Full wave expression for the electromagnetic fields scattered by a rough interface between two chiral materials with laterally varying electromagnetic properties are obtained from generalized telegraphists equation for irregular media. The telegraphists equation are a set of coupled differential equations for the forward and backward wave amplitudes of the transverse components of the magnetic field and the electric field. They can be used to determine the electromagnetic near and far fields scattered above and below the interface. This has direct applications to the detection of chiral materials, the discrimination between different chiral media and the optimization of desired electromagnetic characteristics of artificial chiral materials.
To derive the generalized telegraphists equations, no simplfying assumptions are made about the characteristics of the rough interface, the frequency of the source, or the locations of the source and observation points. Therefore, they provide advantageous starting points for deriving solutions to a broad variety of physical problems. In electrical engineering possible applications include integrated optic devices, polarization transformers, modulators and directional couplers. In all these applications, sub-wavelength fluctuations at the interfaces between the media can significantly affect the physical characteristics of the chiral structure. The analysis can be used in the detection, characterization and design of chiral structures consisting of complex media with engineering, biomedical, agricultural and biosecurity applications.
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.
The full wave approach is applied to one and two dimensionally rough surfaces that are characterized by Gaussian surface height probability density functions. The full wave solutions are compared with published analytical and numerical solutions for one dimensional rough surfaces. The decomposition of the rough surface into smaller and larger rough scale surfaces is not restricted by the small perturbation limitations when the two-scale full wave approach is used. Thus the mean square height of the smaller scale surface is not restricted to small values. In the small slope limit, the total rough surface is regarded as a small scale surface and the corresponding solution is given by the single scatter original full wave solution. In the high frequency limit, the total rough surface is regarded as a large scale surface and the full wave solution reduces to the physical optics solution. For the intermediate two-scale case, the radar cross sections are obtained by regarding the rough surface as an ensemble of arbitrarily oriented patches of small scale surfaces that ride upon the large scale surface. The rough surface radar cross sections are expressed as weighted sums of two cross sections. It is shown that the full wave solutions are stationary over a wide range of patch sizes.