A grating has a high diffraction efficiency into the minus first diffracted order in transmission, for both TE and TM polarizations. The incident angle may optionally be chosen so that the minus first diffracted order in reflection would be retroreflected back to the incident beam. The grating may be formed from various materials and/or layers, where the thicknesses of the individual layers may be determined by an optimization or simulation process. In one aspect, the grating may have four or more layers, formed with three or more materials. In another aspect, the grating may have a longitudinal refractive index profile that contains at least two local extrema, such as a maximum and/or minimum. Such a grating may be formed from three or more materials, two materials, or a single material that has a continuously varying refractive index. Any or all of the materials may have a continuously varying refractive index profile, as well. In another aspect, the grating may include a material that has a continuously varying refractive index profile.