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Articles 61 - 82 of 82
Full-Text Articles in Physics
Constant-Psi Constant-Delta Contour Maps: Applications To Ellipsometry And To Reflection-Type Optical Devices, A.-R. M. Zaghloul, R. M.A. Azzam
Constant-Psi Constant-Delta Contour Maps: Applications To Ellipsometry And To Reflection-Type Optical Devices, A.-R. M. Zaghloul, R. M.A. Azzam
Electrical Engineering Faculty Publications
Constant-psi constant-delta contour maps in the reduced angle-of-incidence-film-thickness plane that are useful in ellipsometry and in design of reflection-type optical devices are discussed. As a specific example, a contour map is given for the SiO2-Si film-substrate system at the 6328-Å He-Ne laser wavelength.
Contours Of Constant Principal Angle And Constant Principal Azimuth In The Complex Ε Plane, R. M.A. Azzam
Contours Of Constant Principal Angle And Constant Principal Azimuth In The Complex Ε Plane, R. M.A. Azzam
Electrical Engineering Faculty Publications
For light reflection at a planar interface between two homogeneous isotropic media with complex relative dielectric function ε, we show that the constant-principal-angle contours are a family of semicircles, whereas the constantprincipal-azimuth contours are a family of (segments of) hyperbolas in the complex ε plane. We also find the exact envelope curve of both families and hence determine the domain of the ε plane of multiple (three) principal angles that is bougded by the envelope curve and the real axis. A unique and peculiar interface with ε = (5 - j√2)/27 is shown to have three coincident principal angles of …
Explicit Determination Of Thickness Of A Transparent Film On A Transparent Substrate From Angles Of Incidence Of Equal P And S Reflectivities, R. M.A. Azzam
Electrical Engineering Faculty Publications
No abstract provided.
Inversion Of The Nonlinear Equations Of Reflection Ellipsometry For Uniaxial Crystals In Symmetrical Orientations, M. Elshazly-Zaghloul, R. M.A. Azzam
Inversion Of The Nonlinear Equations Of Reflection Ellipsometry For Uniaxial Crystals In Symmetrical Orientations, M. Elshazly-Zaghloul, R. M.A. Azzam
Electrical Engineering Faculty Publications
The complex ordinary (No) and extraordinary (Ne) refractive indices of an absorbing uniaxial crystal can be determined using reflection ellipsometry. The measurements are taken with the optic axis parallel and perpendicular to the crystal’s surface. The equations obtained are solved without resort to iterative methods; No and Ne are determined separately. Sixteen solution sets (No, Ne) are obtained and the correct solution can be easily identified. We present an optimum angle of incidence that minimizes the relative errors in No and Ne.
Direct Relation Between Fresnel’S Interface Reflection Coefficients For The Parallel And Perpendicular Polarizations, R. M.A. Azzam
Direct Relation Between Fresnel’S Interface Reflection Coefficients For The Parallel And Perpendicular Polarizations, R. M.A. Azzam
Electrical Engineering Faculty Publications
We have found a significant relation, rp = rs (rs -cos2ϕ)/(1-rs cos2ϕ), between Fresnel’s interface complex-amplitude reflection coefficients rp and rs for the parallel (p) and perpendicular (s) polarizations at the same angle of incidence ϕ. This relation is universal in that it applies to reflection at all interfaces between homogeneous isotropic media collectively and, of course, throughout the electromagnetic spectrum. We investigate the properties of this function, rp = f (rs), and its inverse,rs = g (rp), as …
Relations Between Amplitude Reflectances And Phase Shifts Of The P And S Polarizations When Electromagnetic Radiation Strikes Interfaces Between Transparent Media, R. M.A. Azzam
Electrical Engineering Faculty Publications
No abstract provided.
