Proposal for fabrication-tolerant SOI polarization splitter-rotator based on cascaded MMI couplers and an assisted bi-level taper

A novel silicon-on-insulator (SOI) polarization splitter-rotator (PSR) with a large fabrication tolerance is proposed based on cascaded multimode interference (MMI) couplers and an assisted mode-evolution taper. The tapers are designed to adiabatically convert the input TM0 mode into the TE1 mode, which will output as the TE0 mode after processed by the subsequent MMI mode converter, 90-degree phase shifter (PS) and MMI 3 dB coupler. The numerical simulation results show that the proposed device has a < 0.5 dB insertion loss with < −17 dB crosstalk in C optical communication band. Fabrication tolerance analysis is also performed with respect to the deviations of MMI coupler width, PS width, slab height and upper-cladding refractive index, showing that this device could work well even when affected by considerable fabrication errors. With such a robust performance with a large bandwidth, this device offers potential applications for CMOS-compatible polarization diversity, especially in the booming 100 Gb/s coherent optical communications based on silicon photonics technology. ©2014 Optical Society of America OCIS codes: (130.3120) Integrated optics devices; (230.7370) Waveguides; (130.5440) Polarization-selective devices. References and links 1. D. Xu, J. H. Schmid, G. T. Reed, G. Z. Mashanovich, D. J. Thomson, M. Nedeljkovic, X. Chen, D. V. Thourhout, S. Keyvaninia, and S. K. Selvaraja, “Silicon photonic integration platform-have we found the sweet spot?” IEEE J. Sel. Top. Quantum Electron. 20(4), 189–205 (2014). 2. J. Wang, C. Qiu, H. Li, W. Ling, L. Li, A. Pang, Z. Sheng, A. M. Wu, X. Wang, S. Zou, and F. Gan, “Optimization and demonstration of a large-bandwidth carrier-depletion silicon optical modulator,” J. Lightwave Technol. 31(24), 4119–4125 (2013). 3. J. Wang, Z. Sheng, L. Li, A. Pang, A. Wu, W. Li, X. 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Introduction
Silicon photonics, which takes advantages of the mature complementary metal oxide semiconductor (CMOS) process and strong optical confinement in the SOI waveguide, has been considered to be one of the most promising candidates of the next-generation photonics market for many applications, including the optical communications, optical interconnects and high-performance computers (HPCs) [1].Although silicon photonics has been developed considerably in the past few years with respect to the key active and passive components [2][3][4][5], one of the challenges which limit photonics in the SOI platform from large-scale commercialization lies in the striking polarization sensitivity of the SOI functional devices due to the large index-contrast of SOI materials [6].Tremendous efforts have been done towards polarization-insensitive structures for specific applications in different material systems [7,8], but it would be difficult to achieve the tradeoff between polarization insensitivity and good performance especially for the thin SOI wafers with 220 nm top silicon thickness which are preferred by the silicon photonic foundries [9].
Another promising approach which may be more suitable for SOI photonics platform is the polarization diversity scheme [10].Incoming light with random polarization from the outside fibers will be separated and converted into a single polarization along two paths where the functional components operating at one polarization well are located.Compared to the approaches using polarization beam splitters (PBSs) together with polarization rotators (PRs) [11,12], the integrated polarization splitter-rotator offers some potentially significant advantages, including CMOS-compatible fabrication, simple structure and low insertion loss (IL).Particularly in recent years, the booming silicon photonic transmitters and receivers for 100 Gb/s coherent optical communication requires a robust polarization diversity scheme which should have a large fabrication tolerance and ensure a high manufacture yield because of the high cost of this complex silicon photonic module [13][14][15][16].Various structures have been reported based on asymmetric directional couplers (DCs) [17][18][19][20][21][22] and Y-junctions [23] so far.However, most of these previously reported DC-based PSRs require strict phase matching conditions and thus the performances are usually sensitive to the size deviation due to the imperfect fabrication process [17][18][19][20][21][22].The PSR based on mode-evolution Y-junctions has a considerably large bandwidth, but a low-loss asymmetric Y-junction is difficult to achieve in practice [23].
In this work, we propose a novel SOI PSR based on some fabrication-tolerant basic structures (i.e., adiabatic taper, multimode interference coupler, and phase shifter (PS)).For the ease of the fabrication, only the assisted taper requires an additional etch to break the symmetry of the cross-section in the waveguide and the mode conversion from the TM 0 mode to the TE 1 mode could be achieved in a large wavelength range.The numerical simulation shows that this device has a < 0.5 dB loss with better than −17 dB crosstalk in C optical communication band.Besides, we further analyze the fabrication tolerance of this device, showing that the performance is very robust even for large fabrication deviations in terms of etch depth, MMI width, PS width and refractive index of the upper-cladding.This PSR could be fabricated in a standard CMOS process and integrated with other functional components to realize a more complex function in the coherent optical communications beyond 100 Gb/s.

