as shown in Figure 3d. TM 0 mode is gradually attenuated at a wavelength of 1.496 µm due to being located in the PBG (Figure 3f), while freely propagating at a wavelength of 1.509 µm as a purely Bragg-guided mode (Figure 3e).
To reduce insertion loss and suppress back-reflection incurred by mode mismatch between strip waveguide and uniform MWG, two linearly tapered gratings are utilized at both ends of the uniform MWG with minimum sidewall corrugation δw min , minimum period Λ min , and grating number N , as seen in Figure 4a. The TM 0 -TE 1 conversion efficiency is equal to the fraction of power reflected into TE 1 mode, which can be extracted utilizing the Mode Expansion Monitor. The transmission and reflection as a function of Λ min are shown in Figure 4b. We can see that there is a linear variation region (340 nm < Λ min < 390 nm) for TE 0 mode, and a local minimum reflection of −46 dB for TM 0 mode when Λ min = 380 nm, which corresponds to the highest TM 0 -TE 1 conversion efficiency. This means that we need to make a trade-off between the transmission of TE 0 mode and the reflection of TM 0 mode. Here, the optimal Λ min is determined to be 380 nm, which guarantees an acceptable transmission of 94.2% for TE 0 mode and the lowest reflection of TM 0 mode, and the highest conversion efficiency of TM 0 -TE 1 . In the following simulation, linearly tapered gratings with δw min = 10 nm, Λ min = 380 nm and N = 20 are adopted.  We investigate the influence of grating number N on spectra, keeping ᴧ = 0.414 μm, W2 = 0.9 μm, δw = 0.1 μm, and ff = 50%, as shown in Figure 5a. It is seen that as N increases, the stopband edge becomes much steeper, and the maximum reflection increases significantly. Figure 5b presents the conversion efficiency and transmission as a function of grating number. As seen, the transmission of TE0 mode is higher than 92% (−0.36 dB) when N = 200, and the conversion efficiency of TM0 -TE1 is improved by up to 98% (−0.22 dB). The transmission of TM0 mode is about −46.9 dB at 1.546 μm, which could be even lower by increasing the grating number. Next, we change the grating period ᴧ while keeping W2 = 0.9 μm, δw = 0.1 μm and N = 200. The reflection spectra shown in Figure 6a indicates that stopband is red-shifted sig- We investigate the influence of grating number N on spectra, keeping Λ = 0.414 µm, W 2 = 0.9 µm, δw = 0.1 µm, and ff = 50%, as shown in Figure 5a. It is seen that as N increases, the stopband edge becomes much steeper, and the maximum reflection increases significantly. Figure 5b presents the conversion efficiency and transmission as a function of grating number. As seen, the transmission of TE 0 mode is higher than 92% (−0.36 dB) when N = 200, and the conversion efficiency of TM 0 -TE 1 is improved by up to 98% (−0.22 dB). The transmission of TM 0 mode is about −46.9 dB at 1.546 µm, which could be even lower by increasing the grating number.  We investigate the influence of grating number N on spectra, keeping ᴧ = 0.414 μm, W2 = 0.9 μm, δw = 0.1 μm, and ff = 50%, as shown in Figure 5a. It is seen that as N increases, the stopband edge becomes much steeper, and the maximum reflection increases significantly. Figure 5b presents the conversion efficiency and transmission as a function of grating number. As seen, the transmission of TE0 mode is higher than 92% (−0.36 dB) when N = 200, and the conversion efficiency of TM0 -TE1 is improved by up to 98% (−0.22 dB). The transmission of TM0 mode is about −46.9 dB at 1.546 μm, which could be even lower by increasing the grating number. Next, we change the grating period ᴧ while keeping W2 = 0.9 μm, δw = 0.1 μm and N = 200. The reflection spectra shown in