Transformation Of Fresnel’S Interface Reflection And Transmission Coefficients Between Normal And Oblique Incidence, R. M.A. Azzam
Transformation Of Fresnel’S Interface Reflection And Transmission Coefficients Between Normal And Oblique Incidence, R. M.A. Azzam
Electrical Engineering Faculty Publications
If w denotes an interface Fresnel reflection or transmission coefficient for s- or p-polarized light at an oblique angle of incidence ø, and z denotes the same coefficient at normal incidence, we find that w is an analytic function of z, w = ƒ(z), that depends on ø but not on the specific optical properties of the two media on both sides of the interface. All four functions that correspond to the four distinct Fresnel coefficients and their inverses are determined. We single out for detailed examination, as an example, the relationship between the reflection of s -polarized light at …
Reflection Of An Electromagnetic Plane Wave With 0 Or Π Phase Shift At The Surface Of An Absorbing Medium, R. M.A. Azzam
Reflection Of An Electromagnetic Plane Wave With 0 Or Π Phase Shift At The Surface Of An Absorbing Medium, R. M.A. Azzam
Electrical Engineering Faculty Publications
An electromagnetic plane wave incident obliquely from a transparent medium onto the surface of an absorbing medium can be reflected with 0 or π phase shift if (i) the wave is p (TM) polarized, and (ii) the complex relative dielectric function ε is such that 0 ≤|ε| 2/2Re(ε) ≤ 1. Furthermore, the locus of ε such that the reflection coefficient for the p polarization is real at the same angle of incidence, is a circle, and that of ε½ (the complex relative refractive index) is Bernoulli’s lemniscate.
Principal Angle, Principal Azimuth, And Principal-Angle Ellipsometry Of Film-Substrate Systems, R. M.A. Azzam, A.-R. M. Zaghloul
Principal Angle, Principal Azimuth, And Principal-Angle Ellipsometry Of Film-Substrate Systems, R. M.A. Azzam, A.-R. M. Zaghloul
Electrical Engineering Faculty Publications
When the film thickness is considered as a parameter, a system composed of a transparent film on an absorbing substrate (in a transparent ambient) is characterized by a range of principal angle ø¯min ≤ ø¯ ≤ ø¯max over which the associated principal azimuth ψ¯ varies between 0° and 90° (i.e., 0° ≤ ψ¯ ≤ 90°) and the reflection phase difference Δ assumes either one of the two values: +π/2 or −π/2. We determine the principal angle ø¯(d) and principal azimuth ψ¯(d) as functions of film thickness d for the vacuum-SiO2-Si system at …
Propagation Of Partially Polarized Light Through Anisotropic Media With Or Without Depolarization: A Differential 4 × 4 Matrix Calculus, R. M.A. Azzam
Propagation Of Partially Polarized Light Through Anisotropic Media With Or Without Depolarization: A Differential 4 × 4 Matrix Calculus, R. M.A. Azzam
Electrical Engineering Faculty Publications
We extend the scope of the Mueller calculus to parallel that established by Jones for his calculus. We find that the Stokes vector S of a light beam that propagates through a linear depolarizing anisotropic medium obeys the first-order linear differential equation dS/dz = mS, where z is the distance traveled along the direction of propagation and m is a 4 × 4 real matrix that summarizes the optical properties of the medium which influence the Stokes vector. We determine the differential matrix m for eight basic types of optical behavior, find its form for the most general anisotropic nondepolarizing …
Consequences Of Light Reflection At The Interface Between Two Transparent Media Such That The Angle Of Refraction Is 45°, R. M.A. Azzam
Consequences Of Light Reflection At The Interface Between Two Transparent Media Such That The Angle Of Refraction Is 45°, R. M.A. Azzam
Electrical Engineering Faculty Publications
The reflection of light at the interface between two transparent, homogeneous and optically isotropic media such that the angle of refraction is 45° has the following interesting consequences: (i) the interface relfectivity for the parallel (p) polarization is the square of that for the perpendicular (s) polarization; (ii) the angular deviation of the propagation direction upon refraction is equal to the polarization (or ellipsometric) angle ψ and (iii) the complex reflection coefficient for the ppolarization is stationary, in both magnitude and phase, with respect to small charges of the (refractive and/or absorptive) optical properties of …
Generalized Ellipsometry Based On Azimuth Measurements Alone, R. M.A. Azzam
Generalized Ellipsometry Based On Azimuth Measurements Alone, R. M.A. Azzam
Electrical Engineering Faculty Publications
