This study delves into the exploration of wave propagation in spatially homogeneous systems governed by a Klein-Gordon–type equation with a periodically time-varying cutoff frequency. Through a combination of analytical calculations and numerical simulations, intriguing and distinctive features in the dispersion diagram of these systems are uncovered. Notably, the examined configurations demonstrate some remarkable transitions as the modulation frequency increases. These transitions encompass a transformation from a frequency gap to a wave-number (q) gap around q=0, with the transition point corresponding to a gapless Dirac dispersion with an exceptional point of degeneracy. Subsequently, the q gap undergoes a bifurcation into two symmetric gaps at positive and negative wave numbers. At this second transition point, the dispersion diagram takes the form of an imaginary Dirac dispersion relation and exhibits an isolated exceptional point at the center of the q=0 gap. These findings contribute to a deeper understanding of wave dynamics in periodically modulated media, uncovering tunable phenomena.

Metamaterials are a fascinating class of photonic materials since they allow us to control optical responses (largely) at will. Besides being an intellectual challenge, adding time variations into spatial metamaterials increases the degrees of freedom to tune their effective response, which motivates their exploration. However, to exploit such materials in the future design of functional devices, we may wish to treat them at the effective level to avoid considering all the mesoscopic details. To permit such effective treatment, we describe here an eigenmode-based approach to homogenize spatiotemporal metamaterials composed of a periodic arrangement of scatterers made from a time-varying material. Practically, we consider the periodic arrangement of spheres within one layer. In our two-step homogenization scheme, we first temporally homogenize that metasurface using the eigenmodes of the bulk time-varying material. Following this, we perform spatial homogenization by inverting the Fresnel coefficients of a slab made from a stationary material. These steps effectively describe the optical response of the spatiotemporal metasurface as a homogeneous slab. We validate our results by comparing the optical observables, i.e., reflectivity and transmissivity, of the metasurface with those of the homogenized slab, and we assess the limitations of the homogenization.

A proper generalization of the extended boundary condition method to calculate the transition matrix, T, for electromagnetic scattering from a homogeneous and isotropic body of arbitrary shape, characterized by a periodically time-varying electric permittivity, is presented. The application of the method on a specific example of a spheroidal dielectric particle confirms that time modulation induces strong inelastic scattering, accompanied by energy transfer between the scatterer and the light field, when the difference of the incident wave frequency to a particle optical resonance matches an integer multiple of the modulation frequency. Moreover, it is shown that, for nonspherical scatterers, these effects can be selectively tuned by external means such as the polarization and the propagation direction of the incident light beam. The method is readily implementable in available dynamic multiple-scattering computer codes, and, because of its versatility and computational efficiency, it can offer new opportunities for studying more complex time-varying photonic structures.

An extension of the photonic layer multiple scattering methodology to dynamic spherical scatterers, which exhibit a periodic time-varying response, is presented. The applicability of the method is demonstrated on specific examples of single- and bi-layers of periodically modulated high-refractive-index spherical particles arranged on a square lattice. The results provide compelling evidence for strong and tunable inelastic scattering effects under the triple resonance condition, fulfilled for optical transitions between neighboring high-Q lattice modes of the appropriate symmetry, which originate from multipolar Mie resonances. A consistent interpretation of the underlying mechanisms is provided and potential applications in the design of nonreciprocal devices are discussed.

This work reports on light scattering by a homogeneous dielectric sphere with a periodically time-varying radius. The off-shell inelastic scattering T matrix, which describes the dynamically changing particle, is evaluated using the Floquet method, and some remarkable phenomena, emerging in the strong- and weak-coupling regimes, are discussed. In particular, the limits of validity of the approximate quasistatic solution are established through comparison with the results of fully dynamic calculations, and the scattering in the strong-coupling regime is analyzed in terms of the general behavior of parametrically driven oscillators. Additionally, the influence of damping of the sphere vibrations on the optical spectra is also investigated.

A time Floquet transfer-matrix method for the description of acoustic wave propagation through dynamic stratified structures, modulated by another, low-frequency, pump acoustic wave, is reported. The method is applied to a specific example of a GaAs/AlAs periodic superlattice, subject to a spatiotemporal modulation induced by an evanescent pump wave with frequency in the lowest acoustic band gap of the structure. By means of systematic numerical calculations, we provide compelling evidence for the occurrence of significant nonreciprocal transmission of an acoustic signal with frequency in a high-order acoustic band gap, through inelastic multiple-scattering processes. Our results indicate a promising route to design nonreciprocal acoustic devices.

We study magnon-mediated optical transitions in micrometer-sized axially symmetric yttrium iron garnet (YIG) particles, which act as optomagnonic cavities, by means of electromagnetic calculations, treating the magneto-optical coupling to first order in perturbation theory, in the framework of a fully dynamic approach. Such particles with engineered shape anisotropy exhibit high-quality-factor Mie resonances in the infrared part of the spectrum, with a separation of few gigahertz, which matches the typical frequencies of magnons. This allows for optical transitions mediated by spin waves, while the micrometer volume favors stronger overlap between the optical modes and the precessing magnetization. Our results predict that photon-magnon coupling strengths of tens of kilohertz could be realized with cylindrical or spheroidal particles, since mainly the reduced volume, but also shape anisotropy, can lead to strong, up to four orders of magnitude, enhancement of the coupling strengths compared to submillimeter YIG spheres.

A variety of multidispersive, localized, or extended in frequency, bands, induced by inductance-based external electric circuits in piezoelectric phononic plates, is studied both theoretically and experimentally in this work. Their origin, tightly related to an equivalent LC-circuit behavior, is analyzed in detail and their interaction with the Lamb-like guided modes of the plate is also discussed. These bands, easily tuned by the choice of the parameters of the external electric circuitry, lead to a non-destructive, real-time control of the dispersion characteristics of these structures. Our device and analysis can find application in the improvement of surface acoustic wave components by offering additional degrees of freedom.

We employ the extended boundary condition method (EBCM) that we properly extend so as to describe gyroelectric and gyromagnetic (i.e., gyrotropic) anisotropy and report on the electromagnetic (EM) complex resonances of magnetooptic (i.e., gyroelectric) bodies of revolution (BoRs), as well as on the complex magnetic plasmon resonances (MPRs) of ferrite (i.e., gyromagnetic) BoRs. The proposed extension is based on an alternative scheme for the expansion of the EM field inside a gyrotropic medium, namely, a discrete eigenfunction (DE) expansion in terms of spherical vector wave functions (SVWFs). This approach provides the transition matrix (namely, T-matrix) that allows not only for the direct computation of the scattered field from the incident one, but also for the determination of the complex resonances of open (i.e., situated in free space) gyrotropic BoR resonators. The EBCM is validated on two levels: first, by calculating the EM scattering from various BoRs, including anisotropic spheroids, cylinders, and rods, and comparing with HFSS commercial software; second, by computing the complex eigenfrequency spectrum of gyroelectric spheroidal resonators and comparing with a recently developed rigorous technique for the EM modeling of anisotropic spheroids.

This chapter first summarizes the fundamentals of classical electrodynamics in continuous media, placing emphasis on the optical response of gyrotropic materials. It, subsequently, develops in a concise but rigorous manner the scattering- and transfer-matrix methods for general stratified photonic media, based on a versatile six-vector formulation of Maxwell equations. Applications are reported for periodic and defect one-dimensional (1D) magnetophotonic structures in different configurations. A consistent interpretation of some remarkable phenomena, such as occurrence of photonic gaps and localized defect modes, enhanced magnetooptical effects, non-reciprocal optical response, etc., is provided through a thorough analysis of relevant dispersion diagrams in conjunction with transmission/reflection spectra. Finally, the concept of a dual optomagnonic cavity, formed in judiciously designed stratified magnetophotonic structures, for strong photon–magnon interaction is introduced. Methods for its theoretical description, namely the Green’s function-based perturbation expansion, the quasi-static adiabatic approximation, and a fully dynamic time-Floquet approach, are developed, and their accuracy and limits of validity are assessed. Proof-of-concept demonstrations are presented for enhanced interaction of light, trapped in optical defect modes, with perpendicular standing spin waves, in a dielectric magnetic film sandwiched between two dielectric Bragg mirrors.

A rigorous time Floquet method for the calculation of scattering of electromagnetic waves by a homogeneous spherical object, characterized by a periodically varying-in-time isotropic permittivity, is presented. The method is applied to the study of Mie scattering by such a modulated dielectric particle. Our results are in excellent agreement with the quasistatic adiabatic approximation in the slow-modulation limit. At higher modulation frequencies, a remarkable spectral response, including resonant inelastic scattering and frequency conversion as well as energy transfer between the dynamic sphere and the electromagnetic field, is revealed and consistently explained.

A thorough theoretical study of the optical properties of periodic Si nanosphere arrays is undertaken, placing a particular emphasis on the synergy between multipolar, electric and magnetic, Mie resonances, which occur in high-refractive-index nanoparticles and can lead to a rich variety of phenomena ranging from perfect reflection to controlled diffraction. Systematic calculations using the layer-multiple-scattering method, which we properly extended to describe periodic arrays with many different scatterers per unit cell, in conjunction with finite-element simulations are presented. It is shown that rectangular arrays of pairs of Si nanospheres can efficiently diffract light in reflection or transmission mode at large angles as well as split light with minimum backreflection by properly adjusting the geometry of the structure. Our rigorous full-electrodynamic calculations highlight the importance of higher-order multipoles, which are not taken into account in the commonly employed dipole approximation, in the description of these effects.

A generalized rigorous Floquet scattering-matrix method for stratified anisotropic optical media, subject to a periodic spatiotemporal modulation, is formulated and implemented. The method is applied for studying an optomagnonic cavity formed by an in-plane magnetized ferrite film, in which a magnetostatic surface spin wave propagates, sandwiched between two nonmagnetic dielectric Bragg mirrors. Our results provide unambiguous evidence that externally incident light, when trapped in a cavity mode, experiences a strongly enhanced interaction with the spin wave due to the increased coupling time, which can give rise to pronounced effects if the appropriate selection rules are fulfilled. By means of systematic calculations we reveal and explain some remarkable features of this interaction, such as formation of spectral gaps, controllable transmission, and the emergence of inelastic diffracted beams, and show that efficient conversion of the optical wave can be achieved by triply resonant inelastic scattering through (multi)magnon absorption and emission processes.

We report a thorough theoretical investigation of magnon-assisted photon transitions in magnetic garnet micron-sized spheres, which operate as optomagnonic resonators. In this case, matching the intraband splitting of optical Mie modes, induced by particle magnetization, to the eigenfrequency of the uniform-precession spin wave, high-efficiency triply resonant optical transitions between these modes, through respective emission or absorption of a cavity magnon, are enabled. By means of rigorous full electrodynamic computations, supported by corresponding approximate analytical calculations, we provide compelling evidence of greatly increased optomagnonic interaction, compared to that in similar processes between whispering gallery modes of corresponding submillimeter spheres, due to the reduced magnon mode volume. We explain the underlying mechanisms to a degree that goes beyond existing interpretation, invoking group theory to derive general selection rules and highlighting the role of the photon spin as the key property for maximizing the respective coupling strength.

