Topological States Of Non-Hermitian Square Lattice And Fibonacci Super Lattice Photonic Crystals

In recent years,photonic topological insulators have been widely studied because the edge states possess properties of backscattering suppression and defects immunity,providing solutions for low-loss transmission in the field of optical communication and optical integration.Non-Hermitian topological photonics introduces gain and loss in topological systems.The higher degree of freedom is conducive to more flexible manipulation of light waves and realize novel physical properties different from traditional topological insulators,which has attracted the attention of researchers.Based on non-Hermitian topology,many optical devices with important significance and practical application value have been developed,such as topological laser,light collector,adjustable topological waveguide and so on.At present,the non-Hermitian topological systems affect the topological properties by the imaginary part of eigen frequencies.The gain and loss are little in these studies,the topological states are little influenced by nonHermiticity,such as changing the position or energy of the topological states.In systems with large gain and loss,the non-trivial gap of the system degenerates,resulting in the mixing of topological states and bulk states,and the localization and robustness are affected,whether new topological states can be realized in these systems still needs to be explored.Expanded lattice and shrunk lattice have the same energy band in some conditions,which has great advantages in constructing common bandgaps.In this thesis,large gain and loss are introduced in expanded and shrunk lattice,and the influence of nonHermiticity on topological properties is studied in photonic crystals and photonic quasicrystals.The outcomes of the thesis mainly include the following contents.1.Non-Hermitian box-shaped structure is designed based on expanded and shrunk lattice to realize dual-band topological waveguide.By introducing and adjusting the gain and loss of diagonally symmetric distribution,the variation of band structure of expended and shrunk lattice with different gain and loss is studied,and the topological properties in the band gap are studied by Zak phase of the structure.The dual-band topological edge states are realized.Compared with the low-frequency edge state,the high-frequency edge state has larger field strength,better localization and higher sensitivity to gain and loss.After the introduction of non-Hermitian parameters,the original corner state and bulk state are mixed at the lower frequency,and a new corner state different from the Hermitian system appears at higher frequency,and its energy is localized at the four vertices of the box-shaped structure respectively.2.The one-dimensional Fibonacci quasicrystal is designed based on the expanded and shrunk lattice,and periodly repeat along the y direction to obtain the two-dimensional Fibonacci superlattice structure,and realize the topological edge state introduced by non-Hermiticity.By adjusting the gain and loss,the varation of band structure is studied.When the gain and loss is large enough,the band gap will be opened and the topological edge states with multiarea characteristics appear.The shrunk lattice,non-Hermitian Fibonacci superlattice and expanded lattice are combined to design a dual-linear waveguides.The topological properties of this structure are studied,the results show that the topological edge states are realized on both waveguides in different frequency ranges.The topological edge states can be applied to optical devices requiring frequency conversion,such as topological beam splitter,filter and so on.Because the three structures have trivial properties,quasi-periodic topology and Zak phase topology respectively,this study is helpful to analyze the relationship between Zak phase topology and quasi periodic topology.