Fresnel Reflection Coefficients Research Articles

Radar Cross Section Analysis Using Physical Optics and Its Applications to Marine Targets

Radar Cross Section (RCS) is one of the most considerable parameters for ship stealth design. As modern ships are larger than their predecessors, RCS must be managed at each design stage for its reduction. For predicting RCS of ship, Radar Cross Section Analysis Program (RACSAN) based on Kirchhoff approximation in high frequency range has been developed. This program can present RCS including multi-bounce effect in exterior and interior structure by combination of geometric optics (GO) and physical optics (PO) methods, coating effect by using Fresnel reflection coefficient, and response time pattern for detected target. In this paper, RCS calculations of ship model with above effects are simulated by using this developed program and RCS results are discussed.

EXTENSION AND VALIDATION OF AN ADVANCED INTEGRAL EQUATION MODEL FOR BISTATIC SCATTERING FROM ROUGH SURFACES

This paper deals with the modeling of bistatic scattering from a randomly rough surface. An advanced integral equation model is presented by giving its general framework of model developments, model expressions, and predictions of bistatic scattering for various surface parameters. Extension work to improve the model accuracy is also reported in more detail. In particular, the transition function for the Fresnel reflection coefficient is in more general form. Model predictions are illustrated, demonstrated, and validated by extensive comparisons with numerical simulations. The updated advanced integral equation model remains a compact algebraic form for single scattering and substantially improves prediction accuracy in bistatic scattering that is drawing more emerging applications in earth remote sensing.

Casimir force between metal and graphene sheets

The Casimir force between neutral plates is attractive. For the Casimir force to be really useful one must be able to switch from attraction to repulsion. Exploiting the experimentalist’s ability to change the sign of the charge carriers in graphene, we show how the sign of the Fresnel reflection coefficients can be reversed. This gives rise to a Casimir force between a metal sheet and graphene, which can be either attractive or repulsive; we illustrate it for a dielectric cylinder and graphene sheet.

Modeling Light Propagation Through Bragg Reflection Gratings With an AdaptedMonte Carlo Method

Conventional Monte Carlo light propagation methods use Fresnel reflection coefficients to determine the probability that a photon reflects when reaching an interface. However, in structures, where the wave nature of light is important, such as Bragg reflection gratings, Fresnel coefficients cannot be used due to interference effects. The reflection coefficients for such structures can be calculated by applying wave equations for each wavelength to be simulated in the structure. These reflection coefficients are then used in the Monte Carlo simulation to model light propagation through interference-producing media. A number of Bragg gratings are modeled as an example and the results of the simulation are corroborated by analytic calculations.

High sensitivity lossy mode resonance sensors

We propose a sensor based on spectral as well as angular interrogation of lossy mode resonance between absorbing thin film lossy modes and the evanescent wave for measurement of variation in the refractive index of the bulk media. It is shown that a low index dielectric matching layer introduced between the prism and the lossy waveguiding layer can produce an efficient refractive index sensor. The obtained sensitivity (4000–5000nm/RIU) is comparable to some of the best surface plasmon resonance (SPR) sensors. Unlike the SPR sensor in which surface plasmons can be excited only by p-polarized (TM) light, the proposed sensor can operate at either of these polarizations. Detailed theoretical analysis of the proposed sensor based on Fresnel reflection coefficients and transfer matrix method is presented. Effect of losses (imaginary part of refractive index) on the sensor parameters is also presented in sufficient details. Various parameters such as resonance angle, film thickness and refractive index of various layers are optimized for maximum evanescent field enhancement and increased sensitivity.

Estimation of Soil Permittivity in Presence of Antenna-Soil Interactions

This work deals with a technique for estimating the soil permittivity starting from Ground-Penetrating-Radar (GPR) measurements collected under a reflection mode single view (one transmitting antenna) multistatic (plurality of receivers) configuration. The technique consists of two steps: i) first the soil Fresnel reflection coefficient is estimated; ii) then the soil electromagnetic parameters are inferred from the retrieved reflection coefficient. In real scenarios, the transmitting antenna couples with the soil as it is in close proximity of the air-soil interface so that mutual interactions arise. Accordingly, the transmitting antenna plane-wave spectrum depends on the electromagnetic properties of the medium under investigation. This strongly complicates the problem as the first step becomes a non-linear inverse problem. To overcome such a drawback, a pre-processing stage consisting of a suitable time gating procedure is here introduced. This allows to restore linearity of the Fresnel coefficient estimation. Moreover, it is also able to mitigate negative effect due to not matched transmitting antenna. Numerical examples are presented to assess the feasibility of the proposed technique.

