Brewster Effect Research Articles

Guided-mode resonance Brewster filters with multiple channels

In this letter, a type of guided-mode resonance (GMR) reflection filter incorporating multimode resonance and the Brewster effect is presented. Long-range, low sidebands, and multiple channels are found to be obtainable for a single-layer GMR reflection filter with a TM-polarized plane wave incident at the Brewster angle. Detailed characteristics are calculated using rigorous coupled-wave analysis. In our calculation, for TM-polarized incident wave, we find it sufficiently accurate to calculate the effect index by using the zero-order permittivity ε0,TM of the effective media theory, and narrowband multichannel reflectance can be achieved at the Brewster angle by tuning the grating depth.

Observation of Brewster’s effect for transverse-electric electromagnetic waves in metamaterials: Experiment and theory

We have experimentally realized Brewster's effect for transverse-electric waves with metamaterials. In dielectric media, Brewster's no-reflection effect arises only for transverse-magnetic waves. However, it has been theoretically predicted that Brewster's effect arises for TE waves under the condition that the relative permeability ${\ensuremath{\mu}}_{\mathrm{r}}$ is not equal to unity. We have designed an array of split-ring resonators as a metamaterial with ${\ensuremath{\mu}}_{\mathrm{r}}\ensuremath{\ne}1$ using a finite-difference time-domain method. The reflection measurements were carried out in a $3\text{\ensuremath{-}}\mathrm{GHz}$ region and the disappearance of reflected waves at a particular incident angle was confirmed.

Unattenuated light transmission through the interface between two materials with different indices of refraction using magnetic metamaterials

We report on the application of a magnetic composite metamaterial. The magnetic response of the metamaterial in the light region of the spectrum can realize the Brewster condition for $s$-polarized light. By introducing a uniaxial magnetic metamaterial consisting of stacked two-dimensional arrays of split-ring resonators, the Brewster effect can be produced for both $p$ and $s$ polarizations simultaneously. We also propose optical components that can interconnect two materials of different refractive index and that can transmit the light across the material boundary without any reflection at the interface.

Interaction of polarized light with three-dimensional opal-based photonic crystals

We studied polarization- and angle-resolved optical transmissivity of high quality synthetic opals and found a strong anisotropy in the intensity of the transmitted light at different polarizations for most directions of propagation in the opal photonic crystal. The differential transmissivity ${T}_{\ensuremath{\Vert}}\ensuremath{-}{T}_{\ensuremath{\perp}}$ at two orthogonal polarizations is nearly frequency-independent for the $\ensuremath{\Gamma}\text{\ensuremath{-}}L$ incident light, but it is positive in the energy range of the {111} photonic stop gaps and negative in the energy range of the {200} stop gaps in the case of the $\ensuremath{\Gamma}\text{\ensuremath{-}}K$ incidence. The polarization-resolved transmission spectra can be qualitatively analyzed in terms of the Fresnel theory and the Brewster effect taking into account the relative orientation of the ${hkl}$ crystallographic planes in the opal structure.

Electromagnetic wave propagation in anisotropic metamaterials created by a set of periodic inductor-capacitor circuit networks

We propose a complete set of periodic circuit networks which can realize electromagnetic wave propagation in different two-dimensional (2D) isotropic and anisotropic metamaterials (AMMs). We synthesize the periodic circuits with unit cells of series capacitor or inductor in orthogonal directions, together with either capacitor or inductor shunted to ground. The dispersion relations of the periodic circuits are derived by applying Bloch boundary conditions to the unit cell, which show either elliptic or hyperbolic dispersion surface in phase space. The effective constitutive parameters are obtained by choosing different types and values of the impedance elements in the unit cell. The validity of the circuit models is proved by showing examples that the anisotropic $L\text{\ensuremath{-}}C$ circuits could exhibit the wave propagation characteristics of two 2D AMMs with different cutoff properties, called never-cutoff or anti-cutoff medium. We construct interfaces between isotropic normal medium and AMMs with properly designed $L\text{\ensuremath{-}}C$ circuits and analyze the electromagnetic wave propagation using microwave circuit simulations. We demonstrate extraordinary electromagnetic wave reflection and refraction phenomena including negative refraction, total reflection with reversion of the critical angle and anomalous Brewster effect that have good agreements with the theoretical analysis. Furthermore, we show that the $L\text{\ensuremath{-}}C$ circuit models of AMMs could lead to different approach of actual implementation of 2D AMMs through capacitance loaded transmission line metamaterials. The simulation on actual microstrip line structure demonstrates similar wave propagation phenomena of AMMs, and the losses in the structure only affect the magnitude of the propagating energy.

