Distribution of electromagnetic field and group velocities in two-dimensional periodic systems with dissipative metallic components

We study the distribution of the electromagnetic field of the eigenmodes and corresponding group velocities associated with the photonic band structures of two-dimensional periodic systems consisting of an array of infinitely long parallel metallic rods whose intersections with a perpendicular plane form a simple square lattice. We consider both nondissipative and lossy metallic components characterized by a complex frequency-dependent dielectric function. Our analysis is based on the calculation of the complex photonic band structure obtained by using a modified plane-wave method that transforms the problem of solving Maxwell's equations into the problem of diagonalizing an equivalent non-Hermitian matrix. In order to investigate the nature and the symmetry properties of the eigenvectors, which significantly affect the optical properties of the photonic lattices, we evaluate the associated field distribution at the high symmetry points and along high symmetry directions in the two-dimensional first Brillouin zone of the periodic system. By considering both lossless and lossy metallic rods we study the effect of damping on the spatial distribution of the eigenvectors; Then we use the Hellmann-Feynman theorem and the eigenvectors and eigenfrequencies obtained from a photonic bandstructure calculation based on a standard plane-wave approach applied to the nondissipative system to calculate the components of the group velocities associated with individual bands as functions of the wave vector in the first Brillouin zone. From the group velocity of each eigenmode the how of energy is examined. The results obtained indicate a strong directional dependence of the group velocity, and confirm the experimental observation that a photonic crystal is a potentially efficient tool in controlling photon propagation.