Abstract
An analytical theoretical model for the waveguide grating coupler is developed and applicable to practical deep gratings. The grating-assisted input coupling efficiency is calculated by considering the reciprocal out-coupling problem. The deep grating structure is modelled as an optical layer filled with polarization dipole sources, and the scattered fields are then calculated using the associated Green’s functions and taking into account the multiple reflections and interference from the adjacent layers. The joint loss between the grating region and the waveguide is also considered. Comparison with numerical simulations shows very good agreement and validates the accuracy of the analytical model. The model explicitly describes the importance of multilayer interference of the scattered fields and guided-mode joint loss on the total grating-assisted coupling efficiency and can be used for practical waveguide grating coupler design with negligible computation workload.
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