## Abstract

A polarization-independent grating coupler is proposed and demonstrated in a 3-layer silicon nitride-on-silicon photonic platform. Polarization independent coupling was made possible by the supermodes and added degrees of geometric freedom unique to the 3-layer photonic platform. The grating was designed via optimization algorithms, and the simulated peak coupling efficiency was −2.1 dB with a 1 dB polarization dependent loss (PDL) bandwidth of 69 nm. The fabricated grating couplers had a peak coupling efficiency of −4.8 dB with 1 dB PDL bandwidth of over 100 nm.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

## 1. Introduction

Grating couplers (GCs) have emerged as effective optical input/output interfaces between standard optical fibers and silicon (Si) photonic circuits [1–4]. In conventional silicon (Si) photonic platforms, GCs are formed with the single Si waveguide layer using partially or fully etched features. One dimensional (1D) Si GCs are highly polarization sensitive, which can be intuitively explained using the grating equation. For a GC to couple optical power from a waveguide mode propagating in the chip to an emission angle, *θ*, away from the normal of the plane of the chip, it must satisfy the phase-matching condition,

*k*

_{0}is the free-space wavevector of the light, ${\overline{n}}_{eff,m}$ is the effective index of mode

*m*in the GC,

*n*is the cladding refractive index of the GC, Λ is the grating period, and

_{c}*q*is an integer indexing the diffraction order. In a typical periodic 1D GC formed in a single waveguide layer, ${\overline{n}}_{eff,m}$ depends on the grating duty cycle,

*f*. It is usually not possible to choose a duty cycle such that Eq. 1 is simultaneously satisfied for both transverse electric (TE) and transverse magnetic (TM) polarized modes, i.e., generally, ${\overline{n}}_{eff,TE}(f)\ne {\overline{n}}_{eff,TM}(f)$, leading to polarization-dependent characteristics.

Therefore, to realize a single layer polarization-independent GC (PI-GC), more degrees of freedom, beyond *f*, is needed such that TE and TM modes can satisfy the same condition in the right hand side in Eq. 1. This can be achieved through 2D patterns [5, 6], an intersection of 1D TE and TM gratings [7], or full freedom in the grating geometry [8]. However, thus far, such PI-GCs have exhibited limited coupling efficiency and bandwidths. Proposals require back-reflectors [5] or subwavelength features [5,7,8]. Defining the polarization dependent loss (PDL) bandwidth Δ*λ*_{1dB} PDL as the bandwidth where PDL is under 1 dB, and *η*_{PI} to be the maximum coupling efficiency in either polarization within the PDL bandwidth, to date, the best experimental demonstration of a PI-GC has a Δ*λ*_{1dB} PDL of 12 nm with *η*_{PI} of −6 dB.

Here, we present 1D PI-GCs for the O-band in the 3-layer silicon nitride (SiN)-SiN-on-silicon (Si) platform reported in [9] and [10]. The three layers supported 5 confined supermodes which allowed polarization independent coupling to be realizable using available degrees of freedom. The PI-GCs were designed by a combination of heuristics and optimization algorithms, achieving in simulation *η*_{PI} = −2.1 dB at 1310 nm with Δ*λ*_{1dB} PDL = 69 nm. The best fabricated device had *η*_{PI} = −4.8 dB at 1306 nm Δ*λ*_{1dB} PDL of >100 nm. To the best of our knowledge, this is the highest *η*_{PI} with largest Δ*λ*_{1dB} PDL amongst experimentally realized PI-GCs to date. This result complements the ongoing work on broadband and high peak coupling efficiency bi-layer GCs [11–15] and demonstrates the versatility of multi-layer GCs.

This work is organized as follows. In Section 2, we elaborate on the feasibility of polarization independence in the 3-layer stack, and the optimization process. Section 3 provides experimental measurements of the fabricated devices. Section 4 compares the results with a representative selection of polarization independent and polarization splitting gratings from literature, after which we summarize and conclude.

## 2. Design

#### 2.1. Polarization independent coupling in a 3-layer GC

Figure 1(a) shows the waveguide layers of the 3-layer platform. To intuitively illustrate why a 1D PI-GC can potentially be designed, we examine the modes supported by slab waveguides in this platform. The purpose is to identify whether sufficient degrees of freedom exist to tailor ${\overline{n}}_{eff}$ for the relevant grating modes such that the modes simultaneously satisfy Eq. 1. Full numerical simulations need to be carried out for the PI-GC design to account for substrate reflections and the strong index perturbation (i.e., the guided modes alone do not fully predict the GC performance). The cross-section consisting of the thin Si etch slab and the two fully etched SiN layers, each individually single-mode for TE and TM polarizations, supports a total of 6 supermodes (modes of a system of multiple coupled optical waveguides), as illustrated in Fig. 1(b). To directly couple light from the multi-layer grating into a single layer waveguide, we consider how the supermodes are excited by an input mode from a SiN1 slab waveguide. While a TE input mode couples into the 3 TE supermodes in the 3-layer region [Fig. 2(a) and Fig. 2(c)], a TM input mode couples into only 2 TM supermodes [Fig. 2(b) and Fig. 2(d)]. This is because Mode 6 is not well confined and has very poor overlap with a TM input mode. Therefore, in total, there are 5 modes relevant for polarization independent coupling into an SiN1 slab waveguide.

