Open Access. Powered by Scholars. Published by Universities.®
- Keyword
-
- 4-detector photopolarimeter, general-analysis, optimization, ellipsometry, polarimeter, calibration, light (1)
- Complex epsilon-plane, optical-constants, contours (1)
- Complex reflection coefficient, Discrete values, Fresnel reflection coefficient, Immersion medium, Reflection phase, Relative dielectric, S-polarized light, Total reflection (1)
- Dielectric surface, beam-splitters, polarization, refraction (1)
- Electromagnetic-waves (1)
Articles 31 - 60 of 79
Full-Text Articles in Physics
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), …
Explicit Equations For The Second Brewster Angle Of An Interface Between A Transparent And An Absorbing Medium, R. M.A. Azzam
Explicit Equations For The Second Brewster Angle Of An Interface Between A Transparent And An Absorbing Medium, R. M.A. Azzam
Electrical Engineering Faculty Publications
The second Brewster angle ΦB2, at which the ratio Rp/Rs of intensity reflectances Rp and Rs for the parallel (p) and the perpendicular (s) polarizations of a dielectric-conductor interface reaches a minimum, is determined by Im[(u - ∊)(u - ∊)2/(u - 2∊)2] = 0, where ∊ is the complex ratio of dielectric constants of the media of refraction and incidence, ∊ = ∊/(∊ + 1), and u= sin2ΦB2. An equivalent quartic equation in u …
Simple And Direct Determination Of Complex Refractive Index And Thickness Of Unsupported Or Embedded Thin Films By Combined Reflection And Transmission Ellipsometry At 45° Angle Of Incidence, R. M.A. Azzam
Electrical Engineering Faculty Publications
Measurements of the polarization states (represented by complex numbers Xr and Xt, respectively) of light reflected and transmitted by an unsupported or embedded thin film, for totally polarized light (with nonzero p and s components) incident at 45°, permit simple, direct, and explicit determination of the film's complex refractive index N1 independently of film thickness or input polarization. If α = Xr/Xt, we find that α = rs + rs-1, where rs is Fresnel’s complex reflection coefficient of the ambient-film interface for the s polarization at …
Maximum Minimum Reflectance Of Parallel-Polarized Light At Interfaces Between Transparent And Absorbing Media, R. M.A. Azzam
Maximum Minimum Reflectance Of Parallel-Polarized Light At Interfaces Between Transparent And Absorbing Media, R. M.A. Azzam
Electrical Engineering Faculty Publications
The pseudo-Brewster angle ØpB, of minimum reflectance Rpm for the parallel (p) polarization, of an interface between a transparent and an absorbing medium is determined by Im{(∊ - u)[1 - (1 + ∊-1)u]2} = 0, where ∊ is the complex ratio of dielectric constants of the media and u = sin2øpB. It is shown that, for a given value of the normal-incidence amplitude reflectance |r|, there is an associated normal-incidence phase shift, δ = δmm, that leads to maximum minimum parallel reflectance, …
Single-Reflection Film—Substrate Half-Wave Retarders With Nearly Stationary Reflection Properties Over A Wide Range Of Incidence Angles, R. M.A. Azzam, M. Emdadur Rahman Khan
Single-Reflection Film—Substrate Half-Wave Retarders With Nearly Stationary Reflection Properties Over A Wide Range Of Incidence Angles, R. M.A. Azzam, M. Emdadur Rahman Khan
Electrical Engineering Faculty Publications
The complex reflection coefficient for the p polarization of a transparent film on an absorbing or transparent substrate can be made equal to the negative of that for the s polarization, and hence the film—substrate system acts as a half-wave retarder (HWR), by proper selection of film refractive index N1, film thickness d, and angle of incidence Φ. This condition, which generally holds only at normal incidence, becomes possible at oblique incidence also if N1 is within a certain range, 1 < N1 < N̂1 . For a given substrate and given N1, …
Complex Reflection Coefficients For The Parallel And Perpendicular Polarizations Of A Film-Substrate System, R. M.A. Azzam, M. Emdadur Rahman Khan
Complex Reflection Coefficients For The Parallel And Perpendicular Polarizations Of A Film-Substrate System, R. M.A. Azzam, M. Emdadur Rahman Khan