Mode conversion in the linear tapers
For a normal linear taper which is based on symmetric waveguides such as the strip SOI waveguide with rectangular core and identical upper/bottom cladding, the input mode will not be changed if the taper length is large enough.Figure 1(a) shows a linear SOI taper which has a length of 50 μm with waveguide height of 0.25 μm and waveguide width increasing from 0.50 μm to 0.80 μm.We used a three-dimensional commercial simulation software package (FIMMWAVE) to calculate the effective indices of the first three modes (i.e., the zero-order transverse-electric (TE 0 ), zero-order transverse-magnetic (TM 0 ) and first-order transverseelectric (TE 1 ) mode) in the cross-section along this taper, as shown in Fig. 1(b).The refractive indices of Si and SiO 2 were chosen to be n Si = 3.476 and n SiO2 = 1.455, respectively.It can be seen there is no mode hybridization region and the different quasi-polarized modes (i.e., transverse-electric (TE) and transverse-magnetic (TM) modes where the dominant electric field is parallel and perpendicular to the substrate, respectively) could be distinguished well even when the TM 0 and TE 1 modes have the same effective refractive indices.Therefore, the input TM 0 mode could propagate through this taper without any mode conversion to other guided mode as shown in Fig. 1(c).The mode conversion in another type of linear tapers would be more complex.This type of tapers has an asymmetric waveguide cross-section due to the different upper/bottom cladding or in the case of a rib waveguide.The symmetry in the cross-section is broken, so one cannot make a distinction between different quasi-polarized modes [24].For an example, we consider a linear taper as shown in Fig. 2(a) which is similar to the normal one (see Fig. 1(a)) except the waveguide has a slab height of 0.05 μm. Figure 2(b) shows the calculated effective indices of the first three modes in the cross-section along this taper.One can note that there is hybridization mode region for the second and third modes when the waveguide width is increased from 0.50 μm to 0.80 μm.The mode profiles of these two modes also show that the minor-component (E x or E y ) is comparable to the corresponding major-component (E y or E x ), which may lead to a mode conversion between these two modes in this taper.Figure 2(c) shows the mode propagation in this taper for the incoming TM 0 mode and the mode conversion from the TM 0 to TE 1 mode can be seen very clearly.A more detailed discussion about the mode conversion in the linear tapers could be found in [24].

Mode conversion in MMI couplers
MMI couplers are based on the self-imaging principle [25], where N-fold images of the field at the input plane will be formed at the output after propagation in a multimode waveguide.
The input field can be expressed as the superposition of the guided modes ( ) in the multimode region as below, ( ) where x y dxdy Therefore, the MMI width should be large enough to support enough modes, otherwise some power will be lost when the field is launched into the multimode region.And the field at the position z in the propagation direction can be expressed as where is the beat length of the two lowest-order modes of the multimode region.Here β 0 and β 1 is the propagation constant of the zero-order and first-order modes, respectively.For the general interference where the input field enters into the multimode region from any x position, the field at the position of z = 3L π /2 can be expressed as Therefore, if the input field is even symmetric ( ( , ,0) ( , ,0) x y xy ψ ψ = − , e.g., for TE 0 mode), the field at z = 3L π /2 will be the copy of the input field.That is 3 , , ( , ,0).
Another particular case is the field enters into the multimode region from two symmetric input waveguides, and the fields in these two input waveguides has a 90-degree phase difference.This type of input fields can be expressed as where ( , ,0) 0 x y φ = for x < 0. According to (5) and (7), the field at z = 3L π /2 can be expressed as which means that the field in both two input waveguides can be mapped into only one output waveguide.
Another interference is called symmetric interference which requires the input field launching from the position of x = 0.For the symmetric input field (e.g., TE 0 ), it can be reproduced at the position of z = 3L π /4, where the anti-symmetric field (e.g., TE 1 ) will be split into two parts at the edges of this plane [26].Figures 3(a

