Bragg interactions in periodic media

The interaction of electromagnetic waves of wavelength lambda with periodic structures of spatial period lambda are studied. The emphasis of the work is on Bragg interactions where lambda approximately equal to 2 lambda/N and the Bragg order N takes on the values 1, 2,.... An extended coupled waves (ECW) theory is developed for the case N greater or equal to 2 and the results of the theory are found to compare favorably with the exact results of Floquet theory. Numerous numerical results are displayed as Brillouin diagrams for the first few Bragg orders. Moreover, explicit expressions for coupling coefficients, bandgap shifts and bandgap widths are derived for singly periodic media. Particular note is taken of phase speeding effects.