Oscillating guided modes in a symmetric five-layer slab waveguide with anisotropic-dispersive left-handed material

A symmetric five-layer slab waveguide with anisotropic and dispersive left-handed material (LHM) in the core and righthanded material (RHM) in other layers is investigated. Through Maxwell’s equations and a transfer matrix method, the dispersion equations for the TE oscillating guided modes are obtained. Under consideration of two extremely anisotropic cases, some mode dispersion curves are plotted. The zero-order TE oscillating guided mode exists. Meanwhile, with the increase of mode number, their dispersion curves move to left or right, corresponding to positive or negative dielectric permittivity and magnetic permeability in the longitudinal direction. Besides, as the core thickness increases, mode dispersion properties change and three propagation properties appear: positive group velocity, negative group velocity and zero group velocity. The negative group velocity indicates the characteristics of the left-handed materials, and the zero group velocity implies that electromagnetic waves are trapped in the waveguide completely.