Fig. 1. Schematic of the BSWG coupler in (a) 3D view, (b) cross-section view, and (c) top view. BSWGs in the y direction can be treated as a homogenous EM when Λy is smaller than the light wavelength.

Fig. 2. Simulation results of SWG couplers. (a) Directionality of uniform BSWG couplers with different parameter combinations of fx and fy. Here, fxa, fxb, and fxc are [0.20, 0.50, 0.15], [0.30, 0.40, 0.15], and [0.40, 0.30, 0.15], respectively. (b) Coupling efficiencies of the single-step-etched SWG coupler, uniform BSWG coupler, and apodized BSWG coupler as a function of wavelength. (c) Grating diffracted electric-field distributions of the single-step-etched SWG coupler (i), uniform BSWG (ii), and apodized BSWG coupler (iii).

Fig. 3. SEM images of uniform and apodized BSWG couplers. (a) Top view of the uniform grating coupler. (b) Top view of the apodized BSWG coupler. (c) Zoom-in image of one period of the uniform BSWG coupler. (d) Zoom-in image of one period of the apodized BSWG coupler.

Fig. 4. Experimental results and 3D-FDTD simulations of uniform and apodized BSWG couplers. (a) Coupling spectrum of the uniform BSWG coupler with fx of [0.40, 0.30, 0.15] and fy of 0.5. (b) Coupling spectrum of the apodized BSWG coupler. The maximum coupling efficiency of −4.53  dB with the 3-dB bandwidth of ∼107  nm was measured at the center wavelength of 2336 nm.

Fig. 5. Optical fiber alignment optimization and reproducibility of the apodized BSWG coupler. (a) Dependence of coupling efficiency on the incident angle of the optical fiber at coupling wavelengths of 2375 nm, 2395 nm, and 2415 nm. (b) Dependence of coupling efficiency (red line) and output MFD (blue line) on the optical fiber position in the z direction. Herein, the output MFD was calculated through the Gaussian-shaped beam propagation model. (c) Measurement results of the apodized BSWG coupler with the same design in different dies. (d) Measurement results of the BSWG coupler with different periods of Λx1, Λx2, and Λx3 in die 1.

Fig. 6. Simulation results of the shallowly etched grating coupler and single-step-etched SWG coupler based on two types of SOI wafers. (a), (b) Directionality and coupling efficiency of the shallowly etched grating coupler based on the SOI wafer with the 220-nm-thick top silicon layer and etching depths of 70 nm, 150 nm, and 220 nm. (c), (d) Directionality and coupling efficiency of the single-etched SWG coupler with fx of 0.4, 0.5, and 0.6, and fy of 0.3 based on the SOI wafer with the 220-nm-thick top silicon layer, as well as with fx of 0.4, 0.5, and 0.6, and fy of 0.5 based on the SOI wafer with the 340-nm-thick top silicon layer.

Fig. 7. Schematics and simulations of the BSWG coupler. (a), (b) Schematics of the uniform BSWG coupler (first four periods) and apodized BSWG coupler (first four periods) in the top view. (c) Theoretical coupling strength and required coupling strength of the apodized BSWG coupler. (d) Directionality and overlap factor of the single-step-etched SWG coupler, uniform BSWG coupler, and apodized BSWG coupler as a function of wavelength. (e), (f) Coupling efficiencies of the single-step-etched SWG coupler, uniform BSWG coupler, and apodized BSWG coupler based on the SOI wafer with the 340-nm-thick top silicon layer for center wavelengths of 2250 and 3200 nm.

Fig. 8. Fabrication error analysis of the BSWG coupler. (a) Difference between the designed holes (yellow lines) and fabricated holes (blue lines). (b) Schematic of the fabricated holes in the cross-section view. (c) Dependence of ΔW on the widths of the holes with etching depths of 70 nm, 150 nm, and 220 nm. (d)–(f) Dependence of ΔL on the lengths of the holes for different widths with etching depths of 70 nm, 150 nm, and 220 nm.

Fig. 9. Characterization of the single-step-etched SWG coupler. (a) SEM image of the single-step-etched SWG coupler. (b) Experimental measurement of the single-step-etched SWG coupler.

Table 1. Parameters of the Apodized BSWG Coupler