Broadband Polarization-Independent Edge Couplers With High Efficiency Based on SiN-Si Dual-Stage Structure

Silicon nitride (SiN) plays a critical role in silicon photonics because of its lower refractive index, low waveguide loss, broad operating bandwidth and compatibility with complementary metal oxide semiconductor (CMOS) fabrication process. Here, we propose a polarization-independent sub-wavelength grating (SWG) edge coupler with high efficiency based on SiN-Si dual-stage structure with a length of only 315.8 μm. Such a structure can be fabricated on 8-inch silicon photonics pilot lines and doesn't require special fabrication processes for making it suspended. We simulate the minimum TE/TM light coupling loss from a standard SMF-28 fiber to be 0.61 dB/0.95 dB with polarization dependent loss (PDL) less than 0.4 dB in the whole band between 1500 nm and 1600 nm.

On modern silicon photonics platform, inverse tapers are commonly used for edge coupling [1], [3].In order for better mode matching between the edge coupler and the fiber to reduce the coupling loss, various structural modifications have been made to inverse tapers, such as nonlinear profile tapers [22], multi-stage tapers [23], multi-layer tapers [24] and trident structures [24], [25].However, the high index contrast between Si and SiO 2 (Δn Si-SiO2 ≈ 2) in the C-band inevitably leads to the effective refractive index mismatch between fibers and Si edge couplers, causing low coupling efficiency.Therefore, replacing Si with one material with a lower refractive index as the core of the edge couplers becomes an effective solution to achieve lower coupling loss [26], [27].Silicon nitride (SiN), a common CMOS-compatible material with low index contrast to SiO 2 cladding (Δn SiN-SiO2 ≈ 0.5) is a promising candidate [26], [27], [28].Recently, SiN edge couplers have been extensively studied [27], [29], [38].Siwei Sun et al. proposed an edge coupler design based on a cross-shaped arrangement of SiN waveguides surrounded by SiO 2 cladding on a standard 220 nm-thick silicon SOI platform and it can couple the light from a standard SMF-28 fiber at 1550 nm to silicon wire waveguide with an overall coupling loss lower than 0.44 dB [33].In addition, Martin Papes et al. proposed a new type of fiber-chip edge couplers by adding subwavelength index engineered thin SiN layers in the upper SiO 2 cladding and achieved total coupling loss lower than 0.42 dB [37].Although very high coupling efficiency is achieved in those two work, complex fabrication processes are needed.
In this work, we present edge couplers embedded with SiN sub-wavelength grating (SWG) based on SiN-Si dual-stage structure, which can be easily fabricated in the current 8-inch silicon photonics pilot lines.The simulations done with 3D Finite-Difference Time-Domain (FDTD) calculations show that our structure enables a minimum TE/TM coupling loss of 0.61 dB/0.95dB, respectively.Our work provides a new way to achieve edge coupling with small loss and low cost.

