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.     

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.     

Influence of surface roughness on the reflection of gold films in the region of surface plasmon excitation

The reflection (R) of light at rough gold films has been measured in the region of surface plasmon (SP) excitation and compared with a smooth gold film. The SP resonance minima are shifted to larger wavevectors and their halfwidth is enlarged with increasing surface roughness. Different positions of the reflection minima were observed measuring R(Θ) at constant wavelength λ, and measuring R(λ) at constant angle of incidence Θ. The calculated values prove this observation.     

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.     

Accuracy of ellipsometric monitoring during growth of semiconductor nanostructures

The determination accuracy of the parameters of multilayer structures during their in situ ellipsometric monitoring is analyzed. A qualitative criterion is proposed that makes it possible to evaluate the validity of replacement of the multilayer structure by a certain medium with effective optical constants. According to this criterion, this replacement is possible if the complex reflection coefficients R _{p, s} of the structure satisfy the relation (R _p /R _s + cos2φ)/(R _s + R _p cos2φ) = 1, where φ is the angle of incidence of light. It is shown that, for structures consisting of layers with a high refractive index, this condition is implemented with a high accuracy. This proves that, upon the successive solution of the ellipsometry problem for layers of this structure, errors are not accumulated. In particular, this inference can be applied to structures based on a cadmium-mercury-tellurium ternary compound.     

Applying the phase difference property of polarization angle for measuring the concentration of solutions

This paper proposes a simple method for measuring the concentration of solutions based on the phase difference of internal reflection polarization angle and circularly polarized heterodyne interferometry. For a circularly polarized heterodyne light beam incident on the boundary surface between a hemispherical prism and a test solution, the reflected light passes through a properly oriented analyzer for interference. The phase difference between s- and p-polarized light is sensitive to the solution concentration when the incident angle equals the internal reflection polarization angle. Based on these effects, the resulting phase difference makes it possible to analyze the concentration of solution through heterodyne interferometry. The experiments in this study confirm the feasibility of this method, which provides the advantages of simple installation, ease of operation, and high accuracy.     

Investigations of aluminum films with synchrotron radiation of wavelengths 500 to 1000 Å

Measurements of the photocurrent from thin Al cathodes in a windowless electron multiplier as a function of wavelength, polarization, angle of incidence, and film thickness have been carried out in the extreme vacuum ultraviolet. A normal incidence monochromator utilizing synchrotron radiation provided highly polarized light. A marked difference is found between the photocurrent measured during irradiation of thin films with “s” and “p” polarized light at wavelengths near the Al plasma wavelength (835 Å). For films thicker than about 500 Å pronounced interference effects are found in both “p” and “s” light at wavelengths less than the plasma wavelength. The observations can be explained by assuming the photocurrent is related to the photon density (electromagnetic energy density) in the photocathode. Calculations of the energy density in films irradiated with light give the structure found in the measured photocurrent. The measurements indicate our monochromator yields light with a degree of polarization consistent with the calculated polarization of the synchrotron radiation incident upon our grating (about 85%).     

Determination of optical properties and thickness of nanolayers from the angular dependences of reflectance

The possibility of multiparametric determination of properties of structures from the data on the dependence of reflectances R _p and R _s for polarized radiation and ratio R _p /R _s on the angle of incidence θ and from the angular dependence 1/R _p (ΔR/Δθ) is investigated. The results of natural and computer experiments revealed a high sensitivity of the angular dependence R _p (θ) of the reflectance to the values of optical constants and thickness of layered structures. Quantitative results of multiparametric measurements are verified by the independent method of spectral ellipsometry. The possibility of multiparametric determination of the properties and thickness of nanometer dielectric, metallic, and semiconducting layers on various substrates and the properties of substrates in such structures is established.     

Effects of spatial dispersion at intraband transitions in multiple quantum well structures

Effects of spatial dispersion in reflection of light from multiple quantum well structures of different symmetry have been investigated. It has been shown that with inclined incidence of linearly polarized light on the system of symmetry C _∞v , the reflected wave starts to manifest the circular polarization. Upon the incidence of s(p)-polarized light on the structure of the D _2d symmetry, the reflected wave starts to manifest p(s) component, while in the case of the point symmetry C _2v , this phenomenon also occurs for the normal incidence. The magneto-spatial dispersion in the magnetic field lying in the structure plane leads to the same conversion of polarization. Dependences of the polarization-sensitive reflection coefficients on the incidence angle are calculated. The microscopically gyrotropic contributions to the dielectric permittivity of the multiple quantum well structures are calculated for the intraband frequency range. Evaluations show that the effects of spatial dispersion in such systems can be observed experimentally.     

