C- and O-Band Dual-Polarization Fiber-to-Chip Grating Couplers for Silicon Nitride Photonics

Highly efficient coupling of light from an optical fiber to silicon nitride (SiN) photonic integrated circuits (PICs) is experimentally demonstrated with simple and fabrication-tolerant grating couplers (GC). Fully etched amorphous silicon gratings are formed on top of foundry-produced SiN PICs in a back-end-of-the-line (BEOL) process, which is compatible with 248 nm deep UV lithography. Metallic back reflectors are introduced to enhance the coupling efficiency (CE) from −1.11 to −0.44 dB in simulation and from −2.2 to −1.4 dB in experiments for the TE polarization in the C-band. Furthermore, these gratings can be optimized to couple both TE and TM polarizations with a CE below −3 dB and polarization-dependent losses under 1 dB over a wavelength range of 40 nm in the O-band. This elegant approach offers a simple solution for the realization of compact and, at the same time, highly efficient coupling schemes in SiN PICs.


■ INTRODUCTION
Fiber-to-chip coupling should offer maximum efficiency for high-performance applications while being simple and fabrication tolerant to achieve scalability and allow rapid prototyping.Silicon nitride photonics has gained attention in the past decades due to numerous advantages, such as propagation losses below 0.1 dB/m, dispersion engineering, negligible two-photon absorption, wide transparency window, low thermal sensitivity, and low sensitivity to fabrication variations. 1−7 Yet, a simple and efficient fiber-to-chip coupling scheme compatible with the SiN process flow is still missing.
To couple light efficiently to the SiN platform, two state-ofthe-art methods exist: edge coupling (EC) and grating coupling (GC).EC, on the one hand, is typically known for its high performance in terms of CE, bandwidth, and polarization insensitivity. 8EC on SiN further benefits from the low index contrast of the waveguides, making it easier to match the modal size between on-chip waveguides and the optical fiber, with CEs reaching below 1 dB. 9−11 GC, on the other hand, allows out-ofplane coupling and therefore wafer-level testing, eliminating the need for intensive processing of a sensitive optical facet at the edges of the chips while typically exhibiting relaxed fiber alignment tolerances. 8The main drawbacks of GC compared to EC, however, are the lower bandwidth, lower coupling efficiency, and high polarization dependency.SiN grating couplers have an improved bandwidth in comparison to silicon ones due to the lower index contrast, 12 allowing 1 dB bandwidths of up to 80 nm. 13 The second challenge of low CE, however, is further hampered on SiN, as lower index contrast results in a lower scattering strength, yielding CEs of −4.2 dB in single-etch SiN gratings. 12To address this, different approaches have been proposed and demonstrated.Most commonly, multilayer distributed Bragg reflectors 14−17 consisting of silicon layers beneath the SiN waveguide are employed, yielding CEs as low as −1.17 dB in measurement and −0.31 dB in simulation with a 40 nm 1 dB bandwidth. 14A different approach consists of defining grating bars on multiple layers, 13,18−21 requiring precise planarization and lithographical alignment.Experimental results show CE of −1.29 dB and a high 1 dB bandwidth of 80 nm 13 and simulations of −0.39 dB. 21A simpler dual-layer GC is demonstrated with a SiN grown on SOI yielding −2.5 dB CE in the C-band, 19 although deep trenches through a triple-layer consisting of SiN, SiO 2 , and Si must be etched.Utilizing the self-imaging method, −1.5 dB CE has been achieved with a staircase grating and a fiber placement over 100 μm above the surface. 22Overcoming the third challenge of polarization dependency is vital for applications, such as on−off keying receivers in optical communications, where polarization of the incoming light is not known a priori. 23Solutions are more difficult, however, as matching of the Bragg condition for two polarizations at the same time is hindered by the typical birefringence of planar waveguides.Possible solutions include 2D grating couplers demonstrated on silicon, 24,25 that typically split the polarizations into two different directions.For 1D grating couplers, only a few examples exist, such as combining two grating periods with an experimental CE of −7.8 dB and a polarization dependent loss (PDL) of 0.8 dB over 20 nm 26 or a multilayer grating consisting of two SiN and one silicon layer with a demonstrated CE of −4.8 dB and 1dB PDL of over 100 nm. 18Despite the impressive grating coupler demonstrations, a method that includes fabrication tolerance and simplicity suited for rapid prototyping, while also achieving low loss in the C-and O-bands and polarization insensitivity, is still missing on SiN.
