Coupled-wave model for square-lattice two-dimensional photonic crystal with transverse-electric-like mode

We propose a coupled-wave model for a square-lattice two-dimensional (2D) photonic crystal (PC) with a transverse electric mode. A set of coupled-wave equations is obtained from this model and it is shown that 2D optical coupling occurs between four light waves propagating in the $\Gamma \text{-}X$ direction via higher-order waves propagating in the $\Gamma \text{-}M$ direction. The expressions for the resonant mode frequencies derived from the coupled-wave equations describe the characteristics of experimental results for the band-edge frequencies of the 2D PC laser.