pseudo-Brewster Angle Research Articles

Investigation of temperature dependent tunable Goos—Hanchen shift at the interface of dielectric—nanocomposites containing non- spherical nanoparticles

We develop a theoretical modeling of the temperature-dependent Goos-Hanchen (GH) shift of the reflected waves from the nanocomposites made of spheroidal metal nanoparticles in a dielectric host. The temperature impact on GH shift is explained by the temperature-dependence permittivity of metal nanoparticles with varying volume fraction in the visible and UV wavelength ranges from 250–400 nm for temperatures up to 1200 K. Simulation analysis is performed for both aligned metallic nanoparticles at room temperature and randomly oriented metallic nanoparticles at high temperatures. The effective permittivity of a composite (ϵeff) is calculated using the effective medium approximation theory and the stationary phase method is adopted to study the GH shifts. The impact of the change in the shape of the nanoparticles is simulated by the depolarization factor. Simulation results show that GH shift at elevated temperatures in pseudo-Brewster angle is more negative than the GH shift at room temperature for nanocomposites of small volume fraction with dielectric behavior and we find that the pseudo-Brewster angle is sensitive to the variation of temperature. Using Bruggman theory for numerical results, we show that varying the shape of spheroidal nanoparticles in dielectric nanocomposites leads to significant change in the value of GH shifts for some depolarization factors. Also based on the results, it is possible to obtain a transition from negative to positive GH shift just by adjusting the incident angle in a given depolarization factor. Moreover, the reversal GH shift may occur by adjusting the depolarization factor for a given wavelength, incident angle and volume fraction

Precise identification of graphene layers at the air-prism interface via a pseudo-Brewster angle.

We propose a simple method for the precise identification of graphene layers at the air-prism interface via a pseudo-Brewster angle, where the horizontally polarized reflection is close to zero. We find that the pseudo-Brewster angle is sensitive to the variation of graphene layers where the pseudo-Brewster angle is approximately linearly increased about 0.5deg as the layer numbers increased. Furthermore, the sensitivity of the pseudo-Brewster angle can be greatly enhanced and reaches 0.04deg by eliminating the influence of the cross-polarization effect. Our scheme can provide a simple and effective method to identify the layer numbers of graphene.

Active control of Imbert–Fedorov shifts with graphene-coated chiral metamaterials

We propose a method for controlling the Imbert–Fedorov (IF) shifts of a reflected beam at a graphene-coated chiral metamaterial (CMM) interface, where graphene's chemical potential, the CMM's chirality parameter and the permittivity of dielectric at interface serve as external tunable stimuli to control the IF shifts. The spatial IF (SIF) shift and angular IF (AIF) shift are formulated by the reflection coefficients. The numerical results indicate that for p-polarized incident beam, the IF shifts can be controlled efficiently near the pseudo-Brewster angle through the chemical potential, and that both the high-permittivity dielectric and low-chirality CMM can bring about a broad shift modulation. Actually, the existence of graphene reduces the SIF shifts, but it can play a crucial role in the shift modulation. The above results might be helpful in exploiting various tunable terahertz-wave devices.

Surface sensitivity of optical and magneto-optical and ellipsometric properties in magnetoplasmonic nanodisks

The optical, ellipsometric, and magneto-optical surface sensitivity to dielectric environment of magnetoplasmonic nanodisks is experimentally studied. Here, the shift of the corresponding spectral structures as a function of the thickness of a coating SiO2 layer is characterized. Our results reveal that the so called pseudo-Brewster Angle, easily identified in the ellipsometric phase (Δ) spectrum, is up to four times more sensitive than the conventional features used in surface plasmon resonance based sensors. These results highlight the need of investigating the factual implementation of this technique to develop improved ellipsometric-phase based transducers for bio-chemical sensing purposes.

