Asymptotic study of a two-scale electromagnetic field in a layered periodic structure

We develop an asymptotic method for studying a two-scale monochromatic electromagnetic field in the whole space filled with a periodic layered medium. The frequency of the field is assumed to be close to the frequency of some stationary point of the dispersion surface. In the principle order of the result, the envelopes of the electromagnetic field are governed by a system of hyperbolic or elliptic equations.