Analysis of a metallic reflector grating with the influence of the Joule loss taken into account

In this paper, reflection characteristics of metallic waveguide gratings with rectangular grooves are investigated with the effect of the Joule loss taken into account. For this purpose, the scattering matrix for each step discontinuity is first found by using the mode matching method with an impedance boundary condition at the surface of the conductor. Then, the scattering matrix method for the overall waveguide grating is obtained by a generalized transfer matrix. Numerical results show that Joule loss occurs mainly at planar waveguide sections. In order to suppress the loss of a reflector grating, it is shown that it should have a deep grating depth with a small number of periods. This configuration coincides with that for a compact and wide-band reflector grating, which can well support single-mode operation as was pointed out in our previous work.