In this work we study the electromagnetic scattering by a magnetized cold plasma body, using a surface integral equation (SIE) formulation. To solve the problem, we express the fields inside the anisotropic region using appropriate discrete eigenvalue expansions and, applying the boundary conditions on body's surface, we obtain infinite sets of inhomogeneous algebraic equations from which, upon truncation, the expansion coefficients of the internal field are computed. Then, the expansion coefficients of the scattered field can be evaluated, as well as the bistatic scattering cross section. To conclude on the method's validity, we compute the cross sections, for different values of parameters, for prolate spheroidal bodies, and compare with the results obtained by the HFSS commercial software.

The development of nanostructured semiconductors with tailored morphology and electronic properties for surface-enhanced Raman scattering (SERS) has been attracting significant attention as a promising alternative to conventional coinage metal SERS substrates. In this work, functionalized TiO2 photonic crystals by graphene oxide nanocolloids (nanoGO) are demonstrated as highly sensitive, recyclable, plasmon-free SERS substrates that combine slow-photon amplification effects with the high adsorption capacity and surface reactivity of GO nanosheets. Comparative evaluation of photonic band gap engineered nanoGO–TiO2 inverse opal films was performed on methylene blue SERS detection under different laser excitations in combination with rigorous theoretical simulations of the photonic band structure. A very low detection limit of 6 × 10−7 M and an enhancement factor of 5 × 104 along with excellent self-cleaning performance and reusability could be achieved by the interplay of slow-photon effects assisted by interfacial charge transfer between the analyte and the nanoGO–TiO2 semiconducting substrate. Slow-photon management in combination with judicious engineering of chemical enhancement in photonic nanostructures is accordingly proposed as an advanced approach for the design of efficient dielectric SERS substrates.

Optomagnonic cavities have recently been emerging as promising candidates for implementing coherent photon-magnon interactions, for applications in quantum memories and devices, and next generation quantum networks. A key challenge in the design of such cavities is the attainment of high magnon-mediated optical-to-optical conversion efficiencies, which could, e.g., be exploited for efficient optical interfacing of superconducting qubits, as well as the practicality of the final designs, which ideally should be planar and amenable to on-chip integration. Here, on the basis of a novel time-Floquet scattering-matrix approach, we report on the design and optimization of a planar, multilayer optomagnonic cavity, incorporating a cerium-substituted yttrium iron garnet thin film, magnetized in-plane, and operating in the triple-resonant inelastic light scattering regime. This architecture allows for magnon-mediated optical-to-optical conversion efficiencies of about 5% under realistic conditions, which is orders of magnitude higher than that attained in alternative optomagnonic designs. Our results suggest a viable way forward for realizing practical information inter-conversion, with high efficiencies, between microwaves, strongly coupled to magnons, and optical photons, as well as a platform for fundamental studies of classical and quantum dynamics in magnetic solids and for the implementation of futuristic quantum devices.

A fully dynamic theoretical approach to layered optomagnonic structures, based on a time Floquet scattering-matrix method, is developed. Its applicability is demonstrated on a simple design of a dual photonic-magnonic cavity, formed by sandwiching a magnetic garnet thin film between two dielectric Bragg mirrors, subject to continuous excitation of a perpendicular standing spin wave. Some remarkable phenomena, including nonlinear photon-magnon interaction effects and enhanced inelastic light scattering in the strong-coupling regime, fulfilling a triple-resonance condition, are analyzed and the limitations of the quasistatic adiabatic approximation are established.

We report on judiciously designed stratified periodic structures of magnetic dielectric materials with a localized defect layer, which are able to concurrently confine light and spin waves in the same ultra-small defect region for a long time period, thus resulting in enhanced photon–magnon interaction and large dynamic optical frequency shift. Our results for a specific realization of such a one-dimensional, so-called photomagnonic, crystal magnetized at saturation perpendicular to the interfaces, obtained by means of rigorous calculations using scattering-matrix techniques, show that the inherently weak coupling between visible/near-infrared light and GHz-frequency spin waves can be greatly increased leading to strong modulation of the optical field through multi-magnon exchange mechanisms. Such novel multifunctional composite materials offer a promising platform for tailoring light–spin-wave coupling in view of fast and energy-efficient spin-optical information processing applications.

We report on the optical response of a nonreciprocal bianisotropic metamaterial, consisting of spherical, metal-coated magnetic nanoparticles embedded in an optically active medium, thus combining gyrotropy, plasmonic resonances, and chirality in a versatile design. The corresponding effective medium is deduced by an appropriate two-step generalized Maxwell-Garnett homogenization scheme. The associated photonic band structure and transmission spectra are obtained through a six-vector formulation of Maxwell equations, which provides an efficient framework for general bianisotropic structures going beyond existing approaches that involve cumbersome nonlinear eigenvalue problems. Our results, analyzed and discussed in the light of group theory, provide evidence that the proposed metamaterial exhibits some remarkable frequency-tunable properties, such as strong, plasmon-enhanced nonreciprocal polarization azimuth rotation and magnetochiral dichroism.

The interaction of visible and near-infrared light with spin waves in appropriately designed dual nanocavities, for both photons and magnons, is investigated by means of rigorous calculations, correct to arbitrary order in the magneto-optical coupling parameter. It is shown that the concurrent localization of the interacting photon and magnon fields in the same region of space for a long period of time enhances their mutual interaction, provided that specific selection rules are fulfilled. Our results provide evidence for the occurrence of strong effects, beyond the linear response approximation, which lead to enhanced modulation of light by spin waves through multimagnon absorption and emission processes by a photon.

Using an extension of the full elastodynamic layer-multiple-scattering method to structures of fluid-saturated poroelastic spherical bodies, a comprehensive theoretical study of the acoustic response of double-porosity submerged liquid-saturated granular polymeric materials of specific morphology consisting of touching porous polymer spheres arranged in a fcc lattice, beyond the long-wavelength effective-medium description, is presented. Calculated transmission and absorption spectra of finite slabs of these materials are analyzed by reference to the acoustic modes of the constituent porous spherical grains as well as to relevant dispersion diagrams of corresponding infinite crystals, and a consistent interpretation of the results is provided. In particular, it is shown that resonant modes with very long lifetime, localized in the spheres in the form of slow longitudinal waves, which are peculiar to poroelastic materials, are formed when the viscous length is much shorter than the radius of the inner pores of the spheres. These modes, which can be easily tuned in frequency by adjusting the intrinsic porosity of the spheres, induce some remarkable features in the acoustic behavior of these double-porosity materials, such as narrow dispersionless absorption bands and directional transmission gaps.

The magneto-optical response of a Faraday-active Fabry–Pérot etalon with birefringent mirrors is studied by means of electrodynamic simulations using the finite-element and the scattering-matrix methods. The specific structure under consideration consists of a magnetic garnet film sandwiched between two metallic layers, patterned with periodically spaced parallel grooves on their outer sides. Our results are analyzed by reference to the properties of the individual structural components and a consistent interpretation of the different spectral features observed is provided. It is shown that, by properly adjusting the geometrical parameters involved, strong Faraday rotation enhancement can be obtained through constructive synergy between the Fabry–Pérot resonant mode of the magneto-optical nanocavity and the slot plasmon mode localized in the grooves.

Photonic band gap engineered TiO2 inverse opals were fabricated using self- assembled polystyrene films as sacrificial templates with controlled optical properties, aimed at the identification of the slow-photon effect on dye sensitized TiO2 photocatalysis. The materials’ photocatalytic efficiency was evaluated using Raman spectroscopy, on methylene blue photodegradation following both UVA and monochromatic visible light illumination. Contrary to UVA, where no photonic effect could be traced, laser irradiation within the slow-photon energy range of the TiO2 inverse opals, resulted in a marked increase of the dye photosensitized degradation rate, outperforming not only compact nanocrystalline films but also the benchmark mesoporous Aeroxide® P25 TiO2 films. This effect provides direct evidence for the presence of slow photons that amplify the interaction of visible light with the adsorbed dye molecules on the periodically structured TiO2 film.

We developed an extension of the layer-multiple-scattering method to photonic crystals comprising homogeneous layers of magneto-optical materials. The applicability of the method is demonstrated on a specific architecture of a magnetic garnet thin film coated with a square array of silver nanodisks, supported by a silica substrate. It is shown that enhanced Faraday rotation, driven by hybrid particle plasmon-film quasi-guided collective modes, can be achieved within selected regions of frequency, which can be tuned by properly choosing the geometric and material parameters involved. The results are analyzed in conjunction with numerical simulations by the finite-element method and a consistent interpretation of the underlying physics is provided. Our extended layer-multiple-scattering computational methodology provides a versatile framework for fast and accurate full electrodynamic calculations of magneto-optical structures, enabling physical insight.

An extension of the layer-multiple-scattering method to phononic crystals of poroelastic spheres immersed in a fluid medium is developed. The applicability of the method is demonstrated on specific examples of close-packed fcc crystals of submerged water-saturated meso- and macroporous silica microspheres. It is shown that, by varying the pore size and/or the porosity, the transmission, reflection, and absorption spectra of finite slabs of these crystals are significantly altered. Strong absorption, driven by the slow waves in the poroelastic material and enhanced by multiple scattering, leads to negligible transmittance over an extended frequency range, which might be useful for practical applications in broadband acoustic shielding. The results are analyzed by reference to relevant phononic dispersion diagrams in the viscous and inertial coupling limits, and a consistent interpretation of the underlying physics is provided.

Molecular spontaneous emission and fluorescence depend strongly on the emitter local environment. Plasmonic nanoparticles provide excellent templates for tailoring fluorophore emission, as they exhibit potential for both fluorescence enhancement and quenching, depending on emitter positioning in the nanoparticle vicinity. Here we explore the influence of hitherto disregarded nonclassical effects on the description of emitter–plasmon hybrids, focusing on the roles of the metal nonlocal response and especially size-dependent plasmon damping. Through extensive modelling of metallic nanospheres and nanoshells coupled to dipole emitters, we show that within a purely classical description a remarkable fluorescence enhancement can be achieved. However, once departing from the local-response approximation, and particularly by implementing the recent generalised nonlocal optical response theory, which provides a more complete physical description combining electron convection and diffusion, we show that not only are fluorescence rates dramatically reduced compared to the predictions of the local description and the common hydrodynamic Drude model, but the optimum emitter–nanoparticle distance is also strongly affected. In this respect, experimental measurements of fluorescence, the theoretical description of which requires a precise concurrent evaluation of far- and near-field properties of the system, constitute a novel, more sensitive probe for assessing the validity of state-of-the-art nonclassical theories.

