Showing papers by "Rasheed M. A. Azzam published in 2008"
TL;DR: The complex-amplitude reflection coefficients of p- and s-polarized light by a transparent freestanding, embedded, or deposited quarter-wave layer (QWL) are derived as explicit functions of the angle of incidence and layer refractive index, which provides the basis for the design of 50%-50% beam splitters for incident s- polarized or unpolarization light that use a high-index QWL embedded in a glass cube.
Abstract: The complex-amplitude reflection coefficients of p- and s-polarized light by a transparent freestanding, embedded, or deposited quarter-wave layer (QWL) are derived as explicit functions of the angle of incidence and layer refractive index. This provides the basis for the design of 50%-50% beam splitters for incident s-polarized or unpolarized light that use a high-index (e.g., TiO2 or Ge) QWL embedded in a glass cube in the visible and near infrared spectral range. These simple devices have good angular and spectral response and are insensitive to small film thickness errors to the first order.
6 citations
TL;DR: The pseudo-Brewster angle phi(pB) of minimum reflectance for p-polarized light and the principal anglephi at which incident linearly polarized light of the proper azimuth is reflected circularly polarized are considered as functions of the complex relative dielectric function epsilon of a dielectrics-conductor interface over the entire complex epsilus plane.
Abstract: The pseudo-Brewster angle phi(pB) of minimum reflectance for p-polarized light and the principal angle phi at which incident linearly polarized light of the proper azimuth is reflected circularly polarized are considered as functions of the complex relative dielectric function epsilon of a dielectric-conductor interface over the entire complex epsilon plane. In particular, the spread of phi for a given phi (pB) is determined, and the maximum difference(phi -phi(pB))(max) is obtained as a function of phi(pB). The maximum difference (phi -phi(pB))(max) approaches 45 degrees and 0 in the limit as phi(pB)-->phi 0 and 90 degrees , respectively. For phi(pB)<22.666 degrees , multiple principal angles phi (i), i=1,2,3, appear for each epsilon in a subdomain of fractional optical constants. This leads to an elaborate pattern of multiple solution branches for the difference phi (i)-phi(pB), i=1,2,3, as is illustrated by several examples.
6 citations
TL;DR: A useful algorithm is presented that transforms a three-term Sellmeier dispersion relation of a transparent optical material to an equivalent cubic equation that can be solved for the wavelengths at which the refractive index assumes any desired value.
Abstract: The cumulative retardance
Δt introduced between the p and the s orthogonal linear polarizations after two successive total internal reflections (TIRs) inside a right-angle prism at complementary angles Φ and
90°−Φ is calculated as a function of Φ and prism refractive index n.
Quarter-wave retardation (QWR) is obtained on retroreflection with minimum angular sensitivity when
n=(√2+1)1/2=1.55377 and
Φ=45°. A QWR prism made of N-BAK4 Schott glass
(n=1.55377 at
λ=1303.5 nm) has good spectral response (<5° retardance error) over the 0.5-2 μm visible and near-IR spectral range. A ZnS-coated right-angle Si prism achieves QWR with an error of
<±2.5° in the 9-11 μm (CO2 laser) IR spectral range. This device functions as a linear-to-circular polarization transformer and can be tuned to exact QWR at any desired wavelength (within a given range) by tilting the prism by a small angle around
Φ=45°.
A PbTe right-angle prism introduces near-half-wave retardation (near-HWR) with a ≤2% error over a broad
(4≤λ≤12.5 μm) IR spectral range. This device also has a wide field of view and its interesting polarization properties are discussed. A compact (aspect ratio of
2), in-line, HWR is described that uses a chevron dual Fresnel rhomb with four TIRs at the same angle
Φ=45°.
Finally, a useful algorithm is presented that transforms a three-term Sellmeier dispersion relation of a transparent optical material to an equivalent cubic equation that can be solved for the wavelengths at which the refractive index assumes any desired value.
5 citations
TL;DR: In this article, the first internal angle of incidence φ and prism refractive index n were used to achieve 3λ/4 retardance with minimum angular sensitivity when φ=45° and n=1.900822.
Abstract: The net differential phase shift Δt introduced between the orthogonal p and s linear polarizations after four successive total internal reflections inside an in-line chevron dual-Fresnel-rhomb retarder is a function of the first internal angle of incidence φ and prism refractive index n. Retardance of 3λ/4 (i.e., Δt=270°) is achieved with minimum angular sensitivity when φ=45° and n=1.900822. Several optical glasses with this refractive index are identified. For Schott glass SF66 the deviation of Δt from 270° is ≤4° over a wavelength range of 0.55≤λ≤1.1 μm in the visible and near-IR spectrum. For a SiC prism, whose totally reflecting surfaces are coated with an optically thick MgF2 film, Δt=270° at two wavelengths: λ1=0.707 μm and λ2=4.129 μm. This coated prism has a maximum retardance error of ≈5°over>three octaves (0.5 to 4.5 μm) in the visible, near-, and mid-IR spectral range. Another mid-IR 3λ/4 retarder uses a Si prism, which is coated by an optically thick silicon oxynitride film of the proper composition, to achieve retardance that differs from 270° by <0.5° over the 3-5 μm spectral range.
4 citations
TL;DR: It is shown that the lowest possible reflectance is attained for p-polarized light at phi=45 degrees and that the associated p-reflection phase shift is also minimum at that angle.
Abstract: Conditions for reducing the reflectance of a dielectric-conductor interface for p- and s-polarized light to a minimum at any angle of incidence ϕ are determined. The refractive indices of a transparent immersion medium (liquid) that achieve minimum reflectance at normal incidence, ϕ=0, and at ϕ=45° are independent of polarization. These indices provide sufficient data to determine the real and imaginary parts of the complex refractive index of an absorbing substrate. Reflection at a dielectric-Au interface at 500 nm wavelength is considered as an example. It is shown that the lowest possible reflectance is attained for p-polarized light at ϕ=45° and that the associated p-reflection phase shift is also minimum at that angle. For ϕ≥65° the lowest reflectance of p-polarized light occurs when the ambient is vacuum or air. However, this lowest reflectance at the air-Au interface is not a true minimum in a mathematical sense.
4 citations
TL;DR: The efficiency eta(LC) of linear-to-circular polarization conversion when light is reflected at a dielectric-conductor interface is determined as a function of the principal angle phi and principal azimuth psi.
Abstract: 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 phiv¯ and principal azimuth ψ¯. Constant-ηLC contours are presented in the phiv¯, 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 > or slanted equal to 88% are obtained for light reflection by a Ag mirror in the visible and near-IR (400-1200 nm) spectral range, and ≥40% for the reflection of extreme ultraviolet (EUV) and soft x-ray radiation by a SiC mirror in the 60-120 nm wavelength range.
4 citations