Modeling of low-contrast photonic crystals with coupled-mode equations

Abstract

<p>We show that the coupled-mode equations can be used for analysis of resonant interaction of Bloch waves in low-contrast cubic-lattice photonic crystals. Coupled-mode equations are derived from Maxwell's equations using asymptotic methods. We prove the existence and uniqueness theorem for a solution of the boundary value problem for transmission of N resonant waves in small convex convex domain (linear and non-linear cases). The analytical solutions for linear boundary-value problem for the stationary transmission of four counter-propagating and two oblique waves on the plane are found by using separation of variables and generalized Fourier series. We give the proof that the linear stationary boundary-value problem for four counter-propagating and two oblique waves on the plane is well-posed for arbitrary size of the domain. For applications in photonic optics, we compute integral invariants for the transmission, reflection and diffraction of resonant waves. We recast the problem for four counter-propagating waves on the plane in a multisymplectic Hamiltonian viewpoint, which gives further insights into the problem.</p>