Angularly propagating waves in a radially inhomogeneous, lossy dielectric cylinder and their connection with the natural modes

A physical interpretation is proposed for the natural modes of a radially inhomogeneous, lossy dielectric circular cylinder embedded in a homogeneous, lossless dielectric. These modes are either of the creeping-wave or of the whispering-gallery type. With the aid of a generalized Wentzel-Kramer-Brillouin (WKB) asymptotics, an asymptotic characteristic equation is derived for each type, which can be explained physically. Numerical results obtained from the exact characteristic equation and both approximate equations are presented and discussed.