Supplemental Document
Subwavelength grating couplers for an ultrathin
silicon waveguide: supplement
J IAQI WANG , 1,∗ G UOXIAN W U , 1 S I C HEN , 2,3 Z UNYUE Z HANG , 2,3
H UI Z HANG , 1 X U L I , 1 P ENGHAO D ING , 1 C HUXIAN TAN , 1 Y U D U , 1
YOUFU G ENG , 1 X UEJIN L I , 1 H ON K I T SANG , 4 AND Z HENZHOU
C HENG 2,3,4,5,6
1 College of Physics and Optoelectronic Engineering, State Key Laboratory of Radio Frequency
Heterogeneous Integration, Shenzhen University, Shenzhen 518060, China
2 School of Precision Instrument and Optoelectronics Engineering, Tianjin University, Tianjin 300072,
China
3 Key Laboratory of Optoelectronics Information Technology, Ministry of Education, Tianjin 300072, China
4 Georgia Tech-Shenzhen Institute, Tianjin University, Shenzhen 518055, China
5 Department of Chemistry, The University of Tokyo, Tokyo 113-0033, Japan
6 zhenzhoucheng@tju.edu.cn
∗ jqwang@szu.edu.cn
This supplement published with Optica Publishing Group on 3 March 2025 by The Authors
under the terms of the Creative Commons Attribution 4.0 License in the format provided by the
authors and unedited. Further distribution of this work must maintain attribution to the author(s)
and the published article’s title, journal citation, and DOI.
Supplement DOI: https://doi.org/10.6084/m9.figshare.28381580
Parent Article DOI: https://doi.org/10.1364/OL.554899
Subwavelength grating couplers for an ultrathin silicon
waveguide: supplemental document
This document (Supplement 1) provides supplementary material for Subwavelength grating
couplers for an ultrathin silicon waveguide.
1
1． Simulations of the waveguides with different thicknesses
Fig. S1. Simulation results of (a) mode leakage loss, and (b) ECF of waveguides with different thicknesses.
With a waveguide width of 1.5 μm and different waveguide thicknesses, we calculated the
mode leakage loss defined as the leakage of light to the silicon substrate below the buried oxide
layer and external confinement factor (ECF) in the air [S1] defined as the power ratio in the air
over the total light power of the waveguide, expressed as follows,
ng ∬air ε(x,y)|E(x,y)|2dxdy
ECF = ∬total ε(x,y)|E(x,y)|2dxdy
(S1)
where E is the electric field, ε is the permittivity, ng is the group index. The mode leakage loss
is calculated using the eigenmode solver (Lumerical MODE Solutions), while the ECF is
calculated using the finite element method (COMSOL Multiphysics). As shown in the results
in Fig. S1, the ultrathin waveguide with a thickness of 70 nm has a high ECF factor while
maintaining low mode leakage loss, which is suitable for sensing and optoelectronic
applications. Therefore, we chose 70-nm thick SOI waveguides for this work.
2. Coupling efficiency of the apodized 1D grating couplers
Fig. S2. Coupling efficiency of the apodized 1D grating couplers with different F0 values.
According to Eqs. (3), (4) in the manuscript, we investigated the coupling efficiencies of
apodized 1D grating couplers, which were closely related to the initial grating fill factor (F0),
as shown in Fig. S2. When F0 was 0.9, 0.8, 0.7, 0.6, the linear variation of the filling factor R
2
was optimized as -0.069, -0.019, -0.028, -0.004, and the apodized 1D grating coupler achieved
coupling efficiency of -7.28 dB, -7.60 dB, -7.92 dB, -8.51 dB at the wavelength of 1550 nm,
respectively.
3. The influence of SWG fill factor (Fy) on directionality.
Fig. S3. (a) Directionality and (b) Coupling efficiency of SWG couplers with different Fy at the wavelength of 1550 nm.
We investigated the influence of SWG fill factor (Fy) on the directionality of SWG couplers
at the wavelength of 1550 nm, as shown in Fig. S3(a). The directionality is calculated as the
ratio of optical power diffracted toward the fiber [S2]. The directionalities reach the maximum
with Fy of 0.56 and 0.60 for the uniform and apodized SWG couplers, while the coupling
efficiencies reach the maximum with Fy = 0.62 for the two couplers, as shown in Fig. S3(b).
4. The influence of SWG fill factor (Fy) on back reflection and substrate leakage
Fig. S4. (a) Back reflection and (b) Substrate leakage of the SWG couplers with different Fy at the wavelength of 1550 nm.
We investigated the influence of SWG fill factor (Fy) on the back reflection and substrate
leakage for SWG couplers with different Fy at the wavelength of 1550 nm, as shown in Figs.
S4 (a) and (b). For the SWG couplers with Λy = 320 nm, the apodized device has larger back
reflections than the uniform device when Fy is in the range of 0.54-0.72, while the substrate
leakages are similar for both devices.
3
5. Comparison of the ultrathin grating couplers
Table S1． Comparison of the ultrathin grating couplers.