Tunable lateral and angular shifts of a reflected beam from a graphene-based structure

Abstract We discuss the lateral shift (LS) and the angular shift (AS) of a reflected Gaussian beam from the interface covered with a graphene sheet, which is modeled as an infinitesimally thin surface conductivity. In the two cases where the incident medium is optically rarer or denser than the refractive medium, the LS and AS are numerically analyzed for a TM-polarized beam by using the stationary-phase approach. It is found that both the LS and AS can be controlled by tuning graphene's chemical potential, the frequency or the angle of incidence of incident beam. In particular, when the incident medium is optically denser, since the total internal reflection takes place and the surface plasmon polaritons are excited, the larger AS can be achieved around the critical angle, the pseudo-Brewster angle or resonance angle. Also, a higher chemical potential can tune the directions of the LS (i.e., the positive or negative shifts). The results provide a way to tune flexibly the LS and AS by means of the graphene sheet.

Comparative analysis of two methods for calculating reflectance of black silicon

We report a detailed numerical simulation of the reflection of visible light from a sub-wavelength grating with a rectangular profile on the silicon surface. Simulation is carried out by the effective refractive index method and rigorous coupled-wave analysis. The dependences of the reflectance on the grating depth, fill factor and angle of incidence for TE and TM polarisations are obtained and analysed. Good agreement between the results obtained by the two methods for grating periods of is found. The possibility of reducing the polarised light reflectance to about 1 % by adjusting the depth and the grating fill factor is demonstrated. The characteristics of the Brewster effect manifestation (pseudo-Brewster angle) in the system under study are considered. The possibility of the pseudo-Brewster angle existence and its absence for both polarisations of the incident light is shown as a function of the parameters of a rectangular nanostructure on the surface.

Comparison of Goos–Hänchen shifts of the reflected beam from graphene on dielectrics and metals

The Goos–Hänchen shifts of the reflected beam from graphene-on-dielectric (or metal) in the optical wavelength are investigated by using the stationary-phase method. For the graphene-on-dielectric substrates, it is found that the pseudo-Brewster angle and Goos–Hänchen shift are influenced greatly by the introduced graphene sheets for TM polarization. By changing number of graphene sheets, the lateral shifts can be large positive or negative near the pseudo-Brewster angle. For TE polarization, the lateral shift is still small; however it can also be positive or negative by changing the number of graphene sheets. For the graphene-on-metal substrates, graphene sheets exert a great impact on the reflectance while has little effect on the lateral shifts of both polarizations. Finally, the role of the graphene sheets on the lateral shifts for the different visible wavelengths is discussed.

Effect of damping on Goos–Hänchen shift from weakly absorbing anisotropic metamaterials

The effect of damping on the Goos–Hänchen (GH) shift from weakly absorbing anisotropic metamaterials is investigated. Explicit formulas of the GH shifts are derived and analyzed at three particular angles of incidence: critical angle, pseudo-Brewster angle, and grazing incidence, near which the reflection phases exhibit strong variations and large GH shifts are likely to occur. The damping in the anisotropic metamaterials may result in GH shifts not available in ordinary isotropic media. In particular, a larger GH shift can be associated with a larger rather than a smaller damping, and a small change of damping may even reverse the direction of the GH shift near the pseudo-Brewster angle. This feature is characterized by a parabolic relation determined by the complex components of the permittivity tensor. The GH shifts are also illustrated with the incidence of Gaussian beams based on Fourier integral formulation.

Nonlinear magneto-optic ellipsometry

The ellipsometric parameters for light reflection from a dielectric film with Kerr optical nonlinearity on a bigyrotropic magneto-electric film are theoretically investigated. The combined contributions of cubic optical nonlinearity and magneto-electric coupling allow us to control the ellipsometric parameters and thus, for example, the Kerr rotation with the incoming light intensity, in particular at incidence angles close to the pseudo-Brewster angle.

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).

