Fresnel Laws Research Articles

Lagrangian descriptors for the Bunimovich stadium billiard.

We apply the concept of Lagrangian descriptors to the dynamics on the Bunimovich stadium billiard, a two-dimensional ergodic system with singular families of trajectories, namely, the bouncing ball and the whispering gallery orbits. They play a central role in structuring the phase space, which is unveiled here by means of the Lagrangian descriptors applied to the associated map on the boundary. More interestingly, we also consider the open stadium, which in the optical case (Fresnel's laws) can be directly related to recent microlaser experiments. We find that the structure of the emission profile of these systems can be easily described thanks to the open version of the Lagrangian descriptors.

Determination of the Brewster angle of the wave reflected from a plate with dielectric losses

In free space, the permittivity of materials is usually determined by the value of the Brewster angle using the angular dependences of the amplitude and phase of the wave reflected from the material plate. An expression corresponding to materials without dielectric and magnetic losses is used as a calculation model. Experimental studies of the parameters of the wave reflected from dielectric materials show the discrepancies with theoretical calculations known as deviations from the Fresnel laws. We present the results of determining the Brewster angle of the wave reflected from a plate made of a material with dielectric losses. The angular dependences of the amplitude and phase of the reflected wave were calculated using the numerical solution of the problem of falling at an arbitrary angle of a plane linearly polarized wave with an electric field vector lying in the plane of incidence on a plate of a dielectric material with complex values of the dielectric and magnetic permittivity. They were used to determine the angles corresponding to the minimum reflection coefficient depending on the dielectric losses of the plate material. The differences between the numerical calculations and the data obtained using the Brewster angle formula were noted, which increased with increasing dielectric losses of the material. From the condition that the modulus of the reflected wave amplitude is equal to zero, a different formula for calculating the Brewster angle for a material with losses is analytically obtained. The results of calculations using this formula coincided with the calculations for the reflected wave when solving the classical problem of the inclined incidence of a plane wave on a plate of a dielectric material in the framework of geometric optics. The results obtained can be used to determine the Brewster angle for a wave reflected from a plate with magnetic and dielectric losses.

Dirac fermion optics and directed emission from single- and bilayer graphene cavities

High-mobility graphene hosting massless charge carriers with linear dispersion provides a promising platform for electron optics phenomena. Inspired by the physics of dielectric optical micro-cavities where the photon emission characteristics can be efficiently tuned via the cavity shape, we study corresponding mechanisms for trapped Dirac fermionic resonant states in deformed micro-disk graphene billiards and directed emission from those. In such graphene devices a back-gate voltage provides an additional tunable parameter to mimic different effective refractive indices and thereby the corresponding Fresnel laws at the boundaries. Moreover, cavities based on single-layer and double-layer graphene exhibit Klein- and anti-Klein tunneling, respectively, leading to distinct differences with respect to dwell times and resulting emission profiles of the cavity states. Moreover, we find a variety of different emission characteristics depending on the position of the source where charge carriers are fed into the cavites. Combining quantum mechanical simulations with optical ray tracing and a corresponding phase-space analysis, we demonstrate strong confinement of the emitted charge carriers in the mid field of single-layer graphene systems and can relate this to a lensing effect. For bilayer graphene, trapping of the resonant states is more efficient and the emission characteristics do less depend on the source position.

Demonstrating Arago-Fresnel laws with Bessel beams from vectorial axicons.

Two-dimensional Bessel beams, both vectorial and scalar, have been extensively studied to date, finding many applications. Here we mimic a vectorial axicon to create one-dimensional scalar Bessel beams embedded in a two-dimensional vectorial field. We use a digital micro-mirror device to interfere orthogonal conical waves from a holographic axicon, and study the boundary of scalar and vectorial states in the context of structured light using the Arago-Fresnel laws. We show that the entire field resembles a vectorial combination of parabolic beams, exhibiting dependence on solutions to the inhomogeneous Bessel equation and asymmetry due to the orbital angular momentum associated rotational diffraction. Our work reveals the rich optical processes involved at the interplay between scalar and vectorial interference, opening intriguing questions on the duality, complementarity, and non-separability of vectorial light fields.

