An iterative solution of the rough-surface scattering problem

Abstract

An iterative solution to the problem of scattering from a one-dimensional rough surface is obtained for the Dirichlet boundary condition. The advantages of this method are that bounds for convergence of the solution can be established and that the solution may readily be iterated to sufficiently high order in the interaction to examine the rate at which it converges. Absolute convergence of the iterative solution is also a sufficient condition for the convergence of the operator expansion method for surfaces on which the slope is everywhere less than unity. A numerical example of scattering from an echelette grating is considered, and bounds for convergence established. It is found that for scattering from such surfaces the rate at which the iterative solution converges decreases as the surface slope is increased. Corresponding results are found for the operator expansion method.     

Theoretical and computational aspects of scattering from rough surfaces: one-dimensional perfectly reflecting surfaces

Abstract

We discuss the scattering of acoustic or electromagnetic waves from one-dimensional rough surfaces. We restrict the discussion in this report to perfectly reflecting Dirichlet surfaces (TE polarization). The theoretical development is for both infinite and periodic surfaces, the latter equations being derived from the former. We include both derivations for completeness of notation. Several theoretical developments are presented. They are characterized by integral equation solutions for the surface current or normal derivative of the total field. All the equations are discretized to a matrix system and further characterized by the sampling of the rows and columns of the matrix which is accomplished in either coordinate space (C) or spectral space (S). The standard equations are referred to here as CC equations of either the first (CC1) or second kind (CC2). Mixed representation, or SC-type, equations are solved as well as SS equations fully in spectral space.

Computational results are presented for scattering from various periodic surfaces. The results include examples with grazing incidence, a very rough surface and a highly oscillatory surface. The examples vary over a parameter set which includes the geometrical optics regime, physical optics or resonance regime, and a renormalization regime.

The objective of this study was to determine the best computational method for these problems. Briefly, the SC method was the fastest, but it did not converge for large slopes or very rough surfaces for reasons we explain. The SS method was slower and had the same convergence difficulties as SC. The CC methods were extremely slow but always converged. The simplest approach is to try the SC method first. Convergence, when the method works, is very fast. If convergence does not occur with SC, then SS should be used, and failing that CC.     

Accurately solving the electronic Schrödinger equation of atoms and molecules using explicitly correlated (r 12-)MR-CI IV. The helium dimer (He 2)

The helium dimer interaction potential is computed using the recently proposed (explicitly correlated) r ₁₂-MR-ACPF (averaged coupled-pair functional) method and a [11s8p6d5f4g] basis set. With an MR-ACPF ansatz that contains 121 references we obtain interaction energies that are close to full CI. In a smaller reference space containing 9 functions, however, even by successively adding [3h] and [2i] functions to the basis set mentioned above, the basis set limit could not be reached. While convergence to the basis set limit is slow, it nevertheless is monotonic and therefore allows for extrapolation to the limit. We obtain basis set corrections at R = 4 a ₀ and 5.6 a ₀ which we further extend to all distances and which we apply to the potential energy curve mentioned above. From our calculations, we conclude that a very recent potential which has been calculated using the SAPT (symmetry adapted perturbation theory) method, and which previously was assumed to be the most accurate available, is insufficiently repulsive at short distances. We correct our extrapolated potential for retardation and finally calculate the expectation value of the interatomic distance (?R?) and dissociation energy (D ₀) by solving the Schrödinger equation of the vibrating ⁴He₂. Our results (?R? = 41 ± 13 Å and D ₀ = 2.2 ± 1.0 mK) are in acceptable agreement with very recent calculations in the literature, but they disagree with a recent experiment.     

Perturbation theory results for the diffuse scattering of light from two-dimensional randomly rough metal surfaces

Abstract

Using the unitarity and reciprocity preserving formulation of Brown et al a perturbation treatment, correct to fourth order in the surface profile function, is given for the scattering of electromagnetic waves from a weakly rough, two-dimensional, random metal surface. In this formulation the boundary conditions on the electromagnetic fields are satisfied using the extinction theorem in conjunction with the Rayleigh hypothesis and the vector equivalent of the Kirchhoff integral. The theory is applied to, and results are presented for, several different types of rough surfaces which are characterized by power spectra that are extensions to two-dimensional random surfaces of the power spectrum of some one-dimensional random surfaces recently fabricated by West and O'Donnell. These surfaces, which can be realized experimentally, favor coherent, interferent, multiple scattering of electromagnetic waves via surface plasmon polaritons in intermediate states, and clearly exhibit enhanced backscattering caused by the surface plasmon polariton mechanism. Theoretical results are presented for silver surfaces at optical wavelengths.     

