Some Problems On The Propagation Of Finite-Sized Beams

With the development of integrated optics, the propagations of bounded beams in media have attracted much attention, specially the propagation of spatial optical soliton and Goos-H(a|¨)nchen (GH) displacement of finite-sized beams. These phenomena can greatly predigest the structure of the current optical communication apparatus, and have very important meaning for the optical interconnects, beam steering, and other applications.The spatial soliton is one of major research fields in nonlinear optics, and its existence is correlated with the dynamic balance between diffraction and nonlinear effects for finite-sized beams in the interactions between optical fields and media. Much progress has been achieved in the last 40 years. But all along, attentions were mainly paid to coherent solitons in both theoretical and experimental investigations. With the recent developments in material science and experimental technology, incoherent solitons excited with incoherent light sources were experimentally observed. The findings of incoherent solitons have changed our traditional understanding of soliton phenomena and led to many new research topics. It's hopeful that the application of incoherent solitons shall improve the development of soliton-based all optical communication systems.On the other hand, the GH displacement is the lateral displacement of the totally reflected bounded light beam off dielectric interface from the position predicted by geometrical optics. In recent years, the GH displacements in various microstructures have already become one of the hottest research topics. As a matter of fact, the further investigations of GH displacement will improve our understanding the propagation characteristics of finite-sized beams.In this Ph.D dissertation, we will investigate the GH displacements for finite-sized beams totally reflected from a single interface, and the self-trapping behaviors of incoherent light beams in nonlinear media, including the propagation characteristics of local and nonlocal incoherent solitons, incoherently coupled screening soliton pairs. The main results given by the author include the following four parts:(1) Incoherently coupled screening soliton pairs can be established in biased photorefractive media under steady-state conditions, each constituent of which is not only spatially incoherent with the other, but also with itself. (a) The properties of incoherently coupled soliton pairs in bright-bright, dark-dark and bright-dark configurations are studied with the coherent density approach, and the intensity expressions for these soliton pairs are given. The results show that the existence of coupled soliton pairs has nothing to do with the incoherence property of beams. However, the types of soliton pairs depend on the direction of external bias voltage. (b) The analytical solution of bright-dark soliton pair can be found when the intensity peaks of the two soliton constituents are approximately equal. (c) The propagation characteristics of coherent components that compose each constituent of coupled soliton pairs are discussed in detail. And their intensity distributions depend closely upon the incoherence property of beams.(2) The propagation of incoherent white light beam in logarithmically saturable noninstantaneous nonlinear media is studied by using the mutual spectral density theory. The existing condition and the analytical expression of the beam radii and the coherence radii of white light solitons are obtained. The initial condition of the beam and the nonlinearity of the media decide the propagation of the beam. It is find that the coherence properties of beam evolve periodically with the distance and the spatial correlation distance is smaller for higher frequency constituents of the incoherent light.(3) We present a theoretical investigation of incoherent accessible white-light solitons in strongly nonlocal medium with noninstantaneous Kerr nonlinearity. This soliton has elliptic Gaussian intensity profile and anisotropic spatiotemporal coherence properties. For this soliton to exist, the spatial coherence distance should be larger for lower frequencies and shorter for higher frequencies. When the incident power differs from the critical value, we demonstrate the periodic harmonic oscillations of the accessible white-light solitons.(4) The concept of GH displacement is applicable only when the reflected beam retains the shape of the geometrically reflected or incident beam. The necessary and sufficient condition has been advanced for the totally reflected beam to retain the shape of the incident beam. Numerical simulations have shown that when the angular divergency and the incidence angle of the beam satisfies some condition, the reflection phase shift of the constituting plane wave within the divergency is linearlydependent on k_y, the parallel component of the wave vector to the interface, so that the totally reflected beam retains the shape of the incident beam well. When the incidence angle of the beam is very close to critical angle for total reflection or 90°, the requirement of linear dependence of the reflection phase shift upon k_y cannotbe fulfilled, so that the totally reflected beam is distorted from the shape of the incident beam. The actually displacement of the reflected beam cannot be regarded as a GH displacement.