On the Estimation of Thickness of Marine Oil Slicks From Sun-Glittered, Near-Infrared MERIS and MODIS Imagery: The Lebanon Oil Spill Case Study

The detection of marine oil slicks using satellite sun-glittered optical imagery has been recently assessed. As the nature of the imaging mechanism involves the altered features of the wind-roughened oil-covered sea surface, it is expected that the radiation reflected from the oil-water system carries information about the physical properties of the floating oil layer. In this paper, we report an investigation on the capability to retrieve the average thickness of thin marine oil slicks by using the sun-glittered component of the solar radiation in the near-infrared (NIR) bands of MEdium Resolution Imaging Spectrometer Instrument (MERIS) and MODerate Resolution Imaging Spectroradiometer (MODIS) images. The developed procedure exploits the Cox and Munk model to compute sun glint reflectance at the sea surface level for both clean and oil polluted sea surface as well. It is assumed that the Fresnel reflection coefficient of the oil-water system carries the relevant optical dependence on oil layer thickness and oil type. The expected oil-water system reflectance is computed by taking into account the non-uniform spatial distribution of the oil volume. This is achieved by considering a pdf of oil thicknesses that matches the observations on controlled oil slicks already reported in the scientific literature. MERIS and MODIS images gathered during the Lebanon oil spill occurred on July and August 2006 were selected as case study. When available, co-located SAR imagery was also considered to corroborate NIR-detected oil slicks.

Evanescent wave scattering by particles on a surface: Validation of the discrete dipole approximation with surface interaction against microwave analog experiments

The discrete dipole approximation with surface interaction (DDA-SI) is analyzed and expanded for the modeling of far-field scattering by objects on a surface illuminated by an evanescent wave generated by total internal reflection. More specifically, the electric field scattered in the far zone predicted via the DDA-SI is compared against scaled microwave experiments; additional comparisons are also performed using results from a Finite Element Method (FEM). Three cases are considered: a lossless cube with a side length of λ/1.79 (size parameter x=1.76), a lossless sphere with a diameter of λ/1.92 (x=1.63) and an absorbing sphere with a diameter of λ/0.87 (x=3.63), where λ is the wavelength. For lossless scatterers, a good agreement between the DDA-SI, the FEM and scaled microwave analog experiments is observed, especially when modified Fresnel reflection coefficients are used for computing the surface interaction in the DDA-SI. For an absorbing sphere, the experimental and FEM results are in reasonable agreement, while the DDA-SI exhibits a different trend. This behavior might be due to the fact that the accuracy of the DDA decreases as the permittivity and the size parameter increase. This work suggests that the DDA-SI could be used as a forward model in an evanescent wave-based characterization framework given that a thorough convergence and accuracy analysis is carried on in order to improve the performance when dealing with objects having large permittivity and/or size parameter.

Complex reflection coefficients of p- and s-polarized light at the pseudo-Brewster angle of a dielectric–conductor interface

The complex Fresnel reflection coefficients r(p) and r(s) of p- and s-polarized light and their ratio ρ=r(p)/r(s) at the pseudo-Brewster angle (PBA) φ(pB) of a dielectric-conductor interface are evaluated for all possible values of the complex relative dielectric function ε=|ε|exp(-jθ)=ε(r)-jε(i), ε(i)>0 that share the same φ(pB). Complex-plane trajectories of r(p), r(s), and ρ at the PBA are presented at discrete values of φ(pB) from 5° to 85° in equal steps of 5° as θ is increased from 0° to 180°. It is shown that for φ(pB)>70° (high-reflectance metals in the IR) r(p) at the PBA is essentially pure negative imaginary and the reflection phase shift δ(p)=arg(r(p))≈-90°. In the domain of fractional optical constants (vacuum UV or light incidence from a high-refractive-index immersion medium) 0<φ(pB)<45° and r(p) is pure real negative (δ(p)=π) when θ=tan(-1)(√(cos(2φ(pB)))), and the corresponding locus of ε in the complex plane is obtained. In the limit of ε(i)=0, ε(r)<0 (interface between a dielectric and plasmonic medium) the total reflection phase shifts δ(p), δ(s), Δ=δ(p)-δ(s)=arg(ρ) are also determined as functions of φ(pB).