Device operation principles
Figure 4 schematically illuminate our proposed PSR, which consists of a two-stage bi-level taper and a 90-degree PS sandwiched by two MMI couplers with different functionalities.This device is designed in SOI waveguides with H = 220 nm top silicon thickness and SiO 2 cladding.In this case, an additional etch (e.g., H slab = 90 nm) will be inevitably implemented in the taper to break the symmetry in the waveguide cross-section for the mode conversion between TM and TE modes according to the discussion in section 2.1.The operation principle of this PSR will be described as follows.On one hand, the input TM 0 mode will adiabatically evolve into the TE 1 mode at the end of the first section of the bi-level taper in which the rib width (slab width) linearly increases from W 0 (0) to W 1 (W s ).Then the TE 1 mode remains propagating in the second section of the bi-level taper where the rib width continues increasing from W 1 to W 2 and simultaneously the slab width is reduced to 0 for the ease of fabrication in other areas of the device.To correctly direct the converted TE 1 mode into the TE 0 mode at port 1, we use two MMI couplers based on symmetric interference and general interference, respectively [25].When the first MMI length L MMI1 = 3L π /4, the input TE 1 mode will be mapped into the two TE 0 modes (see Fig. 3(b)) with the same power amplitude and a 180-degree phase difference.Then the upper TE 0 mode will pass through a 90-degree PS with a length of L PS to satisfy the input phase condition of the second MMI coupler.Finally, the two TE 0 modes will be mapped into the TE 0 mode at port 1 of the second MMI which has a length L MMI2 = 3L π /2 according to (8).On the other hand, the input TE 0 mode will not be converted into any other guided modes in the bi-level taper.Then the TE 0 mode will be mapped into the central output of the first MMI (see Fig. 3(a)), enter into the second MMI and finally output port 2 according to (6).Fig. 4. Schematic of the proposed PSR which consists of a bi-level taper, a MMI mode converter, a 90-degree PS and a MMI 3 dB coupler.The overall device is designed in the SOI waveguide with a waveguide height H = 220 nm while the bi-level taper section needs an additional etch (i.e., the slab height H slab = 90 nm). Figure 5 shows the effective indices of the first three modes in the cross-section along this bilevel taper.It can be seen that there is a mode hybridization region for the TM 0 and TE 1 modes when the waveguide rib width (slab width) varies from W 0 = 0.45 μm (0 μm) to W 1 = 0.55 μm (W s = 0.50 μm).After completing the mode conversion from the TM 0 to TE 1 mode in the first section of this taper, the second part of the taper should maintain the completed mode conversion and avoid the TE 1 mode converting back to the TM 0 mode.So we choose W 2 = 0.85 μm to ensure the difference between the effective indices of TE 1 and TM 0 modes of the waveguide cross-section along the second part of this taper is large enough.A larger W 2 will require a longer taper to reduce the mode transition loss while a smaller W 2 may cause a hybridization mode region somewhere in this part of tapers.Figure 6(a) shows the simulated conversion efficiency from the TM 0 to TE 1 mode in the overall bi-level taper with different lengths (L tp1 , L tp2 ).For different L tp2 , the conversion efficiency will be increased with L tp1 increasing.Here we choose L tp1 = 35 μm and L tp2 = 20 μm to achieve a > 99.5% conversion efficiency from 1.50 μm to 1.60 μm.A longer taper will improve the conversion efficiency and bandwidth, but at the expense of a larger device footprint.Figures 6(b)-6(c) show the mode propagation in this bi-level taper for different input modes and one can note that the mode conversion in the taper are achieved as we expected.