The 5 relevant modes are matched by 5 degrees of freedom in the geometry of a periodic 3-layer GC that can be used to adjust ${\overline{n}}_{eff,m}:1$. Fill factor in Si (*f*_{0}), 2. Fill factor in SiN1 (*f*_{1}), 3. Fill factor in SiN2 (*f*_{2}), 4. Spatial offset between the Si and SiN1 features (*o*_{0}), and 5. Spatial offset between the SiN1 and SiN2 features (*o*_{2}). These 5 degrees of freedom allow for the possibility for ${\overline{n}}_{eff,m}$ to be adjusted such that it is equal for all 5 confined supermodes, thus the potential for polarization insensitive operation.

#### 2.2. Optimization assisted design

While satisfying the system of grating equations is a prerequisite for PI-GCs, their good performance (e.g., in terms of *η*_{PI} and Δ*λ*_{1dB} PDL) is not guaranteed. Therefore, in addition to these 5 degrees of freedom that adjust ${\overline{n}}_{eff,m}$, we include the period Λ of the grating, and the fiber position *x _{s}* and polish angle

*θ*in the design process to maximize

*η*

_{PI}and Δ

*λ*

_{1dB}PDL. This results in 8 degrees of freedom for the design of a periodic 3-layer grating. We give a parameterization in Fig. 3, where we have defined the variables

*w*

_{1}=

*f*

_{1}Λ,

*g*= (1 −

*f*

_{1}Λ,

*w*

_{0}=

*f*

_{0}Λ,

*w*

_{2}=

*f*

_{2}Λ for convenience of specifying minimum feature sizes. Apodizing the grating) for this parameterization will result in 2 + 6

*N*variables for apodization of

*N*teeth.

To develop a design, we used a combination of optimization algorithms and heuristics to optimize figures of merits (FOM) extracted from direct 2D Finite-Difference Time-Domain (FDTD) simulations of the design. These 2D-FDTD simulations were set up based on the parameterization in Fig. 3. The GCs are designed to couple light from an angled polished SMF-28 fiber into a SiN1 waveguide. *g*, *w*_{1}, *w*_{0}, *w*_{2} are set between minimum allowable features sizes (0.4 *µ*m for *g*, 0.3 *µ*m for *w*_{1} and *w*_{2}, and 0.18 *µ*m for *w*_{0}) up to coarse features of around 1.3 *µ*m corresponding to an upper limit of roughly wavelength per period, beyond which the resultant grating period would not be efficient for the target wavelength. The offsets *o*_{0} and *o*_{2} are allowed to vary approximately over an entire period, within (−2, 0) *μ*m. Due to substrate reflections and mode matching, the optimal *θ* cannot be known *a priori*. Therefore, the design procedure also searched over coupling angles in the range of *θ* ∈ (0°, 35°) without being limited by the total internal reflection for the cladding-air interface (43.7°). The distance between the SiN1 waveguide and the center of the fiber is *x _{s}*, which is bounded between 4 and 7

*μ*m. A Gaussian source with mode field diameter (MFD) corresponding to SMF-28 fiber at 1310 nm injects 45° polarized light. The TE and TM transmission spectrum of the GC is taken in the SiN1 waveguide using mode overlap integrals.

We first tried to design a periodic 3-layer GC to achieve good coupling efficiency in TE and TM polarizations simultaneously. We used the average between the TE and TM coupled power at 1310 nm as the FOM for this design as it was fast to calculate using only one 2D-FDTD simulation with diagonally polarized light input into the grating. With this FOM, we ran 100 iterations of the particle swarm algorithm [16], using a population of 100 particles initialized with uniform random sampling. Since this FOM does not account for PDL and Δ*λ*_{1dB} PDL, we visually inspected 20 of the top performing designs to eliminate designs with high PDL or narrow Δ*λ*_{1dB} PDL which occur when the TE and TM polarization spectra cross. From this pool of designs, we identified a design balancing good coupling efficiency and large Δ*λ*_{1dB} PDL with low PDL [see Table 1 and Fig. 4(a)]. Excluding variations of the same design from the same local optimum, the remaining designs that we had inspected had lower efficiency, higher PDL, or lower Δ*λ*_{1dB} PDL.