II. PROBLEMS OF SI INVERSE TAPERS AND THE SOLUTIONS
The coupling efficiency can be divided into two factors: the mode overlap efficiency between the optical fiber and the chip facet (η 1 ), and the transformation efficiency of the delocalized mode at the facet to the mode of the waveguide (η 2 ).η 1 can be calculated as [37]: where E 1 and E 2 are the electrical field distribution of the waveguide mode (at the chip facet) and the optical fiber mode respectively, and A is the mode distribution area.The simulation design is performed by mode overlap optimization and mode transformation optimization.Si inverse tapers are standard devices for edge coupling on 8-inch silicon photonics platforms, whose structure is shown in Fig. 1.
Fig. 2(a) shows the simulated coupling loss between an SMF-28 fiber and a 300-μm-long Si inverse taper as a function of wavelength calculated by FDTD compared with the mode overlap efficiency calculated by Finite Difference Eigenmode (FDE) solver.We can see that the Si inverse taper has a large coupling loss and a large PDL.The theoretical upper bound of coupling losses is given by the mode overlap efficiency between the optical fiber and the inverse taper, which is calculated to be 64.9%(1.88 dB)/39.7%(4.01 dB) of the TE/TM mode at 1550 nm with FDE solver, which arises from silicon's large refractive index, leading to large mode index difference between TE and TM modes.The large difference between FDE and FDTD calculations shown in Fig. 2  calculate that both the low overlap efficiency and large mode leakage into the substrate lead to large coupling loss of Si inverse tapers.
Hence, to improve the performance, we shall increase the mode overlap efficiency at the fiber-to-chip facet and reduce the mode leakage at the same time.Because of the low index contrast between SiO 2 and SiN, higher mode overlap efficiency can be achieved by replacing Si with SiN as the core of the edge couplers [26], [27].We replace the Si inverse taper in Fig. 1 with a SiN inverse taper with a cross-section of 0.2 × 0.3 μm 2 at the tip, and the simulations show that the mode overlap efficiency of the TE/TM mode is 72.0%(1.43 dB)/67.2%(1.73 dB).This indicates that using SiN as the core material can reduce both coupling loss and PDL.To eliminate the effects of silicon substrates, suspended structures have been fabricated [39], [40], [41], [42].However, it requires complex etching process and makes packaging more challenging.
Here, we propose a new fabrication method to prevent mode leakage.Fig. 3 shows the fabrication processes of SiN-Si dualstage edge couplers on a standard 220 nm-thick SOI wafer.First, fully etch the Si layer to fabricate Si devices.Next, etch the buried oxide (BOX) layer and the substrate.We intend to  reduce mode leakage to the substrate by etching the substrate.As shown in Fig. 4, at 1550 nm a SMF-28 fiber has a modal radius of roughly 8 μm, which exceeds the BOX thickness of commercial SOI wafers by 5 μm.It can be seen there is almost no energy distribution below the red dashed line (z = −8 μm).The SiN layer is used for fiber coupling, to avoid mode leakage, the thickness of the BOX under the SiN layer at least 8 μm is required, and the corresponding etching depth of the silicon substrate is at least 4.6 μm.Then, deposit SiO 2 and smooth the surface with chemical mechanical polishing (CMP).The surface roughness of the oxide is less than 1 nm after CMP [43], [44], [45], [46].The thickness of the SiO 2 layer above the top Si layer is controlled to be 0.18 μm, which is the commonly used thickness in foundries such as CUMEC.Next, deposit a 300-μm-thick SiN layer.Then, fully etch the SiN layer to fabricate SiN devices.Finally, deposit the SiO 2 cladding, whose thickness should be at least 8 μm.
The structure of the SiN-Si dual-stage edge coupler is shown in Fig. 5. Fig. 5(a) shows the top view of the core of the SiN-Si dual-stage structure edge coupler.The SiN layer consists of two SiN tapers and a 5-μm-long SiN waveguide connecting these two.Fig. 5(b) shows the SiN-Si dual-stage structure.We use SiN with a lower refractive index to enhance mode overlap efficiency and reduce PDL, and reduce the mode leakage to the substrate by etching the substrate, which is shown in Fig. 5(c).The light is coupled from the fiber into the SiN inverse taper, and then using  the SiN-Si inter-layer coupler to eventually couple the light into the Si waveguide [27], [33], thus achieving efficient coupling of the TE/TM mode.We also analyze the fabrication tolerance of the SiN-Si interlayer coupler.Fig. 7(a) shows the its overlay tolerance.Typically, overlay smaller than 30 nm can be achieved with photolithography machines for 8-inch front end of line fabrication.Therefore, overlay errors lead to negligible excess loss.Fig. 7(b) shows the excess loss versus the size of the gap between the SiN and the Si layers.It can be seen the maximum excess loss is only 0.09 dB in the range of 180±50 nm.The SiN-Si interlayer coupler is very robust against fabrication imperfections.The total coupling loss includes fiber-to-SiN coupling loss and SiN-to-Si coupling loss.Fig. 8(a) shows how light is coupled from the fiber to the SiN layer.Comparing Fig. 8(a) with Fig. 2(b), it is found that the light scattered into the substrate is significantly reduced, which indicates the leakage of light to the substrate is reduced by etching the substrate and increasing the thickness of the BOX under the SiN layer.Fig. 8(b) shows the simulated total coupling loss of the TE mode and TM mode as a function of wavelength.It can be seen the PDL is low, which is the same as the calculation of FDE.Comparing Fig. 8(b) with Fig. 2(a), we can see that our proposed structure has much lower coupling loss than conventional Si inverse tapers with similar length, which proves that our method of using SiN with lower refractive index and etching the Si substrate can reduce the coupling loss significantly.