Optimization for the MMI couplers
Figure 7(a) shows the conversion efficiency from the TE 1 input mode to the TE 0 mode at the upper output waveguide of the first MMI with a width of W MMI = 3.4 μm and different input/output taper lengths L tp3 .When the first MMI length L MMI1 = ~19.9μm, there is a maximum conversion efficiency of ~48.3%.And we choose L tp3 = 20 μm as the input/output taper length to reduce the transition loss of the taper.Figure 6(b) shows the phase difference between lights propagating through a straight waveguide and a phase shifter with the same length L PS = 10 μm.Compared to the PS implemented in [27,28], the width of our PS is broadened towards the outside of the central waveguide to reduce the undesired coupling and thus a lower crosstalk can be expected.One can note that a 0.5π phase difference can be achieved when dW = ~0.05μm or 0.3 μm.Here we choose dW = 0.3 μm to relax the fabrication difficulties.In the second MMI coupler, the length L MMI2 is twice L MMI1 based on the MMI operating theory and thus we choose L MMI2 = 38.8μm here.The input/output taper length L tp3 and the MMI width W MMI are chosen as the same as those in the first MMI coupler.Figures 7(c)-7(d) show the mode propagation in the right part of the PSR except the bi-level taper.One can note that there is an output TE 0 mode at port 2 and port 1 for the TE 0 and TE 1 input, respectively.Meanwhile, no additional coupling power can be observed in the central waveguide for the TE 1 mode input.show the mode propagation at 1550 nm wavelength in the overall PSR which confirms the previous simulation result for each section is reliable.Figure 8(c) shows the wavelength difference of the insertion loss (IL) and the crosstalk (CT) for different input modes.This device exhibits a low IL of 0.2 dB (0.29 dB) with a good CT of 20 dB (20.7 dB) when the input is the TE 0 (TM 0 ) mode at 1.55 μm wavelength.The IL performance degradations is more sensitive for the TM 0 input mode in other wavelengths because the mode conversion for the TM 0 mode is more complex.For example, the assisted tapers and the PS will considerably affect the mode conversion for the input TM 0 mode but not for the TE 0 mode.Nevertheless, the device still achieves very stable performances in C optical communication band from 1.53 μm to 1.565 μm with < 0.5 dB IL and < −17 dB CT for both two inputs.And an acceptable performance of < 1 dB IL and < −15 dB CT is also obtained for the TE 0 input in a large operation bandwidth from 1.52 μm to 1.63 μm wavelength, covering C and L bands.The wavelength dependence of the performances may be further improved by adopting some sub-wavelength structures in the MMI couplers [29].And it would also be a useful approach to decrease the crosstalk by cascading a series of polarization filters after the end of this device [21].Fig. 9. Fabrication tolerance analysis to the deviations of (a1-a3) slab height ΔH slab in the bilevel taper, (b1-b3) MMI width ΔW MMI , (c1-c3) PS width ΔdW, and (d1-d3) refractive index of the upper-cladding Δn SiO2 /n SiO2 at wavelengths of 1.52 μm, 1.55 μm and 1.63 μm, respectively.The points with value higher than 30 dB are not shown here.

Device performance characterization and fabrication tolerance analysis
Figures 9(a1)-9(a3) show the fabrication tolerance analysis in terms of the deviation ΔH slab of the slab height in the bi-level taper at wavelengths of 1.52 μm, 1.55 μm and 1.63 μm, respectively.Compared to our previously reported DC-based PSR whose performance is very sensitive to the slab height [21], this new device would not be affected significantly by the slab height deviation in a large range of ± 40 nm because the mode conversion in the bi-level taper is caused by the mode evolution rather than mode interference.Figures 9(b1)-9(b3) discuss the performance variation caused by the deviation ΔW MMI of the MMI width.The device is also benefited from the large fabrication tolerance of the MMI couplers, showing a very stable performance even for a large deviation of ± 50 nm at 1.55 μm wavelength.In other operating wavelengths, the MMI width with optimal performances will shift, such as a smaller optimal MMI width (ΔW MMI ≈-40 nm) for a smaller wavelength (see Fig. 9(b1)) because the beat length L π increases with the wavelength [25].Figures 9(c1)-9(c3) describe the device performances under different deviations ΔdW of the waveguide width in the PS.It can be seen that this type of fabrication errors only affect the performances in the case of TM 0 input, which are also stable and acceptable.Another fabrication imperfection occurs during the upper-cladding oxide deposition, which may lead to a different refractive index of the upper-cladding from that of the bottom-cladding.Fortunately, as shown in Figs.9(d1)-9(d3), even though the refractive index of the upper-cladding has as high as ± 15% variation from the bottom-cladding, corresponding to n SiO2 changing from 1.30 to 1.76, the device performance is still very robust.We believe that these remarkable tolerances will significantly improve the manufacturing yield, which is advantageous to achieve high-density silicon photonic circuits with more complex functionalities.
In addition to the loss caused by the mode conversion in the MMI couplers, the scatting loss due to the waveguide surface (sidewall or top/bottom) roughness is also contributed to the total loss of this device in practice.This kind of loss could be significantly reduced by optimizing fabrication process, such as photolithography and etching processes [5].In addition, we have demonstrated a low-loss MMI coupler fabricated with CMOS technology [4], which will help us decreasing the device loss in our future work.
Another critical issue is the device length.In comparison to the PSR based on asymmetric directional coupler, the footprint of this device is a little large because of the long tapers and MMI couplers.Nevertheless, there will be at least two potential optimizations to reduce the device length.First, the tapers could be further optimized by adopting some other shapes (e.g., parabolic or sinusoidal) and multi-variable optimization (e.g., the genetic algorithm and particle swarm optimization) [30].Second, the MMI width could be improved because the MMI length is proportional to the square of the MMI width [25].

