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.