Electromagnetic energy transport in finite photonic structures.

We have derived, for oblique propagation, an equation relating the averaged energy flux density to energy fluxes arising in the process of scattering by a lossless finite photonic structure. The latter fluxes include those associated with the dispersion relation of the structure, reflection, and interference between the incident and reflected waves. We have also derived an explicit relation between the energy flux density and the group velocity, which provides a simple and systematical procedure for studying theoretically and experimentally the properties of the energy transport through a wide variety of finite photonic structures. Such a relation may be regarded as a generalization of the corresponding one for infinite periodic systems to finite photonic structures. A finite, N-period, photonic crystal was used to illustrate the usefulness of our results.

Zero-width band gap associated with the n[over] = 0 condition in photonic crystals containing left-handed materials.

We demonstrate that the band structure of a photonic crystal consisting of alternating layers of right-handed material (RHM) and left-handed material (LHM) can exhibit two types of zero- n[over ] gaps of zero width. It is shown that each type has an associated null-gap condition which determines the scaling properties of the frequency nu(0) at which the corresponding null gap occurs. Specifically, while scaling in the layer thicknesses does not modify the value of the frequency nu(0) determined by one of these conditions, the frequency nu(0) associated with the other one does not exhibit such a scaling behavior. We have also shown that near the touching point nu(0) (for both types of null gaps) and around the center of the Brillouin zone, the dispersion curves exhibit a linear dependence on the Bloch wave vector k . As a consequence, the corresponding density of states and group velocity are practically flat as functions of k in the neighborhood of k=0 . Another interesting property of the considered structure is that an electromagnetic wave with frequency nu(0) can be transmitted through a finite RHM-LHM photonic crystal without any change in amplitude and phase.