Direct calculation of the optical constants for a thin film using a midpoint envelope

An algebraic method to calculate the optical constants for a weakly absorbing thin film from the spectrum of normal reflectance is described. The calculation of the refractive index of the thin film is simplified by constructing a midpoint envelope through the reflection spectrum. If a portion of the spectrum includes a region where the film is nonabsorbing, the results can be used to calculate an algebraic solution for the refractive index and the absorption coefficient of the thin film throughout the entire spectrum. The method is used to determine the constants for a coating of alumina on a glass substrate. The results are compared to the calculation from the extrema of the spectrum.     

Retrieval of the scattering and microphysical properties of aerosols from ground-based optical measurements including polarization. I. Method

A method has been developed for retrieving the scattering and microphysical properties of atmospheric aerosol from measurements of solar transmission, aureole, and angular distribution of the scattered and polarized sky light in the solar principal plane. Numerical simulations of measurements have been used to investigate the feasibility of the method and to test the algorithm's performance. It is shown that the absorption and scattering properties of an aerosol, i.e., the single-scattering albedo, the phase function, and the polarization for single scattering of incident unpolarized light, can be obtained by use of radiative transfer calculations to correct the values of scattered radiance and polarized radiance for multiple scattering, Rayleigh scattering, and the influence of ground. The method requires only measurement of the aerosol's optical thickness and an estimate of the ground's reflectance and does not need any specific assumption about properties of the aerosol. The accuracy of the retrieved phase function and polarization of the aerosols is examined at near-infrared wavelengths (e.g., 0.870 mum). The aerosol's microphysical properties (size distribution and complex refractive index) are derived in a second step. The real part of the refractive index is a strong function of the polarization, whereas the imaginary part is strongly dependent on the sky's radiance and the retrieved single-scattering albedo. It is demonstrated that inclusion of polarization data yields the real part of the refractive index.     

Optical and structural characterization of r.f. sputtered CeO2 thin films

The optical and structural properties of r.f. sputtered CeO2 thin films deposited on Pyrex substrates have been studied as a function of substrate temperature during deposition. The refractive index, n, extinction coefficient, k, and bandgap of the films were calculated from reflectance, R, and transmittance, T, spectra in the wavelength range 340–900 nm. The refractive index of CeO2 films at 550 nm comprises values from about 2.25–2.4 depending on the substrate temperature during deposition. The extinction coefficient was negligible for wavelength values higher than 400 nm. The value obtained for the bandgap was 3.1 eV. The X-ray diffraction patterns showed the same (f c c) cubic structure with preferential orientation depending on substrate temperature during deposition. The scanning force microscope measurements showed that the roughness and grain size of the CeO2 films increase with increasing substrate temperature. This revised version was published online in November 2006 with corrections to the Cover Date.     

Laser reflectometry in situ measurement of lead zirconate titanate film growth

A convenient method is described for optical characterization of thin films during growth. The method has been demonstrated on lead zirconate titanate (PZT) films deposited by pulsed laser ablation for various temperatures. The optical constants of the PZT films as well as the film growth rate were determined in situ by fitting (with three free parameters) the calculated reflectance as a function of film thickness to the experimental reflectance curve as a function of deposition time, as obtained by unpolarized laser reflectometry. The fitted parameters are the uniform complex PZT refractive index and the layer thickness (assumed proportional to time), with the complex refractive index of the platinum substrate being measured previously. These results compare well with the subsequent ellipsometric measurements made to assess the precision of the reflectometry technique.     

Modeling the optical properties of mineral particles suspended in seawater and their influence on ocean reflectance and chlorophyll estimation from remote sensing algorithms

The optical properties of mineral particles suspended in seawater were calculated from the Mie scattering theory for different size distributions and complex refractive indices of the particles. The ratio of the spectral backscattering coefficient to the sum of the spectral absorption and backscattering coefficients of seawater, b(b)(lambda)/[a(lambda) + b(b)(lambda)], was analyzed as a proxy for ocean reflectance for varying properties and concentrations of mineral particles. Given the plausible range of variability in the particle size distribution and the refractive index, the general parameterizations of the absorption and scattering properties of mineral particles and their effects on ocean reflectance in terms of particle mass concentration alone are inadequate. The variations in the particle size distribution and the refractive index must be taken into account. The errors in chlorophyll estimation obtained from the remote sensing algorithms that are due to the presence of mineral particles can be very large. For example, when the mineral concentration is 1 g m(-3) and the chlorophyll a concentration is low (0.05 mg m(-3)), current global algorithms based on a blue-to-green reflectance ratio can produce a chlorophyll overestimation ranging from approximately 50% to as much as 20-fold.     

