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Full-Text Articles in Physics
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) …