1. Introduction

The silicon-on-insulator (SOI) platform, recently developed for many photonic applications has several advantages over glass-based systems, including small device footprint, low-loss nanowire waveguides, high-speed optical modulators and mature CMOS-compatible fabrication process [1]. However, these SOI devices suffer from strong structural birefringence in waveguides due to the high index-contrast between silicon and SiO₂, leading to a polarization-sensitive performance [2]. Some approaches based on the polarization beam splitters (PBS) [3] and polarization rotators (PR) [4] have been developed recently to achieve polarization diversity [5]. Another efficient and promising polarization-manipulating approach is to use a polarization splitter-rotator (PSR) [6–13], which converts different input polarization modes into the same mode before light passes through functional devices. Compared with the approaches using a PBS cascaded with a PR, the PSR offers potential advantages of simpler structures and lower insertion loss (IL). Various structures have been reported based on asymmetric directional couplers (DCs) [6–11], multimode interference couplers (MMIs) [12] and adiabatic couplers [13]. However, in order to satisfy the phase-matching condition, the DC-based PSRs typically have strict constraints on waveguide widths and coupler lengths, which make the performance sensitive to fabrication imperfections and operating wavelengths. Although a linearly tapered DC has been implemented to relax the requirements on these device sizes, the coupling efficiency is significantly decreased [8]. Another fabrication-tolerant MMI-based PSR with a large bandwidth has been reported recently [12], but this device has complex structures, including a mode-evolution taper, a Y-junction, a phase shifter and a MMI. Very recently, a mode-evolution PSR has been demonstrated in standard silicon photonic platforms, but the coupler length is relatively large [13].

Symmetric Y-junctions, which function as a standard structure in the integrated optics, are well-known as power splitters and often used in the Mach-Zehnder interferometers and optical modulators. However, another type of Y-junctions [14,15], which have two asymmetric output arms, has received much less attention. For an asymmetric Y-junction with a small angle between the output arms, the input mode in the stem will propagate through the Y-junction and adiabatically evolve into the mode in the arm, which has the closest effective refractive index with that of the input mode. By appropriately choosing the arm widths, different modes in the stem will excite the mode in different arms. Previous implementations of asymmetric Y-junctions were focusing on the on-chip mode-division multiplexing (MDM) [16,17] and it is similarly interesting to incorporate this structure into polarization diversity scheme.

In this work, we propose a novel ultra-broadband PSR design based on two basic broadband mode-evolution structures (a mode-evolution taper and a mode-sorting asymmetric Y-junction) in SOI platforms. By optimizing the length of each section of the tapers, high mode conversion efficiency from the TM₀ mode to the TE₁ mode is achieved. Unlike the DC-based PSR which requires a strict phase-matching condition on the waveguide widths and the corresponding coupler lengths, the output arm widths in our device can be chosen in a large range with high mode conversion efficiency as long as the Y-junction length is large enough. Therefore, our device offers a significantly improved operating bandwidth compared to all the existing PSR devices to the best of our knowledge. The simulation results shows that a low IL of < 0.4 dB with > 12 dB extinction ratio (ER) is achieved in a broad wavelength range over 400 nm when the device length is 95 μm. Moreover, the performance degradation caused by the imperfect fabrication is analyzed, showing that our device has a large fabrication tolerance.

2. Device design

Figure 1(a) schematically shows the proposed PSR structures, which consists of a taper and an asymmetric Y-junction. This device is designed in SOI rib waveguides with 250 nm rib height, 50 nm slab height and SiO₂ upper-cladding, which is used to break the symmetry in the waveguide cross-section as well as to protect the device. On one hand, the input fundamental transverse-magnetic mode (TM₀) will be converted into the first-order transverse-electric mode (TE₁) in the taper due to the mode coupling in these two modes [18]. Then the TE₁ mode will evolve into the fundamental transverse-electric mode (TE₀) in the narrow output arm (port 2) of the Y-junction because these two modes have the closely matched effective index. On the other hand, the input TE₀ mode is not converted into any other guided mode in the taper and will excite the TE₀ mode in the wide arm (port 1) if the waveguide width is appropriately chosen.

