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Articles 31 - 60 of 92
Full-Text Articles in Physics
Angular Range For Reflection Of P-Polarized Light At The Surface Of An Absorbing Medium With Reflectance Below That At Normal Incidence, R. M.A. Azzam, Ericson E. Ugbo
Angular Range For Reflection Of P-Polarized Light At The Surface Of An Absorbing Medium With Reflectance Below That At Normal Incidence, R. M.A. Azzam, Ericson E. Ugbo
Electrical Engineering Faculty Publications
The range of incidence angle, 0 < φ < φe, over which p-polarized light is reflected at interfaces between transparent and absorbing media with reflectance below that at normal incidence is determined. Contours of constant φe in the complex plane of the relative dielectric constant ε are presented. A method for determining the real and imaginary parts of the complex refractive index, ε1/2 = n + jk, which is based on measuring φe and the pseudo-Brewster angle φpB, is viable in the domain of fractional optical constants, n, k < 1.
Tilted Bilayer Membranes As Simple Transmission Quarter-Wave Retardation Plates, R. M.A. Azzam, Fadi A. Mahmoud
Tilted Bilayer Membranes As Simple Transmission Quarter-Wave Retardation Plates, R. M.A. Azzam, Fadi A. Mahmoud
Electrical Engineering Faculty Publications
A tilted bilayer membrane, which consists of two thin films of transparent optically isotropic materials of different refractive indices, can function as a transmission quarter-wave retarder (QWR) at a high angle of incidence. A specific design using a cryolite-Si membrane in the infrared is presented, and its tolerances to small shifts of wavelength, incidence angle, and film thickness errors are discussed. Some designs provide a dual QWR in transmission and reflection. Such devices provide simple linear-to-circular (and circular-to-linear) polarization transformers. Bilayer eighth-wave retarders without diattenuation are also introduced.
Differential Reflection Phase Shift Under Conditions Of Attenuated Internal Reflection, R. M.A. Azzam
Differential Reflection Phase Shift Under Conditions Of Attenuated Internal Reflection, R. M.A. Azzam
Electrical Engineering Faculty Publications
The angle-of-incidence dependence of the differential reflection phase shift Δ between p and s polarizations is considered a function of the real and imaginary parts of the relative complex dielectric function ε of an interface in the domain of fractional optical constants, i.e., under conditions of internal reflection. The constraint on complex ε such that oscillatory and monotonic angular responses are obtained is determined. A sensitive and stable technique, which is based on attenuated internal reflection ellipsometry between the Brewster angle and the critical angle, is proposed for measuring small induced absorption (εi∼10−5) in the medium …
Single-Layer-Coated Surfaces With Linearized Reflectance Versus Angle Of Incidence: Application To Passive And Active Silicon Rotation Sensors, R. M.A. Azzam, M. M. K. Howlader, T. Y. Georgiou
Single-Layer-Coated Surfaces With Linearized Reflectance Versus Angle Of Incidence: Application To Passive And Active Silicon Rotation Sensors, R. M.A. Azzam, M. M. K. Howlader, T. Y. Georgiou
Electrical Engineering Faculty Publications
A transparent or absorbing substrate can be coated with a transparent thin film to produce a linear reflectanceversus- angle-of-incidence response over a certain range of angles. Linearization at and near normal incidence is a special case that leads to a maximally flat response for p-polarized, s-polarized, or unpolarized light. For midrange and high-range linearization with moderate and high slopes, respectively, the best results are obtained when the incident light is s polarized. Application to a Si substrate that is coated with a SiO2 film leads to novel passive and active reflection rotation sensors. Experimental results and an error analysis …
Direct Relation Between Fresnel's Interface Reflection Coefficients For The Parallel And Perpendicular Polarizations: Erratum 2, R. M.A. Azzam
Direct Relation Between Fresnel's Interface Reflection Coefficients For The Parallel And Perpendicular Polarizations: Erratum 2, R. M.A. Azzam
Electrical Engineering Faculty Publications
The record is set straight concerning two equations that determine the reflection phase shifts at a single interface from the intensity reflectances forp- and s-polarized light at one angle of incidence. These equations appeared previously in this journal [J. Opt. Soc. Am. 69, 1007 (1979); erratum, J. Opt. Soc. Am. 70, 261 (1980)].