In this work, we introduce a simple and fabrication tolerant method to couple light efficiently into foundry-produced SiN waveguides with silicon overlay gratings; see Figure 1 The work in this paper is in part based on our results first published at the Optica APC congress in 2021 and 2022. 27,28CONCEPT The grating coupler presented in this work consists of amorphous silicon (a-Si) grating bars on top of an 800 nm thick SiN layer separated by a thin interlayer oxide (ILO) between the a-Si and the SiN, see Figure 2a.The overlay approach differs from the usual concept, where the grating is within the SiN waveguide.In this approach, we exploit the Bragg diffraction coupling by placing a grating in the a-Si overlay layer.Yet, we also exploit the multimode section in the grating; see Figure 2c.The multimode section enables a diffraction in a Gaussian-like mode profile along the grating section.
Conceptionally, one can understand the coupling scheme from Figure 2d.First, a fundamental TE 0 mode is propagated from left to right in the SiN waveguide.A sketch of the mode profile is given in Figure 2b.As it is propagating into the multimode grating section, the mode is mapped onto the three eigenmodes (TE 1 , TE 2 , TE 3 ) of the multimode section; see Figure 2c.Initially, the center of the gravity of the light is in the SiN waveguide layer at the bottom.Only a small fraction of the mode is in the overlay layer and is diffracted.As the three modes propagate in the grating multimode section, the modes constructively interfere into the overlay layer, and accordingly, there is stronger diffraction into free space.At some point, the mode fades away and the diffraction decreases.Simulations confirm that this gradual increase and decrease of emission results in an almost ideal excitation of a Gaussian mode profile; see Figure 2d, which is close to the Gaussian mode profile of the fundamental mode in a single mode fiber.
In the next step, we can derive an approximate value for the pitch Λ of the grating.Toward this end, we follow the general design principles of a 1D grating coupler.To diffract the incoming light into a fiber, the phase matching condition or Bragg condition, which relates the wave vectors of the incident beam and the diffracted beams, must be fulfilled.This can be expressed as where k y = 2π•sin(θ)•n cladding /λ is the wave vector component in y-direction, i.e., the out-of-plane wave, β = 2π•n GC /λ is the propagation constant of the multimode waveguide and |K| = 2π/ Λ the grating vector.Assuming a diffraction angle θ toward the normal axis, the phase-matching equation can be rewritten to where n GC is the effective index of the waveguide grating section, n cladding is the refractive index of the cladding, θ is the diffraction angle, λ the center wavelength, and Λ the pitch of the grating. 8his equation can be solved for Λ if the effective index of the multimode grating section were known.Here, we approximate n GC by averaging the effective index of the etched and unetched region weighted by the fill factor (FF): where n M is the effective index in the unetched region, n E is the effective index in the etched region, and FF = L M /(L M + L E ) is the fill factor.To apply this approximation to a multimode structure, see Figure 2c, the effective index n M of the unetched part in the grating waveguide can be approximated by a weighted average of the effective indices of the respective modes. 18The relative weights are given as the fractions by which each mode is excited.
Figure 3a shows the calculated Λ in relation to h Si using the weighted average method with an FF of 0.32.We find a nearly constant value despite a large variation in h Si .This shows a large tolerance of the grating coupler toward a variation of h Si .Following, we investigate the origin of this fabrication tolerance.Toward this goal, we plot in Figure 3b, the effective index (left) and the relative weights (right) of modes TE 1 , TE 2 , and TE 3 from Figure 2c.The relative weights is calculated using eigenmode expansion and refers to the overlap between the three modes to TE 0 , see Figure 2b.Although the individual modes change considerably with h Si , we find that the effective index of the unetched region n M to be near constant for a large range of h Si values.This is an interesting finding as n M is the weighted average of the modes.Next we investigate the variation of n M with the interlayer-oxide thickness (h ILO ). Figure 3c shows the effective index of TE 2 and (d) of TE 3 in relation to h Si .The colors indicate h ILO .It can be seen that h ILO has little influence on the effective index of the two modes.This leads to the conclusion that this a-Si overlay grating coupler has a high tolerance on both h Si and h ILO .