 

Fig. 1 (a) Schematic of the proposed PSR consisting of mode-evolution tapers and a mode-sorting asymmetric Y-junction. (b) Effective indices of the first three modes in a rib waveguide as a function of the waveguide width. The rib waveguide has a 250 nm rib height and 50 nm slab height. The wavelength is 1550 nm in the simulation.

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First, we used a commercial simulation software package (FIMMWAVE) to calculate the effective indices of the first three modes in an SOI rib waveguide, as shown in Fig. 1(b). The refractive indices of Si and SiO₂ are chosen to be n_Si = 3.476 and n_SiO2 = 1.528, respectively. It can be seen that there is a mode hybridization region for the TM₀ mode and the TE₁ mode when the waveguide width varies from W₁ = 620 nm to W₂ = 740 nm. Therefore, in order to convert the input TM₀ mode into the TE₁ mode and simultaneously avoid the mode hybridization at the ends of the taper [7], the taper comprises three sections with linearly tapered widths ranging from W₀ = 500 nm to W₁ = 620 nm, W₁ = 620 nm to W₂ = 740 nm and W₂ = 740 nm to W₃ = 800 nm, respectively. The widths of the arms in the asymmetric Y-junction satisfy the relationship as W_n + W_w = W₃, where W_n and W_w are the widths of the narrow and wide output arms, respectively. One can note that W_n can be chosen from 270 nm to 400 nm based on the mode-sorting principle of the asymmetric Y-junction. The minimum of W_n is determined by the fact that when W_n < 270 nm (corresponding to W_w > 530 nm), |Neff_W3,TE1 - Neff_Ww,TM0| < |Neff_W3,TE1 - Neff_Wn,TE0|, where Neff_w, _mode denotes the effective refractive index of the mode when the waveguide width is w. It means the TE₁ mode in the stem will evolve into the TM₀ mode in the wide arm instead of the TE₀ mode in the narrow arm, leading to an incorrect mode-sorting.

A three-dimensional simulation software package (FIMMPROP) based on eigen-mode expansion (EME) method was used to optimize the mode conversion efficiency in the taper. Figure 2 shows that the mode conversion efficiency from the TM₀ mode into the TE₁ mode is very close to 1 at appropriately chosen L_tp2 for a given L_tp1. In addition, a larger L_tp1 will lead to smaller ripples in the conversion curves, which means a larger fabrication tolerance. Here we choose L_tp1 = 10 μm and L_tp2 = 50 μm to realize a high efficiency mode conversion in a broadband wavelength range. The mode propagation in the taper for the TE₀ mode and the TM₀ mode at the 1550 nm wavelength with the optimal sizes are shown in the insets of Fig. 2.

 

Fig. 2 The mode conversion efficiency for the input TM₀ mode as a function of L_tp2 for L_tp1 varying from 1 μm (black) to 10 μm (dark yellow), where L_tp3 is set to L_tp1(W₃-W₂)/(W₁-W₀). Insets: the mode propagation for TE₀ and TM₀ modes in the taper at the 1550 nm wavelength when L_tp1 = 10 μm, L_tp2 = 50 μm and L_tp3 = 5 μm.

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The simulated mode conversion efficiency in the Y-junction as a function of the Y-junction length L_y at the 1550 nm wavelength is shown in Fig. 3. The modes (TE₁ and TE₀) launched into the stem will evolve into the specific mode in the output arms. The final gap between the output ports is G_out = 1 μm. When W_n varies in a large range from 284 nm to 374 nm, high mode conversion efficiency with correct mode-sorting can be achieved for different input modes and the conversion efficiency increases with the length L_y of the Y-junction as shown in Figs. 3(a) and 3(b). However, some ripples can be seen in Fig. 3(c) when W_n = 274 nm because |Neff_W3,TE1 - Neff_Ww,TM0| is very close to |Neff_W3,TE1 - Neff_Wn,TE0| in this case, leading to a undesirable mode coupling. Nevertheless, the correct mode-sorting with high mode conversion efficiency still occurs when the length is large enough. Figure 3(d) shows an incorrect mode-sorting in the Y-junction, where the input TE₁ mode will evolve into the TM₀ mode in port 1, which should be avoided when choosing the waveguide widths.

