We propose a fabrication tolerant polarization splitter and rotator (PSR) on the silicon-on-insulator platform based on the mode-coupling mechanism. The PSR consists of a silicon wire waveguide coupled to a taper-etched waveguide. Compared to previously reported PSRs based on directional couplers which are sensitive to fabrication variations, the partially etched taper structure can compensate for fabrication inaccuracies. In addition, the taper-etched geometry breaks both the horizontal and vertical symmetries of the waveguide, introducing an additional degree of design freedom to accommodate different upper cladding layers. The proposed PSR can be readily integrated in a planar waveguide circuit using e.g. SiO2 cladding, making it compatible with typical metal back-end-of-line processes. Our simulation results show that the PSR has a low TM-to-TE polarization conversion loss of −0.09 dB in the C-band (or a conversion efficiency of 98%). A low TE-to-TE through insertion loss (−0.07 dB) and a very low polarization crosstalk (−30 dB) over a wide wavelength range exceeding 160 nm with a large fabrication tolerance (>50 nm) are numerically demonstrated.
© 2014 Optical Society of America
Polarization management is an important topic of research in silicon photonic circuits . Polarization splitters and rotators are structures of fundamental importance in polarization diversity systems  and polarization division multiplexed devices . Various types of passive polarization splitters and rotators have been reported [4–12]. Mode-evolution polarization rotators [4–8] have attracted significant attention because of their broad operation wavelength range and robust fabrication tolerance, typically with amorphous silicon or silicon nitride overlayers used to modify the waveguide cross-section in order to break the waveguide vertical symmetry [4–7]. However, such devices generally require a rather complex fabrication process. Another class of polarization rotators are mode-coupling structures, which are inherently wavelength dependent and comparatively sensitive to fabrication variations. Polarization splitter and rotators (PSRs) using asymmetrical directional couplers (DCs) optimized for a single etch process have been reported [9, 10]. However, the air cladding is used to realize vertical asymmetry, which is incompatible with most metal back-end-of-line processes, and these devices are also sensitive to fabrication variations. Recently, double-etch asymmetrical wire and rib DC-based PSRs using silica cladding have been demonstrated [11,12]. The main practical issue of limited fabrication tolerance (typically <10 nm for a loss penalty of −1 dB) still remains.
Here we propose a fabrication tolerant and broadband PSR based on the mode-coupling mechanism. The PSR comprises a taper-etched DC, specifically a silicon wire waveguide evanescently coupled to a taper-etched waveguide. This design is compatible with silica upper cladding. The proposed PSR utilizes a partial etch process, which is available in most silicon photonics foundries.
2. Polarization splitter and rotator design
The proposed PSR is schematically illustrated in Fig. 1(a). It comprises a silicon wire waveguide (waveguide A) of width W and height H, coupled to a taper-etched waveguide (waveguide B) with a width Wt, a ridge width We, a post-etch slab height He, a taper angle θ, and a gap between the waveguides Dgap. The coupling length LDC is the taper end-to-end distance in the waveguide B, where LDC = Wt/tan(θ). Two S-bends with a bending radius of RS are used near the input and the output ports to decouple the waveguides in these two regions.
The operation principle of the PSR is as follows: The dimensions of the waveguide B are chosen based on two conditions: 1) a significant effective index mismatch of the TE-like mode (with dominant Ex component) for the waveguides A and B, i.e. neffB(TE) < neffA(TE), to ensure that the TE-like mode injected in the input port A1 propagates to the through port A2 with a minimal cross-coupling to the waveguide B; 2) a phase matching condition neffB(TE) ~neffA(TM), so that the TM-like mode (with dominant Ey component) injected into port A1 couples to the TE-like mode of the waveguide B. The coupling process from the TM-like mode in the waveguide A to the TE-like mode in the waveguide B is facilitated by hybrid modes supported in the waveguide B, in which both the horizontal and vertical asymmetries are created by the tapered-etch. Under these conditions, a high polarization conversion efficiency CETM-TE = 10log10(P(out)BTE/P(in)ATM) can be achieved.
In our simulations we assume a free-space wavelength of 1550 nm, the refractive index of silicon nSi = 3.476, the bending radius of S-bend RS = 50 µm, and the upper and lower SiO2 cladding with a refractive index nSiO2 = 1.444. The silicon layer thickness is H = 220nm, the width of the waveguide A is W = 450 nm, and the gap in the coupling section is Dgap = 200 nm, which are typical feature sizes used in silicon photonics foundries with public access. The robustness advantage of the proposed PSR can be observed in Fig. 1(b), which shows the TE-like mode effective index in the waveguide B as a function of its ridge width We for a post-etch slab height He = 110 nm. The TM-like mode effective indices of the waveguide A, neffA(TM), are shown for three different waveguide widths. The TE-TM polarization coupling is achieved for the phase matching condition neffB(TE) = neffA(TM). This condition can be fulfilled for a specific combinations of parameters He, We and Wt of the coupling section. As the width of the waveguide A varies, the phase matching is still achieved just for a different We, i.e. at a different position along the taper. Similar behavior is also found for varying the post-etch slab height He. As a result, the TM-TE phase matching condition is remarkably insensitive to variations in waveguide dimensions.
