Perturbation analysis of the TM plane wave scattering from the end-face of a waveguide system

The scattering of a TM plane wave from the end-face of a two-dimensional waveguide system is treated by solving straightforwardly a wave equation for the electric field. The unknown scattered field is expanded into a perturbation series with respect to the difference of refractive indices of core and cladding. The first and second order terms of the series are analytically derived and it is shown that the second order term is sufficiently small compared with the first order term and can be ignored.