Figure 6a indicates that stopband is red-shifted significantly as ᴧ increases. Slight ripple (lower than 1%) in stopband caused by mode mis-  Next, we change the grating period Λ while keeping W 2 = 0.9 µm, δw = 0.1 µm and N = 200. The reflection spectra shown in Figure 6a indicates that stopband is red-shifted significantly as Λ increases. Slight ripple (lower than 1%) in stopband caused by mode mismatch is observed. Figure 6b presents the dependence of central wavelength λc and 1-dB bandwidth on grating period quantitatively. As seen, when Λ increases from 0.414 µm to 0.432 µm, λc increases linearly from 1.545 µm to 1.573 µm with slope dλc dΛ = 1.5, and the bandwidth increases monotonously from 13 nm to 15 nm. Therefore, one can design operation wavelength of PSR by tuning grating period. The effect of corrugation width δw on reflection spectra is investigated when W2 = 0.9 μm, ᴧ = 0.414 μm, and N = 200. As shown in Figure 7a, the stopband is red-shifted significantly as δw decreases, due to a variation of the effective refractive index in MWG. The reflection of central wavelength is diminished from 0.98 to 0.8 because of the decreasing grating strength. Figure 7b presents the dependence of central wavelength and 1-dB bandwidth of the stopband on the δw quantitatively. As seen, when δw increases from 50 nm to 112.5 nm, decreases with δw linearly from 1.578 μm to 1.535 μm with a slope = −0.693, and the 1-dB bandwidth increases monotonously from 6 nm to 14 nm. This indicates that the MWG-based PSR is intrinsically characterized by a narrow operation bandwidth, due to the wavelength dependence of the grating.

Device Performance and Analysis
An adiabatic coupler is adopted for the conversion between backward TE1 mode and TE0 mode because of its high conversion efficiency and large fabrication tolerance. The design parameters of AC and linear taper are optimized by the Eigenmode expansion (EME) method, which are listed as follows: W1 = 0.7 μm, W2 = 0.9 μm, W3 = 0.4 μm, W4 = The effect of corrugation width δw on reflection spectra is investigated when W 2 = 0.9 µm, Λ = 0.414 µm, and N = 200. As shown in Figure 7a, the stopband is red-shifted significantly as δw decreases, due to a variation of the effective refractive index in MWG. The reflection of central wavelength is diminished from 0.98 to 0.8 because of the decreasing grating strength. Figure 7b presents the dependence of central wavelength λc and 1-dB bandwidth of the stopband on the δw quantitatively. As seen, when δw increases from 50 nm to 112.5 nm, λc decreases with δw linearly from 1.578 µm to 1.535 µm with a slope dλc dδw = −0.693, and the 1-dB bandwidth increases monotonously from 6 nm to 14 nm. This indicates that the MWG-based PSR is intrinsically characterized by a narrow operation bandwidth, due to the wavelength dependence of the grating. The effect of corrugation width δw on reflection spectra is investigated when W2 = 0.9 μm, ᴧ = 0.414 μm, and N = 200. As shown in Figure 7a, the stopband is red-shifted significantly as δw decreases, due to a variation of the effective refractive index in MWG. The reflection of central wavelength is diminished from 0.98 to 0.8 because of the decreasing grating strength. Figure 7b presents the dependence of central wavelength and 1-dB bandwidth of the stopband on the δw quantitatively. As seen, when δw increases from 50 nm to 112.5 nm, decreases with δw linearly from 1.578 μm to 1.535 μm with a slope = −0.693, and the 1-dB bandwidth increases monotonously from 6 nm to 14 nm. This indicates that the MWG-based PSR is intrinsically characterized by a narrow operation bandwidth, due to the wavelength dependence of the grating.

