The problem of the propagation of modes along a moving dielectric interface is considered. Two types of dielectric structures were considered in particular: a moving dielectric slab and a moving dielectric circular cylinder. The characteristic equations for modes along these two types of structures are derived and a detailed discussion concerning these characteristic equations is also given. As a specific example, numerical results for the guide wavelength of the dominant TE wave along a moving dielectric slab as a function of frequency for various values of υz/c, where υz, is the velocity of the moving dielectric material and c is the velocity of light in vacuum, were presented. It is found that if υz/c > (±1/±0)-½, the moving dielectric structure can support a forward wave as well as a backward wave and there also exists a high-frequency cutoff for the dominant mode under consideration.
C. YEH, "Propagation along Moving Dielectric Wave Guides," J. Opt. Soc. Am. 58, 767-768 (1968)