The Study On Light Propagation In Nonlinear Photonic Lattices

In recent years, the combination of optical nonlinearity and micro-periodical struc-tures gives rise to the system of nonlinear photonic lattices. Quite a number of novel physical phenomena of the light propagation in the nonlinear photonic lattices are found. All of these imply not only the possibilities for better light controlling and ma-nipulation but also the prosperous applications in all-optical signal and data processing, optical communication and optical networks.By designing and fabricating the structures of nonlinear photonic lattices, one can get the expected band structure to control the light propagating within the lattices. On the other hand, the introduction of the nonlinearity provides one more degree of free-dom. Based on such ideas, the thesis focuses on the exploration of the dynamics of light propagation in nonlinear photonic lattices. Through detailed experimental studies and numerical simulations, we show a number of new physical phenomena and their underlying physics of light propagation in such novel nonlinear photonic lattices. The main contents are as follows:In Chapter 1, we give a brief introduction to the fundamental knowledge about the optical nonlinear effects related to our thesis, especially the photorefractive effect. We show the structure property of the nonlinear photonic lattices and the fundamental principles of light control, and then analyze some of the fundamental phenomena in photonic lattices, such as discrete diffraction and discrete solitons.In Chapter 2, we study both theoretically and experimentally the linear surface waves and their nonlinear switching in a curved waveguide array with a negative re-fractive defect at the edge of the lattices. The results show that the modulated pho-tonic lattices can support three linear surface modes simultaneously only if the bending amplitude is very close to the dynamic localization point A0. As the nonlinearity is increased, interplay of different surface modes enables beam reshaping and switching between different output waveguides. And when the strength of nonlinearity is high enough, light can be trapped at the first waveguide and forms a discrete surface soliton. In Chapter 3, we study both theoretically and experimentally the linear spectrum and their corresponding nonlinear transformation processes in one dimensional straight and curved waveguide arrays. The results show that the output diffraction patterns in both of the straight and curved waveguide arrays are symmetric with respect to the input position in the linear cases. However, the output intensity spectrum will be symmetry-breaking as the nonlinearity is increased. And almost all the spectral components will be trapped back to the input waveguide when the nonlinearity is high enough.In Chapter 4, we fabricate a two-dimensional square backbone lattices by the photo-induced Fourier transformation method based on photorefractive nonlinearity. We observe the linear and nonlinear light propagation dynamics and their correspond-ing power spectrum in the two-dimensional lattices under four different input condi-tions. The result shows that the nonlinearity strength to form four types of gap solitons is different and dependent on the input conditions. The light energy of the gap soli-ton in the power spectrum is localized at the four high-symmetric M points of the first Brillouin zone in the case of on-site excitation, whereas it distributes on the edge of the Bragg band gap in the off-site excitation case.In Chapter 5, we first fabricate a weakly modulated large-area two-dimensional square photonic lattice slab by means of photo-induction method using amplitude mask in LiNbO3:Fe crystal. And then we prove experimentally the discreteness of the lattices slab in transverse and longitudinal dimensions. We study experimentally the linear and nonlinear light propagation dynamics and simulate the process numerically. The results show that the photonic lattice slab is of Bragg-diffraction, discrete diffraction and effective waveguide array in the linear case, while it also support the formation and propagation of discrete soliton in the nonlinear case.