We investigate the azimuth response function, θo = f(θi), of a linear nondepolarizing optical system S, whereθi and θo, are the azimuths (orientations) of the generally elliptic vibrations of totally polarized light at the input and output of S. We find that the azimuth response function depends on five of the six parameters that specify the normalized circular Jones matrix of the optical system. Thus the entire polarization response of an optical system can be nearly completely reconstructed from its azimuth response alone. Five input-output azimuth measurements (θik, θok), k …
Simulation Of Mechanical Rotation By Optical Rotation: Application To The Design Of A New Fourier Photopolarimeter, R. M.A. Azzam
Simulation Of Mechanical Rotation By Optical Rotation: Application To The Design Of A New Fourier Photopolarimeter, R. M.A. Azzam
Electrical Engineering Faculty Publications
The mechanical rotation of an optical element around the axis of a beam of polarized light can be easily simulated by using the phenomenon of optical rotation. Because optical rotation can be magnetically or electrically induced, virtually any kind of mechanical rotation can be mimicked. This interesting principle is applied to the design of a new Fourier photopolarimeter that uses an oscillating-azimuth retarder (OAR). The OAR consists of a quarter-wave plate surrounded by two ac-excited Faraday cells that produce equal and opposite sinusoidal optical rotations. Analysis of the operation of this polarimeter of no moving parts proves its ability to …
Single-Element Rotating-Polarizer Ellipsometer For Film-Substrate Systems, A.-R. M. Zaghloul, R. M.A. Azzam
Single-Element Rotating-Polarizer Ellipsometer For Film-Substrate Systems, A.-R. M. Zaghloul, R. M.A. Azzam
Electrical Engineering Faculty Publications
A novel and very simple ellipsometer for the characterization of film-substrate systems that employs one rotating optical element (a polarizer) is proposed. The ellipsometer is based on detecting the angles of incidence at which a film-substrate system has equal amplitude attenuations for light polarized parallel (p) and perpendicular (s) to the plane of incidence. At a certain wavelength, the film thickness of the filmsubstrate system has to lie within permissible-thickness bands (PTB) for the technique to apply.
Sio2-Si Film-Substrate Reflection Polarizers For Different Mercury Spectral Lines, A.-R. M. Zaghloul, R. M.A. Azzam
Sio2-Si Film-Substrate Reflection Polarizers For Different Mercury Spectral Lines, A.-R. M. Zaghloul, R. M.A. Azzam
Electrical Engineering Faculty Publications
No abstract provided.
Frequency-Mixing Detection (Fmd) Of Polarization-Modulated Light, R. M.A. Azzam
Frequency-Mixing Detection (Fmd) Of Polarization-Modulated Light, R. M.A. Azzam
Electrical Engineering Faculty Publications
When a light beam whose polarization and intensity are weakly modulated at a frequency ωm passes through a periodic analyzer of frequency ωa(<ωm) and the transmitted flux is linearly detected, the resulting total signal St consists of two components: (i) a periodic baseband signal Sbb with harmonics of frequencies nωa (n = 0,1,2,…) and (ii) an amplitude-modulated-carrier signal δSmc with center (carrier) frequency ωm and sideband frequencies at ωm ± nωa(n = 1,2,…). In this paper we show that the average polarization of the beam is determined …ω
Modulated Generalized Ellipsometry, R. M.A. Azzam
Modulated Generalized Ellipsometry, R. M.A. Azzam
Electrical Engineering Faculty Publications
We extend ellipsometry to the direct measurement of small perturbations of the Jones matrix of any linear nondepolarizing optical sample (system) subjected to a modulating stimulus such as temperature, stress, or electric or magnetic field. The methodology of this technique, to be called Modulated Generalized Ellipsometry (MGE), is presented. First an ellipsometer with arbitrary polarizing and analyzing optics is assumed, and subsequently the discussion is specialized to a conventional ellipsometer having either the polarizer-sample-analyzer (PSA) or the polarizer-compensator-sample-analyzer (PCSA) arrangement. MGE provides the tool for the systematic study of thermo-optical, piezo-optical, electro-optical, magneto-optical, and other allied effects for both isotropic …
Design Of Film-Substrate Single-Reflection Linear Partial Polarizers, R. M.A. Azzam, A.-R. M. Zaghloul, N. M. Bashara
Design Of Film-Substrate Single-Reflection Linear Partial Polarizers, R. M.A. Azzam, A.-R. M. Zaghloul, N. M. Bashara
Electrical Engineering Faculty Publications
The results of a preceding paper [J. Opt. Soc. Am. 65, 1464,(1975)] are viewed from a different angleas providing the basis for the design of film-substrate single-reflection linear partial polarizers (LPP),which also operate as reflection optical rotators. The important characteristics of a comprehensive set of discrete designs of SiO2-Si LPP’s at λ = 6328 Å are shown graphically.
