Nonspecular Reflection Research Articles

Direct measurement of the wigner delay associated with the goos-Hanchen effect

It is shown experimentally that the nonspecular reflection of light on an interface induces a time delay, as predicted by Wigner's scattering theory. A differential femtosecond technique is used to directly isolate this delay, associated with the Goos-Hanchen spatial shift produced by a grating near a resonant Wood anomaly. A delay of 4.4 fs is observed between TE and TM pulses, in agreement with the expected Wigner delay obtained from phase shift dispersion measurements.

Surface roughness of sputter-deposited gold films: a combined x-ray technique and AFM study

We applied grazing incidence x-ray specular and non-specular reflectivity (GIXR) and small-angle x-ray scattering (SAXS) to study the surface roughness of gold films on quartz glass substrates. Two model systems were prepared: one series of Au films was sputtered in Ar at 3×10−3mbar (Au1 films) and one in residual air at 3×10−1 mbar (Au2). The combined x-ray experiments showed that the Au1 films are compact and smooth, with-mean-square (rms) roughness values too low to be quantified by means of atomic force microscopy (AFM) or SAXS. The surfaces of film and substrate exhibit a strong cross correlation that is gradually lost with increasing film thickness. The surface height–height correlation functions are well described by a self-affine model. In contrast, as directly proved via AFM, the Au2 films consist of islands that are coarsening with increasing film thickness. The film surface showed no cross-correlation with the substrate surface at all. The SAXS curves from the Au2 films were attributed to a volume scattering effect, by interpreting the films in terms of a two-dimensional array of hard hemispheres. Copyright © 1999 John Wiley & Sons, Ltd.

Long-term stability of a quasiperiodic Ta/Al multilayer: Disintegration at room temperature analyzed by grazing angle x-ray scattering and photoelectron spectroscopy

A three-component Fibonacci (3CF) Ta/Al multilayer has been reinvestigated by specular and diffuse x-ray reflectivity and x-ray photoelectron spectroscopy (XPS) after 41 months of storage at room temperature. The specular reflectivity shows drastically suppressed diffraction peaks, whose positions and intensities are explained by severe interdiffusion of the Ta/Al bilayers building the 3CF sequence. Nonspecular reflectivity scans still indicate a high degree of interfacial roughness correlation in the growth direction that is attributed to the long spatial Fourier components of the interface profiles, which are substantially less affected by interdiffusion. The angle-resolved XPS spectra show that the Ta capping layer is completely oxidized and interdiffused by Al, whereas below the oxide layer Ta and Al coexist in metallic form in the same film. Both x-ray reflectivity and XPS yield an oxide layer of ∼30 Å thickness. Despite the severe structural disintegration, the multilayer diffraction spectrum can still be indexed by means of the projection theory for quasiperiodic sequences, which points to a remarkable stability of quasiperiodic properties against significant disorder. We conclude that Ta/Al bilayers are apparently unsuitable for multilayer applications due to the lack of thermal stability even at room temperature, with grain boundary diffusion pointed out as a possible disintegration mechanism. The design of improved 3CF Ta/Al multilayers is discussed with regard to applications in x-ray optics.

Non-specular reflectivity of spin flipped neutrons

For the first time we observed large intensity non-specular reflection peaks of neutrons incident at small grazing angles on not fully magnetized ferromagnetic samples. In addition to the normal specular reflection spin flipped neutrons are reflected at distinctly higher (lower) angles if the incoming spin down (spin up) neutrons hit the surface at angles near the respective critical angle. The same effect occurs in transmission. The angles at which the non-specular reflection occurs can be calculated by a simple model, which assumes a spin flip without a change of direction and takes into account the different refraction angles of the original and the flipped spin state when the neutrons leave the sample.

Reflection and diffraction in room-acoustic modeling

Many programs for room-acoustic modeling are based on the mirror image source concept. This way, only specular reflections are taken into account such that the resulting wave field is incomplete. Nonspecular reflections, or diffraction phenomena, can be added using an algorithm based on Pierce’s theory. Then, the true wave field is significantly better approximated. However, comparison of both results reveals that, averaged over time and space, the energy is equal in both cases: the added diffraction field so strongly interferes with (i.e., is so strongly correlated with) the specular reflections that no energy is added. This intuitively surprising result can be argued with a thought experiment. In this context, taking into account that acoustic perception is described with energetic criteria (clarity, definition, lateral energy fraction, etc.), it should be critically reconsidered as to how far the physically incomplete mirror image source programs are adequate for the prediction of the global acoustic quality of a hall.

X-ray reflection from self-organized interfaces in an SiGe/Si multilayer

Interface morphology of a strained SiGe/Si multilayer has been investigated by means of non-specular x-ray reflection. Depending on the azimuth of the scattering plane, two types of interface pattern have been observed, namely an asymmetrical random staircase and symmetrical islands superimposed on it. The distribution of the scattered intensity in reciprocal space has been simulated using a structure model of self-similar interface patterns and the distorted-wave Born approximation. The parameters of the interfaces following from the fit of the measured and simulated data were compared with the results of high-resolution x-ray diffractometry and transmission electron microscopy, and a good correspondence has been achieved.

