Analysis in reciprocal space of the band-pass filter effect in uniform and non-uniform grating couplers

A detailed study on the origin of the bandwidth reduction in the CouplingEfficiency (CE) spectrum for non-uniform grating couplers (nu-GCs) due to a band-pass filter effect is reported. This effect is deeply investigated through Finite Difference Time Domain simulations (FDTD) in order to look at the spatial Fourier Transform (sFT) of the nu-GC's emission, which gives the energies and the wavevectors sustained by the overall structure. We show: how to evaluate the bandwidth from the sFT and how the band-pass filter effect arises from the sFT affecting the CE spectrum giving a physical insight on the bandwidth's reduction. Moreover, we also point out how the concept of photonic crystal bandstructure can be applied for such nu-GCs and used as a powerful tool to describe the dispersion of the light inside these non periodic structures. Finally, both the sFT and the bandstructure approaches are shown to give the same outcomes in terms of the bandwidth evaluation and to be in agreement with the CE spectra's behaviours. The entire analysis is proposed also for uniform-GC in order to directly compare the two different types of structures.