Observation and verification of the Fresnel and Arago interference laws using adaptive photodetectors

The Fresnel and Arago interference laws relate the polarization of the electromagnetic field to the interference phenomenon. Different methods and interferometers have been reported to verify these laws; most of them rely on visual inspection to determine the positions of maximum and minimum interference. In this report, the observation and verification of the Fresnel and Arago interference laws using adaptive photodetectors are presented. These photodetectors generate an electrical current proportional to the square of the visibility of the interference pattern; thus the gradual change from the appearance of the interference pattern (maximum visibility) to its disappearance (minimum or null visibility) is detected as an electrical current. The extreme values of the interference pattern visibility can be accurately assessed, in real time and without any signal processing using. A difference of 3 orders of magnitude between the signals measured in the positions of maximum and minimum interference is demonstrated. Due to the adaptive properties of the adaptive photodetectors (compensation of the irregularities of the interfering beams and suppression environmental fluctuations), the proposed method can be suitable for teaching purposes in undergraduate laboratories.

Analytical Fresnel laws for curved dielectric interfaces

Fresnel laws and the corresponding Fresnel reflection and transmission coefficients provide the quantitative information of the amount of reflected and transmitted (refracted) light in dependence on its angle of incidence. They are at the core of ray optics at planar interfaces. However, the well-known Fresnel formulae do not hold at curved interfaces and deviations are appreciable when the radius of curvature becomes of the order of several wavelengths of the incident light. This is of particular importance for optical microcavities that play a significant role in many modern research fields. Their convexly curved interfaces modify Fresnel’s law in a characteristic manner. Most notably, the onset of total internal reflection is shifted to angles larger than critical incidence (Martina and Henning 2002 Phys. Rev. E 65 045603). Here, we derive analytical Fresnel formulae for the opposite type of interface curvature, namely concavely curved refractive index boundaries, that have not been available so far. The accessibility of curvature-dependent Fresnel coefficients facilitates the analytical, ray-optics based description of light in complex mesoscopic optical structures that will be important in future nano- and microphotonic applications.

Nonreciprocal Optical and Magnetooptical Effects in Semiconductor Quantum Wells

Abstract—Effects implying violation of the Fresnel light reflection laws in semiconductor structures with quantum wells (QWs) have been investigated. This violation is related to the manifestation of spatial dispersion caused by spin–orbit coupling in structures without inversion centers. The spin–orbit coupling constants characterizing polarization conversion in symmetric and asymmetric structures with QWs have been measured.

Nonlinear effects in the propagation, reflection and refraction of magnetosonic waves

Reflection and refraction of magnetosonic waves in domains of different sound and Alfvén speeds have been often studied by means of the linearized magnetohydrodynamic equations, obtaining a more complex version of Fresnel laws. However, these waves are intrinsically nonlinear and this method does not describe adequately wave interaction. We consider high-frequency waves by means of the geometric optics approximation to follow the waves evolution until the interface is reached, where this procedure fails because the variation of spatial scales is faster than the frequency. It is shown that a connection with a local linear analysis is feasible, thus yielding the full evolution including reflection, transmission and presence of surface waves, as well as the influence of the interface on the time of shock formation.

Radiation of a charge in presence of a dielectric object: aperture method

We develop an original method for calculation of radiation from a charge moving in the presence of a dielectric object. The method can be applied to objects which are larger than the wavelengths under consideration. First, the field of a charge in an infinite medium (without external boundaries) is calculated. Further the field at the external boundary of the object (“the aperture”) is found using the Snell's and Fresnel's laws. At final step of this technique, we calculate the field outside the target using Stratton-Chu formulae (“aperture integrals”). Contrary to the ray-optic technique, this method is valid for the observation point with arbitrary wave parameter (including Fraunhofer area) as well as in neighborhoods of focuses and caustics. We apply the method developed to the cone with vacuum channel where the charge moves (axially symmetrical problem). As well, this problem is simulated using COMSOL Multiphysics. Comparing results of both techniques one can conclude that the aperture method can be applied even for relatively small objects which have the size of several wavelengths. It is important as well that the accuracy of calculations increases with an increase in the distance from the aperture.

Невзаимные оптические и магнитооптические эффекты в полупроводниковых квантовых ямах

Abstract —Effects implying violation of the Fresnel light reflection laws in semiconductor structures with quantum wells (QWs) have been investigated. This violation is related to the manifestation of spatial dispersion caused by spin–orbit coupling in structures without inversion centers. The spin–orbit coupling constants characterizing polarization conversion in symmetric and asymmetric structures with QWs have been measured.

