The Investigation Of Beams Propagation And Amphoteric Refraction In A Uniaxially Anisotropic Crystal

In recent years, the study of light propagation in anisotropic media has attracted a good deal of attention. In particular, the vectorial nature of light travelling through an anisotropic crystal plays a relevant role and cannot be neglected when designing optical devices. Examples of such devices are polarizers and compensators,switches etc. With the invention of negative index material, the study of negative index material has recently received much attention in the literature, both from theoretical and experimental points of view. Theoretical investigation above indicates that the anomalous refraction can be observed at a planar interface between an isotropic medium and an anisotropic medium, and the negative refraction is a natural result of dispersion relation in anisotropic media.In this thesis we investigate the beam propagation and amphoteric refraction in a Uniaxially anisotropic crystal. The thesis is composed of five chapters, among which are, Chapter 1 is a survey, Chapter 2,3,4 and 5 are the introductions of my own work. The thesis is structured particularly as follows.Chapter 1: We give an introduction of the research background and the research purpose of my thesis.Chapter 2: The vectorial properties of the paraxial beams propagating perpendicular to the optical axis of a uniaxially anisotropic crystal are investigated. By relying on a suitable plane-wave angular spectrum representation of the electromagnetic field, We obtain analytical expressions of optical fields. The longitudinal component is expressible in terms of the first order correction of the transverse field. Moreover the extraordinary beams can induce the ordinary beams in terms of the second order correction of the transverse field.Chapter 3: Based on the method of stationary phase and Fourier components analysis, the definitions of group velocity and group-front velocity are drived rigorously. The group velocity identifies the speed of the maximum intensity of wave packet, while thegroup-front velocity represents the orthogonal propagation of the group front and is the smallest speed at which the group front travels.Chapter 4: By relying on dispersion equation and boundary conditions, the properties of negative refraction in a uniaxial crystal are investigated. The energy and group velocities may undergo negative refraction even the phase and group-front velocities oriented to the positive direction.Chapter 5: Theoretical investigation indicates that the anomalous positive refraction can be observed at a planar interface between an isotropic positive index material (PIM) and an anisotropic negative index material(NIM). When the the optical axis of uniaxial left-handed material is not normal or parallel to the interface, the refraction of Poynting power for the extraordinary waves can be either positive or negative depending on the incident angles, while the refraction of the wave vector is always negative.