Floquet theory of Bragg interactions in an active medium with index modulation

The exact dispersion relation deduced from the Floquet theory for a plane electromagnetic wave progressing parallel to the sinusoidally varying permittivity in an unbounded, active medium is analyzed by singular expansions. For the first four orders of Bragg regions, the wave characteristics are deduced with attention given to their physical explanations. Correct results are reproduced for the special cases of zero modulation and zero gain.