Collective hybridized plasmon modes, which enable strong magnetooptical coupling and consequent enhanced Faraday effect in three-dimensional periodic assemblies of magnetic dielectric nanoparticles coated with a noble-metal shell, are studied by means of rigorous full electrodynamic calculations using an extension of the layer-multiple-scattering method, in conjunction with the effective-medium approximation. A thorough analysis of relevant photonic dispersion diagrams and transmission spectra provides a consistent explanation of the underlying physical mechanisms to a degree that goes beyond existing interpretation. It is shown that properly designed structures of such composite magnetoplasmonic nanoparticles offer a versatile platform for engineering increased and broadband Faraday rotation.

The conditions for the occurrence of strong magnetotransverse anisotropy in light scattering by a single gyrotropic sphere are investigated by means of rigorous full electrodynamic multipole calculations. It is shown that composite magnetoplasmonic spherical scatterers with a core–shell morphology can induce large and tunable plasmon-driven Hall photon currents, which appear even in the case of subwavelength particles. Explicit results for silver-coated bismuth-substituted yttrium iron garnet nanospheres are presented and analyzed.

We report on the influence of elastic waves on the optical response and light emission in simultaneously photonic and phononic resonant cavities. Elastic waves couple with light through the acousto-optic interaction. Concurrent control of both light and sound through simultaneously photonic–phononic, often called phoxonic, band-gap structures is intended to advance both our understanding as well as our ability to manipulate light with sound and vise versa. In particular, co-localization of light and sound in phoxonic cavities could trigger nonlinear absorption and emission processes and lead to enhanced acousto-optic effects. We review our recent work on sound-controlled optical response and light emission in phoxonic cavities and investigate the limits of validity of the photoelastic model that describes light–sound interaction to first-order approximation. Moreover we present some preliminary results on silicon nitride nanobeam phoxonic devices.

A thorough study of localized surface plasmons and associated strong circular dichroism, which can occur in silver-coated metallic and dielectric magnetic nanospheres, is reported by means of both quasistatic and full electrodynamic calculations taking into account the actual (magneto) optical response of the constituent materials, including dispersion and losses. It is shown that such composite magnetoplasmonic nanoparticles offer a versatile platform for engineering hybrid plasmon modes that give rise to sharp absorption resonances and subject to large magneto-optic splitting, leading to giant magnetic circular dichroism signals, by properly choosing the different materials and tuning the geometrical parameters involved.

Composite magnetoplasmonic nanoparticles with a core-shell morphology exhibit intriguing optical properties and offer impressive opportunities for tailoring in a controllable manner the light-matter interaction at subwavelength dimensions. These properties are usually analyzed in the framework of the quasi-static approximation, which, however, is often inadequate; thus, a full electrodynamic treatment is required. In this respect, we developed a rigorous method for an accurate description of electromagnetic scattering by a gyrotropic sphere coated with a nongyrotropic concentric spherical shell, based on the full multipole expansion of the wave field. The method was applied to specific examples of core-shell cobalt-silver spherical nanoparticles, where the occurrence of strong circular dichroism induced by magnetoplasmonic interaction, which largely exceeds that of homogeneous noble metal nanoparticles in an external magnetic field, was found. Our results were also explained by reference to the quasi-static approximation, which, though it reproduces the main features of the absorption spectra, strongly overestimates circular dichroism in the cases we studied.

The limits of validity of the linear photoelastic model are investigated in a one-dimensional dual photonic-phononic cavity, formed by alternating layers of a chalcogenide glass and a polymer homogeneous and isotropic material, which supports both optical and acoustic resonant modes localized in the same region. It is shown that the linear-response regime breaks down when either the acoustic excitation increases or the first-order acousto-optic interaction coupling element vanishes by symmetry, giving rise to the manifestation of multiphonon absorption and emission processes by a photon. Our results provide a consistent interpretation of different aspects of the underlying physics relating to nonlinear acousto-optic interactions that can occur in such cavities.

We present an extension of the layer-multiple-scattering method to photonic crystals of gyrotropic spheres in a homogeneous host medium. The efficiency of the method is demonstrated on specific examples of three-dimensional chiral structures and surfaces of crystals of plasma spheres in an external static uniform magnetic field that lack, simultaneously, time-reversal and space-inversion symmetries, and exhibit a nonreciprocal spectral response.

We present an extended version of the layer-multiple-scattering method, which is ideally suited for the study of photonic crystals of different kinds of particles, encompassing homogeneous and multicoated chiral and nonchiral spheres, gyrotropic spheres, as well as homogeneous nonspherical particles. The efficiency of the method is demonstrated on specific examples of planar magnetoplasmonic nanostructures that lack, simultaneously, time-reversal and space-inversion symmetries. Nonreciprocal transport of light at the (001) surface of a semi-infinite face centered cubic (fcc) crystal of plasma nanospheres under the action of an external, in-plane, static magnetic field and of surface plasmon polaritons at the surface of a plasmonic material coated with an overlayer of magnetized garnet nanospheres is demonstrated in the Voigt geometry.

It is shown that a planar defect in the stacking sequence of an all-dielectric photonic crystal of garnet spheres supports localized optical guided modes, which originate from Mie resonances of the individual spheres. If the defect breaks space-inversion symmetry and the garnet particles are magnetized inplane, nonreciprocal and lossless transport of light on the defect plane, expected on the basis of group theory in the Voigt–Cotton–Mouton configuration, is demonstrated in ultrathin films of the defect crystal by means of full electrodynamic calculations using the layer-multiple-scattering method properly extended to photonic crystals of gyrotropic spheres.

We show that a relatively sparse photonic crystal of high-permittivity magnetic garnet particles can induce a giant Faraday rotation of light transmitted through a finite slab of it. The underlying mechanism resides in wave propagation through collective Bloch modes, which are strongly localized in the particles.

A detailed and rigorous theoretical investigation of the optical properties of a generic three-dimensional chiral structure of plasma spheres, without and under the action of an external static uniform magnetic field, is presented. Corresponding photonic band diagrams in conjunction with relevant transmission spectra, calculated by the full electrodynamic layer-multiple-scattering method properly extended to the case of gyrotropic spherical scatterers, are discussed in the light of the theory of nonsymmorphic space groups. This analysis provides a consistent interpretation of some remarkable features and effects like Dirac points, polarization-dependent transmission, as well as band splitting and non-reciprocal optical response that emerge as a result of time-reversal-symmetry breaking, induced by the external static magnetic field, and the lack of space-inversion symmetry in the crystal.

We report on the occurrence and properties of photonic surface states in periodic structures of magnetized plasma nanospheres by means of rigorous calculations using the full-electrodynamic layer-multiple-scattering method, properly extended to treat gyrotropic spheres with arbitrarily oriented gyration vector. More specifically, dispersion diagrams of Tamm states at the (001) surface of a semi-infinite fcc crystal of plasma nanospheres and of guided modes of a square array of such spheres supported by a quartz substrate, without and under the action of an in-plane static uniform magnetic field, are analyzed and nonreciprocal optical response, which emerges as a result of the simultaneous lack of space-inversion and time-reversal symmetries, is demonstrated in the Voigt geometry.

We report on the occurrence of strong nonreciprocal magnetochiral dichroism in helical structures of magnetic garnet spheres, which emerges as a result of the simultaneous lack of time-reversal and space-inversion symmetries, by means of rigorous full-electrodynamic calculations using the layer-multiple-scattering method. It is shown that a strong effect appears in flat band regions associated with enhanced natural and magnetic optical activity.

Light control through elastic waves is a well established and mature technology. The underlying mechanism is the scattering of light due to the dynamic modulation of the refractive index and the material interfaces caused by an elastic wave, the so-called acousto-optic interaction. This interaction can be enhanced in appropriately designed structures that simultaneously localize light and elastic waves in the same region of space and operate as dual optical-elastic cavities, often called phoxonic or optomechanical cavities. Typical examples of phoxonic cavities are multilayer films with a dielectric sandwiched between two Bragg mirrors or, in general, defects in macroscopically periodic structures that exhibit dual band gaps for light and elastic waves. In the present work we consider dielectric particles as phoxonic cavities and study the influence of elastic eigenmode vibrations on the optical Mie resonances. An important issue is the excitation of elastic waves in such submicron particles and, in this respect, we analyze the excitation of high-frequency vibrations following thermal expansion induced by the absorption of a femtosecond laser pulse. For spherical particles, homogeneous thermalization leads to excitation of the particle breathing modes. We report a thorough study of the acousto-optic interaction, correct to all orders in the acousto-optic coupling parameter, by means of rigorous full electrodynamic and elastodynamic calculations, in both time and frequency domains. Our results show that, under double elastic-optical resonance conditions, strong acousto-optic interaction takes place and results in large dynamical shifts of the high-Q optical Mie resonances, manifested through multiphonon exchange mechanisms.

We report on the calculation of the fundamental plasmon waveguide modes in linear periodic chains of finite silver nanorods, aligned perpendicular to the chain. The results of rigorous full-electrodynamic calculations by the layer-multiple-scattering method are discussed in conjunction with the results of the widely used coupled-dipole model and a critical evaluation of the latter is provided. More specifically, it is shown that both diameter and height of the nanorods must be much smaller than the interparticle distance; otherwise, for relatively long nanorods close to each other, the coupled-dipole model can fail completely to predict the waveguide dispersion diagram. Moreover, the model systematically underestimates the effect of dissipative losses and cannot describe the effect of a supporting substrate, which is always present in realistic cases and induces considerable changes in the waveguide dispersion diagram.

We study, by means of full-electrodynamic calculations using the layer-multiple-scattering method, the effect of diffractive coupling on the enhancement of the local electromagnetic field in periodic arrays of nanolenses consisting of three silver spheres with progressively decreasing sizes and separations. The interaction between the hot-spot modes of an isolated nanolens with the Rayleigh–Wood anomalies of the periodic lattice leads to a further enhancement of the local field intensity, which can be controlled by an appropriate choice of the geometrical parameters involved.

A systematic study, by means of full electrodynamic calculations, of the optical activity of layer-by-layer chiral crystals of finite silver nanorods is presented. The nature of the eigenmodes of the electromagnetic field and the formation of partial gaps for a specific circular polarization in these crystals are analyzed by reference to the hybrid plasmon modes of the structural basis of twisted nanorods. It is shown that collective plasmon modes of the helical assembly give rise to giant optical activity effects, which persist for any angle of incidence and polarization direction. The effects, which are robust against the twisting angle and become more pronounced with increasing particle concentration, can be tuned within a broad range of frequencies in the infrared and visible spectrum by appropriately choosing the rod length. Potential applications of these structures for polarization control in subwavelength optical components are anticipated.

