Determination of specular reflectances in a liquid medium with a variable angle of incidence

We present a technique we developed to measure specular reflectances of mirrors immersed in liquids and in air. The method works with a broad range of angles of incidence (θ = 15-75°). The wavelength range used in this research was from 250 to 800 nm, and the state of polarization of the incident rays could be continuously varied with respect to the phase of incidence. The technique used in this study is based on a low-cost variable-angle reflectometer and a commercial spectrophotometer. Here we discuss the protocol we devised to extract reflectances with this instrument. This procedure was tested with samples that were measured through the use of ellipsometric techniques. The main advantages of the method discussed here are versatility, speed, and the availability of the equipment used; these are particularly useful for controlling the quality of a large number of samples. We present the results of reflectance measurements in water for dielectric coated aluminum intended for use in light concentrators for the Sudbury Neutrino Observatory. The error in our estimate of the overall reflectance, weighted over operational distributions of wavelength and incident angle, is ±3% for one sample and ±5% for the 2000 m(2) of coated material involved in this observatory.     

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.     

一种新型偏振分光棱镜的设计和应用

一种新型的偏振分光棱镜结构,实现了将偏振态相互垂直的光以不同的角度输入后合为一 束的功能,尤其能与双光纤准直器配合使用。通过计算说明二者角度可相互匹配,并分析了在准直器的角度加工出现小的偏差时,通过微量调节输入光束的方向能予以补偿。实验将该棱镜用于偏振光合束器和光学环行器等无源器件中取得了良好效果。     

Polarization effects on scatterer sizing accuracy analyzed with frequency-domain angle-resolved low-coherence interferometry

Angle-resolved low-coherence interferometry (a/LCI) enables us to make depth-resolved measurements of scattered light that can be used to recover subsurface structural information such as the size of cell nuclei. Endoscopic frequency-domain a/LCI (fa/LCI) acquires data by using a novel fiber probe in a fraction of a second, making it a clinically practical system. However, birefringent effects in fiber-based systems can alter the polarization state of the incident light and potentially skew the collected data. We analyze the effect the polarization state of the incident light has on scattering data collected from polystyrene microsphere tissue phantoms and in vitro cell samples and examine the subsequent accuracy of the determined sizes. It is shown that the endoscopic fa/LCI system accurately determines the size of polystyrene microspheres without the need to control the polarization of the incident beam, but that epithelial cell nuclear sizes are accurately determined only when the polarization state of the incident light is well characterized.     

Reflection and transmission of strongly focused light beams at a dielectric interface

The reflection and transmission of tightly focused azimuthally, radially and linearly polarized electromagnetic wave beams with subwavelength spot size and wavefront curvature at a dielectric interface are investigated. For a given wavefront radius, the existence of the optimal radius of beam spot corresponding to a minimal reflectance and maximal transmittance is shown. Significant lateral shift in the transmitted intensity peak is revealed for strongly focused azimuthally and radially polarized beams that are normally incident to an interface. The reflection and transmission of transverse-electric- and transverse-magnetic- polarized extremely narrow wave beams which are obliquely incident on the dielectric interface is analysed. Disappearance of the Brewster angle and total internal reflection effects for the strongly focused beams are predicted. The change in beam profile after reflection and transmission for different polarizations, incident beam spots and incidence angles are analysed.     

Source-optics polarization effects on ellipsometry analysis

Analytical expressions for the Fourier coefficients are presented that permit the effects of source polarization to be included in the analysis of ellipsometric data for the inference of the optical properties of bulk samples. The developed expressions are general and can be obtained for any ellipsometer system as long as the source-optics characteristics are known. In addition, no constraints are imposed on the angle of incidence of the light beam and on the polarizer/analyzer azimuthal angles. We obtained measurements on an amorphous carbon sample at a temperature of 25 °C and in the 400-700-nm wavelength range and analyzed the data using the discrete Fourier transform. Comparisons were carried out for the inferred refractive indices with and without the source-polarization effects. We show that for the source optics and sample used in this study the real part of the index increases by 1.5% when the source-optics parameters are included, whereas the imaginary part of the index decreases by as much as 12%. Thus the correction should not be neglected when accurate values for the indices are to be obtained from the complex ellipsometric parameters of the sample surface.     

Two-dimensional polarization encoding with a phase-only liquid-crystal spatial light modulator

We show how to two dimensionally encode the polarization state of an incident light beam using a parallel-aligned liquid-crystal spatial light modulator (LCSLM). Each pixel of the LCSLM acts as a voltage-controlled wave plate and can be programmed over a 2pi phase range at a wavelength of 514.5 nm. Techniques are reviewed for either rotating the major axis of elliptically polarized light or for converting an input linearly polarized beam into an arbitrary elliptically polarized beam. Experimental results are demonstrated in which we generate various two-dimensional spatial patterns of polarized light. Several potential applications are suggested. We also report an unexpected edge-enhancement effect that might be useful in image processing applications.     

