Plane Wave Method (PWM):
PWM is a very popular numeric technique used to solve periodic electromagnetic problems. This technique expands the periodic structure into a superposition of plane waves with known coefficients and periodic field distribution (periodic structures will cause periodic field distributions) which are going to be solved into a superposition of plane waves with unknown coefficients , where is the number of plane waves used in the expansions.

Under this expansion, the characteristic equation obtained from Maxwell's Equation can be transformed into equations with N unknowns and the problem thus turns into an eigenvalue problem. By solving this eigenvalue problem, the frequencies corresponding to each plane wave (which provides dispersion relationship of the periodic structure) and , i.e., the periodic field distributions, can be obtained.

PWM can be used to solve 1D, 2D, and 3D periodic problems. However, for 3D problems, an impractically tremendous number of plane waves may be needed to ensure accuracy. In this case, Iterative PWM can help. Iterative PWM only solve the interested bands and thus significantly reduce the computation cost and speed up the calculation.