Solution of two-dimensional Helmholtz equation by multipole theory method

A new approach, the multipole theory (MT) method, is presented for calculat ing two-dimensional (2-D) Helmholtz equation problems. By the mathematical deduction, the general MT formula and its applied laws are derived. The new approach has been applied to compute the cutoff wavenumbers of a rectangul ar waveguide, as analytical results are available for this problem. In orde r to further verify the accuracy of this method, the MT method has also bee n applied to compute the TE and TM modes of two high power waveguides and a square offset line. Comparison of accuracy is made whenever data is availa ble. It has been proven that the MT method is an effective approach for cal culating 2-D Helmholtz equation problems.