Guillermo P. Ortiz

Effective optical response of metamaterials

We use a homogenization procedure for Maxwell’s equations in order to obtain in the local limit the frequency-dependent macroscopic dielectric-response tensor ij of metamaterials made of a matrix with inclusions of any geometrical shape repeated periodically with any lattice structure. We illustrate the formalism calculating ij for several structures. For dielectric rectangular inclusions within a conducting material we obtain an anisotropic response that may change from conductorlike at low to dielectriclike with resonances at large , attaining a very small reflectance at intermediate frequencies which can be tuned through geometrical tailoring. A simple explanation allowed us to predict and confirm similar behavior for other shapes, even isotropic, close to the percolation threshold.

Macroscopic optical response and photonic bands

We develop a formalism for the calculation of the macroscopic dielectric response of composite systems made of particles of one material embedded periodically within a matrix of another material, each of which is characterized by a well-defined dielectric function. The nature of these dielectric functions is arbitrary, and could correspond to dielectric or conducting, transparent or opaque, absorptive and dispersive materials. The geometry of the particles and the Bravais lattice of the composite are also arbitrary. Our formalism goes beyond the long-wavelength approximation as it fully incorporates retardation effects. We test our formalism through the study of the propagation of electromagnetic waves in two-dimensional photonic crystals made of periodic arrays of cylindrical holes in a dispersionless dielectric host. Our macroscopic theory yields a spatially dispersive macroscopic response which allows the calculation of the full photonic band structure of the system, as well as the characterization of its normal modes, upon substitution into the macroscopic field equations. We can also account approximately for the spatial dispersion through a local magnetic permeability and analyze the resulting dispersion relation, obtaining a region of left handedness.

Nonadditivity of poynting vector within opaque media.

The energy flux within an opaque medium near an interface is not the sum of an incident plus a reflected term, as there is a synergistic contribution to the time-averaged Poynting vector that involves simultaneously both the incident and reflected fields. Therefore, the well-known formula R + T = 1, where R is the reflectance and T the transmittance, does not hold, and furthermore, R and T lose their accepted meanings. We illustrate the perils of assuming energy flux additivity by calculating the transmission and reflection spectrum of a film over a substrate normally illuminated by incoherent light at frequencies in the neighborhood of an optical resonance. We also show that the usual relation between the scattering, absorption, and extinction cross sections for particles immersed within a dissipative host have to be modified to account for the nonadditivity.

Scaling condition for multiple scattering in fractal aggregates

It is well known that under the first Born approximation, the differential cross-section ds=dO for light scattered by a fractal of dimension df scales with wave vector Q as Qdf : The use of this formula to interpret experiments performed at frequencies close to the resonances of the system for which multiple scattering is not negligible is questionable.We study the scaling properties of the light scattered by colloidal aggregates employing a novel multi-resolution hierarchical algorithm which allows the study of large systems taking fully into account the long range of the interactions in multiple scattering calculations.We obtain the conditions under which scaling may be present and find that even under resonant conditions, the scattering cross-section may scale with the fractal dimension df ; but only if the aggregate is larger than a dissipation and frequency-dependent length-scale Lh; confirming within a full vectorial calculation a result previously found for scalar interactions.For smaller aggregates, d s=dO might scale with a different exponent or it might not scale at all, depending on the frequency of light employed.This could explain the discrepancies between experiments performed on similar systems within the strong scattering regime.

Optical properties and scaling in fractal aggregates

Within the first born approximation, the calculated angular distribution of the light scattered by a fractal decays as a power of the scattering wavevector Q, with an exponent given by the fractal dimension df. This has been frequently used experimentally to characterize optically the geometry of fractal systems. The validity of the result above has been questioned for frequencies close to the resonances of the system, for which the first born approximation fails. In this paper we apply a recently developed hierarchical algorithm to calculate the self-consistent near field and the scattered electromagnetic field for 2D colloidal aggregates excited at their resonant frequencies. The local environment of the strongly polarized regions manifests itself in the angular dependence of these scattered intensity corresponding to large Q. For Q within the mass scaling region, the scattering does decay as Q-df for some frequencies, similar to the geometrical structure factor S(Q), but shows no scaling whatsoever for others.

Optical and electrical properties of nanostructured metallic electrical contacts

We study the optical and electrical properties of silver films with a graded thickness obtained through metallic evaporation in vacuum on a tilted substrate to evaluate their use as semitransparent electrical contacts. We measure their ellipsometric coefficients, optical transmissions and electrical conductivity for different widths, and we employ an efficient recursive method to calculate their macroscopic dielectric function, their optical properties and their microscopic electric fields. The topology of very thin films corresponds to disconnected islands, while very wide films are simply connected. For intermediate widths the film becomes semicontinuous, multiply connected, and its microscopic electric field develops hotspots at optical resonances which appear near the percolation threshold of the conducting phase, yielding large ohmic losses that increase the absorptance above that of a corresponding homogeneous film. Optimizing the thickness of the film to maximize its transmittance above the percolation threshold of the conductive phase we obtained a film with transmittance T = 0.41 and a sheet resistance

Effective non-retarded method as a tool for the design of tunable nanoparticle composite absorbers

R_{\square}^{\mathrm{max}}\approx2.7\Omega

Bulk response of composites from finite samples

. We also analyze the observed emission frequency shift of porous silicon electroluminescent devices when Ag films are used as solid electrical contacts in replacement of electrolytic ones.

Keller’s theorem revisited

We investigate the capabilities of an effective non-retarded formalism (ENR) for the exploration and design of nanoparticle composites with specific optical properties. We consider a composite material comprising periodically distributed metallic spheres in a dielectric host matrix. The effective macroscopic dielectric function of the composite medium is obtained by means of the ENR and is used to calculate the electromagnetic response of a slab made of an inhomogeneous material. This response is compared with that obtained by using the layer Korringa–Kohn–Rostoker wave calculation method (LKKR). We analyze the optical properties for different filling fractions, especially in the vicinity of the resonance frequencies of the macroscopic dielectric function. We notice that for dense systems within the long wavelength regime, the results of some analytical theories developed by other authors do not properly describe the multipolar excitations and interactions of orders higher than the dipole, in contrast with the results obtained by using an ENR. Therefore, those methods are not suitable for the design of compound films with novel properties. We show that by appropriately choosing the parameters of the composite, it is possible to achieve a tunable absorber film, and more generally, we show that ENR is a versatile tool for the design of nanoparticle composite materials with specific properties.

Scaling of light scattered from fractal aggregates at resonance

The bulk macroscopic dielectric response of a disordered composite is calculated employing a large finite sample instead of an infinite one obtained by replicating a unit cell, as has usually been done. We explicitly account for boundary effects through the macroscopic depolarization field, and finite size corrections are minimized by the large size of the system. The generation of the composite and the calculation of the interactions between the great number of particles become feasible using a newly developed hierarchical multi-resolution scheme. The dielectric response of a composite made up of Ag spheres embedded in glass and the composition independent spectral density agree with those from previous simulations and we discuss their differences with analytical theories based on a renormalized polarizability. Confinement effects due to inhomogeneities close to the boundary of the system are also investigated.