Device Performance and Analysis
An adiabatic coupler is adopted for the conversion between backward TE1 mode and TE0 mode because of its high conversion efficiency and large fabrication tolerance. The design parameters of AC and linear taper are optimized by the Eigenmode expansion (EME) method, which are listed as follows: W1 = 0.7 μm, W2 = 0.9 μm, W3 = 0.4 μm, W4 = 0.1 μm, G = 0.12 μm, L1 = 160 μm, L2 = 3 μm. The TE1 to TE0 conversion efficiency is up to

Device Performance and Analysis
An adiabatic coupler is adopted for the conversion between backward TE 1 mode and TE 0 mode because of its high conversion efficiency and large fabrication tolerance. The design parameters of AC and linear taper are optimized by the Eigenmode expansion (EME) method, which are listed as follows: W 1 = 0.7 µm, W 2 = 0.9 µm, W 3 = 0.4 µm, W 4 = 0.1 µm, G = 0.12 µm, L 1 = 160 µm, L 2 = 3 µm. The TE 1 to TE 0 conversion efficiency is up to 98.5% when L 1 = 160 µm at wavelength of 1.546 µm, as shown in Figure 8. Meanwhile, the mode conversion efficiency between the forward TM 0 mode and TE 1 mode decreases significantly, owing to the taper width (from W 1 to W 2 ), which is far away from the mode hybridization region, about 660 nm for the case of air cladding [22]. mode conversion efficiency between the forward TM0 mode and TE1 mode decreases significantly, owing to the taper width (from W1 to W2), which is far away from the mode hybridization region, about 660 nm for the case of air cladding [22].  Figure 9a,b, the injected TE0 mode propagates through the whole structure and outputs at the TRU port. Meanwhile, the injected TM0 mode is first reversely converted to be TE1 mode in the MWG section, then coupled to be TE0 mode in the narrow waveguide of AC section, and finally output at the CRO port. The proposed PSR is evaluated by the performance metrics of insertion loss (IL), extinction ratio (ER), and crosstalk (CT), respectively [42]. The IL, ER, and CT for input TE0 mode are defined as: The IL, ER and CT for input TM0 mode are defined as: where T means the transmission of mode at TRU port or CRO port. The calculated transmission spectra are shown in Figure 9c,d; we note that the IL and IL are both less than 0.5 dB over 10 nm bandwidth (1.54 μm -1.55 μm). The ER is > 50 dB and CT is < −39 dB for the TE0 mode in the wavelength range of 1.53 μm -1.56 μm. Note that CT is theoretically originated from the backward TM1 mode excited by MWG. However, this impact is negligible for a fabricated device considering the large propagation loss of TM1 mode, which is further confirmed by our experimental results. For the input TM0 mode, ER of > 30 dB and CT of −48 dB can be observed, ranging from 1541 nm to 1550 nm. The ER is originated from the weakly reflected TM0 mode.  Figure 9a,b, the injected TE 0 mode propagates through the whole structure and outputs at the TRU port. Meanwhile, the injected TM 0 mode is first reversely converted to be TE 1 mode in the MWG section, then coupled to be TE 0 mode in the narrow waveguide of AC section, and finally output at the CRO port. The proposed PSR is evaluated by the performance metrics of insertion loss (IL), extinction ratio (ER), and crosstalk (CT), respectively [42]. The IL, ER, and CT for input TE 0 mode are defined as: CT TE = 10· log 10 T cro The IL, ER and CT for input TM 0 mode are defined as: ER TM = −10· log 10 (T cro TM /T cro TE ) CT TM = 10· log 10 T tru TE /T cro TE (7) where T port mode means the transmission of mode at TRU port or CRO port. The calculated transmission spectra are shown in Figure 9c,d; we note that the IL TE and IL TM are both less than 0.5 dB over 10 nm bandwidth (1.54 µm-1.55 µm). The ER TE is > 50 dB and CT TE is < −39 dB for the TE 0 mode in the wavelength range of 1.53 µm-1.56 µm. Note that CT TE is theoretically originated from the backward TM 1 mode excited by MWG. However, this impact is negligible for a fabricated device considering the large propagation loss of TM 1 We further investigate the fabrication tolerance of the proposed PSR, assuming there is a width variation of W2 and corrugation δw. As shown in Figure 10a, when TM0 mode is launched, the PSR exhibits a performance of < 0.5 dB IL and > 30 dB CT, when ΔW2 changes from −10 nm to 10 nm. The reason can be explained by the fact that the effective refractive index in MWG is sensitive to the width variation; therefore, the phase-match condition and stopband are affected. However, the transmission of TE0 mode (Figure 10b) is only slightly affected by ΔW2; the CT is > 36 dB, and IL is < 0.6 dB, showing a robust performance. The device performance affected by the corrugation width δw is shown in Figure. 