Contours of constant minimum-reflectance and maximum-reflectance angles in the complex plane of a dielectric constant for incident light of arbitrary polarization

The reflectance of an absorbing medium for incident light of arbitrary polarization can exhibit two extrema at angles of incidence φ(max) and φ(min). The behavior of iso-φ(max) and iso-φ(min) contours in the complex plane of a dielectric constant for various incident polarizations is analyzed.     

Spectroscopic generalized ellipsometry based on fourier analysis

The extension of a spectroscopic ellipsometer that consists of a fixed polarizer, a rotating polarizer, a sample, and a fixed analyzer (PRPSE) to generalized ellipsometry to determining the generalized ellipsometric angles and the optical functions of an anisotropic medium is reported. The PRPSE configuration eliminates the polarization sensitivity of the light source. A general numerical technique has been derived to characterize the optical properties of the anisotropic material without intermediate generalized ellipsometric angles. The proposed method is experimentally verified for uniaxial mercuric iodide. The ordinary and the extraordinary refractive and absorption indices, respectively, N(o) = n(o)--ik(o) and N(e) = n(e)--ik(e), can be extracted directly from the Fourier coefficients measured by the PRPSE on a HgI(2) crystal face that contains the optical axis. The orientations of the optical axis with respect to the plane of incidence were also determined by direct analysis of the measured Fourier coefficients. Measurements were made of reflection across a spectral range of 1.5-4.13 eV at one angle of incidence (Phi = 70 degrees ) for several azimuths phi of the optical axis with respect to the plane of incidence. The generalized ellipsometric angles were obtained from numerical inversion by changes of both polarizer and analyzer azimuth angles P and A.     

Simultaneous measurement of surface geometry and material distribution by focusing ellipsotopometry

A new method for total surface measurement based on reflection ellipsometry is presented. By scanning the surface of the target under test with a focused laser beam, one can measure the surface topography and its material distribution simultaneously with high lateral resolution. Target topography is determined by ellipsometric measurement of local gradient angles gamma(x) and gamma(y) of the target's scanned surface elements. To identify the material, one measures the local complex refractive index n, too. The influence of beam focusing on the measurement results is discussed. We describe successful tests with various dielectric and metallic surfaces by use of He-Ne (632-nm) and He-Cd (442-nm) lasers.     

Depolarization and blurring of optical images by biological tissue

We present a study of the image blurring and depolarization resulting from the transmission of a narrow beam of light through a continuous random medium. We investigate the dependence of image quality degradation and of depolarization on optical thickness, correlation length of the inhomogeneities, and incident polarization state. This is done numerically with a Monte Carlo method based on a transport equation that takes into account polarization of light. We compare our results with those for transport in media with discrete spherical scatterers. We show that depolarization effects are different in these two models of biological tissue.     

Characterization of native and adsorbed thin films on silicon detector surfaces: static and kinetic applications

The photoelectric response of a windowless reflective silicon photodetector for obliquely incident polarized monochromatic light is used to characterize the native passivation dielectric thin film at the detector surface. In the presence of adsorption, the generated photoelectric signal becomes a function of the thickness and refractive index of the adsorbed layer. Higher sensitivity is achieved with s-polarized light and at incidence angles> 60 °. Furthermore, the passivation layer can be optimized for a specific adsorption experiment. A sensor of this kind is used to study the adsorption kinetics of H₂O at the detector surface and the results are interpreted by Bruggeman's effective medium theory. If a second detector is introduced to intercept the light reflected by the first detector, and the polarization of the incident light is modulated, analysis of output signals of this two-detector system determines the responsivity, absolute reflectances, and ellipsometric parameters of the first detector surface.     

White-light ellipsometer with geometric phase shifter

We describe a simple spectroscopic ellipsometer that uses a geometric phase shifter and a white-light source to generate a small number of phase-stepped intensities I(λ), which are recorded by a spectrometer. The ellipsometric angles ψ and Δ are easily calculated from these intensities at each wavelength simultaneously. We show that errors in Δ due to the nonideal behavior of the achromatic quarter-wave plate in the phase shifter can be made small by suitably adjusting the azimuth of the linearly polarized light incident on the sample. Two silicon dioxide films were measured with this instrument between 450 and 850?nm and yielded best fit film thicknesses of 1000.6±0.1 ? and 20.6±0.1 ?, in excellent agreement with those obtained using a commercial ellipsometer.     

Backscattering measurements from double-scale randomly rough surfaces

We present experimental measurements of light backscattered from double-scale randomly rough surfaces (oceanlike surfaces) with different statistical parameters illuminated at small and large angles of incidence. The surfaces are composed of a small-scale roughness superimposed on a slowly (large-scale) varying surface. The large-scale surfaces are diamond-machined periodic surfaces made on aluminum substrates and have either a sinusoidal or a Stokes wave profile. The small-scale roughness is added with lithographic techniques, and the surfaces are then gold coated. For a linearly polarized incident beam, it is found that the backscattered light is strongly depolarized mainly at small angles of incidence and strong shadowing effects are present for large angles of incidence (θ(inc) > 60°).     

