Critical Angle Of Reflection Research Articles

Asymmetric skew X-ray diffraction at fixed incidence angle: application to semiconductor nano-objects

A procedure for obtaining three-dimensionally resolved reciprocal-space maps in a skew X-ray diffraction geometry is described. The geometry allows tuning of the information depth in the range from tens of micrometres for symmetric skew diffraction down to tens of nanometres for strongly asymmetric skew geometries, where the angle of incidence is below the critical angle of total external reflection. The diffraction data are processed using a rotation matrix formalism. The whole three-dimensional reciprocal-space map can be measured by performing a single azimuthal rotation of the sample and using a two-dimensional detector, while keeping the angle of incidence and the X-ray information depth fixed (FIXD method). Having a high surface sensitivity under grazing-incidence conditions, the FIXD method can be applied to a large variety of Bragg reflections, particularly polar ones, which provide information on strain and chemical composition separately. In contrast with conventional grazing-incidence diffraction, the FIXD approach reveals, in addition to the lateral (in-plane) components, the vertical (out-of-plane) component of the strain field, and therefore allows the separation of the scattering contributions of strained epitaxial nanostructures by their vertical misfit. The potential of FIXD is demonstrated by resolving the diffraction signal from a single layer of InGaN quantum dots grown on a GaN buffer layer. The FIXD approach is suited to the study of free-standing and covered near-surface nano-objects, as well as vertically extended multilayer structures.

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.

Simultaneous Surface-Near and Solution Fluorescence Correlation Spectroscopy.

We report the first simultaneous measurement of surface-confined and solution fluorescence correlation spectroscopy (FCS). We use an optical configuration for tightly focused excitation and separate detection of light emitted below (undercritical angle fluorescence, UAF) and above (supercritical angle fluorescence, SAF) the critical angle of total internal reflection of the coverslip/sample interface. This creates two laterally coincident detection volumes which differ in their axial extent. While detection of far-field UAF emission producesa standard confocal volume, near-field-mediated SAF produces a highly surface-confined detection volume at the coverslip/sample interface which extends only ~200 nm into the sample. A characterization of the two detection volumes by FCS of free diffusion is presented and compared with analytical models and simulations. The presented FCS technique allows to determine bulk solution concentrations and surface-near concentrations at the same time.

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.

Theoretical and Experimental Study on Detonation Wave Propagation in Cylindrical High Explosive Charges with a Wave-shaper

The use of a cylindrical high-explosive charge with a wave-shaper is an efficient way to obtain an ultra-high pressure and a convergent detonation wave. An analysis of flow fields corresponding to the regular and Mach reflection of detonation waves in a cylindrical high-explosive charge with a wave-shaper is presented in this paper. The pressure, flow velocity and triple point growth angle of the Mach stem were calculated. The Mach stem height was also determined by using the modified Whitham method. The results show that the Mach stem height rises from zero at the critical angle of Mach reflection and changes to the Chapman-Jouguet detonation state with the propagation of the detonation waves. Shock indentation experiments were conducted, in which a wave-shaper was used in a cylindrical high-explosive charge to form Mach reflection detonation waves. The results showed that the discrepancy between the experimental results and the theoretical calculations was less than 15%, which proves the validity of the proposed theoretical model.

Raman spectroscopy based on plasmon waveguide prepared with mesoporous TiO2 thin film

