Electrical and Electronics Commons^™

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 r_p and r_s of p- and s-polarized light at the planar interface between two linear isotropic media are found to be interrelated by (r_s - r_p)/(1 - r_sr_p) = 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), (r²_s - r_p)/(r_s - r_sr_p) = …

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 …

Investigation Of Electronic Holography Using Spice Computer Simulation Experiments, Monish Ranjan Chatterjee

Electrical and Computer Engineering Faculty Publications

Using SPICE experiments, it has been possible to verify most of the important aspects of electronic holography. The generation and properties of dynamic echoes under different types of nonlinearities have been extensively tested, and some new information has been garnered in the process. The case of pulse and generalized memory echoes has also been tested, and the results have been fairly satisfactory. Most of all, the simplicity with which the intriguing concept of memory echoes has translated into the circuit implementation on SPICE, and the closeness of the results to predicted behavior have been somewhat of a pleasant surprise.

Since …

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

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

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 |g_ν(ø,N_i)| ≤ 1, where g_ν is a function of the angle of incidence ø, the refractive indices N_i(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

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

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

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 = R_p/R_s 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

Electrical Engineering Faculty Publications

No abstract provided.

A Plasma Focus Interrupting Switch, Gregory Francis Knapp

Electrical & Computer Engineering Theses & Dissertations

The feasibility of using a dense plasma focus (DPF) as a current interrupting device has been investigated. Specifically, a 34-kJ, Mather-type DPF was modified to accept a third electrode so that a discharge could be created between this electrode and the center electrode of the DPF by a 10-kJ inductive energy storage circuit. It was anticipated that the accelerating mechanisms of the DPF pinch, which are known to cause a rapid reduction in the DPF current, would interrupt the 1-kA to 10-kA secondary discharge current thus forcing the secondary current through an external load and hence result in power amplification. …

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 = R_p, R_s, or ρ represent the complex amplitude-reflection coefficients for the p and s polarizations and their ratio (ρ =R_p/R_s), …

Self‐Refraction Of Nonlinear Capillary‐Gravity Waves, Partha P. Banerjee, Adrianus Korpel, Karl E. Lonngren

Electrical and Computer Engineering Faculty Publications

Self‐refraction effects have been observed during the propagation of deep‐water capillary‐gravity waves. The observations are shown to be in qualitative agreement with the theory of self‐focusing and defocusing in a cubically nonlinear medium in the presence of diffraction.

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 R_p/R_s of intensity reflectances R_p and R_s 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= sin²_ΦB2. 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 X_r and X_t, 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 = X_r/X_t, we find that α = r_s + r_s^-1, where r_s 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

Electrical Engineering Faculty Publications

The pseudo-Brewster angle Ø_pB, of minimum reflectance R_pm 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 = sin²ø_pB. It is shown that, for a given value of the normal-incidence amplitude reflectance |r|, there is an associated normal-incidence phase shift, δ = δ_mm, 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

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

Electrical Engineering Faculty Publications

The complex reflection coefficients R_v(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 ofR_p and R_s are all presented in the complex plane. Furthermore, the amplitude-reflectance and phase-shift functions, |R_v|(ø,ζ) and argR_v(ø,ζ) …

Subharmonic Generation By Resonant Three‐Wave Interaction Of Deep‐Water Capillary Waves, Partha P. Banerjee, Adrianus Korpel

Electrical and Computer Engineering Faculty Publications

Subharmonic generation has been observed during the propagation of deep‐water capillary waves. The observations are shown to be in agreement with the theory of degenerate resonant noncollinear three‐wave interaction in a nonlinear, dispersive medium.

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

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

Electrical Engineering Faculty Publications

No abstract provided.

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

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 N_o and N_e. N_o and N_e 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

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

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.

A Critical Study Of Nonlinear Echo Phenomena, Monish Ranjan Chatterjee

Electrical and Computer Engineering Faculty Publications

The present thesis attempts to give a concise and critical account of the evolution of the echo phenomena over the last thirty years. Starting with spin and photon echoes, which were among the earliest to be observed and studied, the thesis explores the experimental findings and the models proposed in connection with the more contemporary echo experiments, viz. those involving electroacoustic or polarization echoes in single and polycrystalline piezoelectric materials and in powders. Although the investigations regarding the various mechanisms of short and long term echo formation are by no means complete, a coherent picture is beginning to emerge as …