We report on the optical properties of a layer-by-layer structure of silver nanorods, with their axes aligned perpendicular to the z direction and mutually twisted through an angle of 60° from layer to layer, by means of rigorous full electrodynamic calculations using the layer-multiple-scattering method, properly extended to describe axis-symmetric particles with arbitrary orientation. We analyze the complex photonic band structure of this crystal in conjunction with relevant polarization-resolved transmission spectra of finite slabs of it and explain the nature of the different eigenmodes of the electromagnetic field in the light of group theory. Our results reveal the existence of sizable polarization gaps and demonstrate the occurrence of strong optical activity and circular dichroism, combined with reduced dissipative losses, which make the proposed architecture potentially useful for practical applications as ultrathin circular polarizers and polarization rotators.

We report on the occurrence of strong nonlinear acousto-optic interactions in phoxonic structures, that support, simultaneously, acoustic and optical localized resonant modes, under the influence of acoustic losses. Deploying a detailed theoretical investigation of the acousto-optic coupling in the specific case of a one-dimensional phoxonic cavity, realized by homogeneous SiO2 and Si layers, we demonstrate the possibility for an enhanced modulation of light with sound through multi-phonon exchange mechanisms. A full electrodynamic and elastodynamic multiple scattering approach is employed to describe the optical and acoustic modes, and to account for their mutual interaction and the underlying effects both in time and frequency domains. In particular, we discuss the influence of hypersonic attenuation on the acousto-optic interaction by considering typical acoustic losses in the GHz regime.

We report on the eigenmodes of photonic crystals consisting of submicron homogeneous chiral spheres in a nonchiral isotropic medium, by means of full electrodynamic calculations using the layer-multiple-scattering method. It is shown that resonant modes of the individual spheres give rise to narrow bands that hybridize with the extended bands of the appropriate symmetry associated with light propagation in an underlying effective chiral medium. The resulting photonic dispersion diagram exhibits remarkable features, such as strong band bending away from the Bragg points with consequent negative-slope dispersion inside the first Brillouin zone and sizable frequency gaps specific to each polarization mode. We present a rigorous group-theory analysis to explain features of the calculated photonic band structure, peculiar to a system which possesses time-reversal but not space-inversion symmetry, and discuss some interesting aspects of the underlying physics.

A detailed analysis of the optical properties of photonic structures of metal-coated chiral spheres, calculated by the full electrodynamic layer-multiple-scattering method, is presented. Easily tunable narrow bands, originating from particle-like plasmon modes of the metallic shells, hybridize with the extended bands of the underlying effective chiral medium and give rise to sizable partial gaps and strong band bending with consequent negative-slope dispersion. The photonic band diagram is discussed in the light of group theory, in conjunction with relevant transmission spectra, and the occurrence of polarization-selective transmission and negative refraction for a short range of angles of incidence is demonstrated.

The modulation of spontaneous light emission of active centers through elastic waves in Si/SiO2 multilayer phoxonic structures that support dual photonic-phononic localized modes, in the bulk or at the surface, is studied by means of rigorous full electrodynamic and elastodynamic calculations. Our results show that strong dynamic modulation of the spontaneous emission can be achieved through an enhanced acousto-optic interaction when light and elastic energy are simultaneously localized in the same region.

Unprecedented low-dispersion high-frequency acoustic excitations are observed in dense suspensions of elastically hard colloids. The experimental phononic band structure for SiO 2   particles with different sizes and volume fractions is well represented by rigorous full-elastodynamic multiple-scattering calculations. The slow phonons, which do not relate to particle resonances, are localized in the surrounding liquid medium and stem from coherent multiple scattering that becomes strong in the close-packing regime. Such rich phonon-matter interactions in nanostructures, being still unexplored, can open new opportunities in phononics.

We present an extension of the layer-multiple-scattering method to phononic crystals of nonspherical particles in a homogeneous host medium by employing the extended-boundary-condition technique for the description of the individual scatterers. The efficiency of the method is demonstrated on specific examples of two- and three-dimensional periodic assemblies of spheroidal polymer particles in water and in silicon. We report a thorough analysis of the acoustic properties of these composites and emphasize aspects of the underlying physics that relate to the nonspherical shape of the particles.

We report on the optical response and, in particular, on the refractive properties of an fcc crystal of metallic nanoshells by means of full-electrodynamic layer-multiple-scattering simulations. Exact numerical calculations of the isofrequency surfaces reveal the existence of two frequency regions where negative refraction occurs. A thorough analysis of the photonic band structure, in conjunction with corresponding transmission diagrams, attributes this behavior to the excitation of collective modes, which stem from dipole particle-plasmon resonances, and shows that only in one of the two frequency regions negative refraction without birefringence can be obtained. In addition, we discuss the effect of absorptive losses, and reveal the existence of narrow bands of slab modes in a finite slab of the crystal that can transfer the evanescent components of an incident wave field.

The interaction between acoustic breathing modes and optical Mie resonances in a spherical particle made of a chalcogenide glass material is investigated by means of rigorous calculations, correct to any order in the acousto-optic coupling parameter. Our results reveal the occurrence of strong effects beyond the linear-response approximation, which lead to enhanced modulation of light by acoustic waves through multiphonon exchange mechanisms when both photons and phonons have a very long lifetime inside the particle.

We present a detailed analysis of the optical modes and light propagation in photonic crystals consisting of chiral spheres in a nonchiral isotropic medium, calculated by the full electrodynamic layer-multiple-scattering method. It is shown that resonant modes of the individual spheres give rise to narrow bands that hybridize with the extended bands of the appropriate symmetry associated with light propagation in an underlying effective chiral medium. The resulting photonic dispersion diagrams exhibit remarkable features, peculiar to a system that possesses time-reversal but not space-inversion symmetry, which are analyzed in terms of group theory. In particular, we reveal the occurrence of strong band bending away from the Bragg points with consequent negative-slope dispersion inside the first Brillouin zone, slow-photon bands, and frequency gaps. The calculated band structure is discussed in conjunction with relevant reflection diagrams, providing a consistent interpretation of the underlying physics.

We report on the occurrence and properties of photonic surface states in fcc crystals of metallic nanoshells, by means of full-electrodynamic calculations using the layer-multiple-scattering method, properly extended. Detailed dispersion diagrams of the surface states associated with the (001)  and (111)  surfaces are calculated for such semi-infinite crystals and corresponding finite slabs, and convergence by increasing the slab thickness is discussed. It is shown that these states can be tuned over a broad frequency range by varying the shell thickness and can be characterized, along high-symmetry directions, according to their symmetry. Absorption in the metallic material limits the propagation length which can, however, be as long as several tens of lattice constants for low-loss metals and relatively broad bands.

Periodic media offer impressive opportunities to manipulate the transport of classical waves namely light or sound. Elastic waves can scatter light through the so-called acousto-optic interaction which is widely used to control light in telecommunication systems and, additionally, the radiation pressure of light can generate elastic waves. Concurrent control of both light and sound through simultaneous photonic-phononic, often called phoxonic, bandgap structures is intended to advance both our understanding as well as our ability to manipulate light with sound and vise versa. In particular co-localization of light and sound in phoxonic cavities could trigger nonlinear absorption and emission processes and lead to enhanced acousto-optic effects. In the present communication, we present our efforts towards the design of different phoxonic crystal architectures such as three-dimensional metallodielectric structures, two-dimensional patterned silicon slabs and simple one-dimensional multilayers, and provide optimum parameters for operation at telecom light and GHz sound. These structures can be used to design phoxonic cavities and study the acousto-optic interaction of localized light and sound, or phoxonic waveguides for tailored slow light-slow sound transport. We also discuss the acousto-optic interaction in onedimensional multilayer structures and study the enhanced modulation of light by acoustic waves in a phoxonic cavity, where a consistent interpretation of the physics of the interaction can be deduced from the time evolution of the scattered optical field, under the influence of an acoustic wave.

By employing the layer-multiple-scattering method, properly extended to periodic assemblies of arbitrarily oriented axis-symmetric particles, we investigate the optical response of a three-dimensional spiral-staircase structure of metallic nanorods. We show that the combination of plasmonic modes and helical arrangement of the nanorods results in the formation of collective optical eigenmodes with a specific predominant circular polarization character, sizable polarization gaps, and negative group velocity bands that lead to negative refraction. Moreover, we demonstrate that multilayer slabs of the given crystal exhibit strong optical activity and circular dichroism combined with reduced dissipative losses, which make the proposed structure potentially useful for polarization control applications in miniaturized optoelectronic devices.

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 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 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.

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 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 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.

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.

After a brief description of the multiple-scattering method for photonic crystals, we present some results obtained by this method, relating to various types of plasmonic nanostructures in one, two and three dimensions: cavity plasmon waveguides, systems of metallic particles, and arrays of metallic shells. We analyse the optical response of these structures and emphasise some interesting aspects of the underlying physics.

We present a thorough theoretical study of the optical properties of periodic structures built of silver and silica nanodisks in a sandwich-like configuration, by means of full electrodynamic calculations using the extended layer-multiple-scattering method. The strong coupling of the metallic nanoparticles and the resulting plasmon hybridization lead to collective electric and magnetic resonant modes, which can be tuned by changing the structural parameters, such as nanoparticle size and lattice constant. We analyze the response of single- and multi-layer architectures of ordered arrays of such nanosandwiches on a dielectric substrate to externally incident light and evaluate the corresponding effective permittivity and permeability functions. Our results reveal the existence of optical magnetism, with a strong negative effective permeability over a tunable spectral range at near-infrared and visible frequencies. We introduce the complex photonic band structure as a tool in the study of three-dimensional metamaterials and establish additional criteria for the validity of their effective-medium description. Our work demonstrates the efficiency of the recently developed extended layer-multiple-scattering method in the study of metamaterials of composite metal-dielectric particles of arbitrary shape.

We report a thorough theoretical study of the optical response of two- and three-dimensional periodic assemblies of metallic nanorods by means of full-electrodynamic calculations using the extended layer-multiple-scattering method. We show that these systems support various types of resonant- and bound-collective plasmon modes, which are tunable over a broad spectral range, and provide a consistent interpretation of the underlying physics. In particular, we reveal the existence of slab plasmon modes with zero group velocity, which can cause evanescent-wave enhancement and enable subwavelength imaging. We discuss extinction spectra of single-layer and multilayer slabs of nanorods in conjunction with relevant complex band-structure diagrams and present a rigorous analysis of the results using group theory. Moreover, we explain some peculiar spectral features which are due to the existence of surface resonances. These can modify the optical response of the system in a controllable manner by using a supporting substrate.

