Adiabaticity and random wave propagation

We examine the assumption of adiabaticity that underlies mode-coupling analysis of stochastic phenomena such as roughness and inhomogeneity in passive photonics devices such as couplers, gratings, and simple waveguides. We show that although the adiabaticity condition is formally violated by such phenomena, only the low spatial frequencies actually contribute significantly to such phenomena, thus preserving the validity of the analysis.