Electrical Engineering Faculty Publications
The complex reflection coefficients Rv(ø,ζ) of a film-substrate system for the parallel (v = p) and perpendicular (v = s) polarizations are examined in detail as functions of the angle of incidence ø(0 ≤ ø ≤ 90°) and the reduced normalized film thickness ζ(0 ≤ ζ < 1). For definiteness, the reflection of light of wavelength λ = 0.6328 µm by the air–SiO2–Si system is assumed. Families of circles that represent the constant-angle-of-incidence contours, their envelopes, and the associated constant-thickness contours ofRp and Rs are all presented in the complex plane. Furthermore, the amplitude-reflectance and phase-shift functions, |Rv|(ø,ζ) and argRv(ø,ζ) …
Explicit Determination Of The Complex Refractive Index Of An Absorbing Medium From Reflectance Measurements At And Near Normal Incidence, R. M.A. Azzam
Electrical Engineering Faculty Publications
Measurement of reflectance at normal incidence R and its fractional change ΔR/R caused by a change of the angle of incidence from 0 to a small angle ϕ (ϕ≲ 20°) permits explicit determination of both the refractive index n and extinction coefficient k of an isotropic absorbing medium. The medium of incidence (ambient) is assumed to have a known refractive index (e.g., =1 for vacuum or air), and the incident light is either p or s linearly polarized.
Polarization-Preserving Single-Layer-Coated Beam Displacers And Axicons, R. M.A. Azzam, M. Emdadur Rahman Khan
Polarization-Preserving Single-Layer-Coated Beam Displacers And Axicons, R. M.A. Azzam, M. Emdadur Rahman Khan
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 any input polarization of light is preserved after two reflections at the same angle of incidence from a parallel-mirror beam displacer or an axicon. This is achieved by equalizing the net complex p and s reflection coefficients (also called the radial and azimuthal eigenvalues of an axicon) after two reflections. The net polarization-independent reflectance (insertion loss) of the device is computed and found to exceed the net minimum parallel reflectance of the uncoated device for incidence above …
Scheme To Polarization-Correct A Waxicon, R. M.A. Azzam
Scheme To Polarization-Correct A Waxicon, R. M.A. Azzam
Electrical Engineering Faculty Publications
No abstract provided.
Stationary Property Of Normal-Incidence Reflection From Isotropic Surfaces, R. M.A. Azzam
Stationary Property Of Normal-Incidence Reflection From Isotropic Surfaces, R. M.A. Azzam
Electrical Engineering Faculty Publications
The complex reflection coefficients for the parallel (p) and perpendicular (s) polarizations of light that are normally incident upon an isotropic surface are proved to be stationary with respect to small changes of the angle of incidence in the neighborhood of zero. This is true not only for a single interface between isotropic media but also for any one-dimensionally inhomogeneous or multilayer reflecting structure that is stratified in the direction of the surface normal. For incident light of certain intensity, phase, and polarization, the intensity, phase, and polarization of the reflected light all remain stationary with …
Brewster And Pseudo-Brewster Angles Of Uniaxial Crystal Surfaces And Their Use For Determination Of Optical Properties, M. Elshazly-Zaghloul, R. M.A. Azzam
Brewster And Pseudo-Brewster Angles Of Uniaxial Crystal Surfaces And Their Use For Determination Of Optical Properties, M. Elshazly-Zaghloul, R. M.A. Azzam
Electrical Engineering Faculty Publications
Brewster and pseudo-Brewster angles are defined for surfaces of transparent and absorbing uniaxial crystals parallel and perpendicular to the optic axis. Two Brewster angles of a transparent uniaxial crystal surface parallel to the optic axis, measured when the optic axis is oriented perpendicular and parallel to the plane of incidence, readily determine the ordinary and extraordinary indices No and Ne. No and Ne can also be obtained from two Brewster angles measured on a surface perpendicular to the optic axis in contact with two media of different refractive indices. Conditions for the existence of two …
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.