Convergence of solutions to the rough-surface scattering problem

Abstract

A new formulation of the rough-surface scattering problem is obtained that is closely linked to the Kirchhoff approximation. The governing equation is cast into a form amenable to solution by the method of successive approximations. The domain of convergence of this solution is established and is shown to apply also to the odd-ordered operator expansion, small-slope approximation and perturbation theory provided that the slope of the scattering surface is everywhere less than unity. The analysis is performed for scattering from one-dimensional pressure-release surfaces. Numerical examples are presented for sinusoidal and echelette gratings.     

Isotope effect of protonic conductivity in LiNbO3

Abstract

The electrical DC conductivity [sgrave] of LiNbO₃ :H, D was studied as a function of temperature, electric field and proton/deuteron dopant concentration. The conductivity follows linearly the hydrogen content over two orders of magnitude. Independent holographic measurements on the same samples confirm these results in the temperature range 75 – 150 °C. The activation energy for protonic and deuteronic migration turns out to be equal, E_{act, H} = E_{act, D} = 1.23 ± 0.04eV. The isotope effect of the pre-exponential factor reflects the mass dependence of the attempt frequency and shows the protons to be the migrating species rather than hydroxyl ions.     

Pressure dependence of photoconductivity for hydrogenated amorphous silicon

Abstract

Measurements of steady-state photoconductivity for hydrogenated amorphous silicon (a-Si:H) have been carried out at pressures up to 14 GPa and at room temperature. The ratio of photoconductivity to darkconductivity [sgrave]p/[sgrave]D decreases with increasing pressure. The activation energy for photoconductivity Ep, which is 0.25 eV at ambient pressure, decreases with increasing pressure at the rate -7 meV/GPa. These resultls are discussed with change in density of states.     

Accurately solving the electronic Schrödinger equation of atoms and molecules using explicitly correlated (r12-)MR-CI. VI. The helium dimer (He2) revisited

A recent computation of the helium dimer interaction potential for intermediate distances (2 ≤ R/a₀ ≤ 15) using the (explicitly correlated) r₁₂-MR-ACPF (averaged coupled-pair functional) method [GDANITZ, R. J., 1999, Molec. Phys., 96, 1423] is extended to larger basis sets. Calculations including a large atom centred [11 s8p6d5f4g3h2ilk] set show that the convergence of the energy with respect to enlargement of the basis set has previously been considerably underestimated. The extension of the P_k potential (292.75 ± 0.01, ?10.980 ± 0.004 and ?4.620 = ± 0.002 K at R = 4, 5.6 and 7 _a0) to distances between 2.5 and 15_a0 (P_k?)is close to a recent potential of van Mourik and Dunning [1999, J. Chem. Phys., 111, 9248] and it is believed to be the most accurate available. It gives rise to ⁴He₂ molecular constants of (R) = 46.4 ± 1.4 Å and D₀ = 1.67 ± 0.11 mK.     

The effect of point defects on the ionic conductivity of RbAg4I5 solid electrolytes

Abstract

The effect has been studied of additive coloring on the magnitude of ion conductivity of RbAg₄I₅ crystals. It has been found that slight changes of silver stoichiometry of 10^?3 at.% can lead to considerable variations of the ionic conductivity Δ[sgrave]_i/[sgrave]_i ? 0.1. The dependence has been observed of the magnitude of ion conductivity on the ratio between the integral intensities of the main bands in the photoluminescence spectrum of the γ-phase of RbAg₄I₅ which associated with the luminescence centres containing vacancies and interstitials of silver cations.     

A numerical evaluation of Rayleigh's theory applied to scattering by randomly rough dielectric surfaces

Abstract

We present a numerical simulation of scattering by one-dimensional randomly rough surfaces. It is based on the use of plane-wave expansions to describe the Melds on the surface (i.e. Rayleigh hypothesis). Accuracy and convergence properties of two different numerical implementations are studied. Some examples of results for a dielectric and a metallic Gaussian rough surface are shown to be in good agreement with calculations by a rigorous numerical method. The Rayleigh method appears to be a fast computation tool for dielectric surfaces with slopes of less than 0.2.     

