In order to derive full-wave solutions for electromagnetic wave scattering from rough interfaces between achiral media (free space for instance) and chiral media that satisfy generalized constitutive relations, it is necessary to employ complete modal expansions for the electromagnetic fields above and below the interface. To this end, the familiar Fourier transforms of the fields are expressed as generalized field transforms consisting of the radiation term, the lateral waves, and the surface waves. Maxwell’s equations are converted into generalized telegraphists’ equations [in the companion paper (this issue), J. Opt. Soc. Am. A 30, 335 (2013)] upon the imposition of exact boundary conditions. These telegraphists’ equations are coupled first-order differential equations for the forward- and backward-traveling wave amplitudes associated with all the different species of waves (radiation, lateral, and surface waves) excited at the surface of the chiral medium. The analysis presented here includes the completeness and orthogonal relations of the basis functions associated with the modal expansions. This work is used to distinguish between depolarization due to the chiral properties of the medium and depolarization due to surface irregularities. It has applications in remote sensing and identification of biological and chemical materials based on their optical activity.
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