Experimental study of saturation by visible light transmission in dual-scale fibrous reinforcements during composite manufacturing

A new in situ monitoring strategy is proposed to study void formation during real-time impregnation of dual-scale fibrous reinforcements in liquid composite molding. Void content data from burn-off tests are used to calibrate a refractive index matching approach based on two optical principles: Beer–Lambert and Fresnel laws. Once calibrated, this approach based on visible light transmission is used to study the impact of key process parameters on the saturation footprint of dual-scale fibrous reinforcements during and after mold filling. The injection parameters investigated are the flow front velocity, the pressure distribution inside the mold cavity, the bleeding flow rate, and the mold packing pressure. The experimental setup is a computer-assisted injection system and a transparent resin transfer molding mold is used to perform unidirectional injections. A vinyl ester resin is injected through E-glass bidirectional non-crimp fabrics under various manufacturing conditions. This investigation not only confirms the decreasing trend in void formation by mechanical entrapment of air with the decrease in impregnation velocity, as it converges toward the optimal impregnation conditions for this fibrous reinforcement reported in previous studies, but it also brings insights on void dissolution and transport in liquid composite molding.

Fresnel's laws, ceteris paribus

This article is about structural realism, historical continuity, laws of nature, and ceteris paribus clauses. Fresnel's Laws of optics support Structural Realism because they are a scientific structure that has survived theory change. However, the history of Fresnel's Laws which has been depicted in debates over realism since the 1980s is badly distorted. Specifically, claims that J. C. Maxwell or his followers believed in an ontologically-subsistent electromagnetic field, and gave up the aether, before Einstein's annus mirabilis in 1905 are indefensible. Related claims that Maxwell himself did not believe in a luminiferous aether are also indefensible. This paper corrects the record. In order to trace Fresnel's Laws across significant ontological changes, they must be followed past Einstein into modern physics and nonlinear optics. I develop the philosophical implications of a more accurate history, and analyze Fresnel's Laws' historical trajectory in terms of dynamic ceteris paribus clauses. Structuralists have not embraced ceteris paribus laws, but they continue to point to Fresnel's Laws to resist anti-realist arguments from theory change. Fresnel's Laws fit the standard definition of a ceteris paribus law as a law applicable only in particular circumstances. Realists who appeal to the historical continuity of Fresnel's Laws to combat anti-realists must incorporate ceteris paribus laws into their metaphysics.

Unique Solvability of Stationary Radiative-Conductive Heat Transfer Problem in a System of Semitransparent Bodies

We consider the boundary value problem for a system of differential equations consisting of the stationary nonlinear heat equation and the integro-differential radiative transfer equation and describing stationary radiative-conductive heat transfer in a system of semitransparent bodies, taking into account the effects of reflection and refraction of radiation according to the Fresnel laws at the boundaries of bodies. We take into account the dependence of radiation intensity and optical properties of bodies on the radiation frequency. We establish the existence and uniqueness of a weak solution. We prove the comparison theorem and derive a priori estimates for weak solutions and obtain a regularity result.

Optical Absorption Enhancement in CdTe Thin Films by Microstructuration of the Silicon Substrate.

In this work, the reflectance, optical absorption, and band gap have been determined for CdTe thin films grown on planar and microstructured substrates. The treated surface was prepared by laser ablation of a silicon wafer, forming holes in a periodic arrangement. Thin films were grown by pulsed laser ablation on silicon samples kept at 200 °C inside a vacuum chamber. The presence of CdTe was verified with X-ray diffraction and Raman spectroscopy indicating a nanocrystalline zinc blended structure. The optical absorption of thin films was calculated by using the Fresnel laws and the experimental reflectance spectrum. Results show that reflectance of 245 nm films deposited on modified substrates is reduced by up to a factor of two than the obtained on unchanged silicon and the optical absorption is 16% higher at ~456 nm. Additionally, it was determined that the band gap energy for planar and microstructured films is about 1.44 eV for both cases.

Unique solvability of a nonstationary problem of radiative-conductive heat exchange in a system of semitransparent bodies

A nonstationary initial boundary value problem describing the radiative-conductive heat exchange in a system of semitransparent bodies is considered. The radiation transfer equation with boundary conditions of mirror reflection and refraction according to the Fresnel laws is used to describe the propagation of radiation. The dependence of the radiation intensity and the optical properties of bodies on the radiation frequency is taken into account. The existence and uniqueness of a weak solution are proved. A comparison theorem is proved. Some a priori estimates for the weak solution are derived and its regularity is proved.

