Amplification of Light within a One-dimensional Photonic Crystal with Harmonically Oscillating Dielectric Constant of Each Layer

Photonic crystals made by stacking at equal intervals dielectric plates whose dielectric constant varies with time harmonically have been considered. The exact governing equation in a space-frequency domain and the approximate equation for small frequency of time variation of the dielectric constant have been derived. In the case that the frequency of time variation of the dielectric constant is small enough, the transmission spectra of systems of 21 layers have been investigated using the perturbation method and the transfer matrix method. It has been found that the time variation of the dielectric constant amplifies the incident wave resonantly and that the resonance frequencies change with the phases of the time variation.