A polarizing mirror device including an optical substrate (1) of real refractive index ns; a dielectric multilayer mirror (2), composed of dielectric layers of low and high refractive index; and a corrugated grating layer (6) of local period Λ at the side of a cover medium of refractive index nc. The local period Λ is selected such that upon substantially normal incidence of an incident wave at wavelength λ from the cover medium there is no diffraction order other than the 0th reflected order in the cover medium, such that the field of the +1st and −1st orders diffracted into the layers of the multilayer and into the optical substrate have a non-evanescent propagating character, and such that the respective angles under which the +1st and −1st orders propagate in each layer of said multilayer have an absolute value larger than or equal to the angle corresponding to the angular band edge of the central TM reflection band and, if a central TE reflection band of finite angular width exits, smaller than the angle corresponding to the angular band edge of this central TE reflection band in the angular spectrum of the multilayer at the wavelength λ with a fictive incident medium having the index of the considered layer of this multilayer.