Multiple scattering investigation of the 1T-TaS2 surface termination

Multiple scattering theory based on a cluster model is used to simulate full hemispherical X-ray photoelectron diffraction measurements on a 1T-TaS₂(0001) surface. Key points to determine the surface termination are discussed. As the commonly applied single scattering simulations do not give satisfying results, a multiple scattering approach has to be used to accurately simulate the full hemispherical photoelectron diffraction patterns. Differences and similarities between calculations of Ta and S terminated surfaces are presented along with experimental results at room temperature using both, the single and the multiple scattering approaches. We find that the surface is S terminated and that the quantitative difference between the calculations for both terminations permits to show the limits of the single scattering approach for solving surface termination problems. Moreover, by generalizing the results obtained using the multiple scattering approach, we discuss the application of this method to other similar systems.     

Non-partial-wave Coulomb-Born theory for the excitation of many-electron atomic ions II: Numerical description and application

A non-partial-wave Coulomb-Born theory is recently formulated to treat the excitation of many-electron atomic ions for impact by an arbitrary charged particle [Y.B. Duan et al., Phys. Rev. A 56, 2431 (1997)]. The multiple expansion of the transition matrix element is decomposed into the target form factor and the projectile form factor. These are the matrix elements of the tensor operators between quantum states so that any complicated wave function for the target ion can be employed. In this formal theory, an infinitesimally small positive quantity is introduced artificially to guarantee the convergence of integrals. As a supplementary part of the theory, we discuss how to choose the value of . It is found that the should be taken as functions of the momentum transfer and multipolarity . Illustrations are carried out by calculating the cross-sections for some typical transitions n _a l _a -n _b l _b of hydrogen-like ions for impact by electron, positron, and proton, respectively. The resulting cross-sections are in good agreement with ones produced by using a method available for ion targets with Slater-type orbitals [N.C. Deb, N.C. Sil, Phys. Rev. A 28, 2806 (1993)]. Comparisons demonstrate that the Coulomb-Born theory with non-partial wave analysis provides a powerful method to treat the excitation of many-electron atomic ions impact by an arbitrary charged particle. Received 6 April 1999     

Effect of oxygen segregation on the surface structure of single-crystalline niobium films on sapphire

Single-crystalline Nb films are grown on (1120) oriented sapphire substrates by electron-beam evaporation in ultra-high vacuum. The films are studied in-situ by RHEED and Auger analysis. At a substrate temperature T _S=750° C the RHEED pattern shows a smooth growth of bcc-Nb in the [110] direction. In addition to the fundamental streaks, we observe superlattice streaks of fractional order in several azimuthal directions. The reciprocal lattice of the surface is determined. The basic vectors of the superlattice in real space are given by b ₁=2a ₁, b ₂=–a ₁+3a ₂ where a ₁ and a ₂ are the basic vectors of the Nb (110) surface. Auger analysis shows that the surface of these films is contaminated with oxygen. Therefore, the superstructure is attributed to a modified surface structure due to segregated oxygen, possibly having diffused from the sapphire to the film surface. The superstructure dissappears during further evaporation of Nb at T _S<450° C with a concomitant decrease of the oxygen signal. Nb films on sapphire with a clean, oxygen-free surface can only be prepared at lower temperatures in an island-growth mode.     

Electronic Spectra of a Series of Iron(II) α-iminooxime Macrocyclic Complexes Containing Axial N-Heterocyclic Ligands

Abstract

The influence of the axial N-heterocyclic ligands on the charge-transfer spectra of a series of iron(II)-iminooxime macrocyclic complexes is reported. Spectral correlations are discussed, based on the deconvolution of the absorption profiles and on the dependence of the charge-transfer energies with the Hammett [sgrave]^+/- substituent parameters.     

Scattering of Rayleigh waves by a statistical inhomogeneity of the mass density

The problem of the scattering of a Rayleigh wave by a surface inhomogeneity of the mass density of an isotropic solid is solved in the Born approximation of perturbation theory. The inhomogeneity is statistical with a Gaussian correlation function in the plane parallel to the surface and is deterministic with an exponentially decaying dependence on the coordinate perpendicular to the surface. Expressions are derived for the displacement fields in the scattered longitudinal (P), transverse (SV and SH), and Rayleigh (R) waves at large distances from the inhomogeneity. The Rayleigh wave energy scattering coefficients are calculated as functions of the wavelength λ, the correlation length a of the inhomogeneity, the depth d of the defective layer, and the Poisson ratio of the medium, σ. The angular distribution of the scattered Rayleigh wave energy is determined. Asymptotic expressions are obtained for the scattering coefficient in various limiting cases with respect to the parameters a/λ and λ/d. The relation between the energies in the scattered P, SV, SH, and R waves is established. The resulting equations are used to calculate the scattering coefficients numerically over a wide range of variation of the parameters a/λ, λ/d, and σ; the results are presented in the form of graphs and a table. A physical pattern of the scattering process is constructed and used as a basis for interpreting the results of the study. Fiz. Tverd. Tela (St. Petersburg) 39, 267–274 (February 1997)     