We present an efficient computational methodology for full electrodynamic calculations of metallodielectric nanostructures based on a multiple-scattering formulation of Maxwell's equations. The method, originally developed for systems of spherical particles (MULTEM code), is extended to systems of particles of arbitrary shape and applied to ordered structures of metallic nanodisks with an aspect ratio as large as five. We first discuss the particle plasmon resonances of single metallic nanocylinders of different aspect ratios. Then, we study the plasmonic excitations of square arrays of metal-dielectric-metal nanosandwiches and the optical response of a rectangular lattice of metallic nanodisks on a dielectric waveguide. Finally we analyse the photonic band structure of a simple cubic crystal of metallic nanodisks.

Collective plasmonic modes in two- and three-dimensional periodic assemblies of metallic nanoshells are studied by means of full electrodynamic calculations using the layer-multiple-scattering method. We consider structures made of a single type of nanoshell as well as binary heterostructures made of two different types of nanoshells. The complex photonic band structure of such three-dimensional photonic crystals is analyzed in conjunction with relevant transmission diagrams of corresponding finite slabs and the physical origin of the different optical modes is elucidated. Moreover, we discuss associated absorption spectra and provide a consistent interpretation of the underlying physics. In the case of the binary systems, the plasmonic modes of the two building components coexist, leading to a rich structure of resonances over an extended frequency range and to broadband absorption.

Plasmonic systems of two- and three-dimensional ordered arrays of metallic nanodisks are studied by means of full-electrodynamic calculations using the layer-multiple-scattering method. In particular, we investigate the electromagnetic interaction of waveguide modes of an indium tin oxide film on a quartz substrate with collective-plasmon modes of a two-dimensional periodic overlayer of gold nanodisks and obtain excellent quantitative agreement with experiment. Moreover, we report a thorough analysis of the optical properties of three-dimensional photonic crystals of metallic nanodisks.

We report a theoretical study of two-dimensional periodic arrays of composite particles, consisting of two metallic nanodisks separated by a dielectric spacer, using an efficient and accurate multiple-scattering method, which was originally developed for systems of spherical particles and recently extended to non-spherical shapes. In particular, we discuss the plasmonic excitations in such isolated nanosandwiches and study the influence of geometrical parameters like the thickness of the dielectric spacer. Moreover, we investigate the interaction between such composite particles as they approach each other in a two-dimensional periodic lattice.

Periodic nanostructures for plasmonic engineering, comprising one or two types of silica core - metallic shell spherical particles, are studied by means of full electrodynamic calculations using the layer-multiple-scattering method. The complex photonic band structure of such three-dimensional crystals is analyzed in conjunction with relevant transmission spectra of corresponding finite slabs and the physical origin of the different optical modes is elucidated, providing a consistent interpretation of the underlying physics. In the case of binary structures, collective plasmonic modes originating from the two building components coexist, leading to broadband absorption and a rich structure of resonances and hybridization gaps over an extended frequency range.

We report on the observation of two hypersonic phononic gaps of different nature in three-dimensional colloidal films of nanospheres using Brillouin light scattering. One is a Bragg gap occurring at the edge of the first Brillouin zone along a high-symmetry crystal direction. The other is a hybridization gap in crystalline and amorphous films, originating from the interaction of the band of quadrupole particle eigenmodes with the acoustic effective-medium band, and its frequency position compares well with the computed lowest eigenfrequency. Structural disorder eliminates the Bragg gap, while the hybridization gap is robust.

We report a consistent derivation of a tight-binding formalism, both in the frequency and in the time domain, for the analysis of electromagnetic energy transfer in single-mode cavity-plasmon waveguides. Moreover, we derive closed-form solutions of the relevant tight-binding equations, which describe the response of these waveguides under time-varying excitations by a localized light source. In this context, we discuss the possibility of efficient single-mode waveguiding through coupled cavity-plasmon modes in chains of spheroidal silicon nanoparticles in silver at optical frequencies.

Plasmonic excitations in two- and three-dimensional ordered assemblies of metal-dielectric-metal nanosandwiches are studied by means of full-electrodynamic calculations using the layer-multiple-scattering method. Plasmon hybridization results in collective electric-dipole-like and magnetic-dipole-like resonant modes, which are directly controlled by the lattice constant and the geometrical characteristics of the building units. It is shown that, in planar arrays of such composite nanoparticles on a dielectric substrate, the magnetic resonance induces a negative effective permeability, as large as −2  , which can be tuned within the range of near-infrared and visible frequencies. However, as successive layers are stacked together to build a three-dimensional crystal, the region of negative effective permeability shrinks and disappears for relatively thick slabs. Our analysis demonstrates that the complex photonic band structure is a valuable tool in the study of three-dimensional metamaterials and their effective-medium description.

The present work demonstrates the first application of Brillouin light scattering (BLS) to probe film-guided elastic waves in transparent-substrate supported polymer thin films. In comparison with earlier BLS studies that were restricted to films either free-standing or supported on opaque substrates, the progress made in this work substantially extends the applicability of BLS and permits direct access to the elastic properties of thin films lying on transparent substrates, which is of important practical relevance. A series of thin supported polystyrene and poly(methyl methacrylate) films with thickness in the range of 40−500 nm were explored, and no noticeable trend in elastic properties with thickness has been found, in conformity with earlier BLS results. The first measurement of glass transition temperature, Tg, of supported polymer thin films by BLS is also reported. We observed that the ultrathin (40 nm) films for both polymers exhibit a clear reduction in Tg.

The phononic band structure of two binary colloidal crystals, at hypersonic frequencies, is studied by means of Brillouin light scattering and analyzed in conjunction with corresponding dispersion diagrams of the single colloidal crystals of the constituent particles. Besides the acoustic band of the average medium, the authors’ results show the existence of narrow bands originating from resonant multipole modes of the individual particles as well as Bragg-type modes due to the (short-range) periodicity. Strong interaction, leading to the occurrence of hybridization gaps, is observed between the acoustic band and the band of quadrupole modes of the particles that occupy the largest fractional volume of the mixed crystal; the effective radius is either that of the large (in the symmetric NaCl-type crystalline phase) or the small (in the asymmetric NaZn13 -type crystalline phase) particles. The possibility to reveal a universal behavior of the phononic band structure for different single and binary colloidal crystalline suspensions, by representing in the dispersion diagrams reduced quantities using an appropriate length scale, is discussed.

The optical response of finite slabs of polar materials, containing two- and three-dimensional periodic structures of air cavities, is studied by means of accurate numerical calculations using the layer-multiple-scattering method. Our results reveal the existence of strong resonant modes, originating from the excitation of flat-surface and cavity phonon-polaritons, which may be useful in terahertz applications.

We propose a different type of plasmonic waveguide which consists of identical dielectric nanocavities, periodically arranged along a line, in a metallic material. The dispersion relations for the different guiding modes are obtained by means of exact mutliple scattering calculations and also by a simple tight-binding model which allows a straightforward analysis of the underlying physics. This type of waveguide combines strong lateral localization and no radiative losses with efficient transmission of light through sharp bends. We show how one can overcome absorptive losses by introducing optical gain media into the cavities and, also, how one can design such waveguides for single-mode operation over a given frequency range by using nonspherical cavities.

Guided and quasiguided elastic waves in a glass plate coated on one side with a periodic monolayer of polymer spheres, immersed in water, are studied by means of accurate numerical calculations using the on-shell layer-multiple-scattering method. This system supports, in addition to the modes of the bare plate, almost dispersionless, slow modes which originate from the array of spheres. We calculate and analyze in detail the dispersion diagrams of the interacting modes of the composite slab, and provide a consistent interpretation of the underlying physics.

We present an extension of the layer-multiple-scattering method to photonic crystals of nonspherical particles in a homogeneous host medium. The efficiency of the method is demonstrated on a specific example of a crystal of metallic spheroids. We report a thorough analysis of the optical properties of this crystal and discuss aspects of the underlying physics that relate to the nonspherical shape of the particles.

We discuss acoustic waveguiding through weakly coupled defects along a line in a three-dimensional phononic crystal which possesses an absolute frequency gap. A chain of appropriately chosen defect cells induces modes of the elastic field over a narrow band of frequencies within the gap. We introduce a model of this band in the manner of a tight-binding description of defect bands in semiconductors and demonstrate the applicability of this model through a specific example of phononic crystal: a bubbly liquid. This allows an exact, practically analytic solution and a deeper physical insight into the processes involved.

The propagation of elastic waves in macroscopically periodic composites consisting of core-shell spherical scatterers in a homogeneous host medium is studied by means of numerical calculations using the layer-multiple-scattering method. By an appropriate choice of the constituent materials, these crystals exhibit wide absolute frequency gaps, over which no elastic wave can propagate in the composite medium, whatever the direction of its propagation. We analyze the detailed structure of transmission spectra of finite slabs of such crystals in conjunction with the corresponding complex-band-structure and density-of-states diagrams, and emphasize aspects of the underlying physics which have not been discussed previously.

Composite materials with periodic variations of density and/or sound velocities, so-called phononic crystals, can exhibit bandgaps where propagation of acoustic waves is forbidden. Phononic crystals are the elastic analogue of the well-established photonic crystals and show potential for manipulating the flow of elastic energy. So far, the experimental realization of phononic crystals has been restricted to macroscopic systems with sonic or ultrasonic bandgaps in the sub-MHz frequency range. In this work, using high-resolution Brillouin spectroscopy we report the first observation of a hypersonic bandgap in face-centred-cubic colloidal crystals formed by self-assembly of polystyrene nanoparticles with subsequent fluid infiltration. Depending on the particle size and the sound velocity in the infiltrated fluid, the frequency and the width of the gap can be tuned. Promising technological applications of hypersonic crystals, ranging from tunable filters and heat management to acousto-optical devices, are anticipated.

After a brief description of the layer multiple scattering method as applied to phononic crystals, we present some results obtained by this method, relating to: crystals of polystyrene spheres in water; crystals of silica spheres in air; and crystals of steel spheres in polyester. We relate the transmission characteristics of slabs of these ma terials to the complex band structure of the corresponding infinite crystals. We emphasize aspects of the underlying physics which have not been discussed previously.

We present a computer program to calculate the frequency band structure of an infinite phononic crystal, and the transmission, reflection and absorption of elastic waves by a slab of this crystal. The crystal consists of a stack of identical slices parallel to a given surface; the slice may consist of multilayers of non-overlapping spheres of given periodicity parallel to the surface and homogeneous plates. The elastic coefficients of the various components of the crystal may be complex functions of the frequency.

The optical properties of a dielectric waveguide coated on one side with a periodic monolayer of metallic nanospheres are studied by means of transmission and density-of-states calculations using the on-shell layer-multiple-scattering method. In particular, the strong coupling mechanism between the waveguide and collective particle–plasmon modes is analysed and its influence on the optical response of the system is elucidated.