■ EXPERIMENTAL AND METHODS
Fabrication Tolerant C-Band Grating Coupler.In this section, we show the simulation results of the C-band grating coupler for a maximum CE of −0.42 dB.We analyze the fabrication parameters to show the large fabrication tolerance of our approach.The phase-matching condition allows us to pick a reasonable starting condition for the grating around which we  can apply a thorough 2D FDTD analysis.The optimization routine has led us to an optimized grating coupler with parameter values of h Si = 290 nm, h ILO = 100 nm with a pitch of Λ = 888 nm and fill factor of FF = 0.32.The thicknesses of the SiN (h SiN = 800 nm) and buried oxide (h BOX = 4.1 μm) are kept constant during the optimization.
The wavelength tolerance of the coupling efficiencies of the SiN waveguide toward a SMF fiber tilted by an angle of 7°is shown in Figure 4.The coupling efficiency of a grating coupler without a back reflector is plotted in Figure 4a.The simulated grating is formed only in the a-Si overlay layer and shows a CE of −1.11 dB with a 1 dB bandwidth of 40.5 nm.Simulations show that within 20 grating bars almost 100% of the light is diffracted.For the upward diffracted field there is a 96.6% (−0.15 dB) modal overlap with the fiber.This leaves the reduction of the downward diffracted light as a main method of improvement.Indeed, it is found that the CE can be further increased to −0.44 dB by adding a metallic back reflector below the buried oxide (4.1 μm below the SiN); see Figure 4b.There is no need for changing any parameters of the grating coupler.The 1 dB bandwidth stays large with 39 nm.
In a next step, we analyze the fabrication tolerance of our ideal grating coupler without metal mirror; see Figure 2. We sweep in 2D-FDTD the most important parameters, which are h Si , h ILO , Λ, FF, h BOX , and the thickness of the top oxide (h TOX ).In each sweep, we kept the other parameters constant.In Figure 5a, the CE of the grating coupler is plotted in relation to h Si .Each color indicates a different h ILO .In (b), we plot the coupling efficiency as a function of h ILO .Each color indicates a different h Si .The individual simulations are indicated by colored dots.We find a 1-dB tolerance of 86 nm for h Si and 139 nm for h ILO , indicating an exceptional large tolerance over the two parameters.In Figure 5c, the dependence of the CE on Λ (red line) and the FF (yellow line) are shown.The CE is reduced by 1 dB when varying Λ by ΔΛ = 34 nm and when varying the FF by as much as 0.1455, which corresponds to a detuning of L M by as much as 129 nm.Finally, Figure 5d shows the CE in relation to h BOX (red line) and h TOX (yellow line).Varying h BOX results in an oscillating behavior arising from constructive and destructive interference of the reflections at the interface of the buried oxide and the silicon handle wafer.From the yellow curve, it is seen that h TOX behaves similarly, and a maximum CE is observed at 1.25 μm.Typically, there is a trade-off between efficiency and bandwidth. 29,30If higher optical bandwidth is required, one could potentially utilize an overlay grating material with a lower refractive index than silicon at the price of lower coupling efficiency.
Dual Polarization O-Band Grating Coupler.In the next step, we design and demonstrate a dual-polarization (or polarization insensitive) 1D grating coupler for the O-band using the same principle as the O-band coupler described in the previous section.The use of O-band wavelengths has become the standard for intradatacenter interconnects due to the zerodispersion window around 1310 nm. 31 Furthermore, the dual-  polarization capability of integrated components is essential for the realization of polarization multiplexing schemes or the compensation of polarization rotating effects in the system.
We overcome the polarization sensitivity of 1D grating couplers, which arises due to the birefringence of rectangular waveguides, by taking advantage of the large fabrication tolerances to exploit and the degree of freedoms provided by the overlay structure to find a low loss grating coupler for the TE as well as the TM modes.In contrast to the C-band grating coupler, there are not three but four modes in the multilayer structure because of the smaller wavelength.In Figure 6, the effective index (left) and the relative weights (right) of modes (a) TE 1 , TE 2 , TE 3 , and TE 4 and (b) TM 1 , TM 2 , TM 3 , and TM 4 is shown in relation to h Si .Similar to the C-band, the weighted average is almost constant.With the addition of TE 0 and TM 0 , the effective indices in the grating region can be designed to be nearly equal for TE and TM polarization (n GC,TE ≈ n GC,TM ).This yields a similar pitch through the approximation of the phase matching equation.To achieve similar behavior in the C-band, control over h BOX and h SiN is necessary, which are fixed by the foundry in our work.We used the weighted average approximation described in the Concept section to calculate a starting point for the optimization routine.The result can be observed in Figure 6c.The simulated grating coupler operates for both polarizations with the same fiber angle and position, resulting in a CE of −2.6 dB.The polarization-dependent loss, defined as PDL = |CE TE,dB − CE TM,dB |, is below 0.15 dB over a wavelength range of 30 nm.The grating has a pitch of Λ = 765 nm and a fill factor of 0.484.The thickness of the a-Si is 305 nm and of the interlayer oxide 100 nm.
Fabrication.The a-Si overlay grating coupler was fabricated with a back-end-of-the-line process on a foundry-produced thick SiN platform.Amorphous silicon was deposited on a planarized sample with plasma-enhanced chemical vapor deposition, patterned with electron beam lithography, and etched by using inductively coupled reactive ion etching (ICP-RIE) in HBr plasma.The fabrication of the devices with metallic reflector included a backside oxide etch with ICP-RIE and a subsequent deep reactive ion etching (DRIE) of the Si substrate.Electron beam evaporation was used to deposit gold on the backside.Figure 1d shows a cross-sectional scanning electron microscopy (SEM) image generated with a focused ion beam of the grating coupler without metallic reflector.Figure 1b shows an optical microscopy image of the grating coupler with a metallic back reflector on the same chip.Finally, the chip was coated with poly(methyl methacrylate) (PMMA) as cladding material.It serves as an easy-to-deposit substitute for SiO 2 with a comparable refractive index (n ≈ 1.48).We fabricated the dual-polarization grating coupler in the same way as the C-band gratings with h Si = 305 nm and without a back reflector.The SEM image of the O-band grating coupler is found in Figure 1c.

