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Electrical Engineering Faculty Publications

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Articles 121 - 146 of 146

Full-Text Articles in Electrical and Electronics

Mapping Of Fresnel’S Interface Reflection Coefficients Between Normal And Oblique Incidence: Results For The Parallel And Perpendicular Polarizations At Several Angles Of Incidence, Rasheed M.A. Azzam Oct 1980

Mapping Of Fresnel’S Interface Reflection Coefficients Between Normal And Oblique Incidence: Results For The Parallel And Perpendicular Polarizations At Several Angles Of Incidence, Rasheed M.A. Azzam

Electrical Engineering Faculty Publications

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.

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Determination Of The Optic Axis And Optical Properties Of Absorbing Uniaxial Crystals By Reflection Perpendicularincidence Ellipsometry On Wedge Samples, Rasheed M.A. Azzam Sep 1980

Determination Of The Optic Axis And Optical Properties Of Absorbing Uniaxial Crystals By Reflection Perpendicularincidence Ellipsometry On Wedge Samples, Rasheed M.A. Azzam

Electrical Engineering Faculty Publications

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 N …

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Inversion Of The Nonlinear Equations Of Reflection Ellipsometry For Uniaxial Crystals In Symmetrical Orientations, M. Elshazly-Zaghloul, R. M.A. Azzam Jul 1980

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.

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Direct Relation Between Fresnel’S Interface Reflection Coefficients For The Parallel And Perpendicular Polarizations, R. M.A. Azzam Jul 1979

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 …

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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 Jun 1979

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.

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Transformation Of Fresnel’S Interface Reflection And Transmission Coefficients Between Normal And Oblique Incidence, R. M.A. Azzam Apr 1979

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 …

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Reflection Of An Electromagnetic Plane Wave With 0 Or Π Phase Shift At The Surface Of An Absorbing Medium, R. M.A. Azzam Mar 1979

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.

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Principal Angle, Principal Azimuth, And Principal-Angle Ellipsometry Of Film-Substrate Systems, R. M.A. Azzam, A.-R. M. Zaghloul Dec 1978

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 …

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Propagation Of Partially Polarized Light Through Anisotropic Media With Or Without Depolarization: A Differential 4 × 4 Matrix Calculus, R. M.A. Azzam Dec 1978

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 …

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Consequences Of Light Reflection At The Interface Between Two Transparent Media Such That The Angle Of Refraction Is 45°, R. M.A. Azzam Nov 1978

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 …

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Simulation Of Mechanical Rotation By Optical Rotation: Application To The Design Of A New Fourier Photopolarimeter, R. M.A. Azzam Apr 1978

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 …

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Generalized Ellipsometry Based On Azimuth Measurements Alone, R. M.A. Azzam Apr 1978

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 …

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Single-Element Rotating-Polarizer Ellipsometer For Film-Substrate Systems, A.-R. M. Zaghloul, R. M.A. Azzam Sep 1977

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.

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Sio2-Si Film-Substrate Reflection Polarizers For Different Mercury Spectral Lines, A.-R. M. Zaghloul, R. M.A. Azzam Jun 1977

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.

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Ellipsometer Nulling: Convergence And Speed, Rasheed M.A. Azzam, D. L. Confer, N. M. Bashara Oct 1976

Ellipsometer Nulling: Convergence And Speed, Rasheed M.A. Azzam, D. L. Confer, N. M. Bashara

Electrical Engineering Faculty Publications

The process of nulling in ellipsometry is studied by a graphical presentation using the trajectories of two significant polarization states in the complex plane, XPC and XSA. These states are determined by (1) the polarizer and compensator (XPC) and (2) the specimen and the analyzer (XSA) in the polarizer-compensator-specimen-analyzer ellipsometer arrangement. As the azimuth angles of the ellipsometer elements are varied, XPC and XSA move closer to one another in a stepwise fashion until they coincide when a null is reached. Thus, at null, the polarization states are matched, and XPC = XSA. For …

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Frequency-Mixing Detection (Fmd) Of Polarization-Modulated Light, R. M.A. Azzam Jul 1976

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 …

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Modulated Generalized Ellipsometry, R. M.A. Azzam Jun 1976

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 …

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Design Of Film-Substrate Single-Reflection Linear Partial Polarizers, R. M.A. Azzam, A.-R. M. Zaghloul, N. M. Bashara Dec 1975

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.

