Periodic And Quasi-periodic Photonic Lattices

In recent years, an artificial microstructure called photonic lattices is manufactured by an all-optics means that can make non-linear photorefractive crystal have periodic refractive index modification nature in space. The controllable band-gap structure of these new optical materials has great potential value in optical communication, optical switching, optical soliton, singular optics and other fields, and it causes a lot of attentions of researchers. The traditional methods to make optical crystals have some defects such as complex technology, high costs and fewer lattice period. All these problems are well solved by a new popular optical induced method. The most important part to fabricate optical lattices is design of the corresponding discrete non-diffracting optical field. Currently, researchers have designed some periodic lattice like two-dimensional Kagome lattice, optical graphene and honeycomb lattice, some quasi-periodic optical lattices, hexagonal gradient photonic lattices, defective photonic lattices, three-dimensional helical optical lattices, superlattices and so on. All these lattice structures can either see common in nature or have significant research value. Therefore, research and design non-diffracting discrete optical fields become a very interesting subject.In this subject, the following aspects were mainly done:1. Briefly introduces the history and background of optical crystals and optical lattices,periodic and quasi-periodic optical lattices and research suggestive of this subject.2. We present the physical mechanism of light-induced method. Two kinds of light-induced methods and their advantages and disadvantages were introduced. Non-diffracting wave fields and their prominent position in fabricating two-dimensional optical lattices were also proposed.3. We designed a series of complex masks with arbitrary intensity and phase modulator that constructed by computer programs to generate a variety of non- diffracting beams with lattice patterns. Later, we analyzed the phase distributions of these generated beams, and present the connection between wave field transverse structures and topological values of vortex phases. At last, phase pictures of all these designed wave field, generated by Matlab, were loaded in phase-only spatial light modulator in order to realize the corresponding beams in experiment.4. We proposed a method for generating periodic discrete non-diffracting beams(PDNBs) via superposing two identical rotated quadrilateral or hexagonal lattice wave fields. The rotating angle was calculated theoretically, and on the experiment, a 4f Fourier filter system and a phase-only spatial light modulator imprinting synthesis phase patterns of these PDNBs were used for forming desired wave fields. We also acquired other new PDNBs by modulating initial phase difference of elected adjacent frequency components. Finally, for superposition of two hexagonal wave fields with a special angle, each cell of these PDNBs is quite akin to the center patterns of twelve-fold quasi-periodic lattice waves and few differences between them are also discussed in this chapter.