Photonic crystals are inhomogeneous materials whose dielectric properties vary periodically in space on a macroscopic scale. These materials have novel and interesting properties concerning both basic physics and technological applications. After a brief description of the main properties of photonic crystals, we present some specific applications related to wave guiding and Anderson localization of light due to stacking faults in these crystals.

The optical response of a two-dimensional periodic array of metallic nanoparticles on a dielectric waveguide is investigated by means of numerical calculations using the on-shell layer-multiple-scattering method. We find that the strong interaction between particle-plasmon and waveguide modes influences drastically the extinction spectrum of the system. Our results explain successfully available experimental data and provide a transparent physical picture of the underlying processes.

The optical properties of three-dimensional photonic crystals consisting of polaritonic spheres in a dielectric host medium are studied by means of accurate numerical calculations using the on-shell layer-multiple-scattering method. The transmission characteristics of finite slabs of these materials are related to the complex band structure of the corresponding infinite crystals and the effect of dissipative losses is examined.

We demonstrate the existence of strong Anderson localization in certain disordered phononic systems. As a result, the transmission coefficient of elastic waves through a slab of the material practically vanishes, whatever the angle of incidence, over a region of frequency much wider than the absolute frequency gap of the corresponding ordered system. The phenomenon can be of use in the design of phononic systems with very wide absolute transmission gaps.

We develop a Green’s function multiple-scattering formalism for the calculation of the density of states and the local density of states of the elastic field in periodic and nonperiodic structures consisting of nonoverlapping scatterers in a homogeneous host medium. The formalism is based on concepts and techniques developed in relation to the similar problem of electrons in solids. We apply the method to a specific example which demonstrates the existence of virtual bound states of the elastic field localized about a plane of nonoverlapping steel spheres in polyester. These states are manifested as dips in the transmission spectrum of the monolayer. They develop into narrow frequency bands in a phononic crystal built by a succession of such planes.

Using the first-principles layer-multiple-scattering method we developed in previous work, we analyze recent experimental data on the extinction of light by rectangular two-dimensional arrays of gold nanoparticles on a dielectric waveguide. The theoretical results reproduce accurately the measured spectra and provide a transparent physical picture of the underlying processes.

We describe a photonic crystal disordered by stacking faults which can be realized in the laboratory and which exhibits an Anderson localization of light over certain regions of frequency. The localization length is obtained from a calculation of the transmittance of a slab of the material as a function of the thickness of the slab. The localization length depends on the frequency and the angle of incidence of the incident light. It appears that there are regions of frequency where all states of the electromagnetic field are either localized or delocalized, but we also find regions where localized states coexist with delocalized ones.

We report on the occurrence of absolute elastic band gaps in three-dimensional binary systems made up of steel spheres in polyester, and examine how the width of such gaps depends on the geometry of the structure.

We consider the effect of different approximations to the dielectric function of a silver sphere on the absorption of light by two-dimensional and three-dimensional periodic and non-periodic arrays of non-overlapping silver spheres in a host dielectric medium. We also present some results on the band structure and the absorption coefficient of light by photonic crystals consisting of non-overlapping silver-coated spheres in a dielectric medium.

Using the multiple-scattering formalism we developed in a previous work, and extended here, we analyze available experimental data on the transmission of longitudinal waves in the system: water-slab of polyester-water, the slab of polyester having a plane of glass or lead or steel spheres in the middle. The theoretical results reproduce accurately the measured spectra and provide a transparent physical picture of the underlying processes. In particular, the dips in the observed spectra are attributed to multiple wave scattering between the spheres, and are related to hybridization-induced gaps in the frequency band structure of the longitudinal elastic modes of a corresponding infinite crystal.

We develop a two-stage multiple-scattering formalism for the calculation of photonic bands generated by chains of defects in photonic crystals consisting of nonoverlapping spheres, and for the calculation of the transmission of light through straight and bent waveguides of such chains. We apply the method to a specific example which demonstrates that transmission through a bent waveguide occurs with the same efficiency as for a straight waveguide.

We developed a multiple scattering method for the calculation of the frequency band structure of a phononic crystal consisting of non-overlapping elastic spheres arranged periodically in a host medium of different elastic properties. Using a variation of the same method we can also calculate, with the same ease and accuracy, the coefficients of transmission, reflection and absorption of elastic waves incident on a slab of the material of finite thickness. The elastic coefficients of the spheres and/or the host medium can be complex and frequency dependent. We demonstrate the effectiveness of the method by applying it to specific examples.

Using a coherent-potential approximation, in conjunction with the on-shell method we developed for the study of photonic crystals, we study the effect of moderate disorder on light absorption by composite materials consisting of plasma spheres embedded in a host dielectric medium. We analyze our results by reference to the properties of a single sphere and to those of an infinite crystal. We find, in particular, that the absorption of light by a thin slab (a two-dimensional array of plasma spheres) is affected more strongly by disorder, in comparison to the absorbance of thick slabs consisting of many layers of spheres.

A brief introduction of the layer-Korringa-Kohn-Rostoker method for calculations of the frequency band structure of photonic crystals and of the transmission and reflection coefficients of light incident on slabs of such crystals is followed by two applications of the method. The first relates to the frequency band structure of metallodi-electric composites and demonstrates the essential difference between cermet and network topology of such composites at low frequencies. The second application is an analysis of recent measurements of the reflection of light from a slab of a colloidal system consisting of latex spheres in air.

Stacking faults appear to be the most common type of defect in inverted opals which are good candidates for photonic crystals with absolute gaps in the visible range of light. In this Letter we present for the first time a systematic study of the effect of stacking faults on the optical properties of self-assembled photonic crystals, by means of large-scale transmittance calculations for macroscopic slabs of inverted opals with randomly distributed stacking faults. We show that frequency gaps, as seen in optical transmission experiments, will in general appear wider in the presence of stacking faults. We attribute the above to Anderson localization of light due to disorder.

We examine the optical properties of metals containing a periodic arrangement of nonoverlapping spherical mesopores, empty or filled with a dielectric material. We show that a slab of such a porous metal transmits light over regions of frequency determined by the dielectric constant of the cavities and the fractional volume occupied by them, with an efficiency, which is many orders of magnitude higher than predicted by standard aperture theory. Also, the system absorbs light efficiently over the said regions of frequency unlike the homogeneous metal.

We present a theory of electron, electromagnetic, and elastic wave propagation in systems consisting of non-overlapping scatterers in a host medium. The theory provides a framework for a unified description of wave propagation in three-dimensional periodic structures, finite slabs of layered structures, and systems with impurities: isolated impurities, impurity aggregates, or randomly distributed impurities. We point out the similarities and differences between the different cases considered, and discuss the numerical implementation of the formalism.

We present a new version of a program for the calculation of the frequency band structure of an infinite photonic crystal, and of the transmission, reflection and absorption coefficients of light by a slab of this crystal. The crystal consists of a stack of identical slices parallel to a given surface; a slice may consist of a number of different components, each of which can be either a homogeneous plate or a multilayer of non-overlapping spherical particles of given periodicity parallel to the surface. The homogeneous media to the left and right of the slab may be different (have different real and positive dielectric functions and magnetic permeabilities).

We study the effect of planar defects in phononic crystals of spherical scatterers. It is shown that a plane of impurity spheres introduces modes of vibration of the elastic field localized on this plane at frequencies within a frequency gap of a pure phononic crystal; these show up as sharp resonances in the transmittance of elastic waves incident on a slab of the crystal. A periodic arrangement of impurity planes along a given direction creates narrow impurity bands with a width which depends on the position of these bands within the frequency gap of the pure crystal and on the separation between the impurity planes. We show how a slight deviation from periodicity (one impurity plane is different from the rest) reduces dramatically the transmittance of elastic waves incident on a slab of the crystal.

We develop a formalism for the calculation of the frequency band structure of a phononic crystal consisting of nonoverlapping elastic spheres, characterized by Lamé coefficients which may be complex and frequency dependent, arranged periodically in a host medium with different mass density and Lamé coefficients. We view the crystal as a sequence of planes of spheres, parallel to and having the two-dimensional periodicity of a given crystallographic plane, and obtain the complex band structure of the infinite crystal associated with this plane. The method allows one to calculate, also, the transmission, reflection, and absorption coefficients for an elastic wave (longitudinal or transverse) incident, at any angle, on a slab of the crystal of finite thickness. We demonstrate the efficiency of the method by applying it to a specific example.

We present a method, based on the coherent potential approximation, for the treatment of disorder in photonic crystals. We apply the method to the study of light absorption by a three-dimensional array of plasma spheres distributed randomly in a host dielectric medium. We find that the effect of disorder on the absorbance of a thick slab of the material consisting of many layers of spheres is much less pronounced than in the corresponding case of a single layer of spheres.

We show ab initio calculations for vacancy formation energies in Cu and Al. The calculations are based on density-functional theory and the full-potential Korringa–Kohn–Rostoker Green's function method for impurities. The non-local effect beyond the local-spin-density approximation (LSDA) for density-functional theory is taken into account within the generalized-gradient approximation (GGA) of Perdew and Wang. The lattice relaxation around a vacancy is also investigated using calculated Hellmann–Feynman forces exerted on atoms in the vicinity of a vacancy. We show that the GGA calculations reproduce very well the experimental values of vacancy formation energies and bulk properties of Cu and Al, as they correct the deficiency of LSDA results (underestimation of equilibrium lattice parameters, overestimation of bulk moduli, and vacancy formation energies). It is also shown that the GGA calculations reduce the LSDA results for the lattice relaxation energy for a vacancy in Cu.

We present a systematic examination of the optical properties of photonic crystals consisting of metallic particles (plasma spheres) arranged periodically in a host dielectric medium. We calculate exactly the transmission and absorption coefficients of light incident on a slab of the material as functions of the frequency of the incident light and analyze the results by reference to the properties of a single sphere and to the frequency band structure of the corresponding infinite crystal. We examine the dependence of the above coefficients on the fractional volume occupied by the spheres and on the thickness of the slab. Finally we compare our results with those of the Maxwell Garnett effective-medium theory and in this way we establish the limitations of the latter. We show in particular that multipole interactions which the Maxwell Garnett theory does not take into account lead to significant structure in the transmission/absorption spectra.

We examined the properties of photonic crystals that consist of nonoverlapping chiral spheres in a dielectric medium. We considered the effect of the chiral property of the spheres on the frequency band structure of the electromagnetic field in the crystal and on the transmittance properties of a slab of the crystal, and we estimated the optical activity of the crystal.

We review first-principles calculations of the size effect in dilute transition-metal alloys. The calculations apply local density functional theory and a Green's function method based on the KKR multiple-scattering formalism. In each cell, the full anisotropic potential in included and the forces on the atoms are calculated by the Hellmann-Feynman theorem. The method is applied to predict the atomic positions around d+sp impurities in Cu and Al. The results compare favorably with experimental data from extended X-ray-absorption-fine-structure and lattice-parameter measurements.