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Polarizer-Surface-Analyzer Null Ellipsometry For Film-Substrate Systems, R. M.A. Azzam, A.-R. M. Zaghloul, N. M. Bashara Dec 1975

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 …

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Design Of Film—Substrate Single-Reflection Retarders, A.-R. M. Zaghloul, R. M.A. Azzam, N. M. Bashara Sep 1975

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 …

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Combined Reflection And Transmission Thin-Film Ellipsometry: A Unified Linear Analysis, Rasheed M.A. Azzam, M. Elshazly-Zaghloul, N. M. Bashara Jul 1975

Combined Reflection And Transmission Thin-Film Ellipsometry: A Unified Linear Analysis, Rasheed M.A. Azzam, M. Elshazly-Zaghloul, N. M. Bashara

Electrical Engineering Faculty Publications

A scheme of combined reflection and transmission ellipsometry on light-transmitting ambient-film-substrate systems is proposed and the required sample design and instrument operation are investigated. A comparative study of the sensitivity of external and internal reflection and transmission ellipsometry is carried out based on unified linear approximations of the exact equations. These approximations are general in that an arbitrary initial film thickness is assumed. They are simple, because a complex sensitivity function is introduced whose real and imaginary projections determine the psi (Ψ) and delta (Δ) sensitivity factors. Among the conclusions of this paper are the following. (1) External reflection ellipsometry …

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Application Of Generalized Ellipsometry To Anisotropic Crystals, R. M.A. Azzam, N. M. Bashara Apr 1975

Application Of Generalized Ellipsometry To Anisotropic Crystals, R. M.A. Azzam, N. M. Bashara

Electrical Engineering Faculty Publications

No abstract provided.

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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 Mar 1975

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. …

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Trajectories Describing The Evolution Of Polarized Light In Homogeneous Anisotropic Media And Liquid Crystals, Rasheed M.A. Azzam, N. M. Bashara, B. E. Merrill Apr 1973

Trajectories Describing The Evolution Of Polarized Light In Homogeneous Anisotropic Media And Liquid Crystals, Rasheed M.A. Azzam, N. M. Bashara, B. E. Merrill

Electrical Engineering Faculty Publications

Trajectories are given that describe the evolution of the ellipse of polarization in the complex plane for light propagating in a homogeneous anisotropic medium and along the helical axis of a cholesteric liquid crystal. For the general homogeneous anisotropic medium that exhibits combined birefringence and dichroism the trajectory is a spiral that converges to the low-absorption eigenpolarization. For pure birefringence the trajectory becomes a complete circle that encloses one eigenpolarization, whereas for pure dichroism the trajectory becomes an arc of a circle that ends at the low-absorption eigenstate. The case of a cholesteric (or twisted nematic) liquid crystal leads to …

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Loci Of Invariant-Azimuth And Invariant-Ellipticity Polarization States Of An Optical System, Rasheed M.A. Azzam, N. M. Bashara Jan 1973

Loci Of Invariant-Azimuth And Invariant-Ellipticity Polarization States Of An Optical System, Rasheed M.A. Azzam, N. M. Bashara

Electrical Engineering Faculty Publications

The loci of polarization states for which either the ellipticity alone or the azimuth alone remains invariant upon passing through an optical system are introduced. The cartesian equations of these two loci are derived in the complex plane in which the polarization states are represented. The equations are quartic and are conveniently expressed in terms of the elements of the Jones. matrix of the optical system. As an exple the loci are determined for a system composed of a π/4 rotator followed by a quarter-wave retarder.

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Analogy Between Linear Optical Systems And Linear Two-Port Electrical Networks, Rasheed M.A. Azzam, N. M. Bashara Oct 1972

Analogy Between Linear Optical Systems And Linear Two-Port Electrical Networks, Rasheed M.A. Azzam, N. M. Bashara

Electrical Engineering Faculty Publications

Attention is called to the analogy between linear optical systems and linear two-port electrical networks. For both, the transformation of a pair of oscillating quantities between input and output is of interest. The mapping of polarization by an optical system and of impedance (admittance) by a two-port network is described by a bilinear transformation. Therefore for each transfer property of a system of one type, there is a similar property for the system of the other type. Two-port electrical networks are synthesized whose impedance-(or admittance-) mapping properties are the same as the polarization-mapping properties of a given optical system. The …

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