Floquet and coupled-waves analysis of higher-order Bragg coupling in a periodic medium
The paper considers wave propagation in longitudinally periodic media near the first- and higher-order Bragg resonances. An extended coupled-waves (ECW) approach is applied to media with single or multiharmonic periodicities and is numerically compared with the Floquet theory. The ECW approach predicts coupling coefficients that vary as the magnitude of the perturbation raised to the power of the Bragg order. Explicit expressions are also given for the band-gap width and band-gap shift for all Bragg orders. A number of applications are discussed.