An improved form of Bessel functions for efficiently and accuratly numerical computation

Abstract

For higher order mode excitation in a system with a cylindrical symmetry such as a cylindrical waveguide, a higher order Bessel function is required and numerically an expansion of this function in terms of a series is mostly used. However, the accuracy of mode pattern excited is getting worse when one pushes it to higher and higher order mode with a limited number of expansion series. This inaccuracy usually introduces unwanted or unphysical spurious modes and causes numerical errors in the simulation results. In order to excite a clean higher order mode, we have developed a delicate wave launcher using an improved form of Bessel functions. Since the excitation is located either in the ends (ports) or a cross section somewhere along the waveguide, for a TE or TM mode, the longitudinal magnetic or electric field component respectively is used only for the wave launching source according to the waveguide theory, i.e., all six components of electric and magnetic fields are not independent and all the transverse components can be expressed in terms of the two longitudinal components. This technique has been demonstrated successfully in our finite difference time domain simulations. An introduction of this approach and detailed results will be presented.