10c,d. For the TM0 mode, a high CT of > 20 dB is obtained, when Δδw varies from −7.5 nm to 7.5 nm, assuming W2 = 0.9 μm. However, this influence is slight for TE0 mode (Figure 10d). Overall, the proposed PSR exhibits different performance according to the structure variations, for TE0 mode and TM0 mode, respectively. Additionally, for the injected TM0 mode, the influence of Δδw is more significant than ΔW2. The proposed device can be fabricated by advanced fabrication technologies. We further investigate the fabrication tolerance of the proposed PSR, assuming there is a width variation of W 2 and corrugation δw. As shown in Figure 10a, when TM 0 mode is launched, the PSR exhibits a performance of < 0.5 dB IL and > 30 dB CT, when ∆W 2 changes from −10 nm to 10 nm. The reason can be explained by the fact that the effective refractive index in MWG is sensitive to the width variation; therefore, the phase-match condition and stopband are affected. However, the transmission of TE 0 mode (Figure 10b) is only slightly affected by ∆W 2 ; the CT is > 36 dB, and IL is < 0.6 dB, showing a robust performance. The device performance affected by the corrugation width δw is shown in Figure 10c,d. For the TM 0 mode, a high CT of > 20 dB is obtained, when ∆δw varies from −7.5 nm to 7.5 nm, assuming W 2 = 0.9 µm. However, this influence is slight for TE 0 mode (Figure 10d). Overall, the proposed PSR exhibits different performance according to the structure variations, for TE 0 mode and TM 0 mode, respectively. Additionally, for the injected TM 0 mode, the influence of ∆δw is more significant than ∆W 2 . The proposed device can be fabricated by advanced fabrication technologies.

Fabrication and Measurement
We fabricated the proposed PSR on the SOI platform with a 220 nm thick silicon layer and a 2 μm thick oxide layer. The silicon waveguides were first patterned via electron beam lithography (EBL), then etched by the inductively coupled plasma (ICP) etching process. The focused TM grating couplers (pitch = 1.19 μm, duty cycle = 0.5) and linearly tapered TE grating couplers (pitch = 0.662 μm, duty cycle = 0.5) were adopted for fiberchip coupling and polarization selectivity, with the same coupling angle of 20°. To make a full characterization for different polarization conversion scenarios, four sets of PSRs with TE/TM grating couplers at the input/output ports were fabricated, as shown in Figure 11a. It should be noted that the length of AC was chosen as 350 μm for complete mode conversion [4]. Figure 11b,c show the scanning electric microscopy (SEM) image of the taper and uniform grating section. We can see that the taper section and the designed corrugations on MWG have been accurately fabricated.

Fabrication and Measurement
We fabricated the proposed PSR on the SOI platform with a 220 nm thick silicon layer and a 2 µm thick oxide layer. The silicon waveguides were first patterned via electron beam lithography (EBL), then etched by the inductively coupled plasma (ICP) etching process. The focused TM grating couplers (pitch = 1.19 µm, duty cycle = 0.5) and linearly tapered TE grating couplers (pitch = 0.662 µm, duty cycle = 0.5) were adopted for fiberchip coupling and polarization selectivity, with the same coupling angle of 20 • . To make a full characterization for different polarization conversion scenarios, four sets of PSRs with TE/TM grating couplers at the input/output ports were fabricated, as shown in Figure 11a. It should be noted that the length of AC was chosen as 350 µm for complete mode conversion [4]. Figure 11b,c show the scanning electric microscopy (SEM) image of the taper and uniform grating section. We can see that the taper section and the designed corrugations on MWG have been accurately fabricated.

