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Waveguide structures with an antisymmetric gain/loss profile were studied more than a decade ago as benchmark tests for beam propagation methods. These structures attracted renewed interest, recently e.g. as photonic analogues of quantum mechanical structures with parity-time symmetry breaking. In this paper, properties of both weakly and strongly guiding two-mode waveguides and directional couplers with balanced loss and gain are described. Rather unusual power transmission in such structures is demonstrated by using numerical methods. We found that the interface between media with balanced loss and gain supports propagation of confined unattenuated TM polarized surface wave and we have shown that its properties are consistent with the prediction of a simple analytical model.

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We study the scattering of an electromagnetic wave from a cylinder of infinite length fabricated from a combined split-ring resonator ͑SRR͒ and thin metal wire medium that is characterized by an effective frequency-dependent permittivity ⑀ eff () and permeability eff () that can both be negative in a certain frequency region, and thus constitutes a left-handed ͑LH͒ metamaterial. We evaluate the scattering width of the cylinder in terms of the most general form of the Mie coefficients a n ,b n that takes into account the magnetic effects through the effective refractive index n eff ()ϭͱ⑀ eff ()ͱ eff (). Incident waves of both E polarization ͑where the electric field is parallel to the axis of the cylinder͒ and H polarization ͑where the magnetic field is parallel to the axis of the cylinder͒ are considered. We find that in the case when the magnetic field is perpendicular to the plane of the SRR, the scattering width as a function of the frequency of the incident wave reveals the resonances of the Mie coefficients a n and b n , for both E-and H-polarized incident waves. These peaks occur in the frequency range where the effective refractive index is negative, and they arise from modes that propagate with a negative group velocity. This behavior is consistent with the results of transfer-matrix calculations and transmission experiments on two-dimensional LH metamaterials, which show that the medium becomes transparent to the electromagnetic radiation in this frequency region.

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.

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