Integral equation solution method of two-dimensional electromagnetic fields. A method to employ the transverse field components

New integral equations are introduced in which the transverse electromagnetic field components are unknown for the two-dimensional (2-D) electromagnetic scattering problems and electromagnetic waveguide problems. A numerical analysis by the boundary element method is proposed. The conventional integral equations in which the longitudinal electromagnetic field components are unknown are difficult to determine at certain angular frequencies and at certain longitudinal propagation constants for the electromagnetic scattering problem. In the waveguide problem, the spurious modes may enter as nonphysical solutions. The integral equations proposed in this paper do not have conventional difficulties. Here, the integral equations using the transverse electromagnetic fields are derived and the uniqueness of the solution is proven. Further, for practical examples, the integral equations are analyzed numerically by the boundary element methods so that the validity and effectiveness are investigated.