Effective Complex Refractive Index Research Articles

Emission polarization of roughened glass and aluminum surfaces

Ellipsometer measurements of the effective complex refractive index at a wavelength of 10.6 μm are made on a series of glass and aluminum surfaces of increasing surface roughness. The measured values are then used to calculate the degree of emission polarization and are shown to be in agreement with the experimentally determined values when depolarization is small. Comparisons are also made with calculations based on the Kirchhoff scattering theory. Both the theory and the experimental results indicate that it is the local surface slope and not the roughness magnitude that is the prime factor in determining the degree of emission polarization from the samples studied.

Pertinent Data for Modelling Pigmented Materials in Realistic Rendering

AbstractThis article discusses the important problem of determining pertinent data to describe a pigmented medium. The first part deals with optical characteristics of pigments and the general properties of binders and fillers. It also exposes the limits and conditions of applicability of single scattering. In the second part the connection between individual optical properties, size, and form of particles is made with phenomenological theories of multiple scattering in absorbing media, Progressively, it appears that pertinent data in realistic modelling are always in relation with true or effective complex refractive indices and size parameters.

Characterization of thin films and their structures in surface plasmon resonance measurements

An approach to quantitative evaluation of surface plasmon resonance (SPR) measurements is given. In order to determine thicknesses and refractive indices, measured SPR curves were fitted numerically with a theoretical model based on the Fresnel equations. The model also takes into account additional roughness layers, representing real properties of the interfaces, which significantly improves the fitting accuracy. The intermediate layers have physical thicknesses and effective complex refractive indices, responsible for light losses at the interfaces. This model has been verified by direct measurement of surface roughness with the help of an atomic force microscope (AFM). It has turned out that the fitting procedure can reveal microstructures of a substrate and deposited layer, and when combined with the AFM for roughness measurement, this model can find simultaneously both the thickness and the refractive index of the metal film.

A simple, effective‐medium model for water saturation in porous rocks

A general equation for water saturation is derived from effective‐medium theory. A simpler low‐frequency equation is also derived. Both equations are directly solvable for water saturation. The model should be applicable to any granular, water‐wet formation. Additional relationships are derived specifically for application to shaly sandstones, but the model should be applicable to a wide range of rock types, water conductivities, and tool frequencies. In the derivation, hydrocarbons are included in the matrix component of the equation and the combined “matrix” elements are treated as resistors in parallel. The low‐frequency equation is compared to various approaches to calculation of water saturation, such as Dual‐Water, Waxman‐Smits, and Bussian. The general equation is compared to three‐component effective medium, porosity index, and complex refractive index models (CRIM). The model is proven to work on experimental data under a wide range of frequencies and water conductivities. It is recommended that the new saturation model be used for nearly all types of electrical saturation calculation, whether the measurements are from standard resistivity tools or from dielectric tools.

Theory of optical identification of submicron particles in high atmosphere

Interaction between planetary atmospheres and small bodies is connected with radiation effects. Submicron particles in the Earth's upper atmosphere strongly influence the scattering of the shortwave solar radiation. Based on the mutual connection between the environmental and radiation field structures it is possible to determine the physical characteristics of the particle set in this environment. Generaly, the diffused radiation field in the real atmosphere is given by a sum of elementary and multiple scattering components. Solving the inverse problems always leads to complicated integral equations. A major part of the diffused radiation field in the upper atmosphere is due to the first order scattering. The paper presents a new method for determination of the effective complex refractive index and size distribution of the particles based on the radiance data. The solution of integral equations is to be found in the space of quadratically integrable and continuous functionsf ∈L2.

Field rate equation and linewidth of semiconductor laser with inhomogeneous resonator medium

The spontaneous emission noise of an axially inhomogeneous laser structure is evaluated by Green functions. Explicit analytical expressions are given for the field rate equation and linewidth in the case of soft variations of the complex effective index of refraction and are applied to a gain-lever laser.

