Critical Angle For Total Reflection Research Articles

Lead Detection in a Gig-Lox TiO2 Sponge by X-ray Reflectivity.

The importance of lead analysis in environmental matrices becomes increasingly relevant due to the anthropogenic spread of toxic species in nature. Alongside the existing analytical methods to detect lead in a liquid environment, we propose a new dry approach for lead detection and measurement based on its capture from a liquid solution by a solid sponge and subsequent quantification based on X-ray analyses. The detection method exploits the relationship between the electronic density of the solid sponge, which depends on the captured lead, and the critical angle for total reflection of the X-rays. For this purpose, gig-lox TiO2 layers, grown by modified sputtering physical deposition, were implemented for their branched multi-porosity spongy structure that is ideal for capturing lead atoms or other metallic ionic species in a liquid environment. The gig-lox TiO2 layers grown on glass substrates were soaked into aqueous solutions containing different concentrations of Pb, dried after soaking, and finally probed through X-ray reflectivity analyses. It has been found that lead atoms are chemisorbed onto the many available surfaces within the gig-lox TiO2 sponge by establishing stable oxygen bonding. The infiltration of lead into the structure causes an increase in the overall electronic density of the layer and, thus, an increment of its critical angle. Based on the established linear relationship between the amount of lead adsorbed and the augmented critical angle, a standardized quantitative procedure to detect Pb is proposed. The method can be, in principle, applied to other capturing spongy oxides and toxic species.

The GISANS instrument at the HBS

This manuscript describes a concept of a grazing incidence small-angle neutron scattering (GISANS) instrument for the high brilliance source (HBS). The HBS being a compact pulsed neutron source using a moderate energy proton accelerator which allows for very compact moderators and shielding, and flexible pulse repetition rates. Similar to many other instrument concepts for this source, the lowest proposed HBS pulse frequency of 24 Hz with a relatively large detector distance is the optimal choice for the instrument described here in terms of obtained intensity and Q-range (i.e. scattering vector range). Such a configuration has the added advantage of good Q-resolution, which is important when scattering depths need to be resolved well. This is especially the case for GISANS when the incident angle is close to the critical angle of total reflection. The performance obtained from detailed ray-tracing computer simulations predict a high performance instrument that will be comparable to reflectometers and small angle neutron scattering (SANS) instruments at high-flux reactor sources such as the Forschungsreaktor Munich (FRM-2) and others.

A Calculation Method of Electromagnetic Wave Reflection in Plasma Sheath Environment

Due to its high-speed movement, the reentry object is enveloped with a plasma sheath featuring complex electromagnetic (EM) characteristics. Based on the physical process of EM wave transmission/reflection in plasma sheath, we propose a calculation method of EM wave reflection suited for plasma sheath environment. The proposed method comprehensively considers the resonance shielding surface, the critical angle of total reflection, and the damping effect. Our method is simulated and verified using typical blunt cone computational fluid dynamics (CFD) simulation data. We analyze the reflection intensity distributions of EM waves in the plasma sheath with different altitudes and speeds, revealing the reflection law of EM wave under scenarios of complex EM environment and oblique incidence of plasma sheath. Simulation/experimental results suggest that our proposed method exhibits excellent performance under the conditions of sparse data grid and grazing incidence.

Anderson localization and Brewster anomaly of electromagnetic waves in randomly-stratified anisotropic media

Anderson localization of p-polarized waves and the Brewster anomaly phenomenon, which is the delocalization of p-polarized waves at a special incident angle, in randomly-stratified anisotropic media are studied theoretically for two different random models. In the first model, the random parts of the transverse and longitudinal components of the dielectric tensor, between which the longitudinal component is the one in the stratification direction, are assumed to be uncorrelated, while, in the second model, they are proportional to each other. We calculate the localization length in a precise way using the invariant imbedding method. From analytical considerations, we provide an interpretation of the Brewster anomaly as a phenomenon arising when the wave impedance is effectively uniform. Similarly, the ordinary Brewster effect is interpreted as an impedance matching phenomenon. We derive the existence condition for the Brewster anomaly and concise analytical expressions for the localization length, which are accurate in the weak disorder regime. We find that the Brewster anomaly can arise only when disorder is sufficiently weak and only in the second model with a positive ratio of the random parts. The incident angle at which the anomaly occurs depends sensitively on the ratio of the random parts and the average values of the tensor components. In the cases where the critical angle of total reflection exists, the angle at which the anomaly occurs can be either bigger or smaller than the critical angle. When the transverse and longitudinal components are uncorrelated, localization is dominated by the the transverse component at small incident angles. When only the longitudinal component is random, the localization length diverges as θ−4 as the incident angle θ goes to zero and is also argued to diverge for all θ in the strong disorder limit.

