Rigorous coupled-wave analysis of multilayered grating structures

Using a rigorous coupled-wave analysis, a (2 × 2) matrix method in homogenous layered media is generalized for a grating-embedded multilayer structure with (2M × 2M) dynamic and propagation matrices in both transverse-electric and transverse-magnetic polarizations, where M is the number of harmonics retained in the field expansion. A numerically stable algorithm to implement the method is described. Numerical results are presented for a diffraction-based optoacoustic sensor that consists of a reflective movable membrane and fixed grating fingers on a transparent quartz substrate and are compared with the scalar diffraction method to illustrate the limited applicability of the scalar approach.