Conversion ratio to F-H center pairs from self-trapped excitons in alkali chloride crystals

Abstract

The time delayed double excitation spectroscopy has been utilized to determine the conversion ratio to F-H center pairs from self-trapped excitons(STE_L) at the lowest state (1s[sgrave]_g;a_1g). The final conversion ratios, η_F/(η_F+η_X), were 0.86, 0.49 and 0.20 for NaCl, KCl and RbCl at 14K, respectively. The conversion efficiency (η =η_F+η_X) from STE_L to F-H center pairs(η_F) and to unknown states(η_X) were 0.25, 0.90 and 0.76 for the hole excitation to π_g, while 0.03, 0.01 and 0.01 for the electron excitation to b_1u, b_2u or b_3u, in NaCl, KCl and RbCl, respectively.     

The influence of cone-covered surface structures on sputtering and secondary electron emission: Model

Abstract

The yield and the polar angular distributions of secondary particles emitted from cone-covered surfaces were studied. A model taking into account both the influence of the local incidence angle I and the blocking of the emitted particles by the surface relief was elaborated. For an emission angle a, the transport effect of the particles generated inside the solid was simulated by the standard relation F(a) = (cos a) ⁿ and the emission dependence on the local incidence angle was assumed to behave as E(I) = (cos I) ^-m . Calculations showed that for m= 1 the surface topography only slightly alters the polar angular distribution shape but the yield of the collected particles is always higher than that from a flat surface when m is more than unity. For n= 2, the shape of the distribution curve is significantly different from that of the corresponding flat surface whatever the m values. For n=0, when E(I) very rapidly increases with the incidence angle both the angular distributions shape and the yield are strongly modified by the surface topography.     

Precision measurement of the coherent neutron scattering length of 3He through neutron interferometry

Improved knowledge of the real part of the neutron scattering length of ³He is important for further development of nuclear few-body theory, as well as for a thorough understanding of neutron scattering off quantum liquids. The real part of the bound incoherent neutron scattering length b_i' has recently been measured directly with an experimental uncertainty of better than 1% by means of spin echo spectrometry. The uncertainty of the more fundamental bound multiplet scattering lengths b_±' is thus limited by today's 1.2% uncertainty of the spin-independent coherent part b_c'. Employing the skew-symmetric perfect crystal Si-interferometer at the S18 experimental site at ILL, Grenoble, we have re-measured the real part of the bound coherent neutron scattering length b_c' of ³He. Our result b_c' = 6.010(21)fm exhibits a significant deviation compared to the latest accepted value b_c' = 5.74(7)fm (H. Kaiser, H. Rauch, G. Badurek, W. Bauspiess, U. Bonse, Z. Phys. A 291, 231 (1979)). Including the known value of the incoherent neutron scattering length, we obtain new values for the real parts of the free singlet and triplet scattering lengths, a_-' = 7.573(30)fm and a₊' = 3.480(18)fm. Our result contravenes by more than 7 standard deviations the measurement of the same physical quantity that has recently been performed by a group at NIST in a very similar experiment (P.R. Huffman, D.L. Jacobson, K. Schoen, M. Arif, T.C. Black, W.M. Snow, S.A. Werner, Phys. Rev. C 70, 014004 (2004)) which yielded b_c' = 5.853(7)fm.     

Pulse broadening of enhanced backscattering from rough surfaces

Abstract

Recently, we presented a study of pulse scattering by rough surfaces based on the first-order Kirchhoff approximation which is applicable to rough surfaces with RMS slope less than 0.5 and correlation distance l?λ. However, there has been an increased interest in enhanced backscattering from rough surfaces, study of which requires inclusion of the second-order Kirchhoff approximation with shadowing corrections. This paper presents a theory for the two-frequency mutual coherence function in this region and shows that the multiple scattering on the surface gives rise to an additional pulse tail in the direction of enhanced backscattering. The theory predicts pulse broadening approximately 20% greater than that caused by single scattering alone for a delta-function incident pulse and typical surface parameters. Analytical results are compared with Monte Carlo simulations and millimetre-wave experiments for the one-dimensional rough surface with RMS height 1λ and correlation distance 1λ, showing good agreement.