Research On The Validity Of The Eigenmode Expansion Method In Acoustical Waveguide

In ocean acoustics, the propagation of waveguide in an infinite domain is usually solved by the Eigenmode Expansion Method (EEM) under the Helmholtz equation. The EEM expands the wave field by a complete set of the waveguide modes. The modes of an infinite planar acoustic waveguide are composed by a finite number of propagation modes and continuous-spectrum radiation modes. Because of the radiation modes, one needs to compute the infinite integral numerically, which is seriously difficult. Therefore, a mostly used method in the practical calculation is to truncate the unbounded domain into a finite one with the perfectly matched layer (PML). The obtained bounded waveguide has a set of discrete modes, i.e., the propagation modes, leaky modes and PML modes. And the radiation modes can be replaced by the latter two kinds of modes so as to avoid the infinite integral. Though this replacement is widely used, the rigorous theoretical proof is still an open problem. Our paper will study the validity of the EEM with PML. In fact, all the discrete modes of the finite PML-truncated waveguide will be computed by the asymptotic approximation together with the Chebyshev pseudospectral method. Then these modes will be taken as basis functions to approximate the given wave field by computing the expansion coefficients and the approximation error. Through lots of experiments, this paper verifies numerically the validity of the EEM with PML.