Localization of transverse waves in randomly layered media at oblique incidence

We investigate the oblique incidence of transverse waves on a randomly layered medium in the limit of strong disorder. An approximate method for calculating the inverse localization length based on the assumptions of zero energy flux and complete phase stochastization is presented. Two effects not found at normal incidence have been studied: dependence of the localization length on the polarization, and decrease of the localization length due to the internal reflections from layers with small refractive indexes. The inverse localization length (attenuation rate) for P-polarized radiation is shown to be always smaller than that of S-waves, which is to say that long enough randomly layered sample polarizes transmitted radiation. The localization length for P-polarization depends non-monotonically on the angle of propagation, and under certain conditions turns to infinity at some angle, which means that typical (non-resonant) random realizations become transparent at this angle of incidence (stochastic Brewster effect).

Anisotropy and oblique total transmission at a planar negative-index interface

We show that a class of negative index (n) materials has interesting anisotropic optical properties, manifest in the effective refraction index that can be positive, negative, or purely imaginary under different incidence conditions. With dispersion taken into account, reflection at a planar negative-index interface exhibits frequency selective total oblique transmission that is distinct from the Brewster effect. Finite-difference-time-domain simulation of realistic negative-n structures confirms the analytic results based on effective indices.

Analogs of the brewster effect and total internal reflection for cylindrical waves

Analogs of the Brewster effect and total internal reflection were investigated for cylindrical waves passing through a cylindrical interface. It was found that, in the case of cylindrical geometry, the Brewster effect is also observed but weakens with decreasing moment of momentum of a cylindrical wave. Wave reflection from a small-radius cylindrical interface is analyzed. Asymptotic expressions for the reflection factor of a cylindrical wave are obtained when the radius of the interface tends to zero. It was found that, as the radius the interface decreases, the reflection factor of a cylindrical wave with a nonzero moment of momentum approaches unity from the left but does not reach this value.

Density of states for a dielectric superlattice. II. TM polarization

We present an analysis of the band structure, the equifrequency surfaces, and the density of states (DOS) for the transverse magnetic (TM) polarization mode of the dielectric superlattice, modeled by means of Dirac-delta functions. This complements a recent article [Phys. Rev E 59, 3624 (1999)] that analyzes the case of transverse electric (TE) polarization. Unfortunately, for this simple model, there is no manifestation of the Brewster effect in the band structure for the TM modes. For large values of the frequency or the grating strength, the equifrequency surfaces essentially degenerate into a set of concentric, hollow, and narrow cylinders centered on the superlattice axis. The DOS is enhanced relative to free space for any frequency and it exhibits discontinuities in the slope at the band edges. These results are relevant to the spontaneous emission by an atom or to dipole radiation in one-dimensional periodic structures. The differences between TE and TM modes are discussed. We take the opportunity to correct an error in the DOS calculation for TE polarization in the article referred above.

Bragg reflectors for cylindrical waves

Abstract A transfer matrix method is developed to calculate the electromagnetic field in a dielectric structure with circular cylindrical symmetry. The equations for the reflection and transmission coefficients of cylindrical waves from a single cylindrical boundary between two dielectrics and from a cylindrical multilayered structure are obtained. For a single dielectric interface, enhanced reflection at small interface radii and the analogue of the Brewster effect are predicted and investigated. The design of an optimized cylindrical Bragg reflector (CBR) for cylindrical waves is proposed and its optical properties are studied. It is found that the thicknesses of the layers in the CBR must be different, to provide the adjustment of the phase of the waves, that are reflected from the interfaces at different radii.

Bragg reflectors for cylindrical waves

A transfer matrix method is developed to calculate the electromagnetic field in a dielectric structure with circular cylindrical symmetry. The equations for the reflection and transmission coefficients of cylindrical waves from a single cylindrical boundary between two dielectrics and from a cylindrical multilayered structure are obtained. For a single dielectric interface, enhanced reflection at small interface radii and the analogue of the Brewster effect are predicted and investigated. The design of an optimized cylindrical Bragg reflector (CBR) for cylindrical waves is proposed and its optical properties are studied. It is found that the thicknesses of the layers in the CBR must be different, to provide the adjustment of the phase of the waves, that are reflected from the interfaces at different radii.

Guided-mode resonance Brewster filter

A new type of optical filter is predicted theoretically and verified experimentally. The filter operates under guided-mode resonance conditions in a thin-film waveguide grating. A high-efficiency reflection filter response is produced at the Brewster angle at which TM reflection is classically prohibited. Low-reflectance sidebands are obtained that are adjacent to the resonance peak induced by the Brewster effect in the neighborhood of the resonance peak. A double-layer waveguide grating yields 94% experimental reflectance at the thin-film Brewster angle for a Gaussian laser beam with TM polarization at the 1064-nm wavelength.