Sensitivity of a dielectric layered structure on a scale below the periodicity: A fully local homogenized model

We inspect the unusual scattering properties reported recently for structures alternating dielectric layers of subwavelength thicknesses near the critical angle for total reflection. In TE polarization, the unusual scattering properties are captured by an effective model with an accuracy less than 1% up to $kd\ensuremath{\sim}0.1$. It is shown that the propagation is simply dispersive with local dispersion while the boundary layer effects are captured through a nonintuitive transmission condition. The resulting model involves two parameters depending only on the characteristics of the multilayer and which are given in closed forms. Besides, we show that a discrete description of the spectrum using the layer thickness $d$ as unit of measure misses the complexity of the continuous spectrum exhibiting strong variations within the scale $d$. This ultrasensitivity to variations below $d$ is attributable to strong boundary layer effects and, for large structures, to a cooperation between the boundaries and the phase accumulation within the structure.

Light extraction efficiency enhancement of flip-chip blue light-emitting diodes by anodic aluminum oxide.

We produced an anodic aluminum oxide (AAO) structure with periodic nanopores on the surface of flip-chip blue light-emitting diodes (FC-BLEDs). The nanopores had diameters ranging from 73 to 85 nm and were separated by distances ranging from approximately 10 to 15 nm. The light extraction efficiency enhancement of the FC-BLEDs subjected to different durations of the second pore-widening process was approximately 1.6–2.9%. The efficiency enhancement may be attributed to the following mechanism: periodic nanopores on the surface of FC-BLEDs reduce the critical angle of total reflection and effective energy transfer from a light emitter into a surface plasmon mode produced by AAO.

Time-resolved total reflection detects mass transfer along thickness direction of bulk Nafion® film

To elucidate a bulk membrane (Nafion®) with respect to channel connectivity or mass transfer (water or ions) through the channels, we propose to utilize time-resolved neutron reflectivity and deuterium exchange method. We performed the experiment on time-of-flight spectrometer iMATERIA at pulsed neutron spallation source J-PARC in Tokai, Japan. To exchange water (D2O or H2O) in the film during RF measurements, we specially designed a sample environment with Si substrates. A bulk film (50 μm thickness) is sandwiched by Si substrate (5 mm thickness) and Al mesh plate. The incident neutron incomes from edge of Si substrate and reflects at a front surface of bulk film. When we exchange water (D2O or H2O), water flows through Al mesh and starts to diffuse in the film. When exchanged water reaches to a front surface of the film, critical angle for total reflection (or critical wave number) changes, according to the chemical composition and therefore the averaged coherent scattering length (bav) at the front surface. Consequently, diffusion coefficient is determined from time-dependence in bav.

Light extraction enhancement of AlGaN-based ultraviolet light-emitting diodes by substrate sidewall roughening

The effect of sapphire substrate's sidewall roughening on light extraction of AlGaN-based ultraviolet light-emitting diodes (UV LEDs) is investigated. Finite-difference time-domain simulation reveals that a roughening region for effective light extraction enhancement exists on the substrate's sidewall. Roughening outside the effective roughening region will result in undesirable inward photon scattering and absorption. For TM-polarization-dominated deep-UV LEDs, the effective roughening region is from the substrate's backside to the position about L/2 × tan(θc) away from the substrate's front side, where L is the side length of the LED device and θc is the critical angle of total reflection. In the LED device fabrication, picosecond laser dicing is employed to realize roughening layers on the sapphire substrate's sidewalls. The UV LEDs with three roughening layers have 13.2% higher average light output power (LOP) at 20 mA than those with two roughening layers, thanks to the larger roughening area in the effective roughening region. When additional roughening layers beyond the effective roughening region are applied, the LOP decreases as the simulation predicts. Furthermore, the values of leakage current and forward voltage of these LEDs are consistently below 0.2 μA at −10 V and 5.8–6.0 V at 20 mA, respectively, showing no thermal damage to intrinsic diode performance by the laser processing.