■ RESULTS AND DISCUSSION
Measurement of C-Band Grating Coupler. Figure 7 shows the coupling efficiencies as a function of the spectra of the a-Si overlay grating couplers presented in this work.The red curves are from measurements.The yellow curves correspond to the simulated grating coupler.The parameters of (a) were adapted to the fabrication result through thickness measurements and SEM images of cross sections generated with a focused ion beam.For (b), we assume the same parameters with the only difference of a 50 nm thinner h BOX due to over etching.The plots in Figure 7a show the CEs of the a-Si overlay GCs without a back reflector.Coupling efficiencies of −2.2 dB were found with a 1 dB bandwidth of 45 nm.By adding a metallic back reflector, see Figure 7b, a CE of −1.4 dB and a 1 dB bandwidth of 37.5 nm was measured.The GCs of Figure 7a,b have identical geometries, and they stem from devices fabricated on the same chip.Characterization of the devices were conducted with optical transmission measurements using a tunable laser source in the C-band.A polarization controller was used to set the correct polarization.The setup losses were subtracted from the measurement and the SiN waveguides were assumed to be lossless.In practice we found propagation losses of ∼0.4 dB/cm.Yet, as our waveguides were as short as 1.5 mm, we disregarded such losses.Standard 90°-cleaved single-mode SMF28 fibers were used for coupling.The measurements and simulations of the a-Si GC are in very good agreement.The lower efficiency in the measured vs the simulated GC with metallic mirror potentially arises from utilizing the buried oxide as an etch stop for the DRIE process, which leads to a slightly thinner BOX thickness.Overetching had to be conducted to make sure all silicon is removed.
Table 1 summarizes different approaches for low loss grating couplers on the SiN platform and compares our measurements to the literature results.Our result of −2.2 dB is, to the best of our knowledge, the highest efficiency reported for a single-etch grating coupler without back reflector.The efficiencies of the a-Si grating coupler with a metallic mirror as shown in this work are comparable to the more complex DBR approaches.
Measurement of O-Band Dual Polarization Grating Coupler. Figure 7c shows the measured results of −2.3 dB with a 32 nm 1 dB bandwidth for the TM polarization and −3.0 dB CE with a 41 nm 1 dB bandwidth for the TE polarization.The PDL is below 1 dB over a wavelength range of 40 nm.The measurement was conducted using a similar setup as for the Cband grating coupler with a tunable laser source in the O-band.Polarization-sensitive reference grating couplers were used to set and adjust the polarizations with a polarization controller.
Analog to the C-band, we subtracted the setup losses and assumed that the SiN waveguides are lossless.The angle of the standard 90°-cleaved single-mode SMF28 fibers was set to 10.5°f or both polarizations.The small dips in the spectrum originate from ring resonators coupled to the SiN waveguide.Table 2 summarizes the literature results for polarization diversity schemes with 1D grating couplers for reference.We find that our approach offers a significantly higher coupling efficiency than other 1D grating approaches on silicon or silicon nitride photonics.Furthermore, in contrast to literature, we do not see an efficiency penalty in comparison to single polarization grating couplers.

