I have a two-dimensional array of periodic structure. Without getting into rigorous couples-wave analysis, can anyone provide an easy method to estimate the the transmission of a broadband optical spectrum?
Just a very rough scalar approximation. Let the structure plane be the XOY plane and the refractive index of the structure n(x,y,z), periodical in the X and Y directions, and consider the normal incidence. You integrate product k0 (wavenumber in vacuum) times n(x,y,z) over z through the structure thickness and get the phase diagram t(x,y). Transforming exp(jt(x,y)) into the 2D Fourier series yields the complex amplitudes of the transmitted diffraction orders.