Polarization dependence of plasmonic near-field enhanced photoemission from cross antennas

The field enhancement of individual cross-shaped nanoantennas for normal incident light has been measured by the relative photoemission yield using a photoemission electron microscope. We not only measured the electron yield in dependence on the intensity of infrared light (800 nm, 100 fs), but also the polarization dependence. In the normal incidence geometry, the electrical field vector of the illuminating light lies in the surface plane of the sample, independent of the polarization state. Strong yield variations due to an out-of-plane field component as well as changes in the polarization state described by the Fresnel laws are avoided. The electron yield is related to the near-field enhancement as a function of the polarization state of the incident light. The polarization dependence is well explained by numerical simulations.

Sensitivity enhancement of metal clad planar waveguide sensor using metamaterial layer as a guiding layer

In the present paper, a comprehensive study of sensitivity and reflectance of metal clad planar waveguide biosensor having metamaterial in guiding layer has been done. The sensitivity and reflectivity of proposed waveguide sensor are calculated using Fresnel's laws. It is observed that the sensitivity of a waveguide is highly affected by the presence of metamaterial layer. The calculated sensitivity has been compared with those reported in the earlier studies. It is observed that the sensitivity increases in the presence of metamaterial.

The Conjugate Boundary Value Problem for Radiation Transfer Equation with Reflection and Refraction Conditions

We consider the conjugate problem of the boundary value problem for radiation transfer equation with mirror reflection and refraction conditions subject to the Fresnel laws, describing radiation transfer in a system of semitransparent bodies. We show that the resolving operator A ∗ of the conjugate problem is the adjoint of the resolving operator A of the original problem and A ∗ = UA U, where Uf(ω, x) = f(−ω, x). Bibliography: 7 titles.

The Radiation Transfer Equation with Reflection and Refraction Conditions. Continuous Dependence of Solutions on the Data and Limit Passage to the Problem with “Shooting Conditions”

We study the boundary value problem for the radiation transfer equation with reflection and refraction conditions subject to the Fresnel laws which governs radiation transfer in a system of semitransparent bodies. We establish the continuous dependence of the solution on the data and prove that the solution of this problem converges to the solution of the radiation transfer equation with the “shooting condition” as the refraction exponent tends to 1. Under natural assumptions on the dependence of optic properties of bodies on the radiation frequency ν, we show that the radiation intensity I ν , regarded as a function of ν with values in , is a strongly measurable function, the Bochner integral (where is the absorption coefficient) is defined in L 1(D) and can be estimated in terms of the data of the problem. Bibliography: 9 titles.

Benchmarking of L-band soil microwave emission models

A first step before assimilating Soil Moisture and Ocean Salinity (SMOS) L-band brightness temperatures (Tb) over land is to couple land surface models (LSMs) to microwave emission models. In this study, the Interactions between Soil Biosphere and Atmosphere (ISBA) LSM is coupled to the Community Microwave Emission Modelling platform (CMEM). Simulations of Tb are performed over a 3-yr period (2003–2005) for a bare soil field in southwestern France, at the Surface Monitoring Of the Soil Reservoir EXperiment (SMOSREX) experimental site. Both ISBA and CMEM present several options for the representation of the soil moisture and soil temperature profiles. Simplified 2-layer simulations are compared with more detailed multilayer simulations. In the 2-layer simulations, the soil is divided into two layers (a thin surface layer and a bulk reservoir), and Fresnel laws are used in CMEM to model the smooth surface emissivity. In the multilayer simulations, the ISBA soil diffusion scheme is used (with 11 soil layers represented) together with either the Wilheit or Fresnel option of CMEM. The Tb simulations are compared to the Tb ground observations available for the SMOSREX site, at H and V polarizations and at different angles, and the impact of soil roughness is assessed. It is shown that taking surface soil moisture into account in the calculation of soil roughness improves the representation of the seasonal cycle and increases the correlation for all the versions of CMEM. The Tb derived from the most complex multilayer simulations correlate slightly better to the observations than the Tb derived from the 2-layer model (r=0.84 and r=0.82, respectively, for the pooled dataset). This is partly due to a better representation of the soil moisture profile. Finally, the multilayer model is used to investigate the L-band sampling depth for contrasting soil texture profiles. For a variety of soil textures, it is found that Tb are mainly driven by the top 15cm soil layer.