Size effects in the internal reflection in gold cluster films in polarization modulation experiments

The internal reflection in gold nanocluster films in the Kretschmann geometry is studied using polarization modulation of electromagnetic radiation. The reflection coefficients R _s and R _p for s- and p-polarized light, respectively, as well as their difference ΔR = R _s − R _p , are measured as functions of the angle of incidence of electromagnetic radiation at different wavelengths in the range of 0.6–1.6 μm. A topological size effect is found in the interaction of light with the cluster electronic system, which consists of the fact that the surface plasmon resonance in gold cluster films can be excited by both p- and s-polarized light. It is found that the magnitude and the sign of curvature of the angular dependence of ΔR are related to the degree of resonance with light of either only p-polarization or both polarizations simultaneously.     

Polarization modulation spectroscopy of surface plasmon resonance

The features of surface plasmon resonance in gold nanofilms deposited on the surface of a total-internal-reflection prism have been investigated theoretically, using the Fresnel equation, and experimentally, with application of the polarization modulation technique. The angular characteristics of the polarization difference of the reflection coefficients for s-and p-polarized light, Δρ = R _s ² ? R _p ² , were measured in the wave-length range λ = 0.4–2.0 μm. It is shown that the characteristics of Δρ, in contrast to the results of standard measurements by the surface plasmon resonance method, have a resonance peak. Due to this, the characteristics of the polarization difference contain nonresonant components whose magnitudes are determined by the internal reflection coefficients for the metal and insulator; these parameters depend on the film thickness. The calculated and experimental data coincide when the model assumes exponential dependence of the refractive indices and extinction coefficients on the thickness of the metal film. It is established that the characteristic parameter of the exponential is a metal film thickness of 11.0 ± 0.5 nm, at which the film optical parameters correspond to the bulk characteristics.     

Polarization properties of porous gold and silver films

Using the method of polarization modulation of electromagnetic radiation and the Kretschmann geometry, we perform comparative studies of surface plasmon resonance in porous and continuous gold and silver films. The spectral dependences of the polarization difference of the reflection coefficients of nano-composites are obtained for the first time and are supplemented by angular characteristics of this parameter. We show that these dependences characterize particular features of the optical properties related to the structure, morphology, and topology of porous films. We reveal that surface plasmon-polaritons and local plasmons in porous films can be excited both by radiation that is p polarized with respect to the plane of incidence, as is the case with continuous films, and by s polarized radiation. We demonstrate that the measurement results can yield information on the structural properties of films, such as their thickness, roughness height, degree of dispersion of nanoparticles, and so on.     

Polarization stokes polarimetry of the amplitude and phase characteristics of surface plasmon polariton resonance

The amplitude and phase characteristics of internal reflection of gold nanofilms have been investigated using polarization modulation of electromagnetic radiation in the Kretschmann geometry. The component Q (the difference between the reflection coefficients R _s ² and R _p ² for the s and p polarizations, respectively) and the component V of the Stokes vector (the difference between the phases of the orthogonal components of linearly polarized radiation) of light reflected from a half-cylinder of the total internal reflection with gold films of different thicknesses on its flat surface have been measured as a function of the angle of incidence of light in the wavelength range 500–1000 nm. It has been demonstrated that, in the range of parameters corresponding to the manifestation of the plasmon polariton resonance (the angle of incidence of light, the wavelength, the metal film thickness), the dispersions of the amplitude and phase characteristics are in quantitative and qualitative agreement with the model concepts of a classical oscillator.     

Polarization-modulation spectroscopy of linear dichroism in uniaxially deformed silicon crystals

The effect of linear dichroism in uniaxially deformed samples of single-crystal silicon in the range of edge absorption is studied with the application of polarization modulation. The differential transmission spectrum representing the difference between the values of transmission for linearly polarized radiation with the polarizations that are parallel and perpendicular to the optical axis is obtained. The fine structure of the spectrum, associated with the participation of phonons in indirect optical transitions, is revealed. From the results of measurement of the integral and differential transmission characteristics, the spectral characteristic of the absorption coefficient increment is determined, in which the same specific features are found. The possibility of applying this method for investigating the band spectrum of crystals is shown.     

