Research On The Properties And Applications Of Non-Hermitial On-chip Photonics System

Recently,the area of topological insulator and topological phase transition has got rapid development in past decades,and also won the Nobel Price,so the non-Hermitian quantum mechanics is drawing more and more attentions of all the physics area.Due to the similarity between the Maxwell equation and Schordinger equation,a lot of novel non-Hermitian quantum mechanics phenomena are found and observed in photonics experiment,which promoted development of non-Hermitian photonics,and numerous researchers on photonics,especially nano-photonics researchers,join to the research of non-Hermitian photonics.The nano-photonics researchers found that non-Hermitian photonics provide solutions to many technology problems of Hermitian nano-photonics.Thus,more and more researchers are getting interest in non-Hermitian photonics.Under this background,this dissertation focuses on theory and application of non-Hermitian photonics.The main contents of this dissertation can be arranged as the following branches: 1.I research non-Hermitian symmetries,includind the Parity-Time symmetry,Particle-Hole symmetry and Complex Mirror symmetry,on cross section of nano-photonics system.Starting from the physical definition of them,I derive the condition of refractive index distribution to achieve the symmetries discussed,and then exploit gain or loss waveguides to construct nano-photonics system with the symmetries I research.Further,the properties of eigen-mods and eigen-values of these systems are analyzed.Then the topological transition points and band structures of the non-Hermitian symmetric systems are further discussed deeply.Meanwhile,the corresponding simulated cases are calculated to validate the results.2.Based on researches of Parity-Time(PT)symmetry,Particle-Hole symmetry and Complex Mirror symmetry,band structure of Particle-Hole symmetry and dispersion curves neighboring topological phase transition point of Parity-Time and Complex Mirror symmetry are further researched,and I find something novel and interesting.The topological phase transition point can be employed to construct slow and fast light waveguide;for the band structure of Particle-Hole symmetry,I observed propagating constant displacement effect of ‘defect mode',and find it can be used to detect defect of waveguide array.3.I do some researches of non-Hermitian symmetries,including the PT symmetry,Rotation-Time(RT)symmetry and Inverse-Time(IT)symmetry,on the light propagating direction of nano-photonics system.According to the physical meaning of the three symmetries,the conditions of refractive index distribution are figured out.I found that the Parity-Time symmetry,Rotation-Time symmetry and Inverse-Time symmetry only occurs on the one-dimensional(1D),two-dimensional(2D)and three-dimensional(3D)space,respectively.Then gain and loss waveguides are connected following the condition of refractive index distribution derived before to construct nano-photonic systems with the non-Hermitian symmetries discussed.Based on these researches,the properties of light propagating in the PT,RT and IT symmetric photonics systems are analyzed,and then constant equations of them are given.Simulated cases are also calculated to validate the results.4.On the basis of constant equations of PT,RT and IT symmetry,the reflection and transmission matrix are further analyzed,I found asymmetric property of the reflection and transmission matrix,which is exploited to design unidirectional reflective mirror and mode converter.5.Based on research on PT symmetry,PT symmetry is induced in nonlinear photonic system.I mainly discuss PT symmetry and PT symmetry broken in nonlinear balanced gain/loss coupled waveguide system,and researched the transition point between them.Inducing nonlinear balanced gain/loss coupled waveguide to a nonlinear oscillator waveguide array which emerges superfluidity,it can be found that nonlinear balanced gain/loss coupled waveguide isolates the superfluidity.