We present a program for the calculation of the frequency band structure of an infinite photonic crystal, and of the transmission, reflection and absorption coefficients of light by a slab of this crystal. The crystal consists of a stack of identical slices parallel to a given surface; a slice may consist of a number of different components, each of which can be either a homogeneous plate or a multilayer of spherical particles of given periodicity parallel to the surface.

We present first-principles calculations of the electronic structure and hyperfine fields of 3d and 4sp impurities on the (001) surface of Ni. The calculations are based on the local-spin-density-functional theory and employ a Korringa-Kohn-Rostoker Green's function method for impurities at surfaces. The systematic behaviour obtained for the hyperfine fields of the 4sp adatoms or impurities in the first surface layer is completely different from that found in the bulk. Instead of a single maximum with a very large hyperfine-field value at about the end of an sp series, the adatoms exhibit two maxima with a pronounced minimum in between. This behaviour can be traced back to the reduced coordination number of the adatoms which leads to a much smaller relative splitting of the bonding and antibonding peaks, and to the lower symmetry at the surface which results in an on-site s-p: hybridization. The hyperfine fields found for the 3d impurities at the surface are determined basically by the ferromagnetic or antiferromagnetic coupling of the local impurity moment to the substrate magnetization and are therefore in more or less similar to those for bulk impurities.

We present first-principles calculations of the electronic structure and hyperfine fields of 4sp  impurities on the (001) surfaces of Ni and Fe. The calculations are based on the local-spin-density-functional theory and employ a Green's function method for impurities at surfaces. The systematic behavior obtained for the hyperfine fields of adatoms or impurities in the first surface layer is completely different from that found in the bulk, mainly due to the reduction of the symmetry and the coordination number at the surface. Our results explain the surprisingly small hyperfine-field values measured for Se adatoms and provide challenging predictions to be confirmed by future experiments.

A chain of impurity cells in a photonic insulator introduces impurity modes of the electromagnetic field over a narrow band of frequencies. We introduce a model of this band in the manner of a tight-binding description of impurity bands in semiconductors, and use it to describe waveguiding along the chain, and, in particular, across a corner of 90°  . We also point out the possibility of using impurity bands in photonic insulators to study wave propagation along an effectively one-dimensional disordered chain.

The role of the anisotropic impurity scattering in the determination of the low-field Hall coefficient of Al-4d dilute alloys is investigated by means of systematic theoretical calculations, as well as experimental measurements for AlZr and AlMo. The theoretical results, obtained without using any adjustable parameter, are in excellent agreement with the experimental data and a consistent interpretation of the systematic variation of the low-field Hall coefficient for aluminium-based dilute alloys with transition-metal impurities is given.

We report a systematic study of the spin-polarization energy of 3d impurities in monovalent simple-metal hosts, by means of self-consistent, local-spin-density-functional, impurity-in-jellium calculations, and propose a phenomenological model for the interpretation of our results.

We report a systematic study of lattice relaxation effects around 3d and 4sp impurities in aluminum, using the full-potential Korringa-Kohn-Rostoker Green function method. Our results for the magnetic properties of the impurities seem to resolve the discrepancy between experiment and previous calculations. In addition, the calculated atomic displacements and total volume changes are in good agreement with the corresponding experimental data.

The full-potential Korringa-Kohn-Rostoker Green function method is extended to treat the lattice distortion in the vicinity of a point defect. The method is applied to predict the atomic positions in the neighborhood of d and sp substitutional impurities in Cu. Both the total energy and the Hellmann-Feynman force are used for the calculation of the ground-state configuration, while the semicore states of the impurities are treated as valence states. Our results for the atomic displacements are in very good agreement with the experimental data from extended x-ray-absorption fine-structure and lattice-parameter measurements.

We report a systematic study of low-field galvanomagnetic properties of aluminium-based dilute alloys with 3d and 4sp impurities. The low-field magnetoresistivity tensor is determined by exactly solving the linearized Boltzmann equation for the anisotropic vector mean free path, without using any adjustable parameter. Our method of calculation is based on the on-Fermi-sphere approximation which allows us to combine the full anisotropy of the host Fermi surface, obtained by the four-orthogonal-plane-wave method, with the impurity scattering phase shifts, evaluated by self-consistent local-density-functional impurity-in-jellium calculations. Our results for the Hall coefficient and the magnetoresistance are in good agreement with the experimental data.

We present a theoretical analysis of the photonic band structure of fcc colloidal crystals in relation to experimentally available transmission spectra of finite slabs of such crystals.

We describe single and multiple solitonlike solutions of the electromagnetic field in nonlinear superlattices using an effective-medium approximation.

We report systematic calculations of the low-temperature diffusion thermopower of Al-based dilute alloys with 3d and 4sp impurities, by solving self-consistently the linearized Boltzmann equation. The impurity scattering is described by the phase shifts obtained from self-consistent local-density-functional impurity-in-jellium calculations. Moreover, the influence of the full anisotropy of the Al Fermi surface on the scattering process is taken into account within the on-Fermi-sphere approximation. Our results explain successfully the experimentally measured variations in the thermoelectric power, except for Mn impurities. In this case, the presence of a narrow many-body resonance at the Fermi level in the localized spin-fluctuations regime seems to be responsible for the large negative value of thermopower observed.

We present density-functional calculations within the local-density approximation for all transition-metal impurities in the divalent hosts Ca, Sr, and Ba. Our results predict sizable moments, even for impurities of the 4d and 5d series, being only slightly smaller than the moments obtained in the corresponding alkali metals

We consider optically active photonic crystals. We propose a model structure and discuss the factors which determine optical activity by reference to this model.

We report systematic calculations of the residual resistivity and the low-field Hall coefficient of Al-based dilute alloys with 3d and 4sp impurities, by self-consistently solving the linearized Boltzmann equation. We employ the on-Fermi-sphere approximation, which allows us to combine the full anisotropy of the aluminum Fermi surface, obtained by the four-orthogonal-plane-wave method, with the phase shifts associated with isotropic impurity scattering, evaluated by self-consistent local-density-functional impurity-in-jellium calculations. Our results show that the anisotropic scattering increases the residual resistivity, thus obtaining better agreement with the experiment. Moreover, a consistent interpretation of the observed trends of the low-field Hall coefficient is presented.

The electronic structure of the 4d substitutional impurities in Rb is studied by means of self-consistent density functional calculations. Exchange and correlation corrections for localized orbitals, as included in the mean-field solution of Anderson's model, are superimposed on the spin-dependent potential of the traditional local-spin-density approximation. We find ionic-like dn configurations and a quite important spin polarization of the extended sp states. For Nb and Ru impurities we obtain two stable configurations in each case and their energetic stability is studied by means of constrained density-functional calculations. Our results are compared with the results of other calculations and with the available experimental data.

The local magnetic behaviour of impurities in simple monovalent metal hosts is studied systematically by means of ab-initio, local-spin-density-functional electronic structure calculations. Our results predict that besides the 3d and 4d impurities also the 5d and some sp impurities are magnetic in the late alkali metals and that local magnetism can exist for impurities not only on substitutional but also on interstitial sites.

We establish the existence of an absolute frequency gap of the electromagnetic field in photonic crystals with tetragonal symmetry, and examine the dependence of the gap on the geometry of the structure. We calculate the transmittance through a slab of finite thickness of the material, and show that planar defects in the slab produce interface states of the electromagnetic field, at frequencies within the photonic gap, manifested by sharp resonances in the transmittance of these systems.

We present a systematic study of local spin moments of impurities in alkali-metal hosts, by means of ab initio, local-spin-density electronic structure calculations. Our results predict for the first time that besides the well-known cases of 3d and 4d impurities also 5d and some sp impurities are magnetic in the alkali metals both on substitutional and interstitial positions.

The formation of localized moments of impurities in simple-metal hosts is investigated in the case of an Mn solute atom in jellia with continuously varying density. The mean-field critical behaviour of the transition from a spin-polarized to a non-spin-polarized state of the impurity, which is deduced from self-consistent local-spin-density (LSD) functional calculations, is analysed assuming a Landau-type expansion of the energy. This analysis is illustrated and supported by constrained LSD functional calculations.

We present local density functional calculations for magnetic impurities and magnetic monolayers in non-magnetic metals. The calculations employ a multiple scattering (KKR) Green's function method for impurities in the bulk and for ideal surfaces and interfaces. In particular we discuss the moment formation of 3d and4d impurities in alkali and noble metals. Special emphasis is put on an accurate calculation of the host polarization around 3d impurities in Cu and Pd. While the calculated impurity hyperfine fields in Cu contain rather large errors due to the local density approximation, the induced fields of the Cu atoms agree very well with experiments. We also present similar calculations for magnetic monolayers and the corresponding induced host polarization in Cu and Pd.

The spin-orbit scattering (SOS) cross section σso of the 5(s, p) impurities is investigated in two different metal hosts. In the simple Mg host we observe a maximum at half filled p shell. This is the first experimental observation of an impurity p resonance and confirms theoretical predictions. For the transition metal host Cu the maximum in σso is shifted towards Te, the impurity with four p electrons. This is due to the hybridization of the Cu d states with the Te p level. The comparison between experimental and theoretical SOS cross sections represents a compact test of the quality of modern self-consistent electronic structure calculations.

We have developed a formalism which allows one to calculate the transmission, reflection and ansorbance of electromagnetic waves by structures having two-dimensional periodicity parallel to a given surface. The structures considered are single layers or multilayers of non-overlaping spheres, embedded in a host material of different dielectric function. A special case of multilayer is a stack of identical layers whose properties, when the thickness of the slab exceeds a certain limit, are identical with those of the corresponding infinite crystal. We present numerical results for specific examples of single layers and multilayers, and point out some interesting physics which came out of our calculations.

We present a formalism for the calculation of the scattering of electromagnetic waves by a substitutionally disordered two-dimensional array of spherical particles. The formalism, which constitutes an extension of the coherent-potential approximation scheme to electromagnetic waves is valid for any frequency of the incident wave and for any size and/or concentration of the particles. We demonstrate the applicability of our formalism by applying it to the evaluation of the absorbance of disordered arrays of plasma spheres.

The spin-orbit scattering of 4sp and 5sp impurities in a Mg host is investigated theoretically by self-consistent local-density-functional theory. The calculated spin-orbit scattering cross sections sigmaSO agree with the available experimental results for low valent impurities. For higher valent impurities we predict a p resonance behavior. For Cu and Ag impurities our results point to errors of density-functional theory in estimating the d contribution to sigmaSO. In total a consistent interpretation of the trends is given.