The upper limit of the in-plane spin splitting of Gaussian beam reflected from a glass-air interface

Optical spin splitting has a promising prospect in quantum information and precision metrology. Since it is typically small, many efforts have been devoted to its enhancement. However, the upper limit of optical spin splitting remains uninvestigated. Here, we investigate systematically the in-plane spin splitting of a Gaussian beam reflected from a glass-air interface and find that the spin splitting can be enhanced in three different incident angular ranges: around the Brewster angle, slightly smaller than and larger than the critical angle for total reflection. Within the first angular range, the reflected beam can undergo giant spin splitting but suffers from low energy reflectivity. In the second range, however, a large spin splitting and high energy reflectivity can be achieved simultaneously. The spin splitting becomes asymmetrical within the last angular range, and the displacement of one spin component can be up to half of incident beam waist w0/2. Of all the incident angles, the spin splitting reaches its maximum at Brewster angle. This maximum splitting increases with the refractive index of the “glass” prism, eventually approaching an upper limit of w0. These findings provide a deeper insight into the optical spin splitting phenomena and thereby facilitate the development of spin-based applications.

Focusing hard x rays beyond the critical angle of total reflection by adiabatically focusing lenses

In response to the conjecture that the numerical aperture of x-ray optics is fundamentally limited by the critical angle of total reflection [Bergemann et al., Phys. Rev. Lett. 91, 204801 (2003)], the concept of adiabatically focusing refractive lenses was proposed to overcome this limit [Schroer and Lengeler, Phys. Rev. Lett. 94, 054802 (2005)]. We present an experimental realization of these optics made of silicon and demonstrate that they indeed focus 20 keV x rays to a 18.4 nm focus with a numerical aperture of 1.73(9) × 10−3 that clearly exceeds the critical angle of total reflection of 1.55 mrad.

Transverse magnetic-reflected polarizer for application in surface plasmon resonance configuration

We developed a wideband transverse magnetic (TM) −reflected polarizer composed of BK7 prism and Ag/Cr/TiO2 film. Based on the polarization-dependent loss of coupled plasmon-waveguide resonance (CPWR), BK7 prism/Ag/Cr/TiO2/air layered structure can reflect the TM-components of lightwave and severely attenuate the transverse electric (TE) −components in a wavelength range from 600nm to 900nm at incident angles greater than the critical angle of total reflection. In terms of its practical application, a compact, low cost surface plasmon resonance (SPR) configuration with an integrated polarizer for wavelength modulation is presented and experimentally demonstrated.

Spin- and valley-dependent Goos–Hänchen effect in silicene and gapped graphene structures

We investigate the Goos–Hänchen shift for ballistic electrons (i) reflected from a step-like inhomogeneity of the potential energy and (or) effective mass, and (ii) transmitted through a ferromagnetic barrier region in monolayer silicene or gapped graphene. For the electrons reflected from a single interface we found that the Goos-Hänchen shift is valley-polarized for gapped graphene structure, and valley- and spin-polarized for silicene due to the spin-valley coupling. In contrast, for example, to gapless graphene the lateral beam shift in gapped structures occurs not only in the case of total, but also of partial, reflection, i.e. at the angles smaller than the critical angle of total reflection. We have also demonstrated that the valley- and spin-polarized displacement of the electron beam, transmitted through a ferromagnetic silicene barrier, resonantly depends on the barrier width. The resonant values of the displacement can be controlled by adjusting the electric potential, the external perpendicular electric field, and the exchange field induced by an insulating ferromagnetic substrate.

