Exact closed-form expression for the impedance of a rectangular strip and second-order effects in Bleustein-Gulyaev wave scattering

A novel exact expression for the impedance of a rectangular strip of arbitrary width and height, in the case of horizontally polarized waves, is derived. The impedance representation obtained is applied to the problem of Bleustein-Gulyaev wave scattering on a single rectangular strip of small height. The exact asymptotic expressions for the complex amplitudes of the reflection and transmission coefficients are calculated for this problem, taking into account second-order effects with respect to a small parameter such as the ratio between the strip height and the wavelength. It is shown that the second-order effects are not purely quadratic with respect to the small parameter considered and the main contribution contains as multiplier the logarithm of this parameter