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

Abstract

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 frequencydependent 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 flow 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.

Properties of Anisotropic Photonic Band Gaps in Three-Dimensional Plasma Photonic Crystals Containing the Uniaxial Material With Different Lattices

“…(8) can be rewritten as (10) where ε −1 G,G (i) are the Fourier transform coefficients for ε −1 x and ε −1 y , respectively. As we know, the dielectric sphere filling factor can be written as f = (4πR 3 )/(3V m ), V m is the volume of unit cell.…”

The Wavelength Division Multiplexer Realized in Three-Dimensional Unusual Surface-Plasmon-Induced Photonic Crystals Composed of the Epsilon-Negative Materials Shells

“…Among those methods, PWE method is the most popular one to obtain the band structures, although there are many shortcomings, such as convergence problem and large number of plane waves [42,43]. Recently, the band structures for the PCs containing the Drude-type materials, such as plasma [44] and metal [45], can be computed successfully by a modified PWE method, which can compute the general nonlinear eigenvalue equation by a standard linearization technique. Thus, the PCs composed of the core spheres surrounded by the ENG material shells inserted in the air can be calculated easily by such a method.…”

Omnidirectional mirror based on Bragg stacks with a periodic gain-loss modulation

“…18 The propagation of electromagnetic fields in periodic media in the presence of absorption has been studied by different works using the Complex Band Structure (CBS). [19][20][21][22][23] The canonical formulation of the Plane Wave Method (PWM) is well suited to find allowed bands through the calculation of the real eigenfrequencies ω r with real wave vectors k r . 24 To analyze the forbidden bands there are two ways to proceed.…”

“…The role of absorption in PC has been studied by several authors. [21][22][23]28 In particular, the CBS has been used in Ref. 28 to understand the role of the dissipative effects of dielectric-metallic superlattices on the Omnidirectional Mirror (OM).…”