The polarization conversion is further illustrated in Fig. 2, which includes the top views [Figs. 2(a) and 2(b)] and the cross-sectional views [Fig. 2(c)] of the mode evolution along the PSR structure, as calculated by the 3D-FDTD method. The TE-like mode launched in the input port A1 propagates to the through port A2 without cross-coupling [Fig. 2(a)]. On the other hand, the TM-like mode from the input port A1 is gradually coupled to the waveguide B, being transformed into the TE-like mode propagating to the cross port B2 [Fig. 2(b)]. Figure 2(c) shows the cross-sectional views of the mode evolution for the TM-like mode input. In the middle of the taper section, the Ex and Ey components are equalized, yielding an efficient mode hybridization.
In the following we optimize the device design by varying several parameters of the structure. We use the full-vectorial eigenmode expansion (EME) method and some results are cross-checked by the 3D-FDTD simulations.
The PSR performance is examined for three post-etch slab heights: (i) He = 70 nm (deep etch with an etch depth of D = 150 nm); (ii) He = 110 nm (moderate etch depth, D = 110 nm); and (iii) He = 150 nm (shallow etch depth, D = 70 nm). The selection of these parameters is guided by the availability in foundry offerings. Figure 3(a) shows the effective indices of the TE-like mode in the waveguide B for these etch depths, as a function of the width ratio We/Wt. A deep etch introduces a large neffB(TE) change in the coupling region and a longer coupling length LDC is required [Fig. 3(b)].
The width Wt of the waveguide B should be sufficiently smaller than the width W of the waveguide A to avoid the TE-to-TE mode coupling between the two waveguides. Here, the phase matching condition is designed to be fulfilled in the middle of the taper section, i.e. neffB(TE) = neffA(TM) when We = Wt/2. By setting the width of the waveguide A to W = 450 nm, we obtain Wt = 410 nm, 350 nm and 310 nm for He = 70 nm, 110 nm, and 150 nm, respectively. These parameters are summarized in Table 1.
Using the selected values of parameters He and Wt, the polarization conversion efficiency CETM-TE is calculated as a function of the coupling length LDC using the EME method. The results are shown in Fig. 3(b). For each etch depth, the polarization conversion efficiency eventually saturates and reaches its maximum value provided the coupler is long enough. For the shallow etch (He = 150 nm), a comparatively short LDC is required. The LDC values required for reaching the maximum polarization conversion efficiency CETM-TE are listed in Table 1. It is observed that the minimum polarization conversion loss (i.e., maximum CETM-TE) is achieved for a post-etch slab height of He = 110 nm. At this height (He = 0.5H), the mode is efficiently hybridized (50% Ex and 50% Ey) near the phase-matching position, yielding a high polarization conversion efficiency. Some of our results have been also verified using the 3D-FDTD method. For example, using the parameters in Table 1 for He = 110 nm, the calculated polarization conversion efficiency CETM-TE is ~-0.09 dB across the entire C-band (from 1530 nm to 1565 nm), which is slightly better than the result obtained using the EME method.
3. Fabrication tolerances
The designed taper-etched DC structures can be readily fabricated using the standard silicon photonics processing, including the two-step etch process often used for making high-efficiency surface grating couplers . To investigate the fabrication tolerance of our PSR design, we study the polarization conversion efficiency CETM-TE as a function of several device parameters, as shown in Fig. 4 and Table 2. Simulations show that the longer the coupling length LDC, the more fabrication tolerant the PSR is, but with a penalty in device footprint. The reason is that a long coupling length LDC provides a sufficiently long phase-matching region to ensure the full power transfer from the TM-like mode to the TE-like mode. Here, we set LDC = 400 µm, 200 µm and 150 µm for He = 70 nm, 110 nm and 150 nm, respectively, larger than the values indicated in Table 1. Longer LDC will slightly increase the insertion loss of the PSR while shorter LDC decreases the fabrication tolerances. Figure 4(a) illustrates the dependence of polarization conversion efficiency CETM-TE on the variation of the post-etch slab height (ΔHe). All other parameters are assumed constant at their nominal design values listed in Table 1. It is observed that CETM-TE is rather tolerant to over-etching (ΔHe<0) in the taper section. On the other hand, CETM-TE drops dramatically for substantial under-etching errors as the neffA(TM) exceeds the maximum effective index range for which the phase matching condition holds.