Polarizer-Surface-Analyzer Null Ellipsometry For Film-Substrate Systems, R. M.A. Azzam, A.-R. M. Zaghloul, N. M. Bashara
Polarizer-Surface-Analyzer Null Ellipsometry For Film-Substrate Systems, R. M.A. Azzam, A.-R. M. Zaghloul, N. M. Bashara
Electrical Engineering Faculty Publications
Single-pass polarizer-surface-analyzer null ellipsometry (PSA-NE) can be used to characterize film-substrate systems, provided that the film thickness lies within one of a set of permissible-thickness bands (PTB). For a transparent film on a transparent or absorbing substrate, the PTB structure consists of a small number of finite-bandwidth bands followed by a continuum band that extends from a film thickness of about half the wavelength of light to infinity. We show that this band structure is a direct consequence of the periodicity of the ellipsometric function ρ (the ratio Rp/Rs, of the complex amplitude-reflection coefficients for …
Design Of Film—Substrate Single-Reflection Retarders, A.-R. M. Zaghloul, R. M.A. Azzam, N. M. Bashara
Design Of Film—Substrate Single-Reflection Retarders, A.-R. M. Zaghloul, R. M.A. Azzam, N. M. Bashara
Electrical Engineering Faculty Publications
The design steps for film—substrate single-reflection retarders are briefly stated and applied to the SiO2—Si film—substrate system at wavelength 6328 Å. The criterion of minimum-maximum error of the ellipsometric angle ψ is used to choose angle-of-incidence-tunable designs. Use is made of the (Φ-d) plane (angle of incidence versus thickness) to determine whether a given film—substrate system with known optical properties and film thickness can operate as a reflection retarder and to determine the associated angles of incidence and retardation angles. This leads to the concept of permissible-thickness bands and forbidden gaps for operation of a film—substrate …
Application Of Generalized Ellipsometry To Anisotropic Crystals, R. M.A. Azzam, N. M. Bashara
Application Of Generalized Ellipsometry To Anisotropic Crystals, R. M.A. Azzam, N. M. Bashara
Electrical Engineering Faculty Publications
No abstract provided.
Ellipsometric Function Of A Film-Substrate System: Applications To The Design Of Reflection-Type Optical Devices And To Ellipsometry, R. M.A. Azzam, A.-R. M. Zaghloul, N. M. Bashara
Ellipsometric Function Of A Film-Substrate System: Applications To The Design Of Reflection-Type Optical Devices And To Ellipsometry, R. M.A. Azzam, A.-R. M. Zaghloul, N. M. Bashara
Electrical Engineering Faculty Publications
The ratio ρ = Rp/Rs of the complex amplitude-reflection coefficients Rp and Rs for light polarized parallel (p) and perpendicular (s) to the plane of incidence, reflected from an optically isotropic film-substrate system, is investigated as a function of the angle of incidence ϕ and the film thickness d. Both constant-angle-of-incidence contours (CAIC) and constant-thickness contours (CTC) of the ellipsometric function ρ(ϕ,d) in the complex ρ plane are examined. For transparent films, ρ(ϕ,d) is a periodic function of d with period Dϕ that is a function of ϕ. …