Structural coherence of sputtered Ni3Al/Ni multilayers

Ni 3 Al/Ni multilayers have been grown by magnetron sputtering at room temperature. Structural coherence and interfacial properties were investigated as a function of deposition conditions by means of high angle x-ray diffraction, as well as specular and nonspecular x-ray reflection. High vertical coherence over 3.5 bilayer thickness is obtained in favorable conditions. It is shown that the structural coherence results from a highly textured growth and from a rather constant bilayer thickness over the whole multilayer stack. Surprisingly, the vertical coherence length does not decrease in samples sputtered at high Ar pressure despite a higher mosaic spread of the grains and rougher interfaces. In contrast, a high base pressure prior to sputtering is found to alter the coherence and to favor sharp and smooth interfaces. In all samples the roughness profiles are partially correlated from one interface to the other. The corresponding vertical correlation length is strongly influenced by the sputtering Ar pressure. In a large lateral length scale range (103–104 Å), a relatively slow decrease of the correlation length with decreasing length scale of the roughness is measured with a correlation length significantly smaller for the sample grown at high Ar pressure.

Non-specular X-ray reflection from sputtered Ni 3Al/Ni multilayers

Ni 3Al/Ni multilayers were grown by magnetron sputtering at room temperature. Non-specular X-ray reflection (NSXR) as well as grazing incidence diffraction (GID) measurements were performed in order to study the influence of the bilayer thickness Λ and of the sputtering Ar pressure on the lateral grain size g l and on the lateral correlation length of the interfacial roughness ξ. At low Ar pressure, g l and ξ are found to be of the same order of magnitude and to scale with Λ. At high Ar pressure the two lengths diverge due to the increase of the mosaic distribution of the growing grains.

Non-specular spin-flipped neutron reflectivity from a cobalt film on glass

From polarized neutron reflection experiments on a thin Co layer on glass at various applied fields it is shown beyond doubt that neutron spin-flip reflection in an applied magnetic field is non-specular in agreement with theory. It is shown that the deviations from the specular position at moderate fields is very substantial for wavelengths larger than a few tenths of a nm. The advantages of a curved stacked-mirror polarization analyzer, which recently has been installed on ROG at IRI, are discussed.

Specular and non-specular X-ray reflection from inorganic and organic multilayers

Specular and non-specular X-ray reflectivity measurements can be exploited to obtain interesting properties of layered materials such as electron-density profile and lateral and perpendicular structure of interface roughness. This will be illustrated using results on a nickel–carbon multilayer and a liquid-crystalline polymer.

(Ta/Si) multilayer as a wide-bandpass monochromator material.

Specular and non-specular X-ray reflectivity intensities of a (Ta/Si)(60) multilayer sample were measured to characterize its interface structure. Since the multilayer has a good reflectance at its multilayer peaks, its performance as a wide-bandpass monochromator for X-ray scattering experiments of polymers has been tested.

Bistable nonspecular reflection at a nonlinear–linear local interface

Nonspecular reflection at a nonlinear-linear dielectric interface with local Kerr nonlinearity is analyzed. The Fresnel reflectivity and the variational solution are explicitly given in a closed form. Bistable switching of the interface is demonstrated by numerical simulations based on the monotonic iteration procedure.

Nonspecular reflection of ordinary and extraordinary beams in uniaxial media

We study nonspecular phenomena experienced by two-dimensional ordinary and extraordinary beams propagating in a uniaxial crystal and reflected at a flat uniaxial–isotropic interface. We extend to uniaxial crystals the aberrationless approach used for beams in isotropic media. Analytical expressions for the geometrical nonspecular effects (lateral shift, focal shift, angular shift, and beam waist modification) are given and compared with those predicted by the stationary phase approximation. The theory is applied to the reflection of beams at a flat interface between TiO2 and a vacuum.

Growth mode and asymptotic smoothing of sputtered Fe/Au multilayers studied by x-ray diffuse scattering

The interfacial roughness of sputtered Fe[15 \AA{}]/Au[21 \AA{}] crystalline multilayers on MgO(001) was studied using x-ray specular and nonspecular reflectivity. The nonspecular scattering was collected using an image plate detector that allowed us to map the very weak x-ray diffuse intensity in one in-plane ${(q}_{x})$ and one out-of-plane ${(q}_{z})$ momentum-transfer direction. We have evaluated the interfacial static and dynamic roughness exponents from the in-plane diffuse scattering and the roughness conformality, and found them to be $\ensuremath{\alpha}=0.43\ifmmode\pm\else\textpm\fi{}0.05$ and $z=1.61\ifmmode\pm\else\textpm\fi{}0.15,$ respectively. From this result we show that the growth of this metallic thin film is described well by the Kardar-Parisi-Zhang (KPZ) model. By following the evolution of the interfacial roughness of this multilayer, starting from the MgO/Fe/Au heterostructure used to initiate a coherent lattice, we observe a tendency toward saturation in the growth and interfacial smoothing after the deposition of 40 bilayers. This asymptotic smoothing is induced by the mechanisms of the KPZ model and results in a reduction of the interfacial slope \ensuremath{\rho} as a function of time, according to $\ensuremath{\rho}(t)\ensuremath{\propto}{t}^{\ensuremath{-}0.31}.$ We have also found that the in-plane roughness cutoff length remains finite throughout the multilayer and does not increase to the lateral length of the sample, even after 100 bilayers have been grown.

