Fresnel equations

About: Fresnel equations is a research topic. Over the lifetime, 2770 publications have been published within this topic receiving 54069 citations.

Optical Anisotropy of Black Phosphorus in the Visible Regime.

Abstract: The striking in-plane anisotropy remains one of the most intriguing properties for the newly rediscovered black phosphorus (BP) 2D crystals. However, because of its rather low-energy band gap, the optical anisotropy of few-layer BP has been primarily investigated in the near-infrared (NIR) regime. Moreover, the essential physics that determine the intrinsic anisotropic optical property of few-layer BP, which is of great importance for practical applications in optical and optoelectronic devices, are still in the fancy of theory. Herein, we report the direct observation of the optical anisotropy of few-layer BP in the visible regime simply by using polarized optical microscopy. On the basis of the Fresnel equation, the intrinsic anisotropic complex refractive indices (n–iκ) in the visible regime (480–650 nm) were experimentally obtained for the first time using the anisotropic optical contrast spectra. Our findings not only provide a convenient approach to measure the optical constants of 2D layered materi...

A comparison of theoretical and empirical reflection coefficients for typical exterior wall surfaces in a mobile radio environment

Abstract: This paper presents microwave reflection coefficient measurements at 1.9 GHz and 4.0 GHz for a variety of typical smooth and rough exterior building surfaces. The measured test surfaces include walls composed of limestone blocks, glass, and brick. Reflection coefficients were measured by resolving individual reflected signal components temporally and spatially, using a spread-spectrum sliding correlation system with directional antennas. Measured reflection coefficients are compared to theoretical Fresnel reflection coefficients, applying Gaussian rough surface scattering corrections where applicable. Comparisons of theoretical calculations and measured test cases reveal that Fresnel reflection coefficients adequately predict the reflective properties of the glass and brick wall surfaces. The rough limestone block wall reflection measurements are shown to be bounded by the predictions using the Fresnel reflection coefficients for a smooth surface and the modified reflection coefficients using the Gaussian rough surface correction factors. A simple, but effective, reflection model for rough surfaces is proposed, which is in good agreement with propagation measurements at 1.9 GHz and 4 GHz for both vertical and horizontal antenna polarizations. These reflection coefficient models can be directly applied to the estimation of multipath signal strength in ray tracing algorithms for propagation prediction.

Standard surface-reflectance model and illuminant estimation

Abstract: In the standard reflectance model for inhomogeneous materials it is assumed that light is reflected by two independent mechanisms. One component is reflected at the interface of the material and air. Light reflected by this mechanism does not interact with surface colorant, and its spectral composition is assumed to equal that of the incident light. The second component is reflected after entering and interacting with the subsurface structure of the material. This interaction substantially changes the spectral composition of the reflected light. We adopt a vector analysis technique for testing the standard reflectance model. Further, we develop a computational method to determine the components of the observed spectra, and we obtain an estimate of the illuminant without using a reference white standard. Finally, we evaluate the accuracy of the standard model and the feasibility of the illuminant spectral estimation by using several test objectives.

Realization of a near-perfect antireflection coating for silicon solar energy utilization

Abstract: To harness the full spectrum of solar energy, Fresnel reflection at the surface of a solar cell must be eliminated over the entire solar spectrum and at all angles. Here, we show that a multilayer nanostructure having a graded-index profile, as predicted by theory [J. Opt. Soc. Am. 66, 515 (1976); Appl. Opt. 46, 6533 (2007)], can accomplish a near-perfect transmission of all-color of sunlight. An ultralow total reflectance of 1%-6% has been achieved over a broad spectrum, λ=400to1600 nm, and a wide range of angles of incidence, θ=0°-60°. The measured angle- and wavelength-averaged total reflectance of 3.79% is the smallest ever reported in the literature, to our knowledge.

X-ray diffraction of multilayers and superlattices

Abstract: Recursion formulae for calculating the reflected amplitude ratio of multilayers and superlattices have been derived from the Takagi-Taupin differential equations, which describe the dynamical diffraction of X-rays in deformed crystals. Calculated rocking curves of complicated layered structures, such as non-ideal superlattices on perfect crystals, are shown to be in good agreement with observed diffraction profiles. The kinematical theory can save computing time only in the case of an ideal superlattice, for which a geometric series can be used, but the reflectivity must be below 10% so that multiple reflections can be neglected. For a perfect crystal of arbitrary thickness the absorption at the center of the dynamical reflection is found to be proportional to the square root of the reflectivity. Sputter-deposited periodic multilayers of tungsten and carbon can be considered as an artificial crystal, for which dynamical X-ray diffraction calculations give results very similar to those of a macroscopic optical description in terms of the complex index of refraction and Fresnel reflection coefficients.