The measurement of effective complex refractive indices for selected metal silicides

The measurement of thermally grown silicon dioxide films on selected metal silicides (CoSi2, CrSi2, Ir3Si5, NiSi2, Ru2Si3, and WSi2) via ellipsometry has been investigated. The oxide-thickness calculation requires a knowledge of the complex refractive index of the metal-silicide substrate which can be measured independently by ellipsometry on bare silicide substrates. In order to check the measured refractive indices for the silicide substrates, the thicknesses of thermally grown SiO2 films were compared from ellipsometry which used the measured refractive indices, Rutherford backscattering, and step-height thickness measurements. It is shown that, despite considerable complexities introduced by various surface treatments, procedures have been found so that effective refractive indices for the silicide substrates can be obtained, which in some instances require removal of the oxide and measurement of the complex refractive index of the silicide after oxidation.

Generalized WKB method for the analysis of light propagation in inhomogeneous anisotropic optical waveguides

The generalization of the WKB method for light propagation in planar uniaxially anisotropic inhomogeneous optical waveguides is presented. Both ordinary and extraordinary ray paths and phases along the rays in the medium inhomogeneous in the direction perpendicular to the optic axis are derived. These results are used to formulate the dispersion equations for graded-index anisotropic optical waveguides such as the LiNbO 3 :Ti waveguide. Analytical continuation from the real to the complex effective index of refraction enables one to include leaky modes into the analysis. A simple expression for the leaky-mode loss coefficient is given. Both the polarization conversion and energy leakage effects are well described by this method.

吸収物質を含む大気中のエアロゾルの有効複素屈折率

This paper presents a discussion of the effective complex refractive index of aerosols composed of particles having large and small absorption coefficients in the visible region. Based on Mie theory, the effective complex refractive indices at the wavelength of 0.55μm which give correct values of both the extinction coefficient and the single-scattering albedo were calculated for the following two kinds of aerosol models: one is composed of carbon soot and ammonium sulfate particles and the other is composed of hematite and ammonium sulfate particles in varied proportion. The power law was assumed for the size distribution of the particles, with the exponent being varied from 2.5 to 3.5. The phase functions and the volume backscattering coefficients were also calculated in order to check the validity of using the effective refractive indices.The imaginary part of the effective refractive index increases with increase of carbon soot or hematite content and it also depends on the size distribution of these substances. The imaginary part of the refractive index obtained for a possible range of the soot content is consistent with that so far reported for atmospheric aerosols by several authors. It rarely exceeds 0.05 in this study. Based on these results, the possible effect of aerosol on the heat balance of the earth-atmosphere system is briefly discussed.

A general approach for the analysis of optical waveguides

A general approach for the analysis of optical waveguides with the presence of an active medium is presented. It is shown from first principles that the dispersion and gain (or loss) of the active medium can be incorporated into the modal analysis of the waveguide by defining an effective complex refractive index. The applicability of this approach, in contrast with that of the conventional analysis, is investigated, employing the hollow circular cylindrical waveguide amplifier as a typical example.

Electrode potential scanning ellipsometric spectroscopy: Study of the formation of the anodic oxide film on noble metals

The formation of the anodic oxide film on Pt has been investigated at wavelengths in the visible using voltage scanning ellipsometry. Changes in light intensity in an ellipsometric experiment have been used to determine the changes in Δ 0, ψ 0, and reflectivity of the surface. From these three parameters, the effective complex refractive index and thickness of the surface film have been calculated, using a three-layer model. The oxide film on Pt has been found to have different optical properties above and below 1.1 V versus NHE. The apparent film thickness increases with constant optical properties between 1.1 and 1.6 V, indicating that the oxide may form in patches on the surface. The optical constants of this film show small dependence on wavelength in the visible. The anodic oxide film on Au has also been studied using this technique. The presence of the optical absorption edge of Au in the visible region of the spectrum causes the Au surface to be very sensitive to interactions with the surface oxide. This results in a failure of the simple three-layer model at wavelengths near the absorption edge of Au.