Optical wave parameters for spatially dispersive and anisotropic nanomaterials

Spatial dispersion is an intriguing property of essentially all nanostructured optical media. In particular, it makes optical waves with equal frequencies and polarizations have different wavelengths, if they propagate in different directions. This can offer new approaches to control light radiation and propagation. Spatially dispersive nanomaterials, such as metamaterials, are often treated in terms of wave parameters, such as refractive index and impedance retrieved from reflection and transmission coefficients of the material at each incidence angle. Usually, however, the waves are approximated as transverse, which simplifies the description, but yields wrong results, if spatial dispersion or optical anisotropy is significant. In this work, we present a method to calculate the wave parameters of a general spatially dispersive and optically anisotropic medium without applying such an approximation. The method allows one to evaluate the true impedances and field vectors of the effective waves, obtaining thus the true light intensity and energy propagation direction in the medium. The equations are applied to several examples of spatially dispersive and anisotropic materials. The method introduces new insights into optics of nanostructured media and extends the design of such media towards optical phenomena involving significant spatial dispersion.