Fizeau fringes in wedged resonant gratings

Fizeau fringes are pronounced asymmetric field distributions formed by wedged Fabry-Pérot interferometers also known as the Fizeau interferometers. In this paper, we show that similar effects arise in guided-mode resonant gratings with a wedged waveguide layer. For describing these effects, we develop a formulation of the coupled-mode theory (CMT) with varying parameters, which is shown to be in very good agreement with the results of rigorous electromagnetic simulations of wedged gratings. At the same time, the calculations using the proposed CMT turn out to be by several orders of magnitude faster than solving the Maxwell's equations numerically. We demonstrate that in addition to the Fizeau fringes, the developed CMT captures intricate optical effects such as the appearance of quasi-bound states in the continuum (quasi-BIC) originating from the symmetry-protected BIC supported by the non-wedged grating. We also extend the proposed CMT formulation to the case of stacked wedged gratings exhibiting flat-top reflection peaks. We believe that the obtained results may find application in the design of variable optical filters and resonators based on gratings with spatially varying parameters.