Modified rigorous coupled-wave analysis for multi-layer deformable gratings with arbitrary profiles and materials

In this paper, the rigorous coupled-wave analysis (RCWA) is extended for general multi-layer deformable gratings with arbitrary numbers of layers, surface profiles, layer offsets, and materials. The contribution from the offset between grating layers and/or due to the movement of the deformable grating layer is included in the expansion of the relative permittivity by the Fourier series, enabling the calculations of deformable gratings commonly used in many optical-based displacement sensing devices. The accuracy and efficiency of the extended RCWA are verified by a number of grating models. It is found that the numerical results are in excellent agreement with those from the finite element method, while the RCWA method costs only ∼1/10 in computation time when compared to its counterpart. Our approach can be used for fast calculation and optimization of multi-layer deformable gratings for optical displacement sensing applications.