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Full-Text Articles in Physics
Circular And Near-Circular Polarization States Of Evanescent Monochromatic Light Fields In Total Internal Reflection, R. M. A Azzam
Circular And Near-Circular Polarization States Of Evanescent Monochromatic Light Fields In Total Internal Reflection, R. M. A Azzam
Electrical Engineering Faculty Publications
Conditions for the production of near-circular polarization states of the evanescent field present in the rarer medium in total internal reflection of incident monochromatic p-polarized light at a dielectric-dielectric planar interface are determined. Such conditions are satisfied if high-index (>3.2) transparent prism materials (e.g., GaP and Ge) are used at angles of incidence well above the critical angle but sufficiently below grazing incidence. Furthermore, elliptical polarization of incident light with nonzero p and s components can be tailored to cause circular polarization of the resultant tangential electric field in the plane of the interface or circular polarization of the …
Poincaré Sphere Representation Of The Fixed-Polarizer Rotating-Retarder Optical System, R. M.A. Azzam
Poincaré Sphere Representation Of The Fixed-Polarizer Rotating-Retarder Optical System, R. M.A. Azzam
Electrical Engineering Faculty Publications
The trajectory of the polarization state of a monochromatic light beam after it passes through a fixed linear polarizer and a rotating linear retarder of arbitrary retardance Δ is determined on the Poincaré sphere. The three-dimensional figure-8 contour is shown to be the line of intersection of a right-circular cylinder with the sphere. The cylinder is parallel to the polar (s3) axis, touches the sphere at the equator (at the point that represents the linear polarization transmitted by the fixed polarizer), and has a radius r=sin2(Δ/2). Projections of the trajectory in the coordinate planes of the …
Three-Dimensional Polarization States Of Monochromatic Light Fields, R. M.A. Azzam
Three-Dimensional Polarization States Of Monochromatic Light Fields, R. M.A. Azzam
Electrical Engineering Faculty Publications
The 3×1 generalized Jones vectors (GJVs) [ExEyEz]t (t indicates the transpose) that describe the linear, circular, and elliptical polarization states of an arbitrary three-dimensional (3-D) monochromatic light field are determined in terms of the geometrical parameters of the 3-D vibration of the time-harmonic electric field. In three dimensions, there are as many distinct linear polarization states as there are points on the surface of a hemisphere, and the number of distinct 3-D circular polarization states equals that of all two-dimensional (2-D) polarization states on the Poincaré sphere, of which only two are circular states. The subset of 3-D polarization …
Simplified Design Of Thin-Film Polarizing Beam Splitter Using Embedded Symmetric Trilayer Stack, R. M.A. Azzam
Simplified Design Of Thin-Film Polarizing Beam Splitter Using Embedded Symmetric Trilayer Stack, R. M.A. Azzam
Electrical Engineering Faculty Publications
An analytically tractable design procedure is presented for a polarizing beam splitter (PBS) that uses frustrated total internal reflection and optical tunneling by a symmetric LHL trilayer thin-film stack embedded in a high-index prism. Considerable simplification arises when the refractive index of the high-index center layer H matches the refractive index of the prism and its thickness is quarter-wave. This leads to a cube design in which zero reflection for the p polarization is achieved at a 45 degrees angle of incidence independent of the thicknesses of the identical symmetric low-index tunnel layers L and L. Arbitrarily high reflectance for …
Principal Angles And Principal Azimuths Of Frustrated Total Internal Reflection And Optical Tunneling By An Embedded Low-Index Thin Film, R. M.A. Azzam, F. F. Sudradjat
Principal Angles And Principal Azimuths Of Frustrated Total Internal Reflection And Optical Tunneling By An Embedded Low-Index Thin Film, R. M.A. Azzam, F. F. Sudradjat
Electrical Engineering Faculty Publications
The condition for obtaining a differential (or ellipsometric) quarter-wave retardation when p- and s-polarized light of wavelength λ experience frustrated total internal reflection (FTIR) and optical tunneling at angles of incidence ϕ≥ the critical angle by a transparent thin film (medium 1) of low refractive index n1 and uniform thickness d, which is embedded in a transparent bulk medium 0 of high refractive index n0 takes the simple form: −tanh2x=tanδptanδs , in whichx=2πn1(d/λ)(N2sin2ϕ−1)1/2 , N=n0/n1 , and δp , δs are 01 interface Fresnel reflection phase shifts for the pand s polarizations. From this condition, the …
Transmission Of P- And S-Polarized Light Through A Prism And The Condition Of Minimum Deviation, R. M.A. Azzam, Ryan M. Adams
Transmission Of P- And S-Polarized Light Through A Prism And The Condition Of Minimum Deviation, R. M.A. Azzam, Ryan M. Adams
Electrical Engineering Faculty Publications