Efficient Algorithm for the Evaluation of the Physical Optics Scattering by NURBS Surfaces With Relatively General Boundary Condition

An adaptive integration algorithm is presented for the computation of the Physical Optics (PO) electric and magnetic field scattered by electrically large objects modeled by Non-Uniform Rational B-Splines (NURBS). The algorithm is the customization of a more general-purpose result that has been recently published. By using a unique formulation both impenetrable (e.g., impedance surfaces, coated conductors) as well as transparent thin sheet materials (e.g., thin dielectric panels, or frequency selective surfaces) are treated, via their Fresnel reflection and transmission coefficients. The PO radiation integral is evaluated over the NURBS parametric domain. Since most of the computer-aided geometric design (CAGD) tools are based on NURBS, the proposed algorithm allows a straightforward electromagnetic analysis of the structures by exploiting the standard available geometrical description, with no need of generating new geometrical models. Furthermore, the proposed adaptive sampling requires a number of integration points that is found to be drastically smaller than that resulting from standard Nyquist-based sampling integration algorithms. Such reduction of the sampling points is achieved by resorting to high-frequency technique concepts and allows a significant reduction of the CPU computational burden. Therefore the algorithm is efficient and particulary suitable for the electromagnetic characterization of real-life electrically large objects.

Short surface waves in the Canadian Arctic in 2007 and 2008

[1] We have collected time series data of short oceanic waves as a part of the International Polar Year (IPY) 2007–2008. Using a shipboard laser wave slope (LAWAS) system operating at 900 nm, we have obtained wave slopes measurements up to 60 rad m−1 wave number. We have compared our in situ wave slopes with collocated and concurrent high-resolution upwind Normalized Radar Cross Sections (NRCS) collected by QuikSCAT. The LAWAS measured wave slope spectra were consistent with local wind speeds and QuikSCAT measured NRCS. Our measured short wave mean slopes indicate their enhancement by long waves (0–1 rad m−1) at small values of long-wave slope. Concurrent with wave slope measurements, the strength of the reflected LAWAS light beam was analyzed in terms of the light attenuation coefficient at 900 nm. We have observed a correlation between surface elevation and light attenuation. The mechanism of wave modulated beam attenuation was found to be related to the instantaneous long wave skewness.

Near-field thermal emission from metamaterials

A closed form expression for the local density of electromagnetic states (LDOS) due to a thermally emitting metamaterial bulk is derived from Maxwell's equations combined with fluctuational electrodynamics. The final form is the same as that for nonmagnetic materials, where the influence of the magnetic permeability is embedded in the Fresnel reflection coefficients. Spectral distributions of LDOS near metallic- and dielectric-based metamaterials are investigated. Results reveal that LDOS profiles are dominated by surface polaritons (SPs) in both TE and TM polarization states. A detailed discussion is provided on the necessary conditions for exciting TM- and TE-polarized SPs via a dispersion relation analysis that accounts for losses. Beyond the conventional conditions for excitation of SPs, the lossy dispersion relation analysis demonstrates mathematically that SPs exist when the imaginary parts of the permittivity or permeability, as well as n′n″, are close to zero, where n′ and n″ are the real and imaginary parts of the refractive index, respectively. An asymptotic expression for the extreme near field LDOS is derived, showing a Δ−3 power law relationship, as for nonmagnetic media, between LDOS and distance from the emitting bulk Δ. Results obtained from this study will assist in assessing material properties of arbitrarily electromagnetic materials in applications related to energy harvesting.

Corrections to the classical continuity boundary conditions at the interface of a composite medium

Using the multiple-scales homogenization method, we derive generalized sheet transition conditions (GSTCs) for electromagnetic fields at the interface between two media, one of which is free-space and the other a certain type of composite material. The parameters in these new boundary conditions are interpreted as effective electric and magnetic surface susceptibilities, which themselves are related to the geometry of the scatterers that constitute the composite. We show that the effective tangential E and H fields are not continuous across the interface except in the limit when the lattice constant (the spacing between the scatterers—atoms, molecules or inclusions in the case of a composite material) of the composite medium is very small compared to a wavelength. We derive first-order corrections to the classical continuity conditions. For naturally occurring materials whose lattice constants are on an atomic scale, these effects are shown to be negligible for waves at optical frequencies or lower. However, once the lattice constant becomes a significant fraction of a wavelength (which is the case for many artificial dielectrics and metamaterials), the corrections can be important. In previous work we have alluded to the fact that such a GSTC is needed to correctly account for the surface effects when extracting the effective material properties of a metamaterial. The results of this current paper justify the assumptions made in that previous work. In general, these GSTCs will result in corrections to the classical Fresnel reflection and transmission coefficients (which are themselves merely zeroth-order approximations to the actual reflection and transmission coefficients), and in a separate publication we will use these GSTCs to address this issue.

Effect of melting on the critical ignition energy of condensed explosives by a short laser pulse

A criterion for the initiation of explosives with a melting point below the ignition temperature by a short laser pulse is obtained. The criterion obtained is in good agreement with numerical solutions of the heat conduction equation in the cylindrical coordinate system. This criterion made it possible to explain experiments on the initiation of PETN from an open surface by a laser pulse in the range of transparency with variation in the diameter of the light beam. The calculation results coincided with the experiment at α = 0.065 cm−1 and the Fresnel reflection coefficient.