Theoretical analysis of non-polarizing beam splitters with appropriate amplitude and phase

When used at oblique angles of incidence, the reflectance and transmittance of thin films exhibit strong polarization effects, particularly for the films inside a glass cube. However, the polarization effects are undesirable in many applications. Novel non-polarizing beam splitter designs are shown. Non-polarizing beam splitters with unique optical thin films are achieved through the combination of interference and frustrated total internal reflection. The non-polarizing condition expressions based on frustrated total internal reflection are derived, and examples of the non-polarizing beam splitters are also presented with the optimization technique and the results of R_p=(50±0.5)%, R_s=(50±0.5)%, and Δ_r=(0±0.3) in the wavelength range of 400-700 nm are obtained.     

Polarizing and non-polarizing mirrors for the hydrogen Lyman-<Emphasis Type="Italic">α</Emphasis> radiation at 121.6 nm

Efficient polarizing as well as non-polarizing mirrors for a wavelength of λ=121.6 nm (hydrogen Lyman-α radiation) are necessary to achieve an experimental determination of the magnetic field in the solar corona through the Hanle effect. We have designed, realized and characterized such mirrors. These consist of glass coated with a thin-film stack. The coatings use the most reflective (Al) and most transparent (fluorides) materials at this wavelength. Different coatings were explored which involve an increasing number of films in the coating stack. At the incident angle of maximum polarization where the p-polarized reflectivity R _p is minimized, an s-polarized reflectivity R _s as high as 69% is experimentally obtained with a coating made of a Fabry–Pérot resonator. To our knowledge, this value is the highest ever reported for a polarizing mirror at this wavelength. Additionally, efficient non-polarizing mirrors have been designed and realized by using a two-layer coating (MgF₂/Al/glass). By optimizing the fluoride layer thickness, a mirror with non-polarizing properties in the whole range of incident angles was realized.     

Amplitude-phase reflectance spectra of amorphous silicon-based Bragg structures

Amplitude-phase spectra of light reflection from distributed Bragg reflectors and Fabry-Pérot microcavities based on a-Si: H/a-SiO_x: H thin films have been studied. The frequency dependence of the phase difference between the amplitude p-and s-light reflection coefficients within the photonic band gap is measured. The phase spectrum exhibits predominantly a monotonic, close-to-linear frequency behavior, except for spectral regions near the stop band edges and near the singularities related to the microcavity eigenmodes. The experimental spectra are compared with theoretical calculations based on the transfer matrix method and approximate analytical relations. A method based on analyzing amplitude-phase reflectance spectra is proposed for structural characterization of multilayer microcavity systems.     

Further studies of the sensitivities attainable in using three optical functions to calculate n, k and thickness for thin films

All 56 combinations of three optical functions chosen from R_s, R_p, T_s, T_p, Φ_rs, Φ_rp, Φ_ts and Φ_tp have been investigated to discover their regions of sensitivity in n, k and d/λ coordinate space. When the arrays of error parallelepipeds were plotted, single quadrant patterns of high sensitivity were generated by 21 of these combinations, these being the ones containing one photometric and two polarimetric functions; the best combination was R_pΦ_rpΦ_tp which was viable at all angles of incidence and all thicknesses up to d/λ = 0.08. The remaining 35 combinations produced two-lobe patterns which were insensitive at small angles of incidence but improved as the angle of incidence increased and were best at 60°.     

X-ray scattering from a randomly rough surface

Abstract

On the basis of the method of reduced Rayleigh equations we present a simple and reciprocal theory of the coherent and incoherent scattering of x-rays from one- and two-dimensional randomly rough surfaces, that appears to be free from the limitations of earlier theories of such scattering based on the Born and distorted-wave Born approximations. In our approach, the reduced Rayleigh equation for the scattering amplitude(s) is solved perturbatively, with the small parameter of the theory η(ω) = 1 - ε(ω), where ε(ω) is the dielectric function of the scattering medium. The magnitude of η(ω) for x-rays is in the range from 10^?6 to 10^?3, depending on the wavelength of the x-rays. The contributions to the mean differential reflection coefficient from the coherent and incoherent components of the scattered x-rays are calculated through terms of second order in η(ω). The resulting expressions are valid to all orders in the surface profile function. The results for the incoherent scattering display a Yoneda peak when the scattering angle equals the critical angle for total internal reflection from the vacuum-scattering medium interface for a fixed angle of incidence, and when the angle of incidence equals the critical angle for total internal reflection for a fixed scattering angle. The approach used here may also be useful in theoretical studies of the scattering of electromagnetic waves from randomly rough dielectric-dielectric interfaces, when the difference between the dielectric constants on the two sides of the interface is small.     

