Dielectric constant of a suspension of uniform spheres

Optical microstructures based on surface-selective growth of Ag nanoparticles on thermally poled soda-lime glass

Glass is important as a substrate for coatings in a wide range of applications or as a substrate for the fabrication of optical micro/nano structures. Coating by wet chemistry methods often demands modifications of the glass surface properties involving several steps. In addition, the micro/nano structuring is usually a several-step process. New methods that are simpler and more efficient are being proposed. One of them is glass poling that has been used to obtain surface relief on glass and, together with electric field assisted dissolution, for metal nanostructures in glass/metal systems. In this work, we demonstrate that poling increases the susceptibility of the glass surface for coating with Ag nanoparticles synthesized in situ by silver salt reduction. It is shown that a selectively poled glass surface can be used as a template to obtain optical microstructures consisting of Ag nanoparticles in only three simple steps. As a proof-of-concept, the method is used to fabricate diffraction gratings with an optical response that can be tuned by adjusting the Ag concentration. This approach is more versatile than the standard structuring by electric field assisted dissolution, as it does not require application of an elevated temperature once the coating is formed, which might change or destroy the properties of the thermally sensitive coating species or morphologies.

Fraunhofer diffraction of electromagnetic radiation by finite periodic structures with regular or irregular overall shapes

Based on an essentially different theoretical foundation than common classical diffraction theories that remain in extensive use, this paper discusses from a fresh perspective the theoretical interpretation and prediction of the far-field diffraction of a plane monochromatic wave by a finite periodic array (PA) of identical obstacles. The theoretical treatment rests on the PA extension of the rigorous generalized multiparticle Mie solution (GMM). The truncated periodic structures may have an irregular overall shape with an arbitrary spatial orientation with respect to the incident beam. It is shown that the overall shape and intrinsic geometrical structure of a finite PA play a decisive role in giving rise to an associated far-field diffraction pattern. It is also shown that, when the physical dimensions of individual component units are much smaller than the incident wavelength, the extracted diffraction pattern of a densely packed PA of such small volumes in forward directions exhibits the distinct features predicted from classical diffraction theories for an aperture with the same shape as the overall finite PA. Several typical examples are presented, including two complementary arrays used in the specific discussion concerning Babinet's principle. There are brief preliminary discussions on some fundamental concepts in connection with the involved theoretical basis and on potential further development and application of the present GMM-PA approach.

Quantitative analysis of nanoparticle growth through plasmonics

Plasmon excitation appears to be a powerful and flexible tool for probing in situ and in real time the growth of supported conducting metal nanoparticles. However, although models exist for analysing optical profiles, limitations arise in the realistic modelling of particle shape from the lack of knowledge of temperature effects and of broadening sources. This paper reports on the growth of silver on alumina at 190-675 K monitored by surface differential reflectivity spectroscopy in the UV-visible range. In the framework of plasmonic response analysis, particles are modelled by truncated spheres. Their polarizabilities are computed within the quasi-static approximation and used as an input to the interface susceptibilities model in order to determine the Fresnel reflection coefficient. The pivotal importance of the thermal variation of the metal dielectric constant is demonstrated. Finite-size effects are accounted for. As size distribution fluctuations contribute marginally to the lineshape compared to the aspect ratio (diameter/height) distribution, a convolution method for representing the experimental broadening is introduced. Effects of disorder on the lineshape are discussed. It is highlighted that beside the quality of the fit (not a proof by itself!), physical meaning of the parameters related to the sticking probability, growth and wetting is crucially required for validating models. The proposed modelling opens interesting perspectives for the quantitative study of growth via plasmonics, in particular in the case of noble metals.

On the dielectric function tuning of random metal-dielectric nanocomposites for metamaterial applications

The potential of random metal-dielectric nanocomposites as constituent elements of metamaterial structures is explored. Classical effective medium theories indicate that these composites can provide a tunable negative dielectric function with small absorption losses. However, the tuning potential of real random composites is significantly lower than the one predicted by classical theories, due to the underestimation of the spectral range where topological resonances take place. This result suggests that a random mixture consisting of a metal matrix with embedded isolated dielectric inclusions is a promising design guideline for the fabrication of tunable composites for metamaterial purposes.

Effective-medium theory of surfaces and metasurfaces containing two-dimensional binary inclusions

The paper extends one-body effective-medium theory to incorporate the correct second-order interactions in a two-dimensional Maxwell-Garnett theory. The two-body inclusion problem is solved using the averaged dipole moments that are induced by the scattering electromagnetic field on the medium/inclusion system. By incorporating the appropriate polarizability factor in the solutions, conventional right-handed media with binary embeddings are analyzed while a different form for the polarizability term allows the study of the effective properties of a metasurface. In both cases, it is shown that the two-body coefficient to second order in the low area fraction of inclusions is exact, while the corresponding results of the Maxwell-Garnett and Bruggeman theories are incorrect. This is especially true in the superconducting and holes limits, respectively. In the study of metasurfaces, the requirement for electromagnetic screening of the inclusions as well as the requirement needed to achieve the Fröhlich condition are stated. Negative permittivity and permeability are presented for strong-scattering showing negative resonances for a given frequency spectrum. It is shown that these resonances disappear when we derive the weak-scattering limit. The possibility of obtaining doubly negative effective permittivity and permeability is discussed by using an appropriate polarization for the applied electromagnetic field propagating in the metasurface. Finally, the potential difference and hence voltage and capacitance between binary inclusions is determined for surfaces/metasurfaces which allows, in the case of metasurfaces, the behavior of split-ring-type resonators to be investigated.

Surface plasmon resonance broadening of metallic particles in the quasi-static approximation: a numerical study of size confinement and interparticle interaction effects

The width of the surface plasmon resonance of metallic particles increases as the particle size reduces due to confinement effects that modify the metal dielectric function. In the limit of very low particle concentration, particle size can be directly related to the plasmon width. However, as concentration increases, the interaction among particles induces additional broadening. Numerical computation of the effective dielectric function of systems consisting of monodisperse and randomly distributed particles embedded in a dielectric matrix enable us to quantify the influence of both size and interaction effects. It is shown that for noble metals the contribution of interparticle interaction to plasmon resonance width cannot be neglected even at volume concentrations of a few per cent. The results presented here can be useful in extending nanoparticle sizing from optical extinction spectroscopy beyond the dilute limit required by classical Mie theory.