Photopolarimeter Based On Planar Grating Diffraction, R. M.A. Azzam, K. A. Giardina
Photopolarimeter Based On Planar Grating Diffraction, R. M.A. Azzam, K. A. Giardina
Electrical Engineering Faculty Publications
A division-of-amplitude photopolarimeter (DOAP) is described that employs a diffraction grating in the conventional spectrometer orientation with the grating grooves normal to the plane of incidence. Four coplanar diffracted orders are used for polarimetric analysis to determine all four Stokes parameters of incident light simultaneously and virtually instantaneously (with the speed being determined solely by the photodetectors and their associated electronics); a fifth order is used for alignment by autocollimation or by use of a position-sensing quadrant detector. To sensitize the instrument for the +45° and -45° azimuths of incident linearly polarized light and for the handedness of incident circular …
Limaçon Of Pascal Locus Of The Complex Refractive Indices Of Interfaces With Maximally Flat Reflectance-Versus-Angle Curves For Incident Unpolarized Light, R. M.A. Azzam
Electrical Engineering Faculty Publications
For an interface between two isotropic media the power reflectance Rv (ø) is an even function, Rv (ø) = Rv (--), of the angle of incidence ø; hence all the odd derivatives, Rv(n) = dn Rv /døn (n odd), are identically 0 at ø = 0, independent of the incident polarization v. When the incident light is unpolarized (v = u), the second derivative, Ru(2), is also 0 at ø = 0, so that the flatness of the Ru -versus-ø curve …
Principal Linear Polarization States Of An Optical System, R. M.A. Azzam
Principal Linear Polarization States Of An Optical System, R. M.A. Azzam
Electrical Engineering Faculty Publications
The constraint on the Jones matrix of an optical system such that there exist two linear polarization states at its input that are mapped onto two corresponding linear states at its output is derived. These principal linear polarization (PLP) states, which characterize a broad range of systems, are also found in terms of the Jones matrix elements. Special cases when the PLP states are orthogonal, collapse onto one state, or become infinite in number are indicated. For a deterministic or nondeterministic optical system described by a Mueller matrix, the existence of two PLP states places a constraint on only 3 …
Instrument Matrix Of The Four-Detector Photopolarimeter: Physical Meaning Of Its Rows And Columns And Constraints On Its Elements, R. M.A. Azzam
Instrument Matrix Of The Four-Detector Photopolarimeter: Physical Meaning Of Its Rows And Columns And Constraints On Its Elements, R. M.A. Azzam
Electrical Engineering Faculty Publications
The four-detector photopolarimeter (FDP) is an arrangement of four photodetectors for measuring the state of polarization of light. The output current vector I of the FDP is related to the input Stokes vector S by I = AS, where A is the instrument matrix. The rows of A can be viewed as projection operators that determine the output currents of the detectors. This leads to the recognition of four special totally polarized input states, each of which maximizes the output of one detector. The associated four orthogonal states produce minimum signals. Because each detector is absorptive and its output is …
Accurate Calibration Of The Four-Detector Photopolarimeter With Imperfect Polarizing Optical Elements, R. M.A. Azzam, Ali G. Lopez
Accurate Calibration Of The Four-Detector Photopolarimeter With Imperfect Polarizing Optical Elements, R. M.A. Azzam, Ali G. Lopez
Electrical Engineering Faculty Publications
