As a universal physical scheme, effective light couplings to waveguides favor numerous applications. However, the low coupling efficiency at wide angles prohibits this fundamental functionality and thus lowers the performance levels of photonic systems. As previously found, the transmission gratings patterned on waveguide facets could significantly improve the large-angle-inputted efficiency to the order of 10-1. Here, we continue this study with a focus on a common scenario, i.e., a grating-modified waveguide excited by the Gaussian beam. A simplified 2D theoretical model is firstly introduced, proving that the efficiency lineshape could be well flattened by elaborately arranged diffractive gratings. For demonstration, subsequent explorations for proper grating geometries were conducted, and four structural configurations were selected for later full-wave numerical simulations. The last comparison studies showcase that the analytical method approximates the finite element method-based modelings. Both methods highlight grating-empowered coupling efficiencies, being 2.5 bigger than the counterparts of the previously reported seven-ring structure. All in all, our research provides instructions to simulate grating effects on the waveguide's light-gathering abilities. Together with algorithm-designed coupling structures, it would be of great interest to further benefit real applications, such as bioanalytical instrumentation and quantum photon probes.
Keywords: energy collection; gratings; light coupling; waveguides.