Gold film (40-nm-thick) sputtered on the glass substrate was decorated by using the sol-gel copolymer templated mesoporous TiO2 thin film (275-nm-thick) to fabricate the plasmon waveguide (PW). The Raman spectroscopy based on the Au/TiO2 PW is studied theoretically and experimentally. The surface morphology of the mesoprous TiO2 thin film and the cross-section of the PW chip are obtained by scanning electron microscopy (SEM) and the porosity (P) of mesoporous TiO2 thin film is determined to be about 0.589 by fitting the calculated waveguide coupling dips to the measured resonance wavelengths based on Fresnel equations. The angular distributions of Raman power from the molecular dipole located in the core layer of the waveguide are theoretically investigated based on the optical reciprocity theorem. The calculated results suggest that the Raman light radiated into the substrate consists of the directional Raman signal propagating at the resonant angle and the non-directional Raman signal whose radiation angles are smaller than the critical angle of total reflection. The directional Raman signal could be detected with the aid of the prism coupler, while the non-directional Raman signal can be detected directly on the back of the sensor chip. Furthermore, the angular distribution of the backscattered Raman signal is divergent and it is unaffected by the use of the prism coupler. The highest power of the directional Raman signal is much larger than that of the non-directional Raman signal and the backscattered Raman signal. The Raman spectroscopy based on the PW is studied by experiment with CV molecules adsorbed into the mesoporous TiO2 thin film. The Raman spectrum is obtained with the 532 nm laser radiating directly onto the waveguide surface. The experimental results show that the Raman signal including the directional Raman signal, non-directional Raman signal and the backscattered Raman signal can be detected with the PW chip. Besides, the directional Raman signal can only be detected by using the prism coupler, while the non-directional Raman signal can be detected directly on the back of the chip. Then the results also show that the peak intensity of the directional Raman signal is twice higher than that of the non-directional Raman signal. The further measurements reveal that the backscattered Raman signal hardly changes under the condition with or without the prism coupler. The experimental results mentioned above are in accordance with the theoretical calculations. The Raman spectroscopy based on PW in this work has potential value in further developing the Raman sensing technique.

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.

Two step formation of metal aggregates by surface X-ray radiolysis under Langmuir monolayers: 2D followed by 3D growth.

In order to form a nanostructured metallic layer below a Langmuir monolayer, radiolysis synthesis was carried out in an adapted geometry that we call surface X-ray radiolysis. In this procedure, an X-ray beam produced by a synchrotron beamline intercepts the surface of an aqueous metal-ion solution covered by a Langmuir monolayer at an angle of incidence below the critical angle for total internal reflection. Underneath the organic layer, the X-ray beam induces the radiolytic synthesis of a nanostructured metal–organic layer whose ultrathin thickness is defined by the vertical X-ray penetration depth. We have shown that increasing the X-ray flux on the surface, which considerably enhances the kinetics of the silver layer formation, results in a second growth regime of silver nanocrystals. Here the formation of the oriented thin layer is followed by the appearance of a 3D powder of silver clusters.

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...

Extinction depth in a smooth X-ray waveguide

An approximate solution to the dispersion equation for the dynamics of an X-ray beam trapped in a plane waveguide with smooth walls is used to study the dependence of extinction depth on the optical density of wall material and X-ray energy. For angles of incidence of the X-ray beam that are no greater than the Fresnel angle, the extinction depth in nonabsorbing medium depends only on difference N e1–N e1 of electron densities in the wall material and waveguide layer as (πr 0(N e1–N e2))–1/2, where r 0 ~ 2.81794 × 10–13 cm is the classical electron radius. The results are in good agreement with the penetration depth of X-ray radiation into surface that is obtained using the Fresnel formulas in the approximation of plane waves at grazing angles that range from zero to one half of the critical angle of total external reflection.

Nonlinear acoustic pulse propagation in ocean waveguides containing an elastic seabed

High intensity underwater sources, such as explosions, generate nonlinear finite-amplitude pulses that behave differently than linear acoustic pulses within shallow water waveguides. The nonlinearity is known to decrease the critical angle for total internal reflection from that of the linear case when the seafloor is approximated as a fluid. However, this result has not been extensively studied for elastic seafloors where shear waves are present. In this work, a time-domain model is developed assuming an isotropic linear elastic bottom, inviscid water column, and allowing for nonlinear advective acceleration and a nonlinear equation of state. The model is numerically implemented using a high-order Godunov scheme and then benchmarked against tank experiment data for the linear case. The nonlinear model is used to study the critical grazing angle for ocean bottoms of varying shear speeds to determine the combined effect of nonlinearity and elasticity on bottom penetration.

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.

Large field of view X-ray microscopy with asymmetric bent crystals and a laboratory source

In microscopy, there is a trade-off between the magnification and a workable field of view (FOV). In this paper, bent asymmetric diffraction wafers were used with a conventional X-ray source to accept high divergence and increase the FOV of a two-dimensional X-ray microscope. An FOV of 5 mm with 20× magnification was realized with two independent wafers in a thermomechanically stable setup. Using the knife-edge method, a resolution of 2.5 µm was measured in one dimension. The FOV of such a system is limited by the sizes of the wafers, and the magnification is limited only by the critical angle of external reflection.