The first three columns of the instrument matrix A of the four-detector photopolarimeter (FDP) are determined by Fourier analysis of the output current vector I(P) as a function of the azimuth angle P of the incident linearly polarized light. Therefore 12 of the 16 elements of A are measured free of the imperfections of the (absent) quarter-wave retarder (QWR). The effect of angular beam deviation by the polarizer is compensated for by taking the average, (1/2) [I(P) + I(P + 180°)], of the FDP output at 180°-apart, optically equivalent, angular positions of the polarizer. The remaining fourth column of A …
Analytical Determination Of The Complex Dielectric Function Of An Absorbing Medium From Two Angles Of Incidence Of Minimum Parallel Reflectance, R. M.A. Azzam
Electrical Engineering Faculty Publications
The real and imaginary parts of the complex dielectric function (or complex refractive index) of an opaque substrate or a thick film can be determined from two pseudo-Brewster angles measured in two transparent incidence media of different refractive indices. This two-angle method is simple in that it involves no photometric or polarimetric analysis and in that the solution for the optical properties in terms of the measured angles is explicit, analytical, and direct (i.e. noniterative). The two-angle method is demonstrated for an opaque TiN film on a Cleartran ZnS substrate as a specific example. The effect of angle-of-incidence errors on …
Division-Of-Wave-Front Thin-Film Beam Splitter For Generating Binary Patterns Of Orthogonal Elliptical Polarization States, R. M.A. Azzam
Division-Of-Wave-Front Thin-Film Beam Splitter For Generating Binary Patterns Of Orthogonal Elliptical Polarization States, R. M.A. Azzam
Electrical Engineering Faculty Publications
A division-of-wave-front thin-film beam splitter is described that reflects monochromatic light at oblique incidence with orthogonal elliptical polarization states. It consists of a metallic substrate partially covered with a transparent thin film that inverts the ratio ρ of the complex p and s reflection coefficients at the principal angle of the metal. Any pattern of coated and uncoated areas of the substrate is imprinted upon the reflected wave front as a corresponding two-dimensional spatial binary polarization pattern. A specific design is given that uses a Au substrate at a wavelength of 632.8 nm. The effects of small errors in the …
Thin-Film Devices For Polarized Light- Introduction, R. M.A. Azzam, William H. Southwell
Thin-Film Devices For Polarized Light- Introduction, R. M.A. Azzam, William H. Southwell
Electrical Engineering Faculty Publications
No abstract provided.
Extrema Of The Magnitude And The Phase Of A Complex Function Of A Real Variable: Application To Attenuated Internal Reflection, R. M.A. Azzam
Extrema Of The Magnitude And The Phase Of A Complex Function Of A Real Variable: Application To Attenuated Internal Reflection, R. M.A. Azzam
Electrical Engineering Faculty Publications
Given a complex function F(ω) = |F(ω)|exp[jΔ(ω)] of a real argument ω, the extrema of its magnitude |F(ω)| and its phase Δ(ω), as functions of ω, are determined simultaneously by finding the roots of one common equation, Im[G(ω)] = 0, where G= (F′/F)2 and F′ = ∂F/∂ω. The extrema of |F| and Δ are associated with Re G < 0 and Re G > 0, respectively. This easy-to-prove theorem has a wide range of applications in physical optics. We consider attenuated internal reflection (AIR) as …
General Analysis And Optimization Of The Four-Detector Photopolarimeter, R. M.A. Azzam, I. M. Elminyawi, A. M. El-Saba
General Analysis And Optimization Of The Four-Detector Photopolarimeter, R. M.A. Azzam, I. M. Elminyawi, A. M. El-Saba
Electrical Engineering Faculty Publications
