Topic

# Fresnel equations

About: Fresnel equations is a(n) research topic. Over the lifetime, 2770 publication(s) have been published within this topic receiving 54069 citation(s).

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01 Nov 1974-

Abstract: A compact dyadic diffraction coefficient for electromagnetic waves obliquely incident on a curved edse formed by perfectly conducting curved ot plane surfaces is obtained. This diffraction coefficient remains valid in the transition regions adjacent to shadow and reflection boundaries, where the diffraction coefficients of Keller's original theory fail. Our method is based on Keller's method of the canonical problem, which in this case is the perfectly conducting wedge illuminated by plane, cylindrical, conical, and spherical waves. When the proper ray-fixed coordinate system is introduced, the dyadic diffraction coefficient for the wedge is found to be the sum of only two dyads, and it is shown that this is also true for the dyadic diffraction coefficients of higher order edges. One dyad contains the acoustic soft diffraction coefficient; the other dyad contains the acoustic hard diffraction coefficient. The expressions for the acoustic wedge diffraction coefficients contain Fresenel integrals, which ensure that the total field is continuous at shadow and reflection boundaries. The diffraction coefficients have the same form for the different types of edge illumination; only the arguments of the Fresnel integrals are different. Since diffraction is a local phenomenon, and locally the curved edge structure is wedge shaped, this result is readily extended to the curved wedge. It is interesting that even though the polarizations and the wavefront curvatures of the incident, reflected, and diffracted waves are markedly different, the total field calculated from this high-frequency solution for the curved wedge is continuous at shadow and reflection boundaries.

2,478 citations

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Abstract: The directional distribution of radiant flux reflected from roughened surfaces is analyzed on the basis of geometrical optics. The analytical model assumes that the surface consists of small, randomly disposed, mirror-like facets. Specular reflection from these facets plus a diffuse component due to multiple reflections and/or internal scattering are postulated as the basic mechanisms of the reflection process. The effects of shadowing and masking of facets by adjacent facets are included in the analysis. The angular distributions of reflected flux predicted by the analysis are in very good agreement with experiment for both metallic and nonmetallic surfaces. Moreover, the analysis successfully predicts the off-specular maxima in the reflection distribution which are observed experimentally and which emerge as the incidence angle increases. The model thus affords a rational explanation for the off-specular peak phenomenon in terms of mutual masking and shadowing of mirror-like, specularly reflecting surface facets.

1,596 citations

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Abstract: Optical thin-film materials with low refractive index for broadband elimination of Fresnel reflection

1,082 citations

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TL;DR: A method is described for finding the optical properties of a slab of turbid material by using total reflection, unscattered transmission, and total transmission measurements and the intrinsic error in the method is < 3% when four quadrature points are used.

Abstract: A method is described for finding the optical properties (scattering, absorption, and scattering anisotropy) of a slab of turbid material by using total reflection, unscattered transmission, and total transmission measurements. This method is applicable to homogeneous turbid slabs with any optical thickness, albedo, or phase function. The slab may have a different index of refraction from its surroundings and may or may not be bounded by glass. The optical properties are obtained by iterating an adding–doubling solution of the radiative transport equation until the calculated values of the reflection and transmission match the measured ones. Exhaustive numerical tests show that the intrinsic error in the method is <3% when four quadrature points are used.

699 citations

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Abstract: Explicit formulas are derived for the mean-square electric fields induced by plane electromagnetic radiation in a two-phase, three-phase, and N-phase stratified medium. The first (incident) and last phases are semi-infinite in extent. Boundaries separating phases are plane and parallel. Phases are isotropic with arbitrary optical constants. Simple relationships follow for special cases such as at the critical angle for a two-phase system. Equations for reflectance, transmittance, and phase changes on reflectance and transmittance are given. Details are given concerning the energy absorption process, especially in the two- and three-layer cases. Equations for the N-layer case are in terms of characteristic matrices which can be readily programmed for a computer.

633 citations