Dispersion and thermal properties of lithium aluminum silicate glasses doped with Cr3+ ions

A series of new lithium aluminum silicate (LAS) glass systems doped with chromium ion is prepared. The reflectance and transmittance of the glass slabs are recorded. By means of an iteration procedure, the glass refractive index n and the extinction coefficient k and their dispersions are obtained. Across a wide spectral range of 0.2-1.6 microm, the dispersion curves are used to determine the atomic and quantum constants of the prepared glasses. These findings provide the average oscillator wavelength, the average oscillator strength, oscillator energy, dispersion energy, lattice energy, and material dispersion of the glass materials to be calculated. For optical waveguide applications, the wavelength for zero material dispersion is obtained. Dilatometric measurements are performed and the thermal expansion coefficient is calculated to throw some light on the thermo-optical properties of the present glasses correlating them with their structure and the presence of nonbridging oxygen ions.     

Determination of Optical Constants of Solgel-Derived Inhomogeneous TiO(2) Thin Films by Spectroscopic Ellipsometry and Transmission Spectroscopy

Amorphous and nanocrystalline TiO(2) thin films coated on a vitreous silica substrate by a solgel dip coating method are investigated for optical properties by spectroscopic ellipsometry (SE) together with transmission spectroscopy. A method of analysis of SE data to determine the degree of inhomogeneity of TiO(2) films has also been presented. Instead of the refractive index, the volume fraction of void has been assumed to vary along the thickness of the films and an excellent agreement between the experimental and calculated data of SE below the fundamental band gap has been obtained. The transmission spectrum of these samples is inverted to obtain the extinction coefficient k spectrum in the wavelength range of 300-1600 nm by using the refractive indices and parameters of structure determined by SE. The nonzero extinction coefficient below the fundamental band-gap energy (3.2 eV) has been obtained for the nanocrystalline TiO(2) and shows the presence of optical scattering in the film.     

Optical properties and size distribution of aerosols derived from simultaneous measurements with lidar, a sunphotometer, and an aureolemeter

A new method is proposed to derive the optical properties and size distribution of aerosol in an air column from simultaneous measurements of the backscattering coefficient, the optical thickness, and the solar aureole intensity with lidar, a sunphotometer, and an aureolemeter. Inasmuch as the backscattering properties and the optical thickness depend on both the complex refractive index and the size distribution, whereas the forward-scattering properties depend mainly on the size distribution, real and imaginary indices of refraction and size distributions of aerosol are retrieved from these measurements. The real and the imaginary parts of the complex refractive index of an aerosol at a wavelength of 500 nm during the period from November 1991 to March 1992 obtained in Tsukuba, Japan, were estimated to be 1.46-1.48 and 0.005-0.014, respectively. It is inferred from the size distribution and an optical thickness fraction of stratospheric aerosols in the total columnar aerosols that these results reflect the influences of stratospheric aerosols that originated from the Mt. Pinatubo eruption.     

Determination of optical constants of thin films and multilayer stacks by use of concurrent reflectance, transmittance, and ellipsometric measurements

Using measurements of reflectance, transmittance, and the ellipsometric parameter D, we have determined the thickness, refractive index, and the absorption coefficient of various thin films and thin-film stacks. (D, the relative phase between the p- and s-polarized components, is measured for both reflected and transmitted light.) These optical measurements are performed with a specially designed system at the fixed wavelength of lambda = 633 nm over the 10 degrees -75 degrees range of angles of incidence. The examined samples, prepared by means of sputtering on fused-silica substrates, consist of monolayers and trilayers of various materials of differing thickness and optical constants. These samples, which are representative of the media of rewritable phase-change optical disks, include a dielectric mixture of ZnS and SiO(2), an amorphous film of the Ge(2)Sb(2.3)Te(5) alloy, and an aluminum chromium alloy film. To avoid complications arising from reflection and transmission losses at the air-substrate interface, the samples are immersed in an index-matching fluid that eliminates the contributions of the substrate to reflected and transmitted light. A computer program estimates the unknown parameters of the film(s) by matching the experimental data to theoretically calculated values. Although our system can be used for measurements over a broad range of wavelengths, we describe only the results obtained at lambda = 633 nm.     

Universal antireflection coatings for substrates for the visible spectral region

It is possible to design normal-incidence antireflection coatings that reduce the reflectance of any substrate with a refractive index that lies in the range of 1.48 to 1.75. The performance of such coatings depends on the width of the spectral region over which the reflectance is to be suppressed, on the coating materials used for their construction, and on the overall optical thickness of the layer system. For example, the calculated average spectral reflectance of a set of six different substrates with refractive indices 1.48, 1.55, 1.60, 1.65, 1.70, and 1.75, when coated with a 0.56-μm-thick, eight-layer antireflection coating designed for the 0.40-0.80-μm spectral region, was 0.34%. This is higher than the average reflectance that is attainable with a conventional antireflection coating of similar optical thicknesses designed for a particular refractive index. However, it is an acceptable value for most applications. With the universal type of antireflection coating described, it is thus possible to coat a number of different refractive-index substrates in one deposition run, and this can result in considerable cost and time savings.     

