Effective electromagnetic response of nanostructured metal-dielectric metamaterials

The optical properties of metamaterial layers have been analyzed by the scattering matrix method. The properties of effective ɛ and μ, reconstructed from the transmittance and reflectance of metamaterial layers of finite thickness using the inverse Fresnel formulas, are discussed. It is shown that the optical response of nanostructured metal-dielectric metamaterials is strongly nonlocal and dissipative. Original Russian Text ? S.G. Tikhodeev, 2009, published in Izvestiya Rossiiskoi Akademii Nauk. Seriya Fizicheskaya, 2009, Vol. 73, No. 1, pp. 95–97.     

New assembly route for three-dimensional metamaterials obtained through effective medium theory

In this study,we illustrate the effective medium theories in the designs of three-dimensional composite metamaterials of both negative permittivity and negative permeability.The proposed metamaterial consists of random coated spheres with sizes smaller compared to the wavelength embedded in a dielectric host.Simple design rules and formulas following the effective medium models are numerically and analytically presented.We demonstrate that the revised Maxwell-Garnett effective medium theory enables us to design three-dimensional composite metamaterials through the assembly of coated spheres which are random and much smaller than the wavelength of the light.The proposed approach allows for the precise control of the permittivity and the permeability and guides a facile,flexible,and versatile way for the fabrication of composite metamaterials.     

Effective medium approximation for optical bistability in nonlinear metal-dielectric composites

A general theory based on the spectral representation method and effective medium approximation is adopted to investigate the optical bistable behavior in a nonlinear two-phase composite with symmetrical microstructure, in which the metal particles of the volume fraction p and the dielectric particles of the volume fraction 1−p are randomly dispersed but oriented with respect to one another. The relation between the spatial average of local field squared and the external applied field is established through the spectral density function m(x), obtained from the modified Bruggeman effective medium approximation. We find that the optical bistability (OB) is dependent on the depolarization factor L of the components and the volume fraction p. For a given p, we predict that OB can be observed only when L is larger than the critical value L_c, and bistable behavior is more pronounced at large L. Moreover, numerical results show that both the upper threshold field and the width of OB region increase monotonically as L increases. The field-dependent reflectance at normal incidence R in random composites is also investigated.     

Engineering the point spread function of layered metamaterials

Layered metal-dielectric metamaterials have filtering properties both in the frequency domain and in the spatial frequency domain. Engineering their spatial filtering response is a way of designing structures with specific diffraction properties for such applications as sub-diffraction imaging, supercollimation, or optical signal processing at the nanoscale. In this paper we review the recent progress in this field. We also present a numerical optimization framework for layered metamaterials, based on the use of evolutionary algorithms. A measure of similarity obtained using Hölder’s inequality is adapted to construct the overall criterion function. We analyse the influence of surface roughness on the quality of imaging.     

Computer simulation of surface-enhanced Raman scattering in nanostructured metamaterials

The simulation of local field fluctuations and surface-enhanced Raman scattering in percolation systems at the percolation threshold is described. An approximate real-space renormalization group method was used in the simulation. It allows one to radically reduce the computation time compared to an exact calculation and to obtain detailed information about the electromagnetic field. The local fields in real macroscopic systems can be calculated by using this approximation. A computer simulation of the local fields in metal island (percolation) films has been performed by the developed method. The calculation has confirmed the existence of giant local field fluctuations. In turn, the local electric field excites Raman scattering. The local fields of surface-enhanced Raman scattering have been calculated for the first time. The dependence of the Raman scattering enhancement factor on the reference frequency and Stokes shift has been derived. An experimental observation of this dependence could be considered as a confirmation of the electromagnetic nature of the enhancement.     

Magnetic response of split ring resonator metamaterials: From effective medium dispersion to photonic band gaps

On systematically investigating the electromagnetic response of periodic split-ring resonator (SRR) metamaterials as a function of the size-to-wavelength (a/λ) ratio, we find that the stop bands due to the geometric resonances of the SRR weaken with increasing (a/λ) ratio, and are eventually replaced by stop bands due to Bragg scattering. Our study traces the behaviour of SRR-based metamaterials as the resonance frequency increases and the wavelength of the radiation finally becomes comparable to the size of the unit cell of the metamaterial. In the intermediate stages, the dispersion of the SRR metamaterial can still be described as due to a localized magnetic resonances while Bragg scattering finally becomes the dominant phenomenon as a/λ∼1/2.     

Optical properties of nanostructured 2D metal-dielectric photonic crystals with a lattice defect

Optical properties of 2D nanocomposite-based photonic crystals with a lattice defect are studied. The nanocomposite comprises metallic nanospheres dispersed in a transparent matrix and is characterized by an effective resonant permittivity. Transmission spectrum for s-polarized waves at oblique incidence is calculated. Spectral manifestation of the splitting of the defect mode when its frequency coincides with the resonant frequency of the nanocomposite is studied. The essential dependence of the splitting on the angle of incidence and concentration of metallic nanospheres in the nanocomposite matrix is established. Specific features of spatial distribution of the electric field intensity in defect modes of crystals are analyzed.     