Conclusion
In summary, we propose a novel fabrication-tolerant SOI PSR based on an assisted bi-level taper, a 90-degree PS and two MMI couplers for CMOS-compatible polarization diversity applications.The bi-level is designed to adiabatically convert the TM 0 mode into the TE 1 mode in a large bandwidth.And the MMI couplers are used to separate and correctly direct the different input polarizations into the desired outputs.The device performance is characterized by the numerical simulations, showing a < 0.5 dB IL with better than −17 dB CT in C optical communication band.In addition, we further analyze the fabrication tolerance of this device with respect to the device height, the device width and the imperfect uppercladding oxide deposition, showing a significant improvement compared to the previous reported DC-based PSRs.This novel PSR exhibits a promising application in the 100 Gb/s coherent optical communications realized by silicon photonics technology.

Fig. 1 .
Fig. 1.(a) Schematic of a normal linear taper based on the symmetric strip SOI waveguide.(b) The calculated effective refractive indices of the first three modes in the waveguide crosssection along this taper.Insets: the profiles of the second and third modes.(c) The mode propagation in the taper for the input TM 0 mode.

Fig. 2 .
Fig. 2. (a) Schematic of a linear taper based on the asymmetric rib SOI waveguide.(b) The calculated effective refractive indices of the first three modes in the waveguide cross-section along this taper.Insets: the profiles of the second and third modes.(c) The mode propagation in the taper for the input TM 0 mode.
)-3(b) show the mode propagation in a MMI coupler when the input is the TE 0 and TE 1 mode, respectively.

Fig. 3 .
Fig. 3. (a-b) The mode propagation in the MMI coupler for the input TE 0 and TE 1 mode, respectively.Insets: the mode profile at the input plane and the position of z = 3L π /4.

Fig. 5 .
Fig. 5. (a) Effective refractive indices of the first three modes in the waveguide cross-section along the bi-level taper.Insets: the profiles of the zero-, first-and second-order modes in the cross-section along this taper.All the simulations were run at 1550 nm wavelength.

Fig. 6 .
Fig. 6.(a) Mode conversion efficiency from TM 0 to TE 1 in the bi-level taper as a function of L tp1 with L tp2 varying from 5 μm (red) to 25 μm (pink).Inset: the wavelength dependence of the mode conversion efficiency from TM 0 to TE 1 when L tp1 = 35 μm and L tp2 = 20 μm.(b-c) Mode propagation in the bi-level taper when the input is TE 0 and TM 0 , respectively.All the simulations were run at 1550 nm wavelength.

Fig. 7 .
Fig. 7. (a) Optimization for the first MMI coupler with different input/output taper lengths (i.e., L tp3 = 5, 10, 15, and 20 μm).The MMI width W MMI is chosen to be 3.4 μm here.(b) Phase difference between lights propagating through a straight waveguide and a PS with the same length L PS = 10 μm.(c-d) Mode propagation in the right section of the PSR for the incoming TE 0 mode and TE 1 mode, respectively.All the simulations were run at 1550 nm wavelength.

Fig. 8 .
Fig. 8. (a-b) Mode propagation in our proposed PSR at 1550 wavelength for input TE 0 mode and TM 0 mode, respectively.(c) Wavelength dependence of the PSR performance in terms of the insertion loss (IL) and crosstalk (CT) for different input modes.The points with value higher than 30 dB are not shown here.

Figures 8 (
Figures 8(a)-8(b) show the mode propagation at 1550 nm wavelength in the overall PSR which confirms the previous simulation result for each section is reliable.Figure8(c)shows the wavelength difference of the insertion loss (IL) and the crosstalk (CT) for different input modes.This device exhibits a low IL of 0.2 dB (0.29 dB) with a good CT of 20 dB (20.7 dB) when the input is the TE 0 (TM 0 ) mode at 1.55 μm wavelength.The IL performance degradations is more sensitive for the TM 0 input mode in other wavelengths because the mode conversion for the TM 0 mode is more complex.For example, the assisted tapers and the PS will considerably affect the mode conversion for the input TM 0 mode but not for the TE 0 mode.Nevertheless, the device still achieves very stable performances in C optical communication band from 1.53 μm to 1.565 μm with < 0.5 dB IL and < −17 dB CT for both two inputs.And an acceptable performance of < 1 dB IL and < −15 dB CT is also obtained for the TE 0 input in a large operation bandwidth from 1.52 μm to 1.63 μm wavelength, covering C and L bands.The wavelength dependence of the performances may be further improved by adopting some sub-wavelength structures in the MMI couplers[29].And it would also be a useful approach to decrease the crosstalk by cascading a series of polarization filters after the end of this device[21].