Fig. 1. Schematic of an apodized grating coupler: (a) side view; (b) top view. (c) Relationship of the equivalent refractive index neq,i and longitudinal grating period Λz,i with the lateral duty cycle fy,i. (d) Grating directionality as a function of BOX thickness.

Fig. 2. Calculation results of the Gaussian function and the corresponding leakage factor distribution. Inset, relationship of the leakage factor αi with the duty cycle of the groove fy,i.

Fig. 3. Value distribution along the longitudinal grating period number of duty cycle of the ith groove fy,i, equivalent refractive index neq,i of the grating grooves, and longitudinal grating period Λz,i for apodized grating couplers.

Fig. 4. (a) Coupling efficiency versus wavelength of the apodized grating couplers in three feature sizes; (b) electric field intensity distribution when the light propagates in the grating couplers with gold bottom mirror at the wavelength of 1550 nm.