Center Peak coupling 1 dB
Structure Cladding
wavelength efficiency bandwidth
1D uniform [S3] 1550 nm -3.7 dB 50 nm SiO2
1D uniform [S4] 1565 nm -6.5 dB 40 nm SiO2
Suspended SWG [S5] 2200 nm -7.1 dB 115 nm Air
Apodized SWG with Λy = 560 nm
1544 nm -7.0 dB 40 nm Air
(this work)
Uniform SWG with Λy = 320 nm
1537 nm -7.8 dB 62 nm Air
(this work)
We compared our device with published ultrathin grating couplers. Due to the weak optical
confinement of ultrathin waveguides, researchers have adopted thick upper cladding [S3, S4]
and suspended structures [S5] to improve the coupling efficiency. However, these methods
require additional deposition and etching fabrication processes, and the upper cladding layer
can hinder the direct interaction between the evanescent field of the waveguide and the external
medium, limiting the sensing and optoelectronic applications. In contrast, our ultrathin SWG
coupler features a straightforward and reproducible structure for fabrication, making it suitable
for developing waveguide sensors and waveguide-integrated optoelectronic devices.
6. Calculations of F-P cavity length from the normalized transmittance
The F-P cavity length (L) is calculated as FSR = ngL), where FSR is the free spectral
range of the F-P ripples in the normalized transmittance, and ng is the group refractive index of
the waveguide. We calculated the F-P cavity lengths of four types of grating couplers at their
center wavelengths to be 247.9 μm, 226.7 μm, 232.2 μm, and 231.9 μm, which is consistent with
the total length of the device (a pair of 20-μm long tapers and a 200-μm long straight waveguide),
confirming that the back reflection causes the F-P ripples. The noise in the spectrum in Fig. 5(d)
is caused by the SWG period (560 nm) being too large to suppress high-order diffractions. At
1550 nm wavelengths, the subwavelength grating condition requires a grating period of
approximately 300 nm [S6]. Therefore, the SWG couplers with a Λy of 320 nm have low noise,
while the SWG coupler with a Λy of 560 nm has high noise.
7. Calculations of back reflections for the four types of grating couplers
The back reflection between the grating and the connected waveguide is extracted from Fabry-
Perot ripples of the measured coupling efficiency spectrum, which has been widely explored
[S7,S8]. Based on the normalized transmittance, the back reflection can be calculated by using
the transmission equation of the F-P cavity [S9],
(1 𝑟2)2
𝑇=
(1 𝑟2)2 (2𝑟)2 sin2 𝛿 2
, (S2)
where T is the normalized transmittance, r is the reflection coefficient, and δ is the phase
difference. When sin2(δ⁄2) is taken as 1, T obtains the minimum value, and the back reflection r2
can be calculated as -13.4 dB, -17.7 dB, -18.0 dB, and -18.7 dB for the four types of devices
shown in Fig. 5 at their center wavelengths. The extracted back reflections of the uniform 1D
grating coupler, uniform SWG coupler (Λy = 320 nm), and apodized SWG coupler (Λy = 320
nm) agree with the 3D FDTD simulation results of the back reflection of the grating couplers in
Fig. 2(c). Further, we calculated the back reflection curves from 1540 nm to 1600 nm
wavelengths similarly, as shown in Fig. S5. As the measured transmission spectrum of the
4
grating coupler is a curve, the calculated back reflections in the region far from the center
wavelengths are higher than the actual values.
Fig. S5. Calculation of back reflections of the four types of grating couplers at different wavelengths based on the measured
transmittance spectra.
References
S1. M. Pi, C. Zheng, H. Zhao, et al., “Ultra-Wideband Mid-Infrared Chalcogenide Suspended Nanorib Waveguide
Gas Sensors with Exceptionally High External Confinement Factor beyond Free-Space,” ACS Nano 17(18),
17761-17770 (2023).
S2. R. Marchetti, C. Lacava, L. Carrol, et al., “Coupling strategies for silicon photonics integrated chips”, Photon.
Res. 7(2), 201-239 (2019).
S3. L. He, Y. He, A. Pomerene, et al., “Ultrathin Silicon-on-Insulator Grating Couplers”, IEEE Photon. Technol.
Lett. 24(24), 2247-2249 (2012).
S4. Z. Zou, L. Zhou, X. Li, et al., “60-nm-thick basic photonic components and Bragg gratings on the silicon-on-
insulator platform”, Opt. Express 23(16), 20784-20795 (2015).
S5. R. Guo, H. Gao, T. Liu, et al., "Ultra-thin mid-infrared silicon grating coupler," Opt. Lett. 47(5), 1226-1229
(2022).
S6. R. Halir, P. J. Bock, P. Cheben, et al., "Waveguide sub-wavelength structures: a review of principles and
applications," Laser & Photonics Rev. 9(1), 25-49 (2014).
S7. T. Watanabe, M. Ayata, U. Koch, et al., “Perpendicular Grating Coupler Based on a Blazed Antiback-Reflection
Structure,” J. Lightwave Technol., 3(21), 4663-4669, 2017.
S8. S. E. Hansen, G. Arregui, A. N. Babar, et al., “Efficient low-reflection fully etched vertical free-space grating
couplers for suspended silicon photonics,” Opt. Express, 31(11), 17424-17436, 2023.
S9. S. Zhang, Z. Zhang, R. Guo, et al., “Silicon subwavelength grating coupler with ultra-high reproducibility, ultra-
wide bandwidth, and ultra-low back reflection”, J. Lightwave Technol. 42(15), 5279-5285 (2024).
