D. Agueev and D.E. Pelinovsky
Modeling of wave resonances in low-contrast photonic crystals
SIAM Journal of Applied Mathematics 65, 1101-1129 (2005)
Coupled-mode equations are derived from Maxwell equations for modelling 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.
PHOTONIC CRYSTALS, COUPLED-MODE EQUATIONS, WAVE RESONANCES, STATIONARY TRANSMISSION, BOUNDARY-VALUE PROBLEMS