The condition of minimum deviation (MD) by a transparent optically isotropic prism is re-derived, and expressions for the intensity transmittances Tp(θ) and Ts(θ) of an uncoated prism of refractive index n and prism angle α for incident p- ands-polarized light and their derivatives with respect to the internal angle of refraction θ are obtained. When the MD condition(θ=α/2) is satisfied, Ts is maximum and Tp is maximum or minimum. The transmission ellipsometric parametersψt,Δt of a symmetrically coated prism are also shown to be locally stationary with respect to θ at θ=α/2 . The constraint on (n,α) for …
Tilted Parallel Dielectric Slab As A Multilevel Attenuator For Incident P- Or S-Polarized Light, R. M.A. Azzam
Tilted Parallel Dielectric Slab As A Multilevel Attenuator For Incident P- Or S-Polarized Light, R. M.A. Azzam
Electrical Engineering Faculty Publications
Under the condition of first-order blooming, a parallel dielectric slab, which is inserted in the path of an obliquely incident p- or s-polarized light beam, introduces multiple discrete attenuation levels given by 1/3, 4/27, 4/243,...... in reflection and 4/9, 4/81, 4/729,...... in transmission. These attenuation levels are independent of the slab refractive index, incident p or s linear polarization, or the presence of identical transparent surface coatings at the front and back sides of the slab. Therefore, the tilted slab provides multidecade reflectance and attenuation reference values that can be used in calibrating spectrophotometers and filters, and also …
Plurality Of Principal Angles For A Given Pseudo-Brewster Angle When Polarized Light Is Reflected At A Dielectric-Conductor Interface, R. M.A. Azzam, A. Alsamman
Plurality Of Principal Angles For A Given Pseudo-Brewster Angle When Polarized Light Is Reflected At A Dielectric-Conductor Interface, R. M.A. Azzam, A. Alsamman
Electrical Engineering Faculty Publications
The pseudo-Brewster angle ϕpB of minimum reflectance for p-polarized light and the principal angle ϕ¯ at which incident linearly polarized light of the proper azimuth is reflected circularly polarized are considered as functions of the complex relative dielectric function ε of a dielectric–conductor interface over the entire complex ε plane. In particular, the spread of ϕ¯for a given ϕpB is determined, and the maximum difference (ϕ¯−ϕpB)max is obtained as a function of ϕpB . The maximum difference (ϕ¯−ϕpB)max approaches 45° and 0 in the limit as ϕpB→0 and 90°, respectively. ForϕpB<22.666° , multiple principal angles ϕ¯i , i=1,2,3 , appear for each ε in a subdomain of fractional optical constants. …
Efficiency Of Linear-To-Circular Polarization Conversion For Light Reflection At The Principal Angle By A Dielectric-Conductor Interface, R. M.A. Azzam, A. Alsamman
Efficiency Of Linear-To-Circular Polarization Conversion For Light Reflection At The Principal Angle By A Dielectric-Conductor Interface, R. M.A. Azzam, A. Alsamman
Electrical Engineering Faculty Publications
The efficiency ηLC of linear-to-circular polarization conversion when light is reflected at a dielectric–conductor interface is determined as a function of the principal angle ϕ¯ and principal azimuth ψ¯ . Constant- ηLC contours are presented in the ϕ¯ ,ψ¯ plane for values of ηLC from 0.5 to 1.0 in steps of 0.05, and the corresponding contours in the complex plane of the relative dielectric function ϵ are also determined. As specific examples, efficiencies ⩾88% are obtained for light reflection by a Ag mirror in the visible and near-IR (400–1200nm) spectral range, and ≥40% for the reflection of extreme ultraviolet (EUV) …
Quarter-Wave Layers With 50% Reflectance For Obliquely Incident Unpolarized Light, R. M.A. Azzam, F. F. Sudradjat
Quarter-Wave Layers With 50% Reflectance For Obliquely Incident Unpolarized Light, R. M.A. Azzam, F. F. Sudradjat
Electrical Engineering Faculty Publications
The conditions under which light interference in a transparent quarter-wave layer of refractive index n1 on a transparent substrate of refractive index n2 leads to 50% reflectance for incident unpolarized light at an angle φ are determined. Two distinct solution branches are obtained that correspond to light reflection above and below the polarizing angle, φp , of zero reflection for p polarization. The real p and s amplitude reflection coefficients have the same (negative) sign for the solution branch φ>φp and have opposite signs for the solution branch φ<φp . Operation at φ<φp is the basis of a 50%–50% beam splitter that divides an incident totally polarized light beam (with p and s components of equal intensity) into reflected and …
Polarizing Properties Of Embedded Symmetric Trilayer Stacks Under Conditions Of Frustrated Total Internal Reflection, Rasheed M.A. Azzam, Siva R. Perla
Polarizing Properties Of Embedded Symmetric Trilayer Stacks Under Conditions Of Frustrated Total Internal Reflection, Rasheed M.A. Azzam, Siva R. Perla
Electrical Engineering Faculty Publications
An error in the application of the design procedure described in a previous paper [Appl. Opt. 45, 1650 (2006)] has been corrected, and new revised figures are included in this erratum.