Reflectance optimization of inhomogeneous coatings with continuous variation of the complex refractive index

A model is derived for the reflectance optimization of an inhomogeneous coating made of absorbing materials. The model is applicable mainly for spectral regions where no transparent materials are available, such as in the extreme ultraviolet. The complex refractive index is assumed to take values within a given continuous domain and in a given sequence. The coating design is generated through a series of layer elements with a small refractive-index contrast across interfaces; the thickness of the element is calculated in terms of the refractive-index increment at the interface. The coating is optimized element by element starting from the substrate. When the refractive index varies both continuously and smoothly, the thickness element is of first order in the refractive-index increment. Suggestions are given on how to optimize a more general coating that alternates continuous and smooth refractive-index domains along with discrete indices, which results in a succession of inhomogeneous coatings and finite layers. An example is given to illustrate the model. A new material selection rule is obtained to discriminate whether the addition of a material on top of a partly grown coating will increase or decrease the reflectance of the coating. As a consequence, the model, which is highlighted toward the maximization of reflectance, can be used analogously for reflectance minimization such as for anti-reflection coatings.     

Thickness dependence of structural and optical properties of indium tin oxide nanofiber thin films prepared by electron beam evaporation onto quartz substrates

Indium tin oxide (ITO) thin films, produced by electron beam evaporation technique onto quartz substrates maintained at room temperature, are grown as nanofibers. The dependence of structural and optical properties of ITO thin films on the film thickness (99-662 nm) has been reported. The crystal structure and morphology of the films are investigated by X-ray diffraction and scanning electron microscope techniques, respectively. The particle size is found to increase with increasing film thickness without changing the preferred orientation along (2 2 2) direction. The optical properties of the films are investigated in terms of the measurements of the transmittance and reflectance determined at the normal incidence of the light in the wavelength range (250-2500 nm). The absorption coefficient and refractive index are calculated and the related optical parameters are evaluated. The optical band gap is found to decrease with the increase of the film thickness, whereas the refractive index is found to increase. The optical dielectric constant and the ratio of the free carrier concentration to its effective mass are estimated for the films.     

Absorption-coefficient-determination method for particulate materials

A method is presented for determining the optical absorption coefficient, or the imaginary refractive index, of particulate material that has been collected from aerosols or hydrosols by means of filtration. The method, based on the Kubelka-Munk theory of diffuse reflectance, is nondestructive and requires no other knowledge of the sample than the amount present, the specific gravity, and an estimate of the real index of refraction. The theoretical development of the method is discussed along with an analysis of photometric and gravimetric errors. We test the method by comparing results obtained for powdered didymium glass with measurements made before the glass was crushed. An example of the method's application to the determination of the absorption coefficient of atmospheric dust at UV, visible, and near-IR wavelengths is also presented.     

Optical and dielectric properties of double helix DNA thin films

In this work, the thin film of wheat DNA was deposited by spin-coating technique onto glass substrate, and the optical and dielectric properties of the double helix DNA thin film were investigated. The optical constants such as refractive index, extinction coefficient, dielectric constant, dissipation factor, relaxation time, and optical conductivity were determined from the measured transmittance spectra in the wavelength range 190–1100 nm. Meanwhile, the dispersion behavior of the refractive index was studied in terms of the single oscillator Wemple–DiDomenico (W–D) model, and the physical parameters of the average oscillator strength, average oscillator wavelength, average oscillator energy, the refractive index dispersion parameter and the dispersion energy were achieved. Furthermore, the optical band gap values were calculated by W–D model and Tauc model, respectively, and the values obtained from W–D model are in agreement with those determined from the Tauc model. The analysis of the optical absorption data indicates that the optical band gap E_g was indirect transitions. These results provide some useful references for the potential application of the DNA thin films in fiber optic, solar cell and optoelectronic devices.     

Optical properties of CeO<Subscript>2</Subscript> thin films

Cerium oxide (CeO₂) thin films have been prepared by electron beam evaporation technique onto glass substrate at a pressure of about 6 × 10⁻⁶ Torr. The thickness of CeO₂ films ranges from 140–180 nm. The optical properties of cerium oxide films are studied in the wavelength range of 200–850 nm. The film is highly transparent in the visible region. It is also observed that the film has low reflectance in the ultra-violet region. The optical band gap of the film is determined and is found to decrease with the increase of film thickness. The values of absorption coefficient, extinction coefficient, refractive index, dielectric constant, phase angle and loss angle have been calculated from the optical measurements. The X-ray diffraction of the film showed that the film is crystalline in nature. The crystallite size of CeO₂ films have been evaluated and found to be small. The experimental d-values of the film agreed closely with the standard values.     

