Using complete modal expansions for the electromagnetic fields above and below a rough interface between free space and chiral media and on imposing exact boundary conditions at the interface, Maxwell’s equations are converted into generalized telegraphists’ equations for the wave amplitudes of different species of waves (radiation far fields, lateral, and surface waves). The local basis functions, used in the complete modal expansions, are functions of the fluctuating surface height and medium parameters. The generalized telegraphists’ equations are coupled first-order differential equations for the forward- and backward-traveling wave amplitudes. The coupling between the different species of waves is due to the fluctuations of the rough surface height and medium parameters. A Taylor series expansion of the surface element scattering matrix in terms of the chiral parameter is used to distinguish between depolarization due to surface roughness and the chiral properties of the medium. The analysis has applications in remote sensing and identification of biological and chemical materials through their optical activity.
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