The four-detector photopolarimeter (FDP) is analyzed for an arbitrary spatial configuration and any reflection characteristics (ri, ψi, Δi) of the first three detectors. The instrument matrix A, which relates the output signal vector I to the input Stokes vector S by I = AS, and its determinant are derived explicitly. The essential condition that A be nonsingular (det A ≠ 0) is satisfied in general with uncoated absorbing detector surfaces, assuming that the plane of incidence (POI) is rotated between successive reflections by other than 90°. Therefore no special coatings on …
Antireflection Of An Absorbing Substrate By An Absorbing Thin Film At Normal Incidence, R. M.A. Azzam, E. Bu-Habib, J. Casset, G. Chassaing, P. Gravier
Antireflection Of An Absorbing Substrate By An Absorbing Thin Film At Normal Incidence, R. M.A. Azzam, E. Bu-Habib, J. Casset, G. Chassaing, P. Gravier
Electrical Engineering Faculty Publications
An absorbing substrate of complex refractive index n2 - jk2 at wavelength λ can be coated by an absorbing thin film of complex refractive index n1 - jk1 and thickness d to achieve zero reflection at normal incidence. For given n2,k2 multiple solutions (n1,k1,d/λ) are found that correspond to infinitely many distinct antireflection layers. This is demonstrated for a Si substrate at two wavelengths (6328 and 4420 Å). The response of these absorbing antireflection layers to changes of the angle of incidence from 0 …
Polarizing Beam Splitters For Infrared And Millimeter Waves Using Single-Layer-Coated Dielectric Slab Or Unbacked Films, R. M.A. Azzam
Polarizing Beam Splitters For Infrared And Millimeter Waves Using Single-Layer-Coated Dielectric Slab Or Unbacked Films, R. M.A. Azzam
Electrical Engineering Faculty Publications
No abstract provided.
Thin-Film Beam Splitter That Reflects Light As A Half-Wave Retarder And Transmits It Without Change Of Polarization: Application To A Michelson Interferometer, R. M.A. Azzam
Electrical Engineering Faculty Publications
The refractive index n1 of a transparent layer of quarter-wave optical thickness coating a transparent substrate of refractive index n2 can be chosen to produce half-wave retardation (HWR) in reflection and no change of polarization in refraction at any angle of incidence ø. The function n1(ø, n2), and the associated polarization-independent reflectance of the film-substrate system R(ø, n2) are determined. Such a coated surface can be used as a beam splitter with excellent characteristics (e.g., split fractions that do not depend on source polarization, a split beam whose polarization is identical …
Relationship Between The P And S Fresnel Reflection Coefficients Of An Interface Independent Of Angle Of Incidence, R. M.A. Azzam
Relationship Between The P And S Fresnel Reflection Coefficients Of An Interface Independent Of Angle Of Incidence, R. M.A. Azzam
Electrical Engineering Faculty Publications
The Fresnel reflection coefficients rp and rs of p- and s-polarized light at the planar interface between two linear isotropic media are found to be interrelated by (rs - rp)/(1 - rsrp) = cos 2β, independent of the angle of incidence ø, where tan2β = ∊ and ∊ is the (generally complex) ratio of dielectric constants of the media of refraction and incidence. This complements another relation (found earlier), (r2s - rp)/(rs - rsrp) = …
Total Refraction At Oblique Incidence By A Transparent Bilayer Coating On A High-Index Transparent Or Absorbing Substrate, R. M.A. Azzam, Karim Javily
Total Refraction At Oblique Incidence By A Transparent Bilayer Coating On A High-Index Transparent Or Absorbing Substrate, R. M.A. Azzam, Karim Javily
Electrical Engineering Faculty Publications
Transparent bilayer coatings that produce total refraction (TR) of obliquely incident monochromatic light into an underlying substrate are considered. When the substrate is transparent, it is shown that TR takes place without any accompanying change of polarization. Totally refracting bilayers are realizable in the IR where high-refractive-index substrates are available. This is illustrated by a BaF2–ZnSe bilayer on a Ge substrate at a 10.6-μm (CO2-laser) wavelength and 45° angle of incidence. Limited changes of the angle of incidence, wavelength, and refractive indices and thicknesses of the two films of the bilayer are introduced, and their effects …