Correlated diffuse x-ray scattering from periodically nanostructured surfaces

Laterally periodic nanostructures were investigated with grazing incidence small angle X-ray scattering. To support an improved reconstruction of nanostructured surface geometries, we investigated the origin of the contributions to the diffuse scattering pattern which is correlated to the surface roughness. Resonant diffuse scattering leads to a palm-like structure of intensity sheets. Dynamic scattering generates the so-called Yoneda band caused by a resonant scatter enhancement at the critical angle of total reflection and higher-order Yoneda bands originating from a subsequent diffraction of the Yoneda enhanced scattering at the grating. Our explanations are supported by modelling using a solver for the time-harmonic Maxwell's equations based on the finite-element method.

Multiple scattering in grazing-incidence X-raydiffraction: impact on lattice-constant determinationin thin films.

Dynamical scattering effects are observed in grazing-incidence X-ray diffraction experiments using an organic thin film of 2,2':6',2''-ternaphthalene grown on oxidized silicon as substrate. Here, a splitting of all Bragg peaks in the out-of-plane direction (z-direction) has been observed, the magnitude of which depends both on the incidence angle of the primary beam and the out-of-plane angle of the scattered beam. The incident angle was varied between 0.09° and 0.25° for synchrotron radiation of 10.5 keV. This study reveals comparable intensities of the split peaks with a maximum for incidence angles close to the critical angle of total external reflection of the substrate. This observation is rationalized by two different scattering pathways resulting in diffraction peaks at different positions at the detector. In order to minimize the splitting, the data suggest either using incident angles well below the critical angle of total reflection or angles well above, which sufficiently attenuates the contributions from the second scattering path. This study highlights that the refraction of X-rays in (organic) thin films has to be corrected accordingly to allow for the determination of peak positions with sufficient accuracy. Based thereon, a reliable determination of the lattice constants becomes feasible, which is required for crystallographic structure solutions from thin films.

Characterization of surface Ag nanoparticles in nanocomposite a-C:Ag coatings by grazing incidence X-ray diffraction at sub-critical angles of incidence

Silver diffusion within nanocomposite films and/or toward the film surface is often observed during annealing of the silver-based nanocomposite films. In order to control and/or minimize this process, it is crucial to characterize the aggregated silver nanoparticles on the films surface. In this paper grazing incidence X-ray diffraction (GIXRD) with both sub-critical and supra-critical angles of incidence is used to characterize the Ag nanoparticles distribution, shape and structure both inside the matrix and on the nanocomposite film surface. The nanocomposite carbon coating containing Ag nanoparticles (a-C:Ag) was deposited by dc magnetron sputtering. The coatings were analyzed by GIXRD using fixed incident angles both below and above the critical angle for total reflection. By using sub-critical angles it was possible to eliminate diffraction from the bulk material allowing to estimate the size distribution of the nanoparticles sitting on the surface. The results obtained by GIXRD analysis were checked through comparison with the observations made by both TEM and SEM analysis. The proposed methodology can be used to characterized nanoparticles deposition on a surface and/or island formation during film growth as long an adequate substrate with high critical angle for total reflection is used.

低エネルギーX線を用いた斜入射小角X線散乱法によるブロック共重合体薄膜のミクロ相分離構造の深さ依存性と配向挙動の解析

In this review, we demonstrated grazing-incidence small-angle X-ray scattering (GISAXS) measurement with tender X-ray to achieve depth-resolved structure analysis of block copolymer systems, polystyrene-b-poly (2-vinylpyridine)(S2VP) and poly (methyl methacrylate)-b-poly (n-butyl acrylate) thin films (approximately 300 - 400 nm in thick). In the case of using tender X-rays, the penetration depth of X-rays in the vicinity of critical angle of total reflection becomes gentle as compared to the case of using hard X-rays. Herein, X-ray energies of 2.40 keV and 4.36 keV were employed to conduct depth-resolved structure analysis. The experimental full width at half maximum (FWHM) magnitudes of a diffraction spot was investigated to estimate the penetration depth. The incident angle dependence of experimental FWHM magnitudes indicated the same tendency as the FWHM values calculated with Laue function considering attenuation decay, meaning that the penetration depth was controlled by varying incident angles. Depth-resolved structure analysis revealed that in the case of the completely oriented thin film, micro-phase separated structures slightly deformed along the depth direction in the inside of the thin film and the deformation gradually relaxed near the surface.