Fabrication and Measurement
We fabricated the proposed PSR on the SOI platform with a 220 nm thick silicon layer and a 2 μm thick oxide layer. The silicon waveguides were first patterned via electron beam lithography (EBL), then etched by the inductively coupled plasma (ICP) etching process. The focused TM grating couplers (pitch = 1.19 μm, duty cycle = 0.5) and linearly tapered TE grating couplers (pitch = 0.662 μm, duty cycle = 0.5) were adopted for fiberchip coupling and polarization selectivity, with the same coupling angle of 20°. To make a full characterization for different polarization conversion scenarios, four sets of PSRs with TE/TM grating couplers at the input/output ports were fabricated, as shown in Figure 11a. It should be noted that the length of AC was chosen as 350 μm for complete mode conversion [4]. Figure 11b,c show the scanning electric microscopy (SEM) image of the taper and uniform grating section. We can see that the taper section and the designed corrugations on MWG have been accurately fabricated.  To experimentally characterize the fabricated devices, light was first generated from a C-band tunable laser, with its polarization state controlled by a polarization controller.
The position and angle of the two coupling fibers were aligned utilizing two six-axis stages. The laser source and power meter were connected by a computer to implement wavelength sweeping and power data recording. Figure 12a,b show the measured transmission spectra of the fabricated PSR when TE 0 mode and TM 0 mode are launched, which are normalized with respect to the transmission of grating couplers on the same chip. As depicted in Figure 12a, the TE 0 mode propagates to the TRU port with average IL TE of 1.2 dB. The ER TE is > 53 dB and CT TE is < −26.4 dB, around the central wavelength of 1555 nm. As shown in Figure 12b, when the TM 0 mode is launched, light outputs from the CRO port; the average IL TM is 1.5 dB, ER TM of > 31 dB, and CT TM of > −30 dB can be observed ranging from 1552 nm to 1562 nm. We can also observe about 10 nm central wavelength shifting, compared with the simulation results, which comes from the fabrication errors such as the variation of waveguide width, corrugation width, or waveguide thickness. To experimentally characterize the fabricated devices, light was first generated from a C-band tunable laser, with its polarization state controlled by a polarization controller. The position and angle of the two coupling fibers were aligned utilizing two six-axis stages. The laser source and power meter were connected by a computer to implement wavelength sweeping and power data recording. Figure 12a,b show the measured transmission spectra of the fabricated PSR when TE0 mode and TM0 mode are launched, which are normalized with respect to the transmission of grating couplers on the same chip. As depicted in Figure 12a, the TE0 mode propagates to the TRU port with average IL of 1.2 dB. The ER is > 53 dB and CT is < −26.4 dB, around the central wavelength of 1555 nm. As shown in Figure 12b, when the TM0 mode is launched, light outputs from the CRO port; the average IL is 1.5 dB, ER of > 31 dB, and CT of > −30 dB can be observed ranging from 1552 nm to 1562 nm. We can also observe about 10 nm central wavelength shifting, compared with the simulation results, which comes from the fabrication errors such as the variation of waveguide width, corrugation width, or waveguide thickness.

Conclusions
In summary, we have presented a novel PSR based on MWG, on the SOI platform. Bloch mode hybridization in MSB is exploited to achieve a high polarization conversion efficiency. The fabricated devices exhibit a high extinction ratio of > 53 dB and > 31 dB, low crosstalk of < −26.4 dB and < −40 dB for the injected TE0 and TM0 mode around the central wavelength. We believe that the proposed PSR could be applied in integrated polarization diversity circuits, especially for applications requiring spectra manipulation such as polarization insensitive wavelength division (de)multiplexer and multichannel polarization-multiplexed differential quadrature phase-shift keying (PM-DQPSK) transceiver. Additionally, the polarization conversion approach provides opportunities to develop novel polarization management devices.

Conclusions
In summary, we have presented a novel PSR based on MWG, on the SOI platform. Bloch mode hybridization in MSB is exploited to achieve a high polarization conversion efficiency. The fabricated devices exhibit a high extinction ratio of > 53 dB and > 31 dB, low crosstalk of < −26.4 dB and < −40 dB for the injected TE 0 and TM 0 mode around the central wavelength. We believe that the proposed PSR could be applied in integrated polarization diversity circuits, especially for applications requiring spectra manipulation such as polarization insensitive wavelength division (de)multiplexer and multichannel polarizationmultiplexed differential quadrature phase-shift keying (PM-DQPSK) transceiver. Additionally, the polarization conversion approach provides opportunities to develop novel polarization management devices.