Second And Third Order EPs In Non-Hermitian Optical Waveguide Systems

Exceptional points(EPs)are exceptional points in the system parameter space where two or more eigenvalues and their eigenvectors degenerate under specific conditions,which are mainly produced by non-Hermitian systems with energy exchange with the outside world.In the past two decades,non-Hermitian systems have been studied extensively,especially non-Hermitian quantum systems with parity time inversion symmetry.In recent years,non-Hermitian systems have attracted extensive attention in the field of optics.With advances in manufacturing technology,gains and losses in optical systems can be easily manipulated and thus can be used to verify various non-Hermitian properties,leading to the design of novel optical artificial materials and structures.When two or three eigenvalues and their corresponding eigenvectors degenerate at the same time,the degenerate point is a second or third order exceptional point.The research results show that the vicinity of the singularity has sensitive sensing and topological characteristics.For the second and third order exceptional point,the origin of exceptional point,the conditions and applications of exceptional point in different systems,and the topological mode transformation around exceptional point are firstly introduced in this paper.Then the conditions for the existence of second order exceptional point in double waveguide systems are introduced.The chiral mode transfer is realized by dynamically changing the two system parameters along the closed path.With the increase of the spacing of waveguides,the orbit becomes larger and closer to the exceptional point,and finally does not contain the exceptional point.No matter clockwise or counterclockwise,the mode conversion efficiency remains high when the loop trajectory is close to the exceptional point.Experimentally,by setting up a test optical path,the even mode and odd mode at both ends of the waveguide are excited and detected respectively.The transmittance spectra measured experimentally are basically consistent with the spectra obtained by numerical simulation,and the output mode is determined by the direction of the surround.Finally,we extend the two-waveguide system to the three-waveguide system,and find the conditions for the existence of the third-order exceptional point in the nonHermitic three-waveguide system through theoretical derivation,and carry out simple numerical verification with MATLAB.The conditions for the existence of third-order exceptional point are introduced into a specific optical waveguide structure,and the third-order exceptional point are discovered by determining the specific values of each parameter in the third-order Hamiltonian matrix.As with the way around exceptional point in the double waveguide system,an adiabatic evolution of the eigenmode results in mode transformation.In a three-waveguide system,if the winding path is the same but the starting point is different,the transformation result of the eigen mode remains unchanged and the electric field distribution in the waveguide changes.