Exact image theory for a three layer medium

In this work an exact formulation and solution for the image source amplitude in a three layer medium is given. To do so a novel generalization of the Sommerfeld integral is employed. Of particular interest in this paper is the time-domain solution for the impulse response between source and observation points in the middle layer. It is shown that global boundary conditions can be accommodated for multiple reflections from media of having infinite extent. A branch integral formulation of inverse Laplace transform of integral powers of the Fresnel reflection coefficient is given for this case. It is shown that only odd-powers of the branch point argument contribute thereby reducing computational effort required to numerically evaluate the impulse response.

Sensitivity analysis of thin-film thickness measurement by vertical scanning white-light interferometry

The spectral nonlinear phase method and the Fourier amplitude method have been applied to measure the thin-film thickness profile in vertical scanning white-light interferometry (VSWLI). However, both the methods have their disadvantages, and accordingly their applications are limited. In the paper we have investigated the dependence of the sensitivities of both the methods on the thin-film thickness and refractive index, the objective numerical aperture, and the incident light spectral range of VSWLI. The relation of the Fresnel reflection coefficients on the wavelength effect is also discussed. Some important research results reveal that the combination of both Fourier amplitude and nonlinear phase methods may provide a new approach to improve the VSWLI measurement sensitivity for thin-film thickness profile.

Fano Interference between Localized Plasmons and Interface Reflections

Layers of subwavelength metal nanostructures that support localized surface plasmon resonances are of broad interest in applied nanotechnology, for example, in optical sensor development and solar energy harvesting devices. We measured specular reflection spectra as a function of incidence angle for two-dimensional layers of gold nanodisks on glass and found highly asymmetric line-shapes and a spectral red-shift of up to 0.2 eV, or 10% of the plasmon resonance energy, as the angle changed from normal toward grazing incidence. This dramatic angular dispersion is the result of a tunable Fano interference between the spectrally narrow plasmon emission and a "white" continuum caused by the interface reflection. The data are found to be in excellent agreement with predictions based on a theory for Fresnel reflection coefficients of an interface with subwavelength inclusions. The theory can also be used to derive analytical expressions for the Fano parameters.

Transformation of Rice’s small perturbation solution for rough surface scattering into the high frequency reciprocal physical and geometric optics solutions

A step by step transformation of the low frequency small height and slope perturbation solution into the high frequency reciprocal and dual, physical and geometrical optic solutions is presented. The familiar Kirchhoff approximations for the fields impressed by the incident plane wave upon the rough surfaces results in nonreciprocal solutions. It is shown that the surface element scattering coefficients based on the Kirchhoff approximations agree with the corresponding reciprocal physical optics solutions only at the stationary phase, specular points on the rough surfaces. While the Kirchhoff approximations and physical optics approximations are based on the characterization of the surface fields by Fresnel reflection coefficients, the corresponding surface element scatter coefficient derived for the small perturbation solution and the full wave solutions are based on the imposition of boundary conditions for the tangential components of the electric and magnetic fields. A flow graph schematically depicting the relationships between these solutions for the scattered fields is also presented.

Effective-medium approach to planar multilayer hyperbolic metamaterials: Strengths and limitations

We express the optical properties of multilayered hyperbolic metamaterials (HMMs) in terms of the Fresnel reflection coefficients at the boundary between the metamaterial and the ambient medium. Formation of a band of bulk propagating modes in HMMs located far outside the lightcone of homogeneous isotropic media is demonstrated. Exotic behavior of HMMs, such as the broadband Purcell effect and suppressed outward scattering, is reproduced. Conditions under which a metal-dielectric multilayer can be approximated by a homogeneous effective medium with extreme anisotropy (indefinite medium) are derived. It is shown that real multilayer HMMs usually have a smaller Purcell factor than the corresponding effective medium; however, the reverse scenario is shown to be possible due to an intermediary role of short-range surface plasmon excitations in the outermost metal layer in a metal-dielectric multilayer.

Assessment of specular radar backscatter from a planar surface using a physical optics approach

Satellite and airborne radar altimeter return signals often contain the specular component primarily in polar regions due to the backscatter from a relatively smooth and planar water or ice surface. It is demonstrated here that the specular backscatter from a planar surface should be estimated taking into account the spherical nature of the incident electromagnetic wave. This article introduces the radar equation derived using the physical optics approach and describes the backscatter as a function of the spatial distribution of the complex Fresnel reflection coefficient across a planar surface. The closed form of the radar equation was obtained for an infinite surface, an annulus and a disk with sizes greater than the radius of the first Fresnel zone.