WKB method is often used to calculate the electromagnetic wave propagation in the inhomogeneous plasma

but the coupling effect between the forward wave and backward wave is neglected in the propagation process of the electromagnetic wave in the medium. Making use of the differential transfer matrix methodology

the solution of modified WKB can be improved to the second order approximation and be more accurate than that of WKB for taking into account the coupling effect. Based on this modified WKB method

the waveform of an electromagnetic pulse through an inhomogeneous plasma region is analyzed. The fast Fourier transform algorithm is used to obtain the distortion of the transmission signal waveforms such as the Gaussian pulse signal through a symmetrical plasma distribution and the results show that the amplitude of signal becomes lower under the consideration of coupling effect and so the modified WKB method is suited to analyze the waveform of the transmitted pulse.