Kinetics and dynamics of heat-flow-induced birefringence in a glass: Modulation polarimetric representation

The birefringence induced by thermal stress in a quartz glass plate sample with a small temperature gradient has been measured using the modulation polarimetry technique. The stress distribution along and across the direction of the heat flow at specific points in time has been obtained, as well as its dependence on the time in specific coordinates of the heat flow. The inverse problem of transient thermoelasticity has been solved by graphical integration of experimental characteristics. The results obtained have the form of temperature dependences varying in time and space. It has been found that the dynamics of the point of maximum curvature of the temperature function T(t) is a characteristic of the thermal front during the establishment of a steady-state heat flow. It has been shown that the characteristics of relaxation of thermal stress and temperature contain information on the properties of a “heater-sample-surrounding air” system.     

Effect of nonreciprocity in the state of polarization of an electromagnetic wave traveling in an inhomogeneously anisotropic crystal

Nonreciprocity in the state of polarization in an inhomogeneously anisotropic crystal is discovered, and the main characteristics of this effect are studied. The effect consists in the appearance of asymmetry of components of the Stokes vector for radiation traveling in forward and backward directions. It is shown to be caused by the presence of a nonlinear gradient of mechanical stress. The effect is theoretically analyzed using the model of a sample whose inhomogeneity is caused by the presence of sections with linear and circular birefringence placed in a series. The theoretical conclusions qualitatively agree with experimental results obtained for a silicon single crystal using the polarization modulation technique.     

Kramers–Kronig relations in modulation polarimetry diagnostics of glass-ceramics

It has been found that, in an aluminosilicate glass-ceramic sample cut from a massive ingot, there is a correlation of the residual stress with the temperature gradient. The magnitude and coordinate dependence of the stress along the temperature gradient have been determined from the stress-induced linear birefringence measured by the modulation polarimetry technique. Its functional relationship has been established in the form of the Poisson equation with the heterogeneity of the composition due to the preparation conditions. It has been shown that, in the absence of a temperature gradient, the birefringence and dichroism related by the Kramers–Kronig relation play the role of thermodynamic variables.     

Surface plasmons in porous gold films

The surface plasmon resonance effects in porous gold (por-Au) films—nanocomposite porous films containing an ensemble of disordered gold nanoparticles—have been investigated by modulation-polarization spectroscopy. Por-Au films have been obtained by pulsed laser deposition (using a direct particle flow from an erosion torch formed by a YAG:Nd³⁺ laser in argon). The spectral and angular dependences of the polarization difference ρ(λ, θ) of internal-reflection coefficients of s- and p-polarized radiation in the Kretschmann geometry and the spectral dependences of isotropic reflection angles at ρ(θ) = 0 are measured. Two types of surface plasmon resonance are found: one occurs on isolated nanoparticles (dipole and multipole modes), and the other is due to the dipole–dipole interaction of neighboring nanoparticles. The frequency of electron plasma oscillations for the nanoparticle ensemble and the frequencies and decay parameters of resonances are determined. Dispersion relations for the radiative and nonradiative modes are presented. The negative sign of the dispersion branch of nonradiative modes of dipole–dipole interaction is explained by the spatial dispersion of permittivity. The relationships between the formation conditions of the films, their structure, and established resonance parameters (determining the resonant-optical properties of films) are discussed.     

Modulation polarimetry of the topological effect in gold-organic nanocomposite films

The phenomenon of surface plasmon resonance in composite films consisting of gold nanoclusters in matrices of organic molecular materials calix[4]arene and poly(N-vinylcarbazole) has been investigated. The internal reflection coefficients R _s ² and R _p ² of s- and p-polarized light and their physical difference ρ = R _s ² ? R _p ² have been measured according to the Kretschmann scheme as a function of the angle of light incidence θ at different wavelengths λ in the range 400–1000 nm. The angular characteristics reflect the cluster structure of the films, which is confirmed by electron microscopy. A topological size effect has been revealed. This effect is associated with the dependence of the excitation energy efficiency of surface plasmons on the azimuth of the linearly polarized light, the shape, and the distribution of nanoclusters in the coordinate space. The dependences ρ(λ) demonstrate that the local plasmon resonance is excited by both s- and p-polarized light, whereas the polariton resonance is excited by s-polarized light. The sign of the curvature of the dependence ρ(θ) determines the predominance of the excitation energy efficiency of electromagnetic modes with one of the two states of polarization of the excitation radiation.