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 interferometer as a proximity sensor

A simple interferometric phasemeter which can be used as a proximity sensor is described. It is based on the measurement of the phase shift between the p- and s- components of a field caused by the processes of attenuation in total internal reflection. The role of the interferometer is to restore the p- and the s- components from the resultant totally reflected field, with minimum amplitude and phase distortions and to let them interfere. The phase shift as a function of the attenuation of the total internal reflection can be determined from the interference signal. The interferometer is of a common path polarization shearing type, consisting of Rochon beamsplitter and a linear polarizer. An experiment for measuring the distance between glass plane surface and a plane attenuater made of Si mono-crystal is described. A good agreement between theory and experiment for separations less than 300 nm is observed. This device can be applied in research and metrology. After further modifications, the optical system could be used for proximity sensing, surface geometry control, variable optical retarders, contamination monitoring, etc.     

New contactless method to control the O/N ratio in SiON films

We propose new experimental method of contactless control of the O/N ratio in SiON films deposited on the Si1 1 1 surfaces. The proposed method consists of direct measurements of reflected light for the parallel R_p and perpendicular R_s light polarisations towards the Si1 1 1 plane. We have shown that the spectral dependence of the anisotropic ratio P=R_s/R_p is strictly connected with O/N ratio. Independently performed spectral measurements show good coincidence with experimental data. We show essentially the advantas by comparing with ellipsometry, XPS and other methods both concerning the precision and the technical realisation.     

Power Reflection,Transmission and Absorption Coefficients for a Moving Plasma Slab

Expressions for power reflection (R), transmission (T) and absorption (A) coefficients for p-polarized wave for a warm, collisional, magnetized and moving plasma slab (with sharp boundaries and thickness d₀) are investigated. The effects of plasma slab velocity (β=v/c), electron density (ωp/ω)² and plasma temperature (K_BT) on reflection (R), transmission (T) and absorption (A) coefficients are discussed numerically. It is observed that for the value β=?0.6, reflection coefficient (R) becomes more than unity, whereas absorption coefficient (A) becomes quite negligible while transmission coefficient (T) shows oscillatory behaviour. The variation with plasma frequency (ω_p/ω)² shows that at lower plasma frequency (ω_p/ω)²=0.2 transmission (T) and absorption (A) coefficients are minimum while reflection coefficient (R) is maximum.     

Fast electro-optical response of a cell with a homeoplanar layer of a nematic liquid crystal

The refraction of light, i.e., the turn of an extraordinary ray in the liquid crystal layer similar to total internal reflection at an interface between two media, has been studied in a cell with the homeoplanar orientation of the director. The rise, τ_on, and decay, τ_off, times of optical responses have been obtained for various angles of incidence of light on a liquid crystal layer subjected to an electric field. The times τ_on and τ_off of optical responses for the angles of incidence much larger than the angle of total internal reflection are 1–2 ms, which is three orders of magnitude smaller than the relaxation time of an optical response in the case of normal incidence of the ray.     

Full-field refractive index measurement with simultaneous phase-shift interferometry

Using the phenomenon of total internal reflection and a beam splitting device, a technique of simultaneous phase-shift interferometry is proposed for measuring the full-field refractive index. Because this method applies a beam splitting device that mimics the characteristics of beam splitting and phase modulation, four interferemetric images of various phase distributions can be simultaneously captured. Therefore, this setup can avoid errors caused by non-simultaneous capturing of images and offers the benefits of high stability, ease of operation, and real-time measurement. Furthermore, using the phenomenon of total internal reflection, the phase difference between p- and s-polarized light varies considerably with the refractive index of a tested specimen. This can substantially increase the measurement resolution. The feasibility of this method is verified using an experiment, and the measurement resolution can be higher than 3.65 × 10⁻⁴ RIU.