A point matching method is applied to the problem of light scattering by non-spherical bodies. The electromagnetic field is expanded into a series of spherical waves which include all multipole terms which contribute significantly to the wavefield. We examine, in particular, the absorbance of light by a plasma particle and demonstrate the existence of various peaks associated with dipole and quadrupole resonances of the induced charge distribution.

The local magnetic properties of 3d and 4d substitutional impurities in noble and alkali-metal hosts are investigated by means of self-consistent local-spin-density-functional calculations using the jellium model as well as the first-principles Korringa-Kohn-Rostoker–Green’s-function method. The results for the impurity moment from both calculations are in good agreement and compare well with the available experimental data. Our calculations give a consistent picture for the formation of local impurity spin moments in free-electron-like hosts.

We describe a method for the calculation of the optical properties of a two-dimensional array of non-overlapping metallic particles (approximated by spheres) adsorbed on a dielectric slab. The interest in such systems arises to a large degree from their possible use as coatings, e.g. for solar energy absorbers and similar technological purposes. The formalism is an extension of the methods which have been developed in relation to electron scattering by two-dimensional atomic layers and takes fully into account multiple scattering of light between the particles of the overlayer and between the overlayer and the substrate. Scattering of light by multilayers or by an infinite crystal of non-overlapping spheres can be dealt with by a straightforward extension of the theory as in the theory of low-energy electron diffraction. Our calculations show that the usual approximation of replacement of the metallic particles by effective dipoles fails when the size of the particles or the concentration of particles increases beyond a limit and that l-pole contribution in interparticle scattering beyond the dipolar (l=1) one introduces new structure in the absorbance versus frequency curve. The reflection and absorption of light as a function of frequency is obtained numerically for selected examples. We consider in particular the variation of these quantities with concentration coverage. We examine also the effect of disorder.

The authors consider periodic structures made of spheres embedded in a host material with a different dielectric function. They show how to calculate the reflection and transmission of electromagnetic waves by a slab of the material parallel to a given crystallographic plane. The method of calculation is based on a doubling-layer scheme which obtains the reflection and transmission matrix elements for the multilayer from those of a single layer. The reflection and transmission characteristics of the slab are related to the complex band structure of the photon field associated with the given crystallographic plane of the corresponding infinite crystal, which is introduced in the manner of the low-energy electron diffraction theory. They present numerical results which demonstrate the applicability of the method to real systems of current interest and point out some interesting physics which arose from their calculations. They show in particular that the nondegenerate bands of the photon field at the centre of the surface Brillouin zone do not couple to the incident radiation, leading to total reflection at normal incidence.

The authors develop a new efficient method for calculating the shape-truncation functions of arbitrary Voronoi polyhedra by combining analytical and numerical techniques. Applications are presented for cells of cubic symmetry as well as for hexagonal close-packed (HCP) atomic polyhedra with different values of the c/a ratio. They also discuss an efficient way for performing three-dimensional integrations in electronic-structure calculations (e.g. solve Poisson's equation) using shape functions.

The authors investigate the formation of local spin moments of transition metal impurities diluted in free-electron-like monovalent hosts by performing self-consistent, local spin density functional calculations for all the 3d elements embedded in jellium. The magnetic behaviour of the impurity is studied systematically by varying continuously the jellium density from zero up to a critical value, at which the magnetic moment disappears. The results are in good agreement with the results of other calculations and the available experimental data.

The authors present numerical calculations of the absorbance of light by a plane of metallic spheres. The absorbance is calculated as a function of frequency for s- and p-polarized light, for different angles of incidence and for different coverages. They demonstrate the importance of l-pole terms beyond the dipole (l=1) term in interparticle scattering. They examine the effect of disorder and consider the influence of a dielectric substrate on the absorbance of the system consisting of a substrate plus adsorbed spheres.

The authors present a method for the calculation of the scattering of light by a periodic two-dimensional array of spherical particles adsorbed on a uniform dielectric slab. Multiple scattering of light between the particles of the overlayer and between the overlayer and the substrate is taken fully into account. The method is applied to light scattering from a square lattice of gold particles on a sapphire substrate for which experimental data are available. The agreement between theory and experiment is reasonably good.

The authors present local-spin-density-functional calculations for the interaction energies of vacancies with 3d and 4sp impurities in Cu as well as with 4d and 5sp impurities in Ag. The calculations are based on the jellium model and first-order perturbation theory, thus enabling an interpretation of the interaction in purely electrostatic terms. The results are in agreement with those obtained by first-principles calculations and confirm the experimentally known trends.

We apply the Korringa-Kohn-Rostoker Green’s-function method and perform ab initio calculations based on local-density-functional theory for the vacancy-solute interaction energies in Cu, Ni, Ag, and Pd. In particular, we calculate the nearest-neighbor interaction of vacancies with 3d and 4sp impurities in Cu and Ni as well as with 4d and 5sp impurities in Ag and Pd. We also calculate the divacancy binding energies in these hosts. Further we demonstrate that the Hellmann-Feynman theorem with respect to the nuclear charge provides a useful tool to calculate and understand interaction energies. We discuss applications to jellium calculations for Cu and to the stability of larger agglomerates.

We present an efficient numerical method to calculate shape truncation functions for Wigner-Seitz atomic polyhedra in crystalline solids. We apply our method to the case of simple cubic (SC), face centered cubic (FCC) and body centered cubic (BCC) lattices. A straightforward comparison of our results and of those obtained by other numerical techniques with the exact ones, analytically known in some simple cases, shows the efficiency and high accuracy of our method.

We present ab initio calculations for dilute Fe alloys with 3d and 4d elements. The calculations are based on local-density approximation of density-functional theory and employ the Korringa-Kohn-Rostoker Green’s-function method. Results are given for the densities of states, the local moments, and the magnetization oscillations around the impurities. A detailed comparison is made with measurements of the electronic specific heat, with neutron-scattering results for the moments of the impurity and the neighboring host atoms, and with magnetization measurements. Contrary to the case of Co and Ni alloys, the majority-spin band contributes most to the screening in the Fe alloys. This arises from the fact that the Fermi energy falls into the minimum of the minority-spin density of states. The results are in qualitative agreement with a proposed pseudogap theory and naturally explain why Fe alloys show such a complicated magnetic behavior.

An expression for the interaction energy between two defects in a metallic compound within the framework of the frozen potential approximation is presented. The numerical application to vacancies in Al or TAl (T=Fe, Ni) shows that the electrostatic contribution of the screening charge around each defect can predominate over the one-particle term.

Self-consistent, first-principles calculations are presented for the electronic structure of some point defects in the binary alloys CoAl and CoGa. All possible structural defects-i.e., antistructure atoms and vacancies-as well as 3d transition-metal impurities on both sublattices are considered. The calculations are based on the Korringa-Kohn-Rostoker Green's-function method and on density-functional theory in the local-spin-density approximation. The calculated densities of states, charge transfers, and magnetic moments are discussed and compared with the results of other theoretical calculations and the available experimental data.

We report about self-consistent calculations for dilute Ni alloys, which are based on density-functional theory and the Korringa-Kohn-Rostoker Green's-function method. In particular, we calculate the charge and magnetization perturbations for four shells of atoms around the impurity. Impurities of the 3d, 4d, and 4sp series are considered. Of central interest is the transition from strong to weak ferromagnetism and the different screening mechanism in these alloys. We compare our results for the perturbations of the local moments as well as the change of the total moment with magnetization and neutron scattering data.

We consider the electronic structure of dilute Pd and discuss reasons for the disagreement between experiment and theory, especially concerning the Pd density of states. The intensity of the low energy Pd peak, obtained in previous calculations, is very sensitive to charge transfer, lattice relaxation and relativistic effects. Realistic ab-initio calculations, which take these effects properly into account, practically remove the intensity of the low energy Pd peak and are in much better agreement with experiments than previous single site and KKR-CPA results.

We develop a formalism to take into account the lattice relaxation around an impurity within the Korringa-Kohn-Rostoker Green's-function method. Using this formalism and the density-functional theory in the local spin-density approximation we perform first-principles, self-consistent calculations for the electronic structure of some dilute metallic alloys. In particular, we investigate the influence of lattice relaxations on the local magnetic moments in CuMn, CuFe, CuCo, and NiMn.

We report on self-consistent ab-initio calculations for the electronic structure of intrinsic defects in CoAl, i.e. antistructure (AS) Co atoms and vacancies on the Co sublattice. The calculations are based on the Korringa-Kohn-Rostoker (KKR) Green's function method and employ the local spin density approximation of the density functional theory. The results for the densities of states, the charge transfers and the local moments are discussed and compared with the available experimental data.

The electronic structure of a simple model for (La, Ce, Th, U)Be13 compounds is determined self-consistently within the density functional theory. The rare earth or actinide atom is considered as a spherically symmetric impurity embedded in a jellium. The width and position of f-localised states result naturally from the scattering of conduction electrons by the impurity potential. The results of the author's calculation for electronic specific heat, position and width of f-resonant states are compared with available theoretical results and experimental data.

The general formalism describing the electronic structure of dilute impurities in ordered compounds within the linear-muffin-tin-orbital approximation is presented. It is derived by considering the proper limit in the Green-function theory within the multiple-scattering formalism. The method thus obtained retains the advantages of the Green-function method for ab initio self-consistent calculations, but with reduced numerical efforts. We discuss in great detail several important aspects of its practical application towards point defects in cubic ordered metallic compounds; the part played by Friedel's screening rule, the calculation of the charge perturbations induced in the host, and the use of the complex-plane integration method are especially stressed.

Ab initio self-consistent electronic-structure calculations of vacancies in ordered stoichiometric FeAl within the linear-muffin-tin-orbital atomic-sphere-approximation method are presented. The potential and local densities of states on the defect and the charge perturbations on its neighboring sites in the matrix are calculated and discussed in relation with numerous experimental results concerning the effect of small departures from stoichiometry for this ordered compound.

Ab initio self-consistent calculations are presented of the electronic structure of sp and 3d impurities in simple and ferromagnetic alloys. The calculations have been performed according to the LMTO-ASA method, fully taking into account the band structure of the host.The density functional theory has been used in the local spin-density approximation; the impurity potential is assumed to be of the muffin-tin form and lattice relaxation effects are neglected. Friedel's sum rule is always satisfied during the calculation. Charge and spin-density perturbation induced in the matrix are computed up to the fourth-nearest neighbour shell.The present theoretical results obtained for local moment, hyperfine field on the impurity, change in the saturation magnetization and magnetic perturbation effects induced by the impurity on the neighbouring atoms are in good agreement with the available experimental data.

We present the results of the calculation of the electronic structure of impurities (Ti, V, Cr, Mn, Co, Ni, Cu) diluted in ferromagnetic iron obtained by the method of linear combination of «muffin-tin» orbitals in the atomic sphere approximation (LMTO-ASA). The local moments and the hyperfine fields on the impurity and the electronic specific heat coefficient charges are compared with the experimental data.