Low-damping epsilon-near-zero slabs: Nonlinear and nonlocal optical properties

We investigate second harmonic generation, low-threshold multistability, all-optical switching, and inherently nonlocal effects due to the free-electron gas pressure in an epsilon-near-zero (ENZ) metamaterial slab made of cylindrical, plasmonic nanoshells illuminated by TM-polarized light. Damping compensation in the ENZ frequency region, achieved by using gain medium inside the shells' dielectric cores, enhances the nonlinear properties. Reflection is inhibited and the electric field component normal to the slab interface is enhanced near the effective pseudo-Brewster angle, where the effective \epsilon-near-zero condition triggers a non-resonant, impedance-matching phenomenon. We show that the slab displays a strong effective, spatial nonlocality associated with leaky modes that are mediated by the compensation of damping. The presence of these leaky modes then induces further spectral and angular conditions where the local fields are enhanced, thus opening new windows of opportunity for the enhancement of nonlinear optical processes.

Novel magneto-optic behaviour from a polysquaraine

We report that poly((2,5-bis(1-methylpyrrol-2-yl)thiophene)squaraine) can be synthesized as a dark green insoluble powder which when subjected to shear force and pressed as a disk exhibits a gold-green near optical quality surface with semi-metallic behaviour. Reflectivity measurements at a wavelength of 819nm reveal a high (72°) pseudo-Brewster angle and non-zero p-reflectivity whilst electrical measurements using a four-point probe return a conductivity of 1×10−5Scm−1. Unexpectedly the disks also exhibit magneto-optic (MO) activity which it appears must arise from a weak magnetic component intrinsic to the samples. In both the longitudinal and transverse Kerr configurations large fractional changes in reflectivity (ΔI/I≈2.5×10−2) are observed across a wide range of angles of incidence for wavelengths between 400nm and 1064nm on application and reversal of a magnetic field. Anomalously for these configurations all the MO effects observed are quadratic in the applied field and no first-order effects linear in applied field are observed for any state of incident polarisation. Examined using conventional magnetometry, disk samples return saturation magnetization values of 4.13×10−3emug−1 on a vibrating sample magnetometer and smaller samples similarly processed and prepared for examination by Squid magnetometer confirmatory values of 4.9×10−3emug−1. Magnetization curves from both instruments have a similar form, saturating at about 1.14kOe, and are also in close correspondence with curves derived by plotting the magneto-optic signal as a function of field after allowance for the quadratic nature of the observed MO response. Similarly, both the magnetic and magneto-optic behaviour of all samples is isotropic in plane.Taken together, all experimental observations on this fully organic polymer appear, surprisingly, to be commensurate with the development at room temperature of some form of magnetic state throughout very limited regions of the material. A very tentative model able to reconcile the magnetic and MO observations on the supposition that the magnetic state may be of a reduced dimensional nature is presented. We are very aware that the appearance of an intrinsic room temperature magnetism in the material studied is highly unlikely and that this interpretation of the results presented is strongly dependent on using MO evidence to support chemical analysis, which included multi-elements scans on an ICP and ESR, in precluding contamination.

基底和膜层-基底系统的赝布儒斯特角计算

基底和膜层-基底系统的赝布儒斯特角计算

Polarimetric characterization of bismuth thin films deposited by laser ablation

A Mueller-Stokes analysis is applied to pure bismuth thin film samples prepared by the laser ablation technique by using a polarimeter with a 632.8 nm continuum wavelength laser. The complex refractive index is determined in the range of 250-1100 nm. Results from the Mueller matrix show the high sensitivity of diattenuation and polarizance parameters as a function of the sample thickness and the incidence angle, except at the pseudo-Brewster angle, where they exhibit the same value. Results show that the knowledge of the polarimetric response, with appropriate incident polarization states, could be used to design photonic Bi-based devices for several applications. Polarization dependence is the result of changes on the surface morphology as a result of the small value of the skin depth.

