Wave functions and phase shifts of amplified modes within a vibrating metallic photonic crystal

Abstract

We have so far investigated the optical properties within a one-dimensional photonic crystal whose stacked metallic plates are artificially driven by using actuators. A simple model was proposed and numerically analyzed, and the following novel phenomena were found out: The lattice vibration generates the light of frequency which added the integral multiple of the vibration frequency to that of the incident wave and also amplifies the incident wave resonantly. On a resonance, the amplification factor increases very rapidly with the number of layers. Resonance frequencies vary with the phases of lattice vibration. The amplification phenomenon was analytically discussed for low frequency of the lattice vibration and is confirmed by numerical works. The conditions of the resonance, however, have not been discovered yet. The lattice vibration is different from the usual phonon, since the photonic crystal is vibrated artificially, so that the dispersion relation of the lattice vibration does not exit. This fact is one of the causes which complicate the problem. In the present study, we compute the wave functions and phase shifts between the transmission and reflection coefficients around the amplifying resonance, and approach and discuss the resonance conditions with the photonic band structures and the Friedel sum rule in one dimension.