pseudo-Brewster Angles Research Articles

Theory of quantized photonic spin Hall effect in strained graphene under a sub-Tesla external magnetic field.

The quantized photonic spin Hall effect (PSHE) in the strained graphene-substrate system is predicted under a sub-Tesla external magnetic field, which is two orders of magnitude smaller than required to produce the quantized effect in the conventional graphene-substrate system. It is found that in-plane and transverse spin-dependent splittings in the PSHE, exhibit different quantized behaviors and are closely related to the reflection coefficients. Unlike the quantized PSHE in the conventional graphene-substrate system formed by the splitting of real Landau levels, the quantized PSHE in the strained graphene-substrate system is attributed to the splitting of pseudo-Landau levels caused by the pseudo-magnetic field and the lifting of valley degeneracy of the n ≠ 0 pseudo-Landau levels induced by the sub-Tesla external magnetic field. At the same time, the pseudo-Brewster angles of the system are also quantized with the change of Fermi energy. The sub-Tesla external magnetic field and the PSHE appear as quantized peak values near these angles. The giant quantized PSHE is expected to be used for direct optical measurements of the quantized conductivities and pseudo-Landau levels in the monolayer strained graphene.

Enhanced and unidirectional photonic spin Hall effect in a plasmonic metasurface with S4 symmetry.

In this Letter, we report the significant enhancement of the photonic spin Hall effect (SHE) in a plasmonic metasurface with ${\rm S}_4$ symmetry. We find that an enhanced SHE of reflected light can occur in both horizontally and vertically polarized incident beams, and the maximum transverse displacement can approach half of the beam waist. Such a large displacement is caused by the non-resonant and near-zero pseudo-Brewster angles in the plasmonic metasurface. Owing to ${\rm S}_4$ symmetry, a unidirectional SHE is obtained in the metasurface, i.e., large and tiny transverse displacements are realized for a linearly polarized beam incident from the opposite side. This Letter provides a new, to the best of our knowledge, way to achieve an enhanced photonic SHE and offers more opportunities for designing spin-based nanophotonic devices.

Modified Brewster and pseudo-Brewster angles at the interface between isotropic lossy media.

Conditions for the appearance of a modified Brewster or polarizing angle θP' at which the magnitude of the reflection coefficient |Γp| vanishes when both media have loss are derived. When these conditions are not satisfied, a pseudo-Brewster angle θPB occurs at which |Γp| is a minimum. Conditions are described under which previous expressions for the pseudo-Brewster angle are valid.

The double Brewster angle effect

Abstract The Double Brewster angle effect (DBE) is an extension of the Brewster angle to double reflection on two orthogonal dielectric surfaces. It results from the combination of two pseudo-Brewster angles occurring in complementary incidence angles domains. It can be observed for a large range of incidence angles provided that double bounces mechanism is present. As a consequence of this effect, we show that the reflection coefficient at VV polarization can be at least 10 dB lower than the reflection coefficient at HH polarization over a wide range of incidence angle – typically from 20 to 70 ∘ . It is experimentally demonstrated using a Synthetic Aperture Radar (SAR) image that this effect can be seen on buildings and forests. For large buildings, the difference can reach more than 20 dB.

Goos-Hänchen shift at the reflection of light from the complex structures composed of superconducting and dielectric layers

The Goos-Hänchen effect of light reflected from sandwich (three-layered) structures composed of a superconducting YBa2Cu3O7 film and two different dielectric films is investigated theoretically. It has been shown that optical anisotropy of YBa2Cu3O7 film, as well as its positions in the three-layer specimen, strongly effects on the lateral shift values. We have shown that, for all positions of the superconducting film in the three-layered structure, variation of temperature makes possible to control the values of the lateral shift of TE-polarized light at the incidence angles close to pseudo-Brewster angles, whereas for TM-polarized light the lateral shift is only significant at grazing incidence.

