Giulio Bosi

Substrate‐related effects on the optical behavior of a granular surface: The Maxwell Garnett theory revisited

An approximate treatment, describing the influence of a dielectric substrate on the optical behavior of a granular surface, is reported. It shows that discrepancies between experimental results and predictions mainly based upon the Maxwell Garnett theory [Philos. Trans. R. Soc. London 203, 385 (1904); 205A, 237 (1906)] cannot be interpreted as substrate‐related effects. The magnitudes and locations of the multiple images of the unperturbed dipole of a small metallic sphere have been carried out in an approximate, though reliable, way in the presence of polarizing fields both parallel and perpendicular to the substrate. The resulting dipole is introduced in a long‐known optical model, describing a granular surface as a planar array of equal dipoles interacting with each other. Graphical results, showing the influence of substrates of various dielectric constants, are presented. A discussion of possible improvements of the available model is also reported.

Extension of Maxwell‐Garnett theory for granular surfaces

The Maxwell‐Garnett theory is generally used to describe the optical behavior of aggregated metallic films. This theory is, however, restricted to ultrafine particles whose main dimension can be considered very small compared to that of the wavelength. With particle dimensions in experiments generally larger than 10 nm, this approach is no longer valid for many metals. The purpose of the present work is, therefore, to revise the dipole approximation to include frequency‐dependent terms. The theory is also extended to quadrupolar terms, in order to assess the relative importance of these latter when the aggregates are no longer very small compared to the wavelength. Applications to real metals are discussed.

Transmission of a thin film of spherical particles on a dielectric substrate : the concept of effective medium revisited

A simple comparison with predictions from a scattering surface model shows discrepancies in treatments of thin island films that are based on the effective-medium model. A new approach is thus proposed, and the transmission of a square network of spherical particles on a dielectric substrate is recalculated in a dipolar approximation. Although a convenient multipolar treatment, which would permit retardation-related effects to be handled in a proper way, is still missing, the present partially retarded treatment shows a clear improvement over available predictions.

Optical properties of granular tin films from 0.22 to 1.0μm

The optical properties of granular tin films were investigated in the spectral region from 0.22 to 1.0 microm. As the particles forming the films increased in size (from ~43.0 to 70.0 nm) the peak observed in the reflectance was shifted to longer wavelengths. Parameters such as the film thickness and the filling factor have been determined and served for the calculation of reflectance using the well-known Maxwell-Garnett approach. An extension of this theory was also used to characterize the granular films. The revised dipole theory that includes frequency-dependent terms neglected in the static approximation seems to give a better description of the optical behavior of granular surfaces.

Third‐order treatment of combined effects of space charge and external fields on cylindrical ion and electron beams

Analytical treatments of the space‐charge spread of cylindrical beams have been based upon a number of restrictive assumptions. Most of them can be removed and a higher accuracy attained with the help of a suitable relation connecting motion and Maxwells equations. As previous treatments appear as paraxial approximations, third‐order formulas applying to arbitrary field forms have been carried out.

Optical response of a thin film of spherical particles on a dielectric substrate: retarded multipolar treatment

Multipolar expansions have recently been used to describe the polarizability of a metal sphere on a dielectric substrate. The same technique may be applied to calculating the optical behavior of a square network of identical spheres sitting upon a flat substrate. It is shown how to relate the image multipoles to the object multipoles, which are in turn related to the applied field carried by the unperturbed incident and reflected waves. Retarded-field forms are consistently used throughout the treatment. The scattered fields are also calculated and the optical response determined. This requires summing up the multipole–multipole interactions. Numerical calculations have been performed, showing that a quadrupolar treatment is needed to define the transmittance of an ideal sample.

Retarded treatment of substrate-related effects on granular films: I. Polarizability of a single sphere

Abstract A multipolar treatment of the retarded fields radiated by a metal sphere on a dielectric substrate under the influence of an incident plane wave described. Unlike previous treatments, the present one allows boundary conditions, both on the spherical surface and on the substrate interface, to be matched by simply solving an adequate number of linear equations. The problem is thus reduced to inverting three complex matrices, whose sizes depend on the number of multipoles included in the field forms. The solutions, which represent the object and image multipoles (both in the incidence and in the transmission media) associated with the polarized sphere, are given the form of linear combinations of the multipoles associated with the unperturbed field (incident and reflected waves).

First−order treatment of combined effects of space charge and external fields on plane−symmetric beams of charged particles

First−order equations describing the space−charge spread of charged particle beams under the influence of plane−symmetric external fields are proposed. The present treatment is confined to elliptic cross−section beams and is based upon an earlier work about axially symmetric systems.

Optical response of a thin film of spherical particles upon a dielectric substrate: retarded multipolar treatment including multiple reflections

Multipolar expansions were recently used to calculate the optical behavior of a square network of metal spheres sitting upon an infinitely thick dielectric substrate. Here a more realistic substrate of finite thickness is treated, and multiple reflections are taken into account. Retarded field forms are consistently used throughout the treatment for calculating multipole-multipole interactions and scattered fields. Transmission and reflection properties are fully described by 2 × 2 matrices, whose elements provide the optical response as a function of the polarization state. Numerical results are presented in graphic form: They apply to a particular sample consisting of gold particles upon a sapphire substrate.

Second‐order treatment of combined effects of space‐charge and external fields on plane‐symmetric zero‐emittance beams of charged particles

An earlier first‐order treatment of the space‐charge spread of zero‐emittance charged particle beams under the influence of plane‐symmetric external fields is revised and extended to include second‐order effects. Elliptic and rectangular cross‐section beams are investiged and conditions for parallel beam transport are carried out.