III. FURTHER INCREASING COUPLING EFFICIENCY WITH SIN SWG EDGE COUPLERS
SWG is a kind of grating structure with the pitch is much smaller than the wavelength, and its pitch is small enough to suppress the diffraction effect arising from the periodicity of the structure [47].It has been widely demonstrated that SWG structure can be used to enhance coupling efficiency [39], [42], [47], [48], [49].Yaqian Li et al. demonstrated an integrated edge coupler embedded with both SWG waveguide and suspended structure based on the Si-SiN hybrid photonic platform, and the corresponding coupling loss of the TE/TM mode is 0.86 dB/0.94dB [39].Tymon Barwicz et al. demonstrated the first O-band SWG between a nanophotonic waveguide and a standard single-mode fiber, and enabled −1.3 dB peak transmission efficiency [42].Those works achieve high coupling efficiency, but there are some limitations of these devices such as large footprint or the need for 12-inch photolithography fabrication process (0.13 μm is the process node of 8-inch silicon photonics lines).In this section, we present our SiN SWG structure.With the same fabrication procedures presented in the previous section, we expect more light can be coupled from an optical fiber to a Si waveguide.
Compared with Si SWG devices [39], [42], [48], there are great advantages of using SiN SWG.Because of the low refractive index of SiN, larger pitch (200 nm half pitch) and larger tip width (200 nm) can be utilized, which can be fabricated on an 8-inch silicon photonics pilot line instead of a 12-inch one.Besides, our SiN SWG edge couplers don't require special fabrication processes for making suspended structure [39], [42].
The 3D schematic diagram of an optical fiber aligned with the SWG SiN-Si dual-stage structure edge coupler is shown in Fig. 9 The pitch (Λ) of Part 1 is 400 nm and the duty cycle (DC) is 50%.The tip width of Part 1 at the two ends is 0.5 μm (w g1 ) and 0.7 μm (w g2 ), respectively.The width of the i-th segment (w i ) of the gratings is given by (2), Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.Fig. 12 shows the simulated coupling loss of the TE and TM modes as a function of wavelength.It can be seen that the minimum coupling loss of the TE/TM mode is 0.61 dB/0.95dB.The PDL is less than 0.4 dB in the band between 1500 and 1600 nm.And particularly, in the C-band, both low coupling loss and low PDL can be achieved.The minimum coupling loss of the TE/TM mode is 0.75 dB/0.95dB, respectively.The performance is wavelength-independent, as the coupling loss variations of the TE/TM mode are less than 0.18 dB/0.04 dB in the C-band.
We compare our designs with other works coupling with the stand SMF-28 fiber in terms of the minimum coupling loss, the total length and the complexity of the fabrication process, which are shown in Table I.Our SWG design only requires dual-stage structure and can be fabricated on an 8-inch silicon photonics pilot line, and it has much smaller footprint with significantly reduced fabrication complexity and comparable performance to the edge couplers reported so far.Therefore, our designs can be used to improve the fiber-to-chip couplings in a variety of optical systems at low costs.

IV. CONCLUSION
In conclusion, we demonstrate a broadband polarizationindependent SWG edge coupler with high efficiency based on SiN-Si dual-stage structure.The minimum TE/TM light coupling loss from a standard SMF-28 fiber can be reduced to 0.61 dB/0.95dB with PDL less than 0.4 dB in the band between 1500 nm and 1600 nm.Particularly, the TE/TM light coupling loss can be reduced to 0.75 dB/0.95dB in the C-band with PDL less than 0.2 dB.Such a structure can be fabricated on 8-inch silicon photonics pilot lines, enabling much better coupling efficiency for various applications.We take advantage of the low refractive index of SiN and deliberately engineer the SWG structure.Besides, the light leakage into the Si substrate is eliminated by etching away the substrate rather than making complex suspended structures.Our designs don't require special fabrication processes and have small footprint, which are essential to achieve low-cost fiber-to-chip couplings.

