ABSTRACT
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.
ABSTRACT
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.