Dual enhancement of light extraction efficiency of flip-chip light-emitting diodes with multiple beveled SiC surface and porous ZnO nanoparticle layer coating

A porous ZnO nanoparticle layer coating composed of columnar ZnO nanoparticle piles and a multiple-beveled substrate was used to enhance the light extraction efficiency of GaN-based flip-chip light-emitting diodes (FC-LEDs), which were grown on high-purity SiC substrates. The SiC substrate was multiple-beveled by fabricating an ‘X’ pattern on the face of it, followed by a deposition of a porous ZnO nanoparticle layer on the ‘X’-patterned surface. A porous ZnO nanoparticle layer was fabricated with gas phase cluster beam deposition in a glancing incidence. The incident angular-resolved light transmission of the ZnO nanostructure beyond the critical angle of total internal reflection (TIR) was greatly enhanced. The light output power of the LED was improved by nearly 60% compared to the original planar GaN-based LED on an SiC substrate (FC-SLED), which contained a significant enhancement supplemental to the 18% electroluminescence (EL) enhancement realized with the ‘X’-pattern beveling. We demonstrated that a dual enhancement of light extraction efficiency was achieved by using the hierarchical surface consisting of microscale textures (the multiple-beveled surfaces) and nanoscale structures (the ZnO nanoparticle layers).

Absolute near-infrared refractometry with a calibrated tilted fiber Bragg grating.

The absolute refractive indices (RIs) of water and other liquids are determined with an uncertainty of ±0.001 at near-infrared wavelengths by using the tilted fiber Bragg grating (TFBG) cladding mode resonances of a standard single-mode fiber to measure the critical angle for total internal reflection at the interface between the fiber and its surroundings. The necessary condition to obtain absolute RIs (instead of measuring RI changes) is a thorough characterization of the dispersion of the core mode effective index of the TFBG across the full range of its cladding mode resonance spectrum. This technique is shown to be competitive with the best available measurements of the RIs of water and NaCl solutions at wavelengths in the vicinity of 1550 nm.

Subwavelength multilayer dielectrics: ultrasensitive transmission and breakdown of effective-medium theory.

We show that a purely dielectric structure made of alternating layers of deep subwavelength thicknesses exhibits novel transmission effects which completely contradict conventional effective medium theories exactly in the regime in which those theories are commonly used. We study waves incident at the vicinity of the effective medium's critical angle for total internal reflection and show that the transmission through the multilayer structure depends strongly on nanoscale variations even at layer thicknesses smaller than λ/50. In such deep subwavelength structures, we demonstrate dramatic changes in the transmission for variations in properties such as periodicity, order of the layers, and their parity. In addition to its conceptual importance, such sensitivity has important potential applications in sensing and switching.

New fabrication method for an ellipsoidal neutron focusing mirror with a metal substrate.

We propose an ellipsoidal neutron focusing mirror using a metal substrate made with electroless nickel-phosphorus (NiP) plated material for the first time. Electroless NiP has great advantages for realizing an ellipsoidal neutron mirror because of its amorphous structure, good machinability and relatively large critical angle of total reflection for neutrons. We manufactured the mirror by combining ultrahigh precision cutting and fine polishing to generate high form accuracy and low surface roughness. The form accuracy of the mirror was estimated to be 5.3 μm P-V and 0.8 μm P-V for the minor-axis and major-axis direction respectively, while the surface roughness was reduced to 0.2 nm rms. The effect of form error on focusing spot size was evaluated by using a laser beam and the focusing performance of the mirror was verified by neutron experiments.

Preliminary Investigation on Design and Fabrication of a Metallic-Ellipsoidal Neutron Focusing Mirror

Neutron beam is a very useful probe for material characterization and non-destructive testing. There are a number of plans to construct neutron instrumens using focusing mirror to improve beam quality with higher intensity and smaller spot size. In this paper, an ellipsoidal mirror made by a metal substrate is proposed. As the metal substrate, electroless nickel is adopted because of its amorphous structure, machinability and relatively large critical angle of neutron reflection. The design of ellipsoidal neutron focusing mirror is made by considering the neutron reflectivity. A mirror is fabricated by ultrahigh precision cutting and 1st polishing process, and the form accuracy of 5 μm P-V with surface roughness of 0.7 nm Ra is obtained. Through this experimental fabrication, the feasibility of the proposed method is verified.