The circularly polarized wave decomposition of Maxwell's equations for electromagnetic wave propagation in chiral materials is the starting point for this analysis. The Fourier transforms of the Green's functions for the electromagnetic waves on both sides of a flat interface between two semi-infinite chiral materials are derived. These harmonic solutions are expressed in terms of the characteristic right and left circularly polarized waves. Through a path deformation in the complex plane, the Green's functions are converted into alternate, modal, representations that are suitable for the complete expansion of the electromagnetic fields above and below a rough interface between two chiral materials with laterally varying material properties. From these representations, generalized Fourier teransform pairs are derived. The generalized Fourier transforms can be used to obtain two sets of coupled ordinary differential equations for the field transforms in terms of the forward and backward wave amplitudes of the transverse fields. Iterative solutions of these generalized telegraphists equations are found. From these solutions the fields can be found under appropriate assumptions. Since no a priori assumptions are made about the surface height, the frequency of the source, or the material parameter this work could be applied to nanotechnology involving stratified chiral structures.
[1]
S. Schelkunoff.
Generalized telegraphist's equations for waveguides
,
1952
.
[2]
S. A. Schelkunoff,et al.
Conversion of Maxwell's equations into generalized Telegraphist's equations
,
1955
.
[3]
E. Bahar.
Nanostructures with small- and large-scale periodic and random rough surfaces and lateral fluctuations in the permittivity and permeability-scattered near fields
,
2002
.
[4]
W. Herman.
Polarization eccentricity of the transverse field for modes in chiral core planar waveguides.
,
2001,
Journal of the Optical Society of America. A, Optics, image science, and vision.
[5]
R. Stephenson.
A and V
,
1962,
The British journal of ophthalmology.
[6]
E. Bahar.
Radio Wave Propagation in Stratified Media with Nonuniform Boundaries and Varying Electromagnetic Parameters: Full Wave Analysis
,
1972
.