Study On Optical Propagation In Modulated Photonic Lattices

Micro/nano photonics is a popular topic in optics. When the structure size is in or under micro meter level, some particular optical phenomenon will happen, such as discrete diffraction, discrete soliton, gap soliton, aperture diffraction enhancement, quantum dots radiation, et. al. Based on these physical phenomenon, people have successfully developed some photonic devices such as optical waveguide array, micro/nano optical diode, quantum dots material, nano laser and nanowire polarizer. These works are great important and have practical application potentials in optical interconnection, optical switching, optical communication and optical integrated circuit. But until now, the majority of the works concern about periodic micro/nano photonic structures. When such periodic structures are systematically modulated, the optical propagation phenomenon will be changed thoroughly. According to these thoughts, we have investigated the following issues in thesis:In the first chapter, we introduced some familiar micro/nano photonic structures and some optical mechanism for these structures. We described the defect photonic lattices firstly, then illustrated a concept called modulated micro/nano photonic lattice. With this concept, we discussed some different modulation types, explained optical propagation behaviors in such systems. At last, some basic knowledge on nonlinear optics is introduced as well.In chapter two, we studied some popular optical propagation theory and numerical methods for micro/nano photonics. In this part, we studied the Schrodinger equation analytically, which is used to describe optical propagation, super mode theory in paralleled waveguides and coupled-mode function. On the other hand, we described two numerical methods used in this thesis, Fast Fourier Transform Beam Propagation Method (FFTBPM) and Planar Wave Expansion (PWE).In chapter three, we numerically studied beam propagation in four kinds of separation modulated micro/nano photonic lattices. The results showed that, the optical beam would be localized and appear self recurrence during propagation in structures with positive hyper secant potentials and positive rectangular potentials. In structures with negative hyper secant potentials, the beam would appear reflectionless propagation, while decay in negative rectangular potentials. Furthermore, with the properties that the negative hyper secant and negative rectangular potentials could capture beam, we studied the linear coupling and nonlinear localization of broad beam between the two potentials. Our works provided new ideas and methods for light controlling in micro/nano photonic lattices.In chapter four, we studied the asymmetric propagation of light beam in transverse separation modulated photonic lattices. One waveguide array was divided into different layers according to spacing between waveguides, with which method we realized the linear asymmetric propagation of light beam. We approached the mathematical expression of optical transmission contrast theoretically and asymmetric propagation patterns numerically. The results showed that the transmission contrast was determined only by the coupling strengths between the chirped lattice and the two boundary uniform lattice portions, but had no relationship with the waveguide numbers in modulated layer and chirped types. The simulations showed a good agreement with theory.In chapter five, we studied light beam propagation in modulated micro/nano photonic lattices (curved waveguides). We designed curved waveguide coupler and transverse separation modulated curved waveguides array. In a two-waveguides coupler, we studied the optical coupling efficiency dependence by varying the structure parameters. In curved waveguide array, with the four kinds of potentials mentioned above, we studied the similar dynamic localization phenomenon of light beam. The results showed that when the modulation obeying sine or cosine functions, in curved waveguide arrays with positive hyper secant or rectangular potentials, the similar dynamic localization would happen even though the dynamic localization condition was not matched.In chapter six, based on the amorphous silicon, we studied the fabrication of photonic crystal and the self phase modulation phenomenon. Firstly, with the slow light condition, we designed two different geometry structures in crystals, discussed two available crystal fabrication methods. We studied the self phase modulation in amorphous silicon photonic crystal with slow light condition. The results showed that because of the enhancement by slow light condition, an obvious pulse split appeared.