We then apodized the periodic GC with the goal of further improving *η*_{PI} and decreasing the PDL, while maintaining the wide Δ*λ*_{1dB} PDL of the periodic GC design. We incrementally performed the apodization. Multiple rounds of optimization are performed, where we select several randomly chosen teeth at a time to be varied, with the result from the previous round as a starting point. At each round, we applied the local optimization algorithm COBYLA [17] bounded to a small region around each starting point to make gradual improvements to one of the following FOM: 1. TE coupling efficiency at 1310 nm *η _{TE}*, TM coupling efficiency at 1310 nm

*η*, the standard deviation of the PDL computed at 100 wavelengths between 1260 and 1360 nm

_{TM}*σ*which is proportional to PDL over the O-band in linear scale, and 4. Δ

_{spread}*η*= log

_{log}_{10}[

*η*/

_{TM}*η*] which reduces the difference in the TE and TM coupling efficiencies at the center wavelength in logarithmic scale. At each round, the FOM was selected heuristically by visual inspection based on the result of the previous round, attempting to balance the increase of the

_{TE}*η*

_{PI}while minimizing the PDL. We first tried to alternate between increasing

*η*and

_{TE}*η*, but this often led to an increased difference between the TE and TM spectra, or a spectral shift between the two polarizations. Applying the FOMs

_{TM}*σ*or Δ

_{spread}*η*usually decreased the PDL but sometimes at a slight cost of coupling efficiency. This prompted additional attempts to increase

_{log}*η*and

_{TE}*η*. Through repeated cycling of the FOM and optimization parameters, improvements became less frequent, and we chose to stop at apodized GC with spectrum shown in Fig. 4(b), with

_{TM}*x*= 5

_{s}*µ*m and

*θ*= 33.9°. Design parameter values are shown in Table 2. Both TE and TM spectra are centered at 1306 nm, with a peak coupling efficiencies of −2.3 dB and −2.1 dB, respectively. The PDL of 0.2 dB at the peak is the lowest value. PDL is below 1 dB between 1329 nm and 1260 nm. Therefore, Δ

*λ*

_{1dB PDL}= 69 nm and

*η*

_{PI}= −2.1 dB.

We show the impact of fabrication variation in fill-factor, interlayer spacer and interlayer offsets in Figs. 5-7 respectively. Fill-factor variations are given in Fig. 5 as deviations from the nominal teeth widths *w* of Tab. 2 in nm while the fixing the corresponding period. While the TM polarization spectra remains relatively robust against most ±60 nm variations, the TE polarization is prone to shifts in the center wavelength or additional losses. The most significant impact on the performance comes from variations in the SiN1 and SiN2 fill-factors, spacer thicknesses, and SiN2 offset. In these variations, the TE coupling efficiency degrade significantly. In all cases, the TE and TM spectra change in different ways with respect to the variations, which impacts PDL and Δ*λ*_{1dB PDL}.

## 3. Experiment

The GCs were fabricated on 200mm wafers with deep UV lithography at IME A*STAR with the back-end-of-line (BEOL) platform described in [10]. The SiN layers are added on top of an active Si platform by plasma-enhanced chemical vapor deposition (PECVD), etching, and chemical mechanical polishing (CMP) steps. The GCs were 12 *µ*m wide, and tapered down to 740 nm waveguides by 500 *µ*m linear tapers. The test structures consisted of pairs of GCs connected by SiN1 waveguides as shown in Fig. 8(a). The devices were measured using a fiber array polished at 34° with index fluid matching fluid (Norland IML150, refractive index *n* = 1.5) applied at the fiber-chip interface. The input laser polarization was set to TE or TM with a polarization controller (Keysight N7788B) with the polarization calibrated to Si TM GCs that were placed nearby. TM Si GCs were used as they had a higher coupling efficiency and higher PDL than TE Si GC designs at 34°. We used the large contrast between the TE and TM spectra in these TM Si GCs to determine the input polarization by minimizing/maximizing measured power at the center wavelength.

The measured spectra for TE, TM, scrambled polarization (SP) inputs, and the PDL from several devices from across the wafer with locations as indicated in Fig. 8(b) are shown in Figure 9. As determined from the free spectral range, the fringes were due to back-reflection of the GCs. From a fringe of at most −0.1 dB near the center wavelength near 1306 nm, we expect at most −22 dB back-reflection. The maximum contrast in the fringe is around −1 dB near 1340 nm, which corresponds to a back-reflection of around −12 dB. Further reduction in back-reflection can be achieved by slanting the grating teeth [18]. Device E4 achieved the best performance, with the TE and TM spectrum overlapping near 1306 nm resulting in a *η*_{PI} = −4.8 dB where Δ*λ*_{1dB PDL} was ≥100 nm between <1260 nm and 1360 nm (over the entire O-band).

