We propose a method for calculating average local effective permittivity and permeability tensors for anisotropic photonic crystals through least-squares fits of sets of data points, obtained by rigorous, systematic complex-band-structure, and reflection calculations for all propagation directions, to appropriate analytic expressions. The proposed methodology is applied on a specific example of a tetragonal structure of metallic nanoshells, which is a uniaxial photonic crystal of resonant units. Our results demonstrate the efficiency of the method at low and moderate frequencies and, at the same time, reveal the inability to define local effective constitutive parameters in regions of resonance gaps.

By means of full electrodynamic and elastodynamic multiple-scattering calculations we study the optical and acoustic properties of three-dimensional lattices of metallic nanospheres implanted in a dielectric host. Our results show that such structures exhibit omnidirectional spectral gaps for both telecom infrared light and hypersound, with relatively low absorptive losses. This class of dual (phoxonic) band-gap materials is an essential step toward the hypersonic modulation of light and could lead to the development of efficient acousto-optical devices.

We apply the layer-multiple-scattering method to study the optical properties of different plasmonic architectures; namely two- and three-dimensional periodic arrays of metallic nanocylinders and of metallodielectric nanosandwiches. These structures exhibit various types of collective plasmonic resonances, tunable over a broad spectral range from infrared to visible frequencies, which cause large enhancement of the local field and give rise to interesting phenomena that we discuss and provide a consistent interpretation of the underlying physics. We analyze extinction spectra of finite slabs of the structures under consideration and explain the different spectral features. In relation to optical metamaterials, we deduce effective electromagnetic parameters by the S-matrix retrieval procedure for single- and multi-layer slabs of periodic arrays of metallodielectric nanosandwiches and propose a method to resolve ambiguities in the determination of the effective refractive index, which become prominent for thick slabs, based on the complex band structure of the corresponding infinite crystal.

We report on the effective optical response of single- and multilayer periodic structures of metallodielectric nanosandwiches on the basis of rigorous, full-electrodynamic calculations by the extended layer-multiple-scattering method. It is shown that the complex photonic band structure and the reflection coefficient of the infinite and semi-infinite crystal, respectively, provide reliable bulk effective parameters, which can be used as a reference in order to resolve ambiguities and problems in the determination of these parameters for finite slabs by the S-matrix retrieval procedure. Our results show that the structures under consideration exhibit strong artificial optical magnetism and thin films consisting of a few layers already behave like the bulk metamaterial.

We report on the effective optical response of a uniaxial crystal of metal–dielectric–metal nanosandwiches, which exhibits artificial optical magnetism, through full-electrodynamic simulations by the extended layer-multiple-scattering method. Using a recently developed all-angle homogenization procedure, which is based on rigorous results of complex-band-structure and reflection-coefficient calculations, we deduce local effective permittivity and permeability tensors, appropriate for this crystal. We show that the effective-medium description breaks down as we approach the region of the magnetic resonance. In a frequency region close to the resonance the retrieved effective parameters, though doubtful, indicate that the crystal under consideration may exhibit negative refraction. This behaviour is demonstrated by rigorous calculation of the isofrequency surfaces of the actual crystal and determination of the relevant group velocities.

By applying a homogenization method based on systematic full-electrodynamic complex-band-structure calculations, we deduce the effective permittivity tensor of a uniaxial photonic crystal consisting of consecutive hexagonal arrays of aligned metallic nanorods of finite length. The form of the obtained permittivity tensor over a relatively broad low-frequency region, where homogenization is applicable, suggests the occurrence of unconventional refractive behavior, namely, negative refraction and self-collimation. This behavior is corroborated by straightforward calculation of the relevant group velocities in the actual photonic crystal. Moreover, it is shown that, in the frequency region where negative refraction occurs, a finite slab of the crystal possesses eigenmodes that form flat bands outside the light cone, as many as the number of its constituent layers. These eigenmodes allow for transfer of the evanescent components of an incident wave field to the other side of the slab, thus enabling subwavelength imaging.

We report on the occurrence of strong nonlinear acousto-optic interactions in a one-dimensional model phoxonic cavity that supports, simultaneously, photonic and phononic localized resonant modes, by means of rigorous electrodynamic and elastodynamic calculations. We show that these interactions can take place when photons and phonons of long lifetime are confined in the same region of space and lead to enhanced modulation of light by acoustic waves through multiphonon exchange mechanisms.