On the effective medium model for particles with a complex structure

We consider a generalization of the effective medium approximation to the case of matrices containing macroscopically inhomogeneous particles with an arbitrary structure (cermet topology). The form of the result is determined to a considerable extent by the heuristic choice of effective cells used to estimate the field and induction values averaged over the volume. The simplest choice of a particle in an unperturbed field as a cell leads to the Maxwell–Garnett approximation, while the self-consistent effective medium approximation corresponds to the replacement of the unperturbed field by the mean field. As an example, we describe particles with a shell, as well as statistically anisotropic media with a single preferred direction.     

Fundamental limits of waves propagating in an inhomogeneous multilayer metal-dielectric medium

The dispersion equations have been derived for various types of orthogonally polarized waves in a five-layer dielectric medium shielded by metal screens. The dispersion characteristics of electromagnetically coupled waves propagating in two waveguide dielectric layers, isolated from each other and from the metal screens by separating and intermediate dielectric layers, have been investigated. The fundamental limits of the spectrum of fundamental, higher-order, waveguide, and reactive types of waves are determined by the relative retardation and reduced-frequency range.     

Retrieval of effective parameters for bianisotropic metamaterials with omega shaped metallic inclusions

Bianisotropic metamaterials including Ω-shaped metallic elements are investigated experimentally and theoretically. A passband is observed for a composite metamaterial (CMM) based on an Ω-medium below the plasmonic frequency of the corresponding closed CMM. The effective parameters (refractive index, impedances, permittivity, permeability, and magnetoelectric coupling coefficient) are retrieved for the Ω-medium and the CMM based on it. Our retrieval results show that the passband observed for the CMM is a band with positive refractive indices. Our retrieval results confirm the deductions of our previous reports.     

Ray theory for a locally layered random medium

We consider acoustic pulse propagation in inhomogeneous media over relatively long propagation distances. Our main objective is to characterize the spreading of the travelling pulse due to microscale variations in the medium parameters. The pulse is generated by a point source and the medium is modelled by a smooth three-dimensional background that is modulated by stratified random fluctuations. We refer to such media as locally layered .

We show that, when the pulse is observed relative to its random arrival time, it stabilizes to a shape determined by the slowly varying background convolved with a Gaussian. The width of the Gaussian and the random travel time are determined by the medium parameters along the ray connecting the source and the point of observation. The ray is determined by high-frequency asymptotics (geometrical optics). If we observe the pulse in a deterministic frame moving with the effective slowness , it does not stabilize and its mean is broader because of the random component of the travel time. The analysis of this phenomenon involves the asymptotic solution of partial differential equations with randomly varying coefficients and is based on a new representation of the field in terms of generalized plane waves that travel in opposite directions relative to the layering.     

Frequency separation of surface acoustic waves in layered structures with acoustic metamaterials

We show theoretically that in elastic layered structures containing an upper layer of smoothly varied thickness and a substrate of a highly dispersive metametarial it is possible to significantly enhance spatial frequency separation of surface acoustic waves. Theory of Love surface acoustic waves propagation in waveguides with varied thickness, taking into account mutual modes coupling, is built. Appropriate structure of metamatererial with resonant frequency dependence of material parameters, making frequency separation effective, is provided. Efficiency of spatial frequency separation and modes coupling is calculated for various metamaterial parameters and wave frequencies.     

An effective mean-field method for describing surface effects in polymer layers

The peeling off of an adsorbed flexible macromolecule from a surface under the action of an effective mean field formed due to intermolecular interactions with the ends of other extended chains is considered. It is shown that there is a first order phase transition in the system that is accompanied by a rise of fluctuations, the existence of metastable states, and jumps of the extension and heat capacity of chains.     

Elastic properties of nanostructured materials with layered grain boundary structure

Atomistic calculations of the elastic constants for a bulk nanostructured material that consists of a layered structure where alternating layers meet along high angle grain boundaries and where atoms interact via a Lennard-Jones potential are presented. The calculations of the elastic constants were performed in the frame of homogeneous deformations for a wide range of layer widths ranging from 2.24 up to 74.62 nm. The results showed that the relaxation of the atomic structure affects the elastic constants for the cases where more than 5% of atoms are located in the GB region. Also it was found that the way that external stresses are applied on the system affects the values of the obtained elastic properties, with the elastic constants related to the characteristic directions of the grain boundary being the most affected ones. The findings of this work are of interest for the fabrication methods of nanostructured materials, the measurement methods of their elastic properties as well as multiscale modeling schemes of nanostructured materials.     

A discrete model of damped acoustic metamaterials

For damped acoustic metamaterials, a discrete model is proposed in the form of a periodic structure with cells of the simplest type. The effective parameters of the model are determined by criteria based on the equality of dispersion of waves. The general properties of the model are studied. An example of one negative type of metamaterials is presented. The model is useful for analyzing wave properties and creating metamaterials with given acoustic properties.     

Band structure and broadband compensation of absorption by amplification in layered optical metamaterials

The frequency dependence of the gain required to compensate for absorption is determined for a layered structure consisting of alternating absorbing and amplifying layers. It is shown that the fulfillment of the same conditions is required for the existence of a band structure consisting of alternating bands allowed and forbidden for optical radiation propagation in the frequency-wave vector parametric region. Conditions are found under which the gain required for compensation is smaller than thresholds for absolute (parasitic lasing) and convective (waveguide amplification of radiation) instabilities.