The measurements agreed well with simulations qualitatively, but had around −2.5 dB lower coupling efficiency. The study of geometry sensitivity of the device in Sec. 2.2 suggests while fabrication variation could partially be responsible, it is unlikely to be the predominant source of loss as we would also expect worsening of PDL and Δ*λ*_{1dB PDL}. Here, we saw that the polarization independent behavior remains well preserved. Instead, we had observed that SiN2 layer waveguides throughout the wafer experienced losses in excess of 100 dB/cm. The GC teeth uses the SiN2 layer, and an additional loss which affects TE and TM equally is consistent with a lossy SiN2 layer. The physical cause of this fabrication issue is still under investigation, but it can be avoided in future runs as this issue was not present in a separate fabrication run of this 3-layer platform reported in [9], and the subsequent fabrication of a similar passive 3-layer C-band platform [19]. Other contributions to losses include the lack of planarization of the oxide cladding, a slight mismatch in the refractive index between the index matching fluid (n = 1.5) and SiO_{2}, variation or uncertainty in the refractive index, slopes in the sidewalls of the grating features, variation in the layer thicknesses from planarization, and the precise position and angle polish of the optical fiber. Wafer-scale characterization of the material composition and layer thicknesses can be done in the future to ensure better fidelity with simulated results.

## 4. Discussion

Table 3 compares this present work with a representative selection of PI-GCs and polarization splitting (PS) GCs from literature. This work is the first demonstration of GCs that uses supermodes in a multi-layer platform to effect polarization insensitive operation. Compared to other PI-GCs in a single waveguide layer, our approach does not require post-processing to add a back-reflector to achieve high coupling efficiency (such as comparing between simulation results in [5]), and uses coarser features more amenable to foundry fabrication. To the best of our knowledge, our design is the current best experimental demonstration of a PI grating with respect to PDL bandwidth and insertion losses.

*η*_{PI} is the best coupling efficiency of either polarization within the PDL bandwidth (Δ*λ*_{PDL}) for the PDL given in parentheses. MFS is the minimum feature size of the device.

Abbreviations: **Meas.** Measured result, **Sim.** Simulation result, **PI** Polarization Independent, **PS** Polarization Splitting, **SWL** Subwavelength, **Shape Opt.** Shape Optimization, **SOI** Silicon on Insulator, **BR** Back-reflector.

The simulated coupling efficiency and bandwidth of our PI-GC is competitive with PS-GCs. PS-GCs are amenable for polarization diversity and are suited to single layer Si photonic platforms. However, with the introduction of SiN waveguide layers on Si, it is possible to realize components in the SiN layer that exhibit much reduced birefringence such that polarization diversity may not be needed for coarse wavelength division multiplexing (e.g., see [23] for a SiN polarization insensitive wavelength demultiplexer), halving the required footprint.

Although optimization methods have been used to automate the generation of designs, the selection of the designs was largely owed to heuristic evaluations of the device performance. The optimizations used simple FOMs (i.e., single objective each time) and thus required human intervention to guide the procedure toward a final design. Because of the cycling of different FOMs, it is difficult to evaluate the optimality of the solution, although the gradual stalling of improvements suggest the design may be at a local optima of some of the FOMs. Other better performing designs may be possible. For future work, we can adopt a more systematic approach that uses multi-objective optimization or re-define a combined FOM of all the relevant metrics (e.g., *η*_{PI}, PDL, Δ*λ*_{1dB PDL}) that is used throughout the optimization. More systematic methods will provide better insight into design trade-offs and optimality in future designs.

## 5. Conclusion

In summary, we have proposed and demonstrated PI-GCs in a 3-layer SiN-on-Si platform. The polarization insensitivity was made possible by the supermodes and degrees of geometric freedom in the platform. A design was found by successively applying optimizations, each of which targeted a different FOM to optimize for a particular spectral feature. The PI GC achieved *η*_{PI} = −4.8 dB at 1306 nm with Δ*λ*_{1dB} PDL of ≥100 nm, the first demonstration of a 3-layer GC and, to the best of our knowledge, the highest measured performance for PI-GCs to date. The work shows the versatility of multi-layer integrated photonic platforms. The results also suggest extensions of multi-layer GCs to spatial division multiplexing, by similarly coupling different input spatial modes to selected layer supermodes. Optimization based design methodologies are particularly necessary to navigate the large number of degrees of freedom in multi-layer photonics.

## Funding

Natural Sciences and Engineering Research Council (NSERC); Huawei Technologies Canada.

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