Plane wave propagation in plasma slabs

Electromagnetic plane wave propagation is studied in an isotropic one dimensionally varying plasma slab. Riccati-type differential equations are derived in terms of reflection and transmission coefficients which are a function of distance into the plasma. A flow diagram method is used to derive the differential equations. The transmission coefficient for a plasma slab with an arbitrary but known profile is derived as the sum of two terms, the classical WKB approximate solution and a WKB error term the error term being the difference between the exact transmission coefficient and the WKB approximate coefficient. The error term is expressed as the integral over distance through the plasma of the incremental error incurred by using the WKB approximation.