The transmission and reflection coefficients of an electromagnetic wave for a gradient dielectric layer

A gradient dielectric layer is considered. In the layer, permittivity ɛ(z) depends on coordinate z as follows: ɛ(z) = ɛLa4/(z − a)4 (a being the gradientness parameter). For this layer, reflection and transmission coefficients rr and rt are determined. It is found that, in a wide frequency range, the considered gradient layer has amplitude- and phase-constant reflection and transmission coefficients and can serve as a low-pass filter in radio devices involved in the transmission of wideband signals.