Constraint On The Optical Constants Of A Film-Substrate System For Operation As An External-Reflection Retarder At A Given Angle Of Incidence, R. M.A. Azzam, Bruce E. Perilloux
Constraint On The Optical Constants Of A Film-Substrate System For Operation As An External-Reflection Retarder At A Given Angle Of Incidence, R. M.A. Azzam, Bruce E. Perilloux
Electrical Engineering Faculty Publications
Given a transparent film of refractive index n1 on an absorbing substrate of complex refractive indexn2-jk2, we examine the constraint on n1, n2, and k2 such that the film-substrate system acts as an external-reflection retarder of specified retardance Δ at a specified angle of incidence φ. The constraint, which takes the form ƒ(n1,n2,k2;φ,Δ) = 0, is portrayed graphically by equi-n1 contours in the n2,k2 plane at φ = 45, 70° and for Δ …
Explicit Equations For The Polarizing Angles Of A High-Reflectance Substrate Coated By A Transparent Thin Film, R. M.A. Azzam
Explicit Equations For The Polarizing Angles Of A High-Reflectance Substrate Coated By A Transparent Thin Film, R. M.A. Azzam
Electrical Engineering Faculty Publications
Simple explicit equations are derived that determine the angles of incidence at which the parallel and perpendicular polarization components of light are extinguished on reflection from a transparent film coating a high-reflectance (metallic) substrate. The polarizing angles obtained from our approximate expressions are in excellent agreement with those determined by iterative numerical solution of the exact nonlinear equations that govern such angles. For the approximation to be valid, the intensity reflectance of the film-substrate interface, evaluated at the critical angle of the film-ambient interface, must exceed 0.5.
Antireflecting And Polarizing Transparent Bilayer Coatings On Absorbing Substrates At Oblique Incidence, R. M.A. Azzam, Karim Javily
Antireflecting And Polarizing Transparent Bilayer Coatings On Absorbing Substrates At Oblique Incidence, R. M.A. Azzam, Karim Javily
Electrical Engineering Faculty Publications
The condition of zero reflection of p- and s-polarized light by a transparent bilayer on an absorbing substrate is derived in the form |gν(ø,Ni)| ≤ 1, where gν is a function of the angle of incidence ø, the refractive indices Ni(i = 0,1,2,3) of the system, and the polarization state ν (= p or s). As an application, the air-Si3N4-SiO2-Si system is considered at two laser wavelengths λ = 6328 and 3250 Å. The thicknesses of the two films of the bilayer and the …
Single-Layer Antireflection Coatings On Absorbing Substrates For The Parallel And Perpendicular Polarizations At Oblique Incidence, R. M.A. Azzam
Single-Layer Antireflection Coatings On Absorbing Substrates For The Parallel And Perpendicular Polarizations At Oblique Incidence, R. M.A. Azzam
Electrical Engineering Faculty Publications
Explicit equations are derived that determine the refractive index of a single layer that suppresses the reflection of p- or s-polarized light from the planar interface between a transparent and an absorbing medium at any given angle of incidence. The required layer thickness and the system reflectance for the orthogonal unextinguished polarization also follow explicitly. This generalizes earlier work that was limited to normal incidence or to oblique incidence at dielectric—dielectric interfaces. Specific examples are given of p- and s-antireflection layers on Si and Al substrates at λ = 6328 Å at various angles of incidence.
