Research On The Properties Of One-dimensional PT Symmetric Periodic Structure

For traditional Hermitian operators have real eigenvalues and the corresponding observable quantity.However,non-Hermitian Hamiltonian system of the parity-time(PT)symmetry may have real eigenvalues and the corresponding observable quantity.Thus the systems of observable quantity are no longer limited to the Hermitian property,which make PT symmetric system have important research significance.Although the scientists not find PT symmetric system in nature,the propagation equation of laser beam under paraxial approximation are similar to Schrodinger equation which make PT symmetric quantum system can utilize the optical system to simulation.In order to research character that the one-dimensional PT symmetric periodical structure.We research energy eigenvalues and light propagation problems in the PT symmetric system through the PT symmetric two optical waveguide,the PT symmetric dimer lattice and the PT symmetric trimer lattices.In the article,the main content is as follows:1)First,we study PT symmetric eigenvalues problem by PT symmetric two coupled waveguides in the second chapter.When the energy eigenvalues are located on real domain,the system is PT symmetric.When the energy eigenvalues are located on complex domain,the PT-symmetry is broken.We take the eigenvalues expression of the PT-symmetric two coupled waveguides and compare diversity of the evolution about the real and imaginary parts of the eigenvalues in the different parameters.Meanwhile we analyze relation of nonlinear effect on eigenvalues.2)Then,we analyze property that the PT symmetry phase transition of the dimer lattices in the third chapter.The results indicate that the PT symmetry phase transition and topological phase transition are two most important factors.Of course the initial conditions also affect evolution.In the PT-symmetric dimer lattice,the intensity show different evolutional features in the unbroken PT symmetry and broken PT symmetry.The former present periodic oscillation distribution,the latter present single and multiple similar Gaussian distribution.3)Finally,we focus on the PT-symmetric trimer lattices in the fourth chapter.The results indicate that the evolution of intensity not only has characteristic similar to the PT-symmetric dimer lattice,but also has specific symmetric distribution and asymmetric distribution.These features are discussed as the on-site energy have equal real part(△ = 0)and unequal real part(△≠0).The topological edge state which energy focused on one side of waveguide arrays could appear in broken PT symmetric system of the PT-symmetric trimer lattices.