An efficient plane-grating monochromator based on conical diffraction for continuous tuning in the entire soft X-ray range including tender X-rays (2-8 keV).

Recently it was verified that the diffraction efficiency of reflection gratings with rectangular profile, when illuminated at grazing angles of incidence with the beam trajectory along the grooves and not perpendicular to them, remains very high for tender X-rays of several keV photon energy. This very efficient operation of a reflection grating in the extreme off-plane orientation, i.e. in conical diffraction, offers the possibility of designing a conical diffraction monochromator scheme that provides efficient continuous photon energy tuning over rather large tuning ranges. For example, the tuning could cover photon energies from below 1000 eV up to 8 keV. The expected transmission of the entire instrument is high as all components are always operated below the critical angle for total reflection. In the simplest version of the instrument a plane grating is preceded by a plane mirror rotating simultaneously with it. The photon energy selection will then be made using the combination of a focusing mirror and exit slit. As is common for grating monochromators for soft X-ray radiation, the minimum spectral bandwidth is source-size-limited, while the bandwidth can be adjusted freely to any larger value. As far as tender X-rays (2-8 keV) are concerned, the minimum bandwidth is at least one and up to two orders of magnitude larger than the bandwidth provided by Si(111) double-crystal monochromators in a collimated beam. Therefore the instrument will provide more flux, which can even be increased at the expense of a bandwidth increase. On the other hand, for softer X-rays with photon energies below 1 keV, competitive relative spectral resolving powers of the order of 10000 are possible.

X-Ray Optics on a Chip: Guiding X Rays in Curved Channels.

We study the propagation of hard x rays in single curved x-ray waveguide channels and observe waveguide effects down to surprisingly small radii of curvature R≃10 mm and a large contour length s≃5 mm, deflecting beams up to 30°. At these high angles, about 2 orders of magnitude above the critical angle of total reflection θ(c), most radiation modes are lost by "leaking" into the cladding, while certain "survivor" modes persist. This may open up a new form of integrated x-ray optics "on a chip," requiring curvatures mostly well below the extreme values studied here, e.g., to split and to delay x-ray pulses.

Depth-Resolved Structure Analysis of Cylindrical Microdomain in Block Copolymer Thin Film by Grazing-Incidence Small-Angle X-ray Scattering Utilizing Low-Energy X-rays

Depth-resolved structure analysis of a polystyrene-b-poly(2-vinylpyridine) (S2VP) thin film (420 nm thick) was achieved by grazing-incidence small-angle X-ray scattering (GISAXS) utilizing low-energy X-rays (“tender” X-rays). In contrast to techniques utilizing hard X-rays, a gradual change of the penetration depth of soft X-rays around the critical angle of total reflection of a polymer surface is anticipated. In this research, X-ray energy of 2.4 keV was chosen to control the penetration depth and achieve depth-sensitive GISAXS measurement. Microphase-separated structure of the annealed S2VP in the thin film was confirmed to be hexagonally packed cylinders (HEX) aligned parallel to the substrate surface. Significant elongation of the Bragg spots in the qz direction was observed for an incidence angle close to the critical angle. The experimental full width at half-maximum (fwhm) values of the (11) HEX diffraction spot was interpreted using the theoretical fwhm values estimated using the Laue function co...

The effect of total reflection in PLIF imaging of annular thin films

Planar laser-induced fluorescence (PLIF) imaging techniques are increasingly used to study wavy annular flows in vertical and horizontal pipes. We present a ray-tracing study that analyzes the imaging properties of the PLIF technique for uniform and wavy annular films. Part of the emitted fluorescence will hit the water–air interface at angles greater than the critical angle of total reflection. As a consequence, PLIF imaging probes the film twice: From bottom to top and then again from top to bottom. Deflected fluorescence widens PLIF images of uniform films by about 30%. Surface waves further increase the contribution of deflected rays to the overall signal. At the steep slopes of large amplitude axial waves, total reflection might widen PLIF signals by up to a factor of two.