SIMPLE APPLICATION OF THE ENVELOPE-FUNCTION APPROXIMATION FOR PHOTONIC CRYSTALS

A useful technique is presented for calculating the approximate behavi or of electromagnetic wavepackets in a periodic dielectric medium. The technique produces an operator equation which describes the time evol ution of the envelope of the wave packet. The operator equation is sho wn to be equivalent to the Helmholtz equation in linear, isotropic. ho mogeneous media and to a Schrodinger-like equation in a photonic band- gap material. A reflection experiment is used to demonstrate the techn ique. In this experiment, a photonic-crystal cavity is excited at a fr equency above its band edge. It is found that the reflection coefficie nt has Fabry-Perot-Like resonances which increase with the square of t he Frequency. Both the frequency and curvature of the band edge are ac curately predicted by fitting the envelope-function theory to the refl ection data.