Analysis of mode dispersion for abnormal total reflection from an isotropic medium to an arbitrarily oriented uniaxial crystal

Mode dispersion is used to study the necessary conditions for the existence of abnormal total reflection, for wave propagating from a rare isotropic medium to a dense anisotropic medium with optical axis oriented arbitrarily in three-dimension space. The conditions can be put down to three inequalities of the relations among relative permittivity parameters in two media and the direction of optical axis of a uniaxial crystal. Based on the different geometrical characteristics of mode dispersion in isotropic and anisotropic media as well as the numerical simulations of spatial field, the physical essence of this abnormal total reflection is revealed, which means that the ray index in incident medium is still larger than that in refracted medium, although the refractive index in incident medium is smaller than that in refracted medium.