Effective-medium theory of zeroth-order lamellar gratings in conical mountings

A formalism is presented for calculating the ordinary and extraordinary refractive indices for a uniaxial film with optical properties equivalent to those of a conically mounted zeroth-order lamellar grating. In the quasistatic limit (grating-period-to-wavelength ratio → 0) this treatment is exact for both dielectric and metallic gratings. For period-to-wavelength ratios approaching unity, the effective anisotropic refractive indices are dependent on the polar and azimuthal incidence angles. The validity of this method as the period-to-wavelength ratio increases is studied by comparison of the method with the predictions of rigorous grating theories. Comparisons are then made with the predictions of other effective-medium theories. Examples of the use of this theory for conically mounted zeroth-order gratings are presented.