Geometrically Lit Region Analysis of the Single-ray Debye Terms for the Transmis- Sion of a High Frequency Plane Wave into a Double-negative Cylinder by the Modified Watson Transformation and Debye Series Ex- Pansion

Abstract—The Debye expansion integrals obtained by application of the Modified Watson Transformation and Debye series expansion to the Mie series for the high frequency plane wave transmitted into a double negative (DNG) cylinder are solved in the geometrically lit regions of the corresponding Debye series terms. The Debye series expansion is made up to the possible maximum term after which double ray field formation is first observed. Using the steepest descent method and the geometrical optics approximation, the role of the lower ray in the double-ray field formation is pointed out. For refractive indices satisfying |n| ≥ 10, it is shown that the maximum Debye series term index up to which simple single-ray tracing can be performed is bigger for a DNG cylinder than that for a DPS cylinder and the difference between the term indices increases as |n| increases.