In lossless periodic media, the concept of group velocity is fundamental to the study of propagation dynamics. When spatially averaged, the group velocity is numerically equivalent to energy velocity, defined as the ratio of energy flux to energy density of modal fields. However, in lossy media, energy velocity diverges from group velocity. Here, we define a modal field velocity which remains equal to the complex modal group velocity in homogeneous and periodic media. The definition extends to the more general situation of modal fields that exhibit spatial or temporal decay due to lossy elements or Bragg reflection effects. Our simple expression relies on a generalization of the concepts of energy flux and density. Numerical examples, such as a two-dimensional square array of silver rods in vacuum, are provided to confirm the result. Examples demonstrate how the dispersion relation of the periodic structure, the properties of its modes, and their group velocities change markedly in lossy media.

We consider thin lamellar and cylinder gratings, composed of silicon carbide and air, and investigate the conditions under which they can totally absorb an incident plane wave, for both p and s polarizations. We also consider thin-film equivalent in the quasistatic limit to the gratings, deriving the effective dielectric tensor for cylinder gratings. We show that the accuracy of the quasistatic models is a strong function of polarization, wavelength, and grating thickness due to the resonant nature of the optical constants of silicon carbide but that these models can be quantitatively accurate and give a good qualitative guide to the parameter values under which thin gratings can deliver high optical absorptance.

A faster method of simulating 2D slabs, both metallic and dielectric, with cylindrical inclusions is proposed. The method is applicable to photonic crystal defect-row waveguides and extraordinary transmssion through metallic films, capable of producing both in-plane dispersion relations and transmission spectra.