Deterministic design of focusing apodized subwavelength grating coupler based on weak form and transformation optics.

The focusing apodized subwavelength grating coupler (F-ASGC) has advantages of high coupling efficiency, small footprint and simple fabrication process, which make it a popular component for chip-scale coupling and testing of integrated optical circuit. However, the design of F-ASGC based on effective medium theory lacks accuracy, causing the drawbacks of peak wavelength deviation and performance degradation. In this work, we propose a deterministic design method of F-ASGC. Our grating coupler is formed by assembling various subwavelength grating units according to their complex effective indexes. The complex effective indexes of these grating units are accurately obtained by the weak form calculation. Then combining with transformation optics, we strictly analyze the F-ASGC for the first time. The simulation results show that the deterministically designed F-ASGC has high coupling efficiency of -2.51 dB, 3 dB bandwidth of 51 nm, and accurate central wavelength of 1553.1 nm. And we also fabricated it on the commercial SOI wafer. The measured maximum efficiency is -3.10 dB, the 3 dB bandwidth is 55 nm, and the central wavelength is 1551.5 nm.