The Rayleigh hypothesis in scattering off photonic crystal interfaces

We examine the Rayleigh hypothesis in the context of scattering of light off photonic crystal interfaces. First, the hypothesis - which was initially suggested for scattering of waves off rough surfaces between homogeneous media - is rephrased to apply to photonic crystal interfaces. Next, an exact and explicit functional form is presented that maps plane photonic crystal surfaces to periodic rough surfaces in free space, so that known criteria for the validity of the Rayleigh hypothesis for scattering at rough surfaces can be applied directly to scattering at the photonic crystal surfaces. The same map also allows the scattering problem to be solved exactly.