The fabrication tolerance of the PSR is also evaluated for other device parameters, with a condition of CETM-TE> −0.5 dB. For each scan of a given parameter, all other parameters are assumed constant at their nominal design values listed in Table 1. In practical implementation, the tip termination of the taper-etched waveguide has a finite width. Figure 4(b) shows the calculated polarization conversion efficiency CETM-TE as a function of tip with Dt. When Dt ~80 nm, CETM-TE is > −0.5 dB while the loss penalty is 0.2 dB. As shown in Table 2 and Fig. 4, the designed device is very fabrication tolerant to W, Dgap and Dt. Meanwhile, the fabrication tolerance of the proposed design is similar for different etching depths, i.e., He = 70 nm, 110 nm and 150 nm. In Table 2, it is also shown that the overall tolerances are better than 50 nm for a penalty of −0.5 dB in CETM-TE. These tolerances are within the process specifications offered by photonic foundries, demonstrating the fabrication resilience of our PSR design.
Finally, we examine the operational wavelength range of our PSR. For a TE-like mode input, the TE-to-TE insertion loss (IL) at the through port A2 and the crosstalk (XT) at the cross port B2 are defined as IL = 10log10(P(out)ATE/ P(in)ATE) and XTTE = 10log10(P(out)BTE /P(out)ATE) respectively. For the TM-like mode input, the polarization conversion loss (PCL) at the cross port B2 and the XT at the through port A2 are defined as PCL = 10log10(P(out)BTE/ P(in)ATM) and XTTM = 10log10(P(out)ATE/P(out)BTE), respectively. Figure 5 shows the wave-length dependence of the loss and crosstalk of the PSR for He = 110 nm. The TE-like mode insertion loss is below −0.07 dB within the wavelength range of 1450 nm to 1650 nm (bandwidth>200 nm), while the TM-to-TE conversion loss is less than −0.5 dB across the entire S, C and L-bands (1460 nm to 1625 nm), and below −0.3 dB over the C-band (1530 nm to 1565 nm). As shown in Fig. 5(b), the crosstalk XTTE and XTTM are below −30 dB in the investigated S, C and L bands. This broad bandwidth is a distinct advantage of our PRS based on the taper-etched directional coupler. In Table 3 we summarize the wavelength dependence of the PSR parameters for the three different post-etch slab heights He. For the deep-etch (He = 70 nm), the TE-to-TE insertion loss is about −0.15 dB and the crosstalk XTTM is below −20 dB. This is because the width Wt = 410 nm of the waveguide B is closer to W = 450nm, resulting in TE-to-TE mode coupling between the two waveguides. In addition, simulations show that fabrication tolerances remain similar over the entire C band. Since neffB(TE) of the waveguide B and neffA(TM) of the waveguide A varies with the wavelength in a similar trend, the phase-matching condition neffB(TE) = neffA(TM) is expected to be achieved at the same position for different wavelengths.
4. Comparison with literature results
Table 4 summarizes several results of the DC-based PSRs from the current literature and compares them with our design. The PSRs using a one-step etch in [9, 10] required an air cladding to break the vertical asymmetry in order to achieve a high polarization conversion efficiency. The two-step etching processes in [11, 12] induced both the horizontal and vertical asymmetry without the need of an air cladding. However, the parallel DC structures in [9, 11, 12] required precisely tuned phase matching. As a result, these DCs are all inherently wavelength dependent and sensitive to fabrication variations. The tapered DC in  was used to compensate the fabrication variations at the cost of a relatively large footprint. However, the improvement of the fabrication tolerance was still limited. The taper-etched DC structure in this work enhances the fabrication tolerance significantly while using a similar footprint as in . Furthermore, the structure reported here has a broadband operation bandwidth without the need for precise lithographic alignments.
We have proposed and investigated a fabrication-tolerant polarization splitter and rotator (PSR) design based on the cross-polarization coupling mechanism. The PSR comprises a silicon wire waveguide coupled to a taper-etched waveguide and it can be fabricated by standard silicon photonics processing without the need for precise lithographic alignments. We used the full-vectorial EME and the 3-D FDTD methods for the numerical evaluation of the device performance. Our calculations show that a high TM-to-TE polarization conversion efficiency can be readily achieved over a broad wavelength range, i.e. −0.5 dB polarization conversion loss within the S, C and L band wavelength range of exceeding 160 nm. The conversion loss in the C-band is below −0.09 dB. A TE-to-TE through insertion loss is better than −0.07 dB for the same wavelength range, with a low polarization crosstalk of −30 dB. Among the PSR structures designed for an SOI platform, our design is among the most fabrication tolerant and broadband reported to date.
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