Nontrivial grating that possesses only specular characteristics: Normal incidence

It is well known that gratings with horizontally pronounced periodicities produce nonspecular reflection (and transmission) modes depending on the frequency and the periodicity. Do gratings with vertically pronounced periodicities always do similarly well? This question is resolved by considering a grating made of an infinitely long slab of constant width in which perfectly conducting gratings are periodically inserted. Only normal incidence is considered, and an elementary modal theory has been used in which diffraction from knife edges has been neglected. From the computed results it is shown that such a grating always reflects and transmits specularly perfectly over wide frequency ranges irrespective of the periodicity of the grating, the dielectric constant of the slab (real), the width of the slab, or the polarization of the incident electromagnetic plane wave.