Electromagnetic propagation in an exponential ionization density

The propagation of a plane electromagnetic (TE) wave into a plane stratified medium in which the ionization density varies as exp ( ) is investigated. The solution of the wave equation appears as a combination of Bessel functions of imaginary order and complex argument, but the magnitude of the reflection coefficient (taken at ) is given by the simple expression exp , where is the angle of incidence, is the free-space wavelength and ( ) is the ratio of electron collision frequency to the frequency of the field. In general, the field components must be obtained from a complex series, but at depths beyond the critical density asymptotic forms are given which display the rapid decay of the evanescent field in terms of elementary functions.