Application of polarimetric sounding to HF ionospheric remote sensing

It is shown that the scattering of electromagnetic waves by refractive index inhomogeneities in a continuous random medium is accompanied by a certain polarimetric phenomenon that is analogous to the Brewster effect of classic electrodynamics. In this paper, an observational method and results are discussed for the case of bistatic HF radar sounding of small‐scale ionospheric inhomogeneities at frequencies above MUF. The height of the scattering layer, its thickness, and characteristic plasma drift velocity in the ionosphere are estimated as a result of statistical processing.

Propagation constant — limited surface modes in dielectric superlattices

The surface modes of a dielectric superlattice — their very existence — depend strongly on the position of the surface (the cut-plane through the last cell). For example, TE and TM surface waves can propagate even when the layer next to the surface is made of lower-index material. In this case we find a novel TE mode where the propagation constant is limited by a bulk band. For TM polarization, the propagation constant may be limited due to a different mechanism, namely the internal (within the dielectric layers ε a, ε b) Brewster effect. This upper bound is k 0[ ε a ε b (ε a + ε b ) ] 1 2 , where k 0 is the vacuum propagation constant.

The Brewster effect for a one-dimensional random surface

Abstract By the use of a unitarity and reciprocity conserving theory for the scattering of p-polarized light from a one-dimensional random dielectric surface the we determine the shift in the Brewster angle toward smaller angles of incidence caused by the surface roughness, and the (non-zero) value of the reflectivity at its minimum. Both quantities may be useful in the characterization of the roughness of such surfaces.

Localization and Resonance Transmission of Light Waves in a One-Dimensionally Disordered Dielectric. Polarization Effects

Using a diagrammatic self-consistent approach the problem of Anderson localization is treated for photons with different polarizations in a layered random dielectric. The diffusion coefficient and localization length are calculated for photons. Two types of anomalies are found whose manifestation is a divergency of the localization length. One of the anomalies, which originates in the total transmission of light through scatterers, is peculiar to both (s and p) polarizations. Another anomaly associated with the Brewster effect is a feature of p-polarized waves only. [Russian Text Ignored].

Spectral behavior of anomalies in deep metallic gratings

An experimental investigation of spectral dependence of two recently discovered anomalies in deep metallic gratings is presented. Good coincidence with theoretical results is obtained. It is shown that the Brewster effect in deep gratings is suppressed with a decrease of wavelength, as the angle of incidence approaches zero. At the same time the groove-depth interval widens, and low values of reflectivity are observed.

Brewster effects for deep metallic gratings

Total absorption of light by highly modulated metallic gratings is demonstrated both theoretically and experimentally. This phenomenon occurs when only the zeroth-order propagates and is linked with the excitation of surface plasmons.

Brewster angle light scattering from bubbles in water: Observations and potential applications to the acoustics of natural microbubbles

Consider the reflection of light from a clean gas bubble in water such that the light is polarized with its electric field parallel to the scattering plane. The Fresnel reflection coefficient should vanish when the local angle of incidence i is at Brewster's angle iB = arctan (n−1) ≈ 36.9 deg, where n = 1.33 is the refractive index of water. When the scattering angle θ is close to that of the Brewster scattering angle, θB = (180 − 2iB) ≈ 106.2 deg, this Brewster effect should be strongly manifested in the scattering pattern [D. L. Kingsbury and P. L. Marston, Appl. Opt. 20, 2348–2350 (1981)]. In the present research the first laboratory observations described are of Brewster effects in the scattering patterns of bubbles rising through water having radii ≈ 70μm. There is a noticeable reduction in the visibility of fringes in the scattering pattern for scattering angles ≈θB. (The fringes arise from the interference of a farside ray with the reflected ray.) Microbubbles of natural origin can be important in ocean and bioacoustics and Brewster effects may be useful in the optical characterization of such bubbles including the discrimination of optical scattering patterns of bubbles from those of particles or cells. Brewster angle scattering may also be useful for characterization of the surfactant coating that is thought to occur on some microbubbles in nature. [Work supported by ONR.]

Brewster effect on amplitude and phase of reflectivity in the exciton spectral region

For the first time the exact Brewster effect has been identified in the exciton reflection spectrum. Experimentally, the amplitude and phase of the reflection coefficient for the ground exciton state in ZnTe at 2 K were studied versus the angle of incidence. It is shown that, in spite of strong excitonic absorption, the reflectivity can be zero either in p- or in s-components of polarization, including the case of normal incidence. The observation conditions for the effect are analysed within the framework of the spatial dispersion theory taking into account the presence of the exciton-free surface layer.