Reflection and transmission characteristics of electromagnetic waves by the uniaxially anisotropic chiral slab

The reflection and transmission characteristics of electromagnetic waves by the uniaxially anisotropic chiral slab with the optical axis parallel to the interface are investigated. Formulas of the reflection and transmission coefficients (power) are derived. The curves of powers of the reflected and transmitted electromagnetic waves are presented for four cases of dielectric constants according to their signs. The effects of chirality parameter on the reflection and transmission are discussed. Especially, the dependences of pseudo-Brewster angles on the chirality parameter are plotted.

Magneto-Optical Ellipsometry: Effect of Cubic Optical Nonlinearity

We investigate optical plane rotation and ellipticity at light reflection from a nonlinear optical dielectric film on a bigyrotropic magneto-electric slab. We have analyzed the optical nonlinearity and the magneto-electric coupling contributions to the ellipsometric parameters for both s- and p-polarized light at the incidence angles close to pseudo-Brewster angles.

Difference between the second-Brewster and pseudo-Brewster angles when polarized light is reflected at a dielectric–conductor interface

For a given pseudo-Brewster angle phi(pB) of minimum reflectance |r(p)| of p-polarized light at a dielectric-conductor interface, the second-Brewster angle phi(2B) of minimum reflectance ratio |rho|=|r(p)|/|r(s)| of the p and s polarizations is determined for all possible values of the complex relative dielectric function epsilon that lead to the same phi(pB). The difference phi(2B)-phi(pB) is considered as a function of phi(pB) and theta=arg(epsilon). For any given phi(pB), the difference phi(2B)-phi(pB)=0 at theta=0(epsilon(r)>0,epsilon(i)=0) increases monotonically as a function of theta and reaches maximum value {phi(2B)-phi(pB)}(max) in the limit as theta-->180 degrees (epsilon(r)<0,epsilon(i)=0). This maximum difference {phi(2B)-phi(pB)}(max) has an upper limit of 15.701 degrees when phi(pB)=28.195 degrees.

Investigation of light reflection at Brewster angles from a nonlinear optical film on a magnetoelectric substrate

We investigate the light reflection from a nonlinear optical dielectric film on a bigyrotropic magneto-electric substrate magnetized parallel to the interface. The reflection matrix has been obtained and reflection coefficients are investigated with respect to the incidence angle for both polarizations of the incident light. We analyzed the optical nonlinearity and the magnetoelectric coupling contributions to the reflection of the electromagnetic waves and the appearance of so-called pseudo-Brewster angles.

Theoretical study of influence of substrate microdefects on optical properties of dielectric thin films

Based on the theory of inhomogeneous thin films, a model for refractive index of stratified dielectric substrate is firstly put forward. The substrate can be divided into surface layer, subsurface layer and bulk layer in turn. Both the s urface layer and subsurface layer, whose refractive indices obey statistical dis tributions, are equivalent to inhomogeneous thin films. They can be separated in to N1 and N2 sublayers respetively which are regarded as homogenous thin films. Subsequently, theoretical analysis was carried out utili zing the characteristic matrix method of optical thin films. Numerical calculati on for optical properties of single layer dielectric thin films was carried out. The computing results indicate that microdefects in surface layer and subsurfac e layer of the substrate alter the equivalent refractive indices of the thin film and the substrate, which leads to the deviation of pseudo-Brewster angles and assembling reflectance from ideal conditions. Meanwhile, these microdefects change the propagation characteristics in thin film and substrate, as a result t he phase shift of reflection and phase difference deviate from ideal conditions. In addition, this model is also suitable for calculating the influence of micr odefects in the substrate on optical propertied of multilayer dielectric thin fi lms.

Contours of constant pseudo-Brewster angle in the complex ∊ plane and an analytical method for the determination of optical constants