Extinction Of The P And S Polarizations Of A Wave On Reflection At The Same Angle From A Transparent Film On An Absorbing Substrate: Applications To Parallel-Mirror Crossed Polarizers And A Novel Integrated Polarimeter, R. M.A. Azzam
Electrical Engineering Faculty Publications
The p- and s-polarized components of light can be suppressed on reflection at the same angle of incidence from an absorbing substrate coated by a transparent thin film if the wave is refracted in the film at 45° and the constraint Re[(ε2 - α)/(l -α)]1/2 = α + | ε2 - α| is satisfied, where 2α and ε2 are the ratios of dielectric constants of the film and substrate, respectively, to that of the ambient. For high-reflectance metal substrates (|ε2| » 1), α≈ 1, the ratio of film to ambient refractive index …
Multiple Determination Of The Optical Constants Of Thin-Film Coating Materials, D. P. Arndt, R. M.A. Azzam, J. M. Bennett, J. P. Borgogno, C. K. Carniglia, W. E. Case, J. A. Dobrowolski, U. J. Gibson, T. Tuttle Hart, F. C. Ho, V. A. Hodgkin, W. P. Klapp, H. A. Macleod, E. Pelletier, M. K. Purvis, D. M. Quinn, D. H. Strome, R. Swenson, P. A. Temple, T. F. Thonn
Multiple Determination Of The Optical Constants Of Thin-Film Coating Materials, D. P. Arndt, R. M.A. Azzam, J. M. Bennett, J. P. Borgogno, C. K. Carniglia, W. E. Case, J. A. Dobrowolski, U. J. Gibson, T. Tuttle Hart, F. C. Ho, V. A. Hodgkin, W. P. Klapp, H. A. Macleod, E. Pelletier, M. K. Purvis, D. M. Quinn, D. H. Strome, R. Swenson, P. A. Temple, T. F. Thonn
Electrical Engineering Faculty Publications
The seven participating laboratories received films of two different thicknesses of Sc2O3 and Rh. All samples of each material were prepared in a single deposition run. Brief descriptions are given of the various methods used for determination of the optical constants of these coating materials. The measurement data are presented, and the results are compared. The mean of the variances of the Sc2O3refractive-index determinations in the 0.40–0.75-nm spectral region was 0.03. The corresponding variances for the refractive index and absorption coefficient of Rh were 0.35 and 0.26, respectively.
Three-Reflection Halfwave And Quarterwave Retarders Using Dielectric-Coated Metallic Mirrors, T. F. Thonn, R. M.A. Azzam
Three-Reflection Halfwave And Quarterwave Retarders Using Dielectric-Coated Metallic Mirrors, T. F. Thonn, R. M.A. Azzam
Electrical Engineering Faculty Publications
A design procedure is described to determine the thicknesses of single-layer coatings of a given dielectric on a given metallic substrate so that a specified net phase retardance (and/or a net relative amplitude attenuation) between the p and s polarizations is achieved after three reflections from a symmetrical arrangement of three mirrors that maintain collinearity of the input and output beams. Examples are presented of halfwave and quarterwave retarders (HWR and QWR) that use a ZnS-Ag film-substrate system at the CO2-laser wavelength λ = 10.6 µm. The equal net reflectances for the p and s polarizations are computed …
Inverting The Ratio Of The Complex Parallel And Perpendicular Reflection Coefficients Of An Absorbing Substrate Using A Transparent Thin-Film Coating, R. M.A. Azzam
Electrical Engineering Faculty Publications
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 …
Division-Of-Wave-Front Polarizing Beam Splitter And Half-Shade Device Using Dielectric Thin Film On Dielectric Substrate, R. M.A. Azzam
Division-Of-Wave-Front Polarizing Beam Splitter And Half-Shade Device Using Dielectric Thin Film On Dielectric Substrate, R. M.A. Azzam
Electrical Engineering Faculty Publications
No abstract provided.
Pseudo-Brewster And Second-Brewster Angles Of An Absorbing Substrate Coated By A Transparent Thin Film, R. M.A. Azzam, T F. Thonn
Pseudo-Brewster And Second-Brewster Angles Of An Absorbing Substrate Coated By A Transparent Thin Film, R. M.A. Azzam, T F. Thonn
Electrical Engineering Faculty Publications
The pseudo-Brewster angle of minimum reflectance for the p polarization, the corresponding angle for thes polarization, and the second-Brewster angle of minimum ratio of the p and s reflectances are all determined as functions of the thickness of a transparent film coating an absorbing substrate by numerical solution of the exact equations that govern such angles of the form Re(Z′/Z) = 0, where Z = Rp, Rs, or ρ represent the complex amplitude-reflection coefficients for the p and s polarizations and their ratio (ρ =Rp/Rs), …