Modeling of Wave Resonances in Low-Contrast Photonic Crystals

Coupled-mode equations are derived from Maxwell equations for modeling of low-contrast cubic-lattice photonic crystals in three spatial dimensions. Coupled-mode equations describe resonantly interacting Bloch waves in stop bands of the photonic crystal. We study the linear boundary-value problem for stationary transmission of four counter-propagating and two oblique waves on the plane. Well-posedness of the boundary-value problem is proved by using the method of separation of variables and generalized Fourier series. For applications in photonic optics, we compute integral invariants for transmission, reflection, and diffraction of resonant waves.