Fig. 1 .
Fig. 1.(a) 3D diagram of fiber-to-chip coupling with a Si inverse taper for C-band.The coordinate system is shown in the lower left corner, and the light propagates along the X-axis direction; (b) The top view of the Si inverse taper; (c) The side view of the Si inverse taper with the length of 300 µm; (d) The cross-section of the Si inverse taper edge coupler near the fiber facet.
(a) is due to the silicon substrate.Fig. 2(b) shows how light couples from the fiber into the Si inverse taper.Inside the red dashed box, severe mode scattering or leakage into the Si substrate can be seen.We

Fig. 2 .Fig. 3 .
Fig. 2. (a) Simulated coupling loss of the TE mode and TM mode along the coupler with the length of 300 µm as a function of wavelength compared with the mode overlap efficiency calculated by FDE.(b) The simulated field distribution in XZ plane of the TE mode at 1550 nm along the coupler with the length of 300 µm propagating 80 µm.The red dashed box indicates the substrate.

Fig. 4 .
Fig. 4. Mode profile of the TE mode at 1550 nm in the SMF-28 fiber.The position of the red dashed line is −8 µm.

Fig. 5 .
Fig. 5. (a) Top view of the core of the SiN-Si dual-stage structure edge coupler (the 5 µm-length part is the SiN rectangle waveguide).(b) The projection of the core of the SiN-Si dual-stage structure edge coupler on the XZ plane.(c) The projection of the SiN-Si dual-stage structure edge coupler on the XZ plane.

Fig. 6 .
Fig. 6.(a) Calculated coupling loss of TE/TM modes at 1550 nm as a function of the length of the SiN-Si interlayer coupler.(b) The simulated field distribution of the TE mode at 1550 nm as it propagates along the SiN-Si interlayer coupler.(c)-(g) The mode distribution at five positions, x = 280.8µm (c), 289.55 µm (d), 298.3 µm (e), 307.05 µm (f), 315.8 µm (g).The chip facet is set as the origin.

Fig. 7 .
Fig. 7. (a) Excess loss versus the misalignment tolerance between the SiN and Si layers along the Y direction.The red dash line indicates the excess loss of 1 dB.(b) The excess loss versus the thickness of SiO 2 between the SiN and the Si layers.

Fig. 6 (
a) shows the calculated coupling loss of TE/TM modes at 1550 nm as a function of the length of the SiN-Si interlayer coupler.An optimized length of 35 μm is chosen to achieve low coupling loss of both TE mode and TM mode simultaneously.Fig. 6(b) shows the simulated field distribution of the TE mode at 1550 nm as it propagates along the SiN-Si inter-layer coupler.Fig. 6(c)-(g) show the evolution of the TE mode (Y-Z plane) as it propagates along the SiN-Si coupler.Set the chip facet as the origin (x = 0), we simulated the mode distribution at five positions.It can also be seen that the mode distribution is coupled from the SiN layer to the Si layer gradually.

Fig. 8 .
Fig. 8. (a) Simulated field distribution in XZ plane of the TE mode at 1550 nm along the SiN-Si dual-stage structure edge coupler.The red dashed box indicates the substrate.(b) The simulated coupling loss of the TE mode and TM mode along the SiN-Si dual-stage structure edge coupler as a function of wavelength.

Fig. 9 .
Fig. 9. (a) 3D schematic diagram of fiber-to-chip coupling with the SWG SiN-Si dual-stage structure edge coupler.(b) The top view of the core of the SWG SiN-Si dual-stage structure edge coupler.(c) The projection of the core of the SWG SiN-Si dual-stage structure edge coupler on the XZ plane.(d) The projection of the SWG SiN-Si dual-stage structure edge coupler on the XZ plane.

Fig. 10 .
Fig. 10.Loss as a function of w g1 and w g2 when Λ = 300 nm, K = 50 and w b = 0 µm.The solid dot corresponds to the minimum loss when w g1 = 0.5 µm and w g2 = 0.7 µm.

Fig. 11 .
Fig. 11.Coupling loss of TE mode at 1550 nm as a function of (a) Λ, (b) K, and (c) w b .

Fig. 12 .
Fig. 12. Simulated coupling loss of the TE and TM modes as a function of wavelength.