Ultrasonic beam reflection from lossy layered cylindrical shells

Nonspecular reflection from a two-layer curved elastic structure consisting of rubber bonded to the outer surface of a steel shell has been studied experimentally and theoretically. The reciever voltage, in a two-transducer experiment, is measured as a function of azimuthal scan angle. The bond rigidity between the rubber and steel is accounted for by a spring model. This model is incorporated into an asymptotic evaluation of the spectral reflection integrals, accounting for the receiver characteristics by electromechanical reciprocity. Decreasing bond rigidity acts to weaken the leaky wave excited in the underlying steel shell and provides a method to assess bond integrity, while the damping loss of the rubber is found to be only a scale factor. A disbond completely suppresses the leaky wave. In comparisons between experimental data and predictions, good agreement is generally seen, also at incident angles different from phase-matched Lamb mode coupling.

Angular measurement of acoustic reflection coefficient for substrate materials and layered structures by V(z) technique

An experimental method to evaluate the acoustic reflection coefficient as a function of the incident angle R(θ) for substrate materials or layered structures is presented. By measuring the acoustic material signature V(z) using a highly focused acoustic lens or transducer at normal incidence, the reflection coefficient R(θ) can be reconstructed from the FFT of the complex V(z) signal (amplitude and phase of the echo). This technique has a great simplicity for the experimental procedure of R(θ) measurement. It overcomes the disadvantages of the conventional method where the finite-aperture plane beam reduces the angular precision and causes the unexpected non-specular reflection at critical incident angles. Results are given for different substrate materials, single plates and a three-layered bonded joint, and are compared to theoretical predictions.

Normal-mode theory of nonspecular phenomena for a finite-aperture ultrasonic beam reflected from layered media

A normal-mode formalism is developed to describe the nonspecular effects of a finite-aperture ultrasonic beam incident onto layered elastic media. Analytical expressions for the reflected field have been obtained for various structures. This model proposed a unique physical picture and resolved the conflict between various explanations made for the nonspecular reflection phenomena. Novel features of leaky wave fields were observed at interfaces of liquid-solid and liquid-solid-liquid structures. These results may be helpful for nondestructive evaluation of layered structures and determination of material signatures in the acoustic microscope.

Quasiballistic model of current transport and formation of the S-type current-voltage characteristic in the lightly doped, double-barrier heterostructure AlxGa1−x As-GaAs-AlAs

The quasiballistic model of current-carrier transport in the lightly doped, double-barrier heterostructure AlxGa1−xAs-GaAs-AlAs is considered. Electron scattering into the X-valley in the GaAs layer, nonspecular electron reflection from the AlAs layer, and energy quantization in the pre-barrier region are all taken into account. The possibility of an S-shaped current-voltage characteristic in lightly doped, double-barrier heterostructures in the absence of electron-electron collision is demonstrated for a comparatively wide AlAs barrier.

Specular versus diffuse reflection of atoms from an evanescent-wave mirror

We tested the specularity of the ref lection of slow atoms from an evanescent-wave mirror at normal incidence. In two of the three prisms that we tested the atoms were ref lected diffusely. This nonspecular ref lection appears to be correlated with the rms roughness of the surface supporting the evanescent wave. Only the highest quality surface (rms roughness of the order of 0.1 nm) leads to specular ref lection. This discovery imposes stringent limits on the use of these mirrors in atomic-optics experiments.

Motion of three inelastic particles on a ring.

In a previous paper [P. Constantin, E. Grossman, and M. Mungan, Physica D 83, 409 (1995)], we have studied in detail the dynamics of three inelastically colliding particles moving on an infinite line. The present paper addresses the effect of boundary conditions by investigating both analytically and numerically the dynamics of three particles confined to a ring. Using the methods developed in [P. Constantin, E. Grossman, and M. Mungan, Physica D 83, 409 (1995)], we reformulate the dynamics as a billiard in an equilateral triangle with nonspecular reflections laws. There are three sharply distinct regimes: (i) perfectly elastic collisions, (ii) slightly inelastic collisions, and (iii) strongly inelastic collisions. In particular, in the limit of the inelasticity going to zero, the asymptotic motion in case (ii) does not reduce to case (i), i.e., perfectly elastic motion is a singular limit. For motion on the line in the strongly inelastic regime, particles can either cluster, undergoing infinitely many collisions while their relative separation goes to zero (inelastic collapse), or they can separate after a finite number of collisions (escape). The confinement to a circle, while greatly enhancing the occurrence of clustering, does not completely eliminate the existence of other asymptotic states. In fact, there exists a fractal set of initial conditions for which collisions proceed indefinitely without clustering. \textcopyright{} 1996 The American Physical Society.