We review the basic physics behind light interaction with plasmonic nanoparticles. The theoretical foundations of light scattering on one metallic particle (a plasmonic monomer) and two interacting particles (a plasmonic dimer) are systematically inv
estigated. Expressions for effective particle susceptibility (polarizability) are derived, and applications of these results to plasmonic nanoantennas are outlined. In the long-wavelength limit, the effective macroscopic parameters of an array of plasmonic dimers are calculated. These parameters are attributable to an effective medium corresponding to a dilute arrangement of nanoparticles, i.e., a metamaterial where plasmonic monomers or dimers have the function of meta-atoms. It is shown that planar dimers consisting of rod-like particles generally possess elliptical dichroism and function as atoms for planar chiral metamaterials. The fabricational simplicity of the proposed rod-dimer geometry can be used in the design of more cost-effective chiral metamaterials in the optical domain.
Wannier function expansions are well suited for the description of photonic- crystal-based defect structures, but constructing maximally localized Wannier functions by optimizing the phase degree of freedom of the Bloch modes is crucial for the effic
iency of the approach. We systematically analyze different locality criteria for maximally localized Wannier functions in two- dimensional square and triangular lattice photonic crystals, employing (local) conjugate-gradient as well as (global) genetic-algorithm-based, stochastic methods. Besides the commonly used second moment (SM) locality measure, we introduce a new locality measure, namely the integrated modulus (IM) of the Wannier function. We show numerically that, in contrast to the SM criterion, the IM criterion leads to an optimization problem with a single extremum, thus allowing for fast and efficient construction of maximally localized Wannier functions using local optimization techniques. We also present an analytical formula for the initial choice of Bloch phases, which under certain conditions represents the global maximum of the IM criterion and, thus, further increases the optimization efficiency in the general case.
The Cherenkov radiation is substantially modified in the presence of a medium with a nontrivial dispersion relation. We consider Cherenkov emission spectra of a point charge moving in general three- (3D) and two-dimensional (2D) photonic crystals. Ex
act analytical expressions for the spectral distribution of the radiated power are obtained in terms of the Bloch mode expansion. The resulting expression reduces to a simple contour integral (3D case) or a one-dimensional sum (2D case) over a small fraction of the reciprocal space, which is defined by the generalized Cherenkov condition. We apply our method to a specific case of an electron moving with different velocities in a 2D square-lattice photonic crystal. Our method demonstrates an excellent agreement with numerically rigorous finite-difference time-domain calculations while being less demanding on computational resources.
The analysis of an angular distribution of the emission intensity of a two-level atom (dipole) in a photonic crystal reveals an enhancement of the emission rate in some observation directions. Such an enhancement is the result of the bunching of many
Bloch eigenwaves with different wave vectors in the same direction due to the crystal anisotropy. If a spatial distribution of the emission intensity is considered, the interference of these eigenwaves should be taken into account. In this paper, the far-field emission pattern of a two-level atom is discussed in the framework of the asymptotic analysis the classical macroscopic Green function. Numerical example is given for a two-dimensional square lattice of air holes in polymer. The relevance of results for experimental observation is discussed.