 

Fig. 3 The mode conversion efficiency in the asymmetric Y-junction for different input modes at the 1550 nm wavelength. (a-b) The correct mode-sorting occurs when W_n varies from 284 nm to 374 nm. (c) The undesirable mode coupling occurs when W_n = 274 nm. (d) The incorrect mode-sorting occurs when W_n = 264 nm.

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Figure 4 shows the required minimum Y-junction length for various levels of mode conversion efficiency from the TE₁ mode into the TE₀ mode in port 2 as a function of W_n. Clearly there is a tradeoff between the Y-junction length and the mode conversion efficiency. By increasing the Y-junction length, improved mode conversion efficiency can be obtained in a large range for W_n, showing a potentially large fabrication tolerance compared to the DC-based PSRs. Besides, the minimum length for 99% mode conversion efficiency is achieved when W_n = 374 nm. In this case, the corresponding Y-junction length is ~30 μm.

 

Fig. 4 The minimum Y-junction length required to achieve various levels of mode conversion efficiency from the TE₁ mode to the TE₀ mode at port 2 as a function of the narrow arm width W_n. The wavelength is 1550 nm in the simulation.

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3. Device performance and fabrication tolerance analysis

Figure 5 shows the mode propagation in the PSR for different input modes at 1550 nm wavelength. According to the analysis above, the proposed PSR device has a taper length L_tp ( = L_tp1 + L_tp2 + L_tp3) = 65 μm and a Y-junction length L_y = 30 μm, corresponding to a total length of 95 μm. The input TM₀ mode is predominantly converted into the TE₀ mode at port 2, while the input TE₀ mode is not converted in the taper and finally exits at port 1.

 

Fig. 5 Mode propagation in the device when the input is (a) the TE₀ mode and (b) the TM₀ mode, respectively. The wavelength is 1550 nm.

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The wavelength dependence of the conversion efficiency at different ports is shown in Fig. 6. The simulated results were further validated by a three-dimensional finite-difference-time-domain (3D-FDTD, Lumerical FDTD) simulation and a good agreement can be seen in the figures. The optimum performance is achieved when the wavelength is ~1550 nm. Since the two basic structures in this PSR is broadband, the entire device exhibits a good performance with > 12 dB ER and < 0.4 dB IL in an ultra-broadband wavelength range from 1350 nm to 1750 nm at both ports, which significantly improved the operation bandwidth compared to all the previously reported PSRs. With such a broad operating bandwidth, this device offers potential applications for polarization diversity operating across every communication bands.

 

Fig. 6 The mode conversion efficiency as a function of the wavelength in the two output ports. The simulation is carried out by 3D-EME and 3D-FDTD methods. The grid size in the FDTD simulation is chosen as Δx = Δy = Δz = 15 nm. The conversion efficiency below −35 dB is not shown.

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We further analyzed the performance variations due to the practical fabrication imperfections. Figures 7(a) and 7(b) show that the device has a low IL of < 0.5 dB with > 10 dB ER at both ports for the device width variation Δw from −40 nm to 70 nm and the slab height variation ΔH_slab from −15 nm to 15 nm. 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 Fig. 7(c), even though the refractive index of the upper-cladding has as high as ± 15% variation Δn_SiO2/n_SiO2 from the bottom-cladding, corresponding to n_SiO2 changing from 1.30 to 1.76, the device performance is still very stable. We believe that these tolerances will significantly improve the manufacturing yield.

 

Fig. 7 Fabrication tolerance analysis for (a) the width variation Δw of the device width, (b) the variation ΔH_slab of the slab height, and (c) the variation of the upper-cladding refractive index. The inset of (a) shows a PSR layout affected by Δw > 0 (solid red) and Δw < 0 (dashed blue).

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4. Conclusion

In summary, an ultra-broadband SOI PSR is proposed by utilizing mode-evolution tapers and a mode-sorting asymmetric Y-junction. By appropriately choosing the waveguide widths and lengths of each section in this device, high mode conversion efficiency with correct mode-sorting is obtained for the two output ports. Moreover, since the taper and Y-junction have advantages of large bandwidth and fabrication tolerance, the entire device exhibits a good performance in a large bandwidth over 400 nm as well as a large fabrication tolerance for the device width variation, the slab height variation and the imperfect upper-cladding oxide deposition.