Optical characterization of organic material bromoindium phthalocyanine thin films grown by electron beam evaporation

This paper presents the optical properties of organic material bromoindium phthalocyanine (BrInPc) thin films grown by electron beam evaporation technique. The paper describes the optical characteristics of BrInPc thin films, which have been determined using spectrophotometric measurements of the absorbance, transmittance and reflectance at normal incident of light in the spectral range 300–1,100 nm. The optical band gap energy and type of the electronic transition have been determined by analysis of spectral behavior of absorption coefficient, which reveals the probability of both direct and indirect transitions. Other optical constants, such as refractive index, extinction coefficient, complex dielectric constant and optical conductivity of thin films have been evaluated. Moreover, the width of band tails of localized states (Urbach energy), steepness parameter and width of the defect states have been determined by studying the absorption coefficient spectra just below the fundamental absorption edge.     

Vector wave analysis for nonnormal incident rays in epimicroscopic refractive index profile measurements

We have investigated the effects of nonnormal incident rays in calculating the refractive index profile of a dielectric sample using the reflectance measurement data obtained with a scanning confocal epimicroscope and also by solving three-dimensional vector wave equations for linearly polarized light. The numerically calculated reflection data of tightly focused Gaussian beams with different numerical apertures (NAs) on planar surfaces with various refractive indices confirm that the reflectance increases with an increase in the NA of a focusing objective lens. This is due to the nonnormal incident ray components of a Gaussian beam. We have found that the refractive index obtained with the assumption of a normal incident beam is far from the real value when the NA of a focusing lens becomes larger than 0.5, and thus the variation in the reflectance for different angular components in a Gaussian beam must be taken into consideration while using a larger NA lens. Errors in practical refractive index calculation for an optical fiber based on a normal incident beam in reflectance measurements can be as large as 1% in comparison to real values calculated by our three-dimensional vector wave equations.     

Estimation of the average residual reflectance of broadband antireflection coatings

We deal with optimal two-material antireflection (AR) coatings for the visible and adjacent spectral regions. It has been shown before that, for a given set of input parameters (refractive indices of the substrate, ambient medium and high- and low-index coating materials, and for a given spectral width of the AR coating), such designs consist of one or more clusters of layers of approximately constant optical thickness and number of layers. We show that, through the analysis of many different optimal coatings, it is possible to derive two parameters for a simple empirical expression that relates the residual average reflectance in the AR region to the number of clusters. These parameters are given for all possible combinations of relative spectral bandwidth equal to 2, 3, and 4; low-index to ambient-medium index ratio equal to 1.38 and 1.45; and high-to-low index ratio equal to 1.4, 1.5, and 1.7. The agreement between the numerically and the empirically calculated values of residual average reflectance is excellent. From the information presented the optical thin-film designer can quickly calculate the required number of layers and the overall optical thickness of an AR coating having the desired achievable residual average reflectance.     

Determination of the refractive index and thickness of holographic silver halide materials by use of polarized reflectances

A method to determine the refractive index and thickness of silver halide emulsions used in holography is presented. The emulsions are in the form of a layer of film deposited on a thick glass plate. The experimental reflectances of p-polarized light are measured as a function of the incident angles, and the values of refractive index, thickness, and extinction coefficient of the emulsion are obtained by using the theoretical equation for reflectance. As examples, five commercial holographic silver halide emulsions are analyzed. The procedure to obtain the measurements and the numerical analysis of the experimental data are simple, and agreement of the calculated reflectances, by use of the thickness and refractive index obtained, with the measured reflectances is satisfactory.     

Diffuse light propagation in a turbid medium with varying refractive index: Monte Carlo modeling in a spherically symmetrical geometry

We report on the development of Monte Carlo software that can model media with spatially varying scattering coefficient, absorption, and refractive index. The varying refractive index is implemented by calculating curved photon paths in the medium. The results of the numerical simulations are compared with analytical solutions obtained using the diffusion approximation. The model under investigation is a scattering medium that contains a spherically symmetrical inclusion (inhomogeneity) created by variation in optical properties and having no sharp boundaries. The following steady-state cases are considered: (a) a nonabsorbing medium with a spherically symmetrical varying refractive index, (b) an inclusion with varying absorption and scattering coefficients and constant refractive index, and (c) an inclusion with varying absorption, scattering, and refractive index. In the latter case it is shown that the interplay between the absorption coefficient and the refractive index may create the effect of a hidden inclusion.