Perturbation calculation of the scattering of electromagnetic waves by an underdense plasma layer

A perturbation technique has been utilized to obtain the scattering of electromagnetic waves by an underdense plasma layer for Gaussian, sech², and parabolic density distribution, and the calculations compared with accurate solutions. The results for the reflection are good at small values of plasma width, but (except for the parabolic case) decrease too rapidly at large plasma widths. The transmission coefficient is more difficult to calculate and, despite the presence of absorption, has a spurious rise to unity at large plasma widths. A Wentzel-Kramers-Brillouin calculation of the transmission yields fairly accurate results and with less labor than required by the perturbation method.