Goos–Hänchen shift of the reflected wave through an anisotropic metamaterial containing metal/dielectric nanocomposites

Goos-Hänchen (GH) shift of a transverse-magnetic (TM) wave reflected from a semi-infinite anisotropic metamaterial consisting of aligned metallic nanowires in a dielectric matrix is investigated. Based on Bruggeman effective medium theory, we obtain the conditions for realizing the negative refraction, which are dependent on both the incident wavelength and the volume fraction of metallic inclusions. Then, we investigate the GH shifts from the composite metamaterial with positive and negative refractions with the stationary-phase method. Numerical results show that the enhancement of GH shift can be achieved near the pseudo-Brewster angle for small volume fractions and at the close-to-grazing incidence for large volume fractions. We further find that for positively refractive metamaterials with weak absorption, one can realize the transition from negative GH shift to the positive one by adjusting the incident wavelength. However, for negatively refractive composite metamaterials, the reversal of the GH shifts may take place by the adjustment of the volume fraction instead of the incident wavelength. In order to demonstrate the validity of the stationary-phase approach, numerical simulations are performed for a Gaussian-shaped beam. In the end, by using COMSOL simulation, a comprehensive understanding is given and the above analysis is confirmed.

Explicit expression of the pseudo-Brewster angle for anisotropic metamaterials

In the conventional optics, the pseudo-Brewster angle (PBA) mainly depends on the permittivity of the optical materials. However, the recent development of metamaterials in the optical wavelength has put magnetic permeability on equal footing. Thus, the conventional PBA needs to be revisited to include the permeability for metamaterial applications in the optical region. By taking into account the loss and anisotropy of the metamaterials, we present the explicit expression of PBA in terms of complex permittivity and permeability through rigorous analysis. Based on the explicit expression, some interesting features and potential applications of the PBA are discussed.

Large positive and negative lateral shifts near pseudo-Brewster dip on reflection from a chiral metamaterial slab

The lateral shifts from a slab of lossy chiral metamaterial are predicted for both perpendicular and parallel components of the reflected field, when the transverse electric (TE)-polarized incident wave is applied. By introducing different chirality parameter, the lateral shifts can be large positive or negative near the pseudo-Brewster angle. It is found that the lateral shifts from the negative chiral slab are affected by the angle of incidence and the chirality parameter. In the presence of inevitable loss of the chiral slab, the enhanced lateral shifts will be decreased, and the pseudo-Brewster angle will disappear correspondingly. For the negative chiral slab with loss which is invisible for the right circularly polarized (RCP) wave, we find that the loss of the chiral slab will lead to the fluctuation of the lateral shift with respect to the thickness of the chiral slab.The validity of the stationary-phase analysis is demonstrated by numerical simulations of a Gaussian-shaped beam.

Return-path, multiple-principal-angle, internal-reflection ellipsometer for measuring IR optical properties of aqueous solutions

A retroreflection (return-path) spectroscopic ellipsometer without a wave plate is described that uses an IR-transparent high-refractive-index hemicylindrical semiconductor substrate to measure the optical properties of aqueous solutions from multiple principal angles and multiple principal azimuths of attenuated internal reflection (AIR) at the semiconductor-solution interface. The pseudo-Brewster angle of minimum reflectance for the p polarization is also readily measured using the same instrument. This wealth of data can also be used to characterize thin films at the solid-liquid interface. Simulated results of AIR at the Si-water interface over the 1.2-11?mum IR spectral range are presented in support of this concept. The optical properties of water and aqueous solutions are important for modeling radiative transfer in the atmosphere and oceans and for biomedical and tissue optics.

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.

Plurality of principal angles for a given pseudo-Brewster angle when polarized light is reflected at a dielectric-conductor interface

The pseudo-Brewster angle phi(pB) of minimum reflectance for p-polarized light and the principal angle phi at which incident linearly polarized light of the proper azimuth is reflected circularly polarized are considered as functions of the complex relative dielectric function epsilon of a dielectric-conductor interface over the entire complex epsilon plane. In particular, the spread of phi for a given phi (pB) is determined, and the maximum difference(phi -phi(pB))(max) is obtained as a function of phi(pB). The maximum difference (phi -phi(pB))(max) approaches 45 degrees and 0 in the limit as phi(pB)-->phi 0 and 90 degrees , respectively. For phi(pB)<22.666 degrees , multiple principal angles phi (i), i=1,2,3, appear for each epsilon in a subdomain of fractional optical constants. This leads to an elaborate pattern of multiple solution branches for the difference phi (i)-phi(pB), i=1,2,3, as is illustrated by several examples.