Phase Shifts In Frustrated Total Internal Reflection And Optical Tunneling By An Embedded Low-Index Thin Film, R. M.A. Azzam
Phase Shifts In Frustrated Total Internal Reflection And Optical Tunneling By An Embedded Low-Index Thin Film, R. M.A. Azzam
Electrical Engineering Faculty Publications
Simple and explicit expressions for the phase shifts that p- and s-polarized light experience in frustrated total internal reflection (FTIR) and optical tunneling by an embedded low-index thin film are obtained. The differential phase shifts in reflection and transmission Δr,Δt are found to be identical, and the associated ellipsometric parameters ψr,ψt are governed by a simple relation, independent of film thickness. When the Fresnel interface reflection phase shifts for the pand s polarizations or their average are quarter-wave, the corresponding overall reflection phase shifts introduced by the embedded layer are also quarter-wave for all values of film …
Achromatic Angle-Insensitive Infrared Quarter-Wave Retarder Based On Total Internal Reflection At The Si–Sio2 Interface, R. M.A. Azzam, Cristina L. Spinu
Achromatic Angle-Insensitive Infrared Quarter-Wave Retarder Based On Total Internal Reflection At The Si–Sio2 Interface, R. M.A. Azzam, Cristina L. Spinu
Electrical Engineering Faculty Publications
An achromatic infrared (λ = 1.2–4 μm), Si-prism quarter-wave retarder (QWR) is described that uses total internal reflection at a buried Si–SiO2 interface at an angle of incidence φ near 33°, where ∂Δ/∂φ = 0. The retardance Δ deviates from 90° by <±2° within a field of view of ±10° (in air) over the entire bandwidth. Because the SiO2 layer at the base of the prism is optically thick, this QWR is unaffected by environmental contamination.
Phase Shifts That Accompany Total Internal Reflection At A Dielectric–Dielectric Interface, R. M.A. Azzam
Phase Shifts That Accompany Total Internal Reflection At A Dielectric–Dielectric Interface, R. M.A. Azzam
Electrical Engineering Faculty Publications
The absolute, average, and differential phase shifts that p- and s-polarized light experience in total internal reflection (TIR) at the planar interface between two transparent media are considered as functions of the angle of incidence φ. Special angles at which quarter-wave phase shifts are achieved are determined as functions of the relative refractive index N. When the average phase shift equals π/2, the differential reflection phase shift Δ is maximum, and the reflection Jones matrix assumes a simple form. For N>√3, the average and differential phase shifts are equal (hence δp=3δs) at …
Optimal Beam Splitters For The Division-Of-Amplitude Photopolarimeter, R. M.A. Azzam, A. De
Optimal Beam Splitters For The Division-Of-Amplitude Photopolarimeter, R. M.A. Azzam, A. De
Electrical Engineering Faculty Publications
Optimal optical parameters of the beam splitter that is used in the division-of-amplitude photopolarimeter are determined. These are (1) 50%–50% split ratio of the all-dielectric beam splitter, (2) differential phase shifts in reflection and transmission Δr and Δt that differ by ±π/2, and (3) ellipsometric parameters (ψr, ψt)= (27.368°, 62.632°) or (62.632°, 27.368°). It is also shown that for any nonabsorbing beam splitter that splits incident unpolarized light equally, the relationship ψr+ψt=π/2 is always satisfied.
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 …