Asymptotic Solutions Of Modes And Its Application In Wave Propagation Computation

Leaky modes play an important role in wave propagation computation of optical and acoustic waveguide ,especially in the on-chip optical interconnection proposed re-cently. They can be used to partially represent the wave field related to the continuous spectrum of the radiation and evanescent modes.For two-dimensional step-index waveguides,the propagation constants satisfy an analysis nonlinear equation,from which asymptotic solutions of leaky modes have been given. B-ut when the refractive index n is varied with the transverse variable x in optical waveguide or acoustic velocity c is varied with z in acoustic waveguide respectively,analysis nonlinear equation of the leaky modes can not be obtained. Asymptotic solutions of leaky modes in unbounded waveguide are given first. In order to get asymptotic solutions of the leaky modes, W.K.B. method is implemented to create an approximate nonlinear equa-tion. Numerical simulations show that our asymptotic solutions are very close to exact leaky modes and the errors become smaller as the norm of the modes become larger. Our asymptotic solutions can be used as initial guesses for computing the more accurate leaky modes by Rayleigh Quotient iteration .PML as an efficient artificial absorbing material is widely used to solve unbounded wave propagation problem, in which Berenger modes(the eigenmodes in a waveguide terminated by a finite PML) appear. High order asymptotic solutions for the Leaky modes and Berenger modes are derived in waveguide with PML. Asymptotic solutions of the modes are useful,because they can be used as initial guesses for solving the exact eigenvalues numerically.Wave propagation computation is implemented when Leaky modes are obtained by asymptotic solutions which are used as initial guesses for Rayleigh Quotation itera-tion. Two cases are considered: first, refractive index is varied with transverse variable and acoustic velocity c is varied with depth,second, they are all varied with two directions. Numerical simulations show that results from this method are better than the methods from Lapack with highly computation efficiently.For optical waveguide,wave propagation computation are compared with or without Berenger modes. Numerical simulations show that results from these two ways will have a slight difference.