Determination of the optic axis and optical properties of absorbing uniaxial crystals by reflection perpendicularincidence ellipsometry on wedge samples

Given an arbitrarily cut uniaxial crystal wedge, a procedure is described using reflection perpendicular-incidence ellipsometry (PIE) for (1) locating the optic axis, and (2) determining the ordinary (No) and extraordinary (Ne) complex refractive indices. The optic axis is located by finding the principal directions of the two wedge faces and subsequently solving three spherical triangles. No and Ne are determined by two complex ratios of principal reflection coefficients (of light normally incident on and linearly polarized along the principal directions of each face) as measured by PIE. The solution for No and Ne is explicit but requires finding the roots of a sixth-degree algebraic equation in No

Mapping of Fresnel’s interface reflection coefficients between normal and oblique incidence: results for the parallel and perpendicular polarizations at several angles of incidence

The functions, w = ƒ(z), that describe the transformation of Fresnel’s reflection coefficients of parallel and perpendicularly polarized light between normal and oblique incidence, as well as their inverses, z = g(w), are studied in detail as conformal mappings between the complex z and w planes for angles of incidence of 15, 30, 45, 60, and 75°. New nomograms are obtained for the determination of optical properties of absorbing isotropic and anisotropic media from measurements of reflectances of s- or p-polarized light at normal and oblique incidence

Photodetector Arrangement for Measuring the State of Polarization of

A photopolarimeter for the simultaneous measurement of all four Stokes parameters of light. The light beam, the state of polarization of which is to be determined, strikes, at oblique angles of incidence, three photodetector surfaces in succession, each of which is partially specularly reflecting and each of which generates an electrical signal proportional to the fraction of the radiation it absorbs. A fourth photodetector is substantially totally light absorbtive and detects the remainder of the light. The four outputs thus developed form a 4x1 signal vector I which is linearly related, I=A S, to the input Stokes vector S. Consequently, S is obtained by S=A-1 I. The 4x4 instrument matrix A must be nonsingular, which requires that the planes of incidence for the first three detector surfaces are all different. For a given arangement of four detectors, A can be either computed or determined by calibration

Photodetector Arrangement for Measuring the State of Polarization of Light

An apparatus and method for the measurement of at least one parameter of the state of polarization of a light beam is described. The apparatus includes only a photo detector and no other optical elements. Thedetector surface is partially specularly re?ecting and intercepts the light beam at an oblique angle of incidence. The absorbed fraction of incident radiation produces a cor responding electrical output signal that is detected and from which the at least one parameter of the state of polarization can be determined; The detector may also be rotated to modulate the electrical output signal to determine the elliptic polarization of light except for handedness. A two detector ellipsometer is disclosed wherein light reflected from one detector is absorbed by the second detector and the entire system is rotated

Complex reflection coefficients of p- and s-polarized light at the pseudo-Brewster angle of a dielectric–conductor interface

The complex Fresnel reflection coefficients rp and rs of p- and s-polarized light and their ratio ρ = rp/rs at the pseudo-Brewster angle (PBA) φpBof a dielectric-conductor interface are evaluated for all possible values of the complex relative dielectric function Ε = |Ε| exp(-jθ) = Εr - jΕi, Εi \u3e 0 that share the same φpB. Complex-plane trajectories of rp, rs, and ρ at the PBA are presented at discrete values of φpB from 5° to 85° in equal steps of 5° as θ is increased from 0° to 180°. It is shown that for φpB \u3e 70° (high-reflectance metals in the IR) rp at the PBA is essentially pure negative imaginary and the reflection phase shift δp = arg(rp) &asyum; -90°. In the domain of fractional optical constants (vacuum UV or light incidence from a high-refractive-index immersion medium) 0 \u3c φpB \u3c 45° and rp is pure real negative (δp = π) when θ = tan-1 (√cos(2φpB)), and thecorresponding locus of Ε in the complex plane is obtained. In the limit of Εi = 0, Εr \u3c 0(interface between a dielectric and plasmonicmedium) thetotal reflection phase shifts δp, δs, Δ = δp - δs = arg(ρ) are also determined as functions of φpB

Inverting the ratio of the complex parallel and perpendicular reflection coefficients of an absorbing substrate using a transparent thin-film coating

An absorbing substrate can be coated with a transparent thin film of refractive index N1 (within a certain range) and thickness d such that the ratio of complex reflection coefficients for the p_and s polarizations of the film-covered substrate ρ = Rp/Rs is the inverse of that of the film-free substrate ρ¯ = R¯p/R¯s at an angle of incidence ø. A method to determine the relationship among ø, N1, and d that inverts ρ (i.e., makes ρ = 1/ρ¯) for a given substrate at a given wavelength is described and is applied to aluminum and silver substrates at 0.6328- and 10.6-μm wavelengths, respectively. Sensitivity of the inversion condition to incidence-angle and film-thickness errors is analyzed. ρ-inverting layers can be applied to one of the two metallic mirrors of a beam displacer or axicon to preserve the polarization state of incident monochromatic radiation

Diffraction Grating Photopolarimeters and Spectrophotopolarimeters

A division-of-amplitude photopolarimeter based on conical grating diffraction includes a diffraction grating and at least four photodetectors. An incident light beam is directed at the grating at an oblique incidence angl

Determination of the optic axis and optical properties of absorbing uniaxial crystals by reflection perpendicularincidence ellipsometry on wedge samples

Given an arbitrarily cut uniaxial crystal wedge, a procedure is described using reflection perpendicular-incidence ellipsometry (PIE) for (1) locating the optic axis, and (2) determining the ordinary (No) and extraordinary (Ne) complex refractive indices. The optic axis is located by finding the principal directions of the two wedge faces and subsequently solving three spherical triangles. No and Ne are determined by two complex ratios of principal reflection coefficients (of light normally incident on and linearly polarized along the principal directions of each face) as measured by PIE. The solution for No and Ne is explicit but requires finding the roots of a sixth-degree algebraic equation in No

Sensor for Rotational Velocity and Rotational Acceleration

Novel rotation sensors are disclosed. sensors with a temporal resolution of one measurement per rotation. A transparent or absorbing substrate can be coated with a transparent thin film to produce a linear response in reflectance versus angle of incidence over a certain range of angles. The best results were obtained when the incident light was s-polarized For example. a Si substrate coated with an SiO2 film was used in constructing a reflection rotation sensor. Experimental results and an error analysis of this rotation sensor are presented

Return-path, multiple-principal-angle, internal-reflection ellipsometer for measuring IR optical properties of aqueous solutions

A retroreflection (return-path) spectroscopic ellipsometer without a wave plate is described that uses an IR-transparent high-refractive-index hemicylindrical semiconductor substrate to measure the optical properties of aqueous solutions from multiple principal angles and multiple principal azimuths of attenuated internal reflection (AIR) at the semiconductor–solution interface. The pseudo-Brewster angle of minimum reflectance for the p polarization is also readily measured using the same instrument. This wealth of data can also be used to characterize thin films at the solid–liquid interface. Simulated results of AIR at the Si–water interface over the 1.2–11 μm IR spectral range are presented in support of this concept. The optical properties of water and aqueous solutions are important for modeling radiative transfer in the atmosphere and oceans and for biomedical and tissue optics