■ CONCLUSION
In this work, we introduce highly efficient grating couplers for an emerging SiN platform.The single etch a-Si gratings have been fabricated by a back-end-of-the-line process at the wafer-scale on foundry-produced SiN waveguides.For TE-polarized light in the C-band, simulations yield high CEs of −1.11 without and −0.44 dB with metallic mirrors.In experiments, we found CEs of −2.2 and −1.4 dB, respectively.Furthermore, we demonstrate efficient and polarization-insensitive 1D grating couplers in the O-band.We measure a PDL below 1 dB within a 40 nm spectral window with a CE of −2.3 dB (TM) and −3.0 dB (TE) in the same device for coupling to a fiber aligned along the same fiber angle.Our approach offers a solution to a pending problem and provides ease of fabrication by taking advantage of a fabricationtolerant design that is compatible with wafer-scale testing.The low fabrication complexity might help to further leverage the SiN platform.

■ AUTHOR INFORMATION
. Coupling efficiencies in the C-band as high as −2.2 dB in measurement and −1.11 dB in simulation are demonstrated, and we show improvement to −1.4 dB in measurement and −0.44 dB in simulation by depositing a metal back reflector without changing any other parameter.The versatility of the approach is further demonstrated with a polarization insensitive design in the Oband reaching −2.2 and −3 dB CE for TM and TE polarizations, respectively.The PDL remains below 1 dB over 40 nm.

Figure 1 .
Figure 1.Fabrication-tolerant back-end-of-the-line amorphous silicon overlay grating couplers for the SiN platform.(a) Three-dimensional illustration of the a-Si overlay grating couplers with back reflector.(b) Optical microscope image of fabricated couplers with a circular back reflector.(c) SEM image of couplers without a backside mirror.(d) SEM image of a FIB-generated cross section of the C-band grating coupler without back reflector.

Figure 2 .
Figure 2. (a) Schematic of the grating coupler with the relevant parameters.(b) Mode in the SiN waveguide without overlay.(c) Modes in the multilayer structure, which have an influence on the diffraction.(d) Normalized electric field in y-direction of the suggested grating coupler, showing that there is an interaction between the different modes.

Figure 3 .
Figure 3. (a) Λ calculated using the weighted average, showing a near constant value in relation to h Si .(b) n eff (left) and the relative weights to TE 0 (right) of the modes TE 1 , TE 2 , and TE 3 in relation to h Si .The weighted approximation of n M is near constant, indicating a large tolerance on to h Si .Simulated to n TE2 (c) and n TE3 (d) in relation to h Si with the colors indicating h ILO .h ILO has a minimal influence on the effective index.

Figure 4 .
Figure 4. Simulated coupling efficiency for (a) a-Si overlay grating and (b) a-Si overlay grating with metallic mirror.The directionality can be improved by including a metallic mirror, increasing the coupling efficiency from −1.11 to −0.44 dB.

Figure 5 .
Figure 5. Simulations showing that the suggested grating coupler offers large fabrication tolerance.(a, b) Simulated CE with varying h Si and h ILO showing large fabrication tolerance with a 1 dB tolerance of 86 and 139 nm, respectively.(c) Tolerance sweeps over Λ (red line) and FF (yellow line) with a 1 dB tolerance of 34 nm for the Λ and 0.1455 for the FF.(d) CE in relation to h BOX (red line) and h TOX (yellow line).

Figure 6 .
Figure 6.Polarization diverse 1D grating coupler enabled by the multilayer approach.(a) The n eff (left) and the relative weights (right) of the modes TE 1 , TE 2 , TE 3 , and TE 4 for the O-band in relation to h Si .(b) n eff (left) and the relative weights (right) for the TM-polarized modes.(c) Optimized 1D grating coupler for TE and TM operation with a coupling efficiency above 2.5 dB with a polarization-dependent loss (PDL) of less than 0.25 dB for over 30 nm.

Figure 7 .
Figure 7. Measured (red line) and simulated (yellow line) coupling efficiency of the grating couplers versus simulated value with the 1 dB bandwidth.(a) CE of the TE C-band grating coupler without a back reflector.(b) CE of the TE C-band grating coupler with a back reflector.(c) Measurement result of the polarization diverse grating coupler with a measured PDL below 1 dB for over 40 nm.

Table 2 .
Polarization Diversity Schemes for 1D GC on Si or SiN Found in the Literature