The locus of all points in the complex plane of the dielectric function ?[?(r) + j?(i) = |?| exp(jtheta)], that represent all possible interfaces characterized by the same pseudo-Brewster angle theta(p)B of minimum p reflectance, is derived in the polar form: |?| = l cos(zeta/3), where l = 2(tan(2)Phi(p)B)k, zeta = arccos(- costheta cos(2)Phi(p)B/k(3)), and k = (1 - 2/3 sin(2)Phi(p)B)(1/2). Families of iso-Phi(p)B contours for (I) 0 degrees </= Phi(p)B </= 45 degrees and (II) 45 degrees </= Phi(p)B </= 75 degrees are presented. In range I, an iso-Phi(p)B contour resembles a cardioid. In range II, the contour gradually transforms toward a circle centered on the origin as Phi(p)B increases. However, the deviation from a circle is still substantial. Only near grazing incidence (Phi(p)B > 80 degrees ) is the iso-Phi(p)B contour accurately approximated as a circle. We find that |?| < 1 for Phi(p)B < 37.23 degrees , and |?| > 1 for Phi(p)B > 45 degrees . The optical constants n,k (where n + jk = ?((1/2)) is the complex refractive index) are determined from the normal incidence reflectance R(0) and Phi(p)B graphically and analytically. Nomograms that consist of iso-R(0) and iso-Phi(p)B families of contours in the nk plane are presented. Equations that permit the reader to produce his own version of the same nomogram are also given. Valid multiple solutions (n,k) for a given measurement set (R(0),phi(p)B) are possible in the domain of fractional optical constants. An analytical solution of the (R(0),Phi(p)B) ? (n,k) inversion problem is developed that involves an exact (noniterative) solution of a quartic equation in |?|. Finally, a graphic representation is developed for the determination of complex ? from two pseudo-Brewster angles measured in two different media of incidence.

Analytical determination of the complex dielectric function of an absorbing medium from two angles of incidence of minimum parallel reflectance

The real and imaginary parts of the complex dielectric function (or complex refractive index) of an opaque substrate or a thick film can be determined from two pseudo-Brewster angles measured in two transparent incidence media of different refractive indices. This two-angle method is simple in that it involves no photometric or polarimetric analysis and in that the solution for the optical properties in terms of the measured angles is explicit, analytical, and direct (i.e. noniterative). The two-angle method is demonstrated for an opaque TiN film on a Cleartran ZnS substrate as a specific example. The effect of angle-of-incidence errors on the determination of the optical properties is investigated, and the domain of applicability of this new and interesting method is also delineated.

Brewster and pseudo-Brewster angles of uniaxial crystal surfaces and their use for determination of optical properties: errata

Brewster and pseudo-Brewster angles of uniaxial crystal surfaces and their use for determination of optical properties: errata

Pseudo-Brewster and second-Brewster angles of an absorbing substrate coated by a transparent thin film

The pseudo-Brewster angle of minimum reflectance for the p polarization, the corresponding angle for the s polarization, and the second-Brewster angle of minimum ratio of the p and s reflectances are all determined as functions of the thickness of a transparent film coating an absorbing substrate by numerical solution of the exact equations that govern such angles of the form Re(Z′/Z) = 0, where Z = Rp, Rs, or ρ represent the complex amplitude-reflection coefficients for the p and s polarizations and their ratio (ρ = Rp/Rs), respectively, and Z′ is the angle-of-incidence derivative of Z. Results that show these angles and their associated reflectance and reflectance-ratio minima are presented for the SiO2–Si film–substrate system at wavelength λ = 0.6328 μm and film thickness of up to four periods (≃1.2 μm). Applications of these results are proposed in film-thickness measurement and control.

Brewster and pseudo-Brewster angles of uniaxial crystal surfaces and their use for determination of optical properties

Brewster and pseudo-Brewster angles are defined for surfaces of transparent and absorbing uniaxial crystals parallel and perpendicular to the optic axis. Two Brewster angles of a transparent uniaxial crystal surface parallel to the optic axis, measured when the optic axis is oriented perpendicular and parallel to the plane of incidence, readily determine the ordinary and extraordinary indices No and Ne. No and Ne can also be obtained from two Brewster angles measured on a surface perpendicular to the optic axis in contact with two media of different refractive indices. Conditions for the existence of two Brewster angles are discussed. The complex No and Ne of an absorbing uniaxial crystal can be derived from pseudo-Brewster-angle and minimum-reflectance data obtained in two symmetrical orientations of a surface parallel to the optic axis. An approximate, but accurate, explicit inversion procedure is presented for this purpose.