Simulation of an absorption-based surface-plasmon resonance sensor by means of ellipsometry

Through numerical simulations, we point out that introduction of an ellipsometric measurement technique to an absorption-based surface-plasmon resonance (SPR) sensor enhances precision and sensitivity in measuring the imaginary part k of the complex refractive index of the sample. By measuring a pair of ellipsometric Delta-Psi parameters, instead of the conventional energy reflectance R(p) of p-polarized light in the Kretschmann optical arrangement, we can detect a small change of k that is proportional to that of the concentration of the sample, especially when k < 1. While one has difficulty in determining the value of k uniquely by the standard technique, when the thickness of Au under the prism is thin (20-30 nm), the ellipsometric technique (ET) overcomes the problem. Furthermore, the value of k and the thickness d(s) of the absorptive sample that is adsorbed on Au can be determined precisely. The ET based on the common-path polarization interferometer is robust against external disturbance such as mechanical vibration and intensity fluctuation of a light source. Although only the p-polarized light is responsible for the SPR phenomenon, we show that the introduction of the ET is significant for quantitative analysis.     

Beam splitter for a wide-angle Michelson Doppler imaging interferometer

The design and construction of a hexagonal interferometer beam splitting prism is described in which the light falls onto the all-dielectric partially reflecting coating at an angle of 300 with respect to the normal. For a beam that undergoes one transmission and one reflection by the device, the average effective transmittance 1/2 (T(parallel)R(parallel) + T(perpendicular)R(perpendicular)) in the 0.55-0.75-microm spectral region is approximately 0.23. This quantity is not strongly dependent on the plane of polarization of the incident light, nor on small changes of the angle of incidence from the design angle of 30 degrees. Ways to improve further the performance of the beam splitter are indicated. Coating designs for other angles of incidence are also given.     

Substrate noise in optical data-storage systems

Noise in optical disk readout has been examined for different polarizations of the incident beam. The disks studied are bare grooved glass substrates, having different groove shapes or differing jaggedness in the sidewalls. We perform measurements for the electric field of the incident laser beam parallel to the track and perpendicular to the track using both differential magneto-optical and conventional phase-change readout schemes. The incident beam of light is focused on the grooved surface of the (bare) substrate either through the substrate or directly from the air. Experiments reveal that the noise level is dependent on the state of polarization, the nature of the track (i.e., land or groove), and the medium of incidence. Surface roughness and sidewall jaggedness are two dominant contributors to the media noise in these substrates.     

Material sensitive scanning probe microscopy of subsurface semiconductor nanostructures via beam exit Ar ion polishing

Whereas scanning probe microscopy (SPM) is highly appreciated for its nanometre scale resolution and sensitivity to surface properties, it generally cannot image solid state nanostructures under the immediate sample surface. Existing methods of cross-sectioning (focused ion beam milling and mechanical and Ar ion polishing) are either prohibitively slow or cannot provide a required surface quality. In this paper we present a novel method of Ar ion beam cross-section polishing via a beam exiting the sample. In this approach, a sample is tilted at a small angle with respect to the polishing beam that enters from underneath the surface of interest and exits at a glancing angle. This creates an almost perfect nanometre scale flat cross-section with close to open angle prismatic shape of the polished and pristine sample surfaces ideal for SPM imaging. Using the new method and material sensitive ultrasonic force microscopy we mapped the internal structure of an InSb/InAs quantum dot superlattice of 18 nm layer periodicity with the depth resolution of the order of 5 nm. We also report using this method to reveal details of interfaces in VLSI (very large scale of integration) low k dielectric interconnects, as well as discussing the performance of the new approach for SPM as well as for scanning electron microscopy studies of nanostructured materials and devices.     

Simple holographic polarogram

A new technique capable of obtaining quantitative values of the rotation angle of the polarization vector by using holography is presented. This is a two-stage holographic process; during the recording stage a hologram of the object of interest is obtained. The reference beam is composed of two beams that form a small angle between them and keep their polarization states at right angles to each other. In the reconstruction stage of the hologram, two images from the hologram are obtained along two different angles. As a result of the interference between these two images, a set of parallel fringes is formed at the image plane. The fringe contrast on the reconstruction is related to the angle of the polarization vector of the light at each position on the image plane. Measurements of the rotation of the polarization angle of a fraction of a degree were obtained. The main application of this technique is in the study of transient phenomena, where single-shot measurements are the only means of obtaining reliable data.     

Interferometric back focal plane microellipsometry

We present a technique for ellipsometric analysis of materials with high lateral resolution. A Michelson-type phase-shifting interferometer measures the phase distribution in the back focal plane of a high numerical aperture objective. Local measurements of the ellipsometric parameter delta are performed over the entire spectrum of angles of incidence. We show that delta is to leading order linearly proportional to the phase change on reflection of normally incident light. We furthermore invert the Fresnel reflection equations and derive expressions for the real and imaginary parts of the refractive index as functions of the phase change on reflection and the reflectivity at normal incidence, both of which are measurable with the same apparatus. Hence we accomplish local measurements of the refractive indices of our samples. Determination of the phase change on reflection permits correction of interferometric topography measurements of heterogeneous specimens.