Strong Nonlocal Vector Spatial Soliton

When the diffraction effect is exactly balanced by nonlinear effect, the optical beam can keep its width unchanged during propagation. This is the spatial optical soliton. In 1997, Snyder and Mitchell present the famous Snyder-Mitchell mode(S-M mode), and obtained the Gaussian-shaped soliton. Their work raised the upsurge in the research of the nonlocal spatial optical solitons. So far, a series of achievement have been obtained. Such as in strong nonlocal media, Laguerre-Gaussian soliton, Hermite-Gaussian soliton, Ince-Gaussian soliton, elliptic Gaussian soliton, surface-wave soliton, vector spatial optical soliton, dark soliton and the interaction of the optical solitons had been studied. The comparison of the optical soliton propagating in weekly, general and strong nonlocal media shows that the critical powers, phase shifts and shapeds of the solitons have large difference in different degree of nonlocal media. Such as the intensity profile is hyperbolic secant shaped in weekly nonlocal media, whereas in strong nonlocal media the intensity profile is Gaussian-shaped. The critical power and phase shift are increase as the increase of the nonlocality. In addition, the propagation of optical beam in nonlocal media with different response functions(such as Gaussian-shaped, exponential shaped and rectangle response functions) has been studied. In experimentally, the strong nonlocal media have been found such as Nematic liquid crystal and lead glass.In the first chapter of this paper, we introduce the concept, classify, history and recently research status of the soliton. The second chapter studied the coupled propagation of Hermite-Gaussian(Laguerre-Gaussian) shaped beam pairs in strong nonlocal media. In the third chapter, we investigated the propagation of the vector soliton-like wave which consisted of Gaussian-shaped beam pairs in strong nonlocal media with Gaussian-shaped and exponential decay response function, respectively. The fourth chapter has three sections. The first and second section investigated the propagation of Gaussian beam in strong nonlocal logarithmic media and(1+2)-dimensional synthetic nonlocal media, respectively. The third section studied the propagation of elliptic Hermite-Gaussian beam in strong nonlocal media with elliptic Gaussian-shaped response function.The concretely contents are as follow:Chapter 1, the history and recently research status of the soliton were introduced. In specially, we sum up the concept and classify of nonlocality, the nonlocal media which have been found, the character of nonlocal soliton and some research methods.Chapter 2, the propagation of two mutually incoherent Hermite-Gaussian(Laguerre-Gaussian) beam pairs in strong nonlocal media was studied by variational approach. The evolution equations for the parameters of the two beams were obtained and the condition of forming a Hermite-Gaussian(Laguerre-Gaussian) vector soliton was found. When the total input power is equal to the critical power, the optical beam pairs both can keep theirs initial widths unchanged during propagation. The numerical result shows that a series of vector Hermite-Gaussian(Laguerre-Gaussian) solitons which consisted of different-order Hermite-Gaussian(Laguerre-Gaussian) beam pairs can be formed in strong nonlocal media.Chapter 3, we studied the propagation of two orthogonally polarized incoherent optical beams in strong nonlocal nonlinear media with Gaussian-shaped and exponential-shaped response functions, respectively. The evolution equations for the parameters of the two beams were obtained and a spatial vector soliton was found. The effects of coupling coefficient and birefringence on the propagation of the two beams were discussed. A soliton-like wave, which is different from the vector soliton, was discovered. Moreover, the phase shifts of the two beams are different under certain conditions and the propagation distance of generating π phase difference can be figured out.Chapter 4 has three sections.The first section investigated the propagation of Gaussian-shaped optical beam in strong nonlocal logarithmic media. When the initial optical beam is on-waist incident and its width is equal to the critical beam width, the spatial optical soliton can be formed. This condition is different from that in strong nonlocal Kerr medium. In addition, we found that the beam width will oscillate periodically when the initial condition is dissatisfied and the initial beam width can influence the oscillating range.The second section discussed the propagation of Gaussian-shaped optical beams in(1+2)-dimensional synthetic nonlocal media. We found that the optical soliton can be formed in “focusing-focusing” synthetic nonlocal media with arbitrary degree of nonlocality. However, for the “focusing-defocusing” synthetic case, the degree of nonlocality must be grater than a certain value which was depended on the other material parameters of the nonlocal media.The last section studies the propagation of elliptic Hermite-Gaussian beam in strong nonlocal media with elliptic Gaussian-shaped response function. For forming elliptic Hermite-Gaussian soliton, the ratio of the square of the beam width must be proportional to the ratio of the characteristic length of the material, and the initial power should be equal to the two critical powers in x- and y-directions. For the anisotropic nonlinearity of this media, the instability of the high-order elliptic Hermite-Gaussian beam is increase as the increase of the order.Chapter 5, we display the inadequacies based on summing up the content and result of this paper, and then discussed the outlook for future work.