Multiple scattering in the high-frequency limit with second-order shadowing function from 2D anisotropic rough dielectric surfaces: II. comparison with numerical results

Abstract

This second part presents illustrative examples of the model developed in the companion paper, which is based on the first- and second-order optics approximation. The surface is assumed to be Gaussian and the correlation height is chosen as anisotropic Gaussian. The incoherent scattering coefficient is computed for a height rms range from 0.5λ 1λwhere λ is the electromagnetic wavelength), for a slope rms range from 0.5 to 1 and for an incidence angle range from 0 to 70°. In addition, simulations are presented for an anisotropic Gaussian surface and when the receiver is not located in the plane of incidence. For a metallic and dielectric isotropic Gaussian surfaces, the cross- and co-polarizations are also compared with a numerical approach obtained from the forward.backward method with a novel spectral acceleration algorithm developed by Torrungrueng and Johnson (2001, JOSA A 18). (Some figures in this article are in colour only in the electronic version)     

Pulse broadening of enhanced backscattering from rough surfaces

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.     

A practical depth distribution function for angle-resolved Auger/photoelectron spectroscopy

It is shown that, to a good approximation, over the range of energies (single scattering albedo, ω 0.5) and angles (take-off angle >30°) used in angle-resolved AES and XPS spectroscopy, the depth distribution function (DDF) is approximately exponential with decay length Λ = λ_i(1 + λ_i/λ_tr)^−1/2, for inelastic mean free path (IMFP) λ_i, and transport mean free path λ_tr.

As Λ is also the length measured for the attenuation length experimentally (with either the overlayer technique or from backscatter spectra, equivalent to λ_i, using an interpretation which neglects elastic effects), the CDP may be obtained by straightforward Laplace inversion using experimentally determined attenuation lengths. That is, the correct composition depth profile may be obtained from systematically ignoring elastic scattering.     

Measurements of light scattering by a characterized random rough surface

Measurements are presented of the angular distribution of four wavelengths of light scattered by a one-dimensional random rough surface, whose probability density function is Gaussian with a standard deviation σ=1.22±0.02 μm and whose lateral correlation function is also Gaussian with 1/e width τ=3.17±0.07 μm. The wavelengths used are 0.63, 1.15, 3.39 and 10.6 μm. The surface is used in two forms: coated with gold and as an almost lossless dielectric. The results are compared to those predicted by a double scattering form of the Kirchhoff formulation. Agreement is good at small angles of incidence but less good at larger angles of incidence.     

The temperature dependence of the short wavelength transmittance limit of vacuum ultraviolet window materials—I. Experiment

The short wavelength transmittance limit or cut-off wavelength, λ_co, of LiF, MgF₂, CaF₂, LaF₃, BaF₂, sapphire, synthetic crystal quartz and fused quartz has been measured from about 100°C to about 10°K. λ_co is not a well denned quantity, so for the purpose of this experiment it has been arbitrarily taken as the wavelength where transmittance could just be measured, usually 0.1-0.5 per cent. With one exception λ_co shifted to shorter wavelengths as the sample was cooled; the shift varied from about 40 to 80 Å over the temperature range from 100°C to 10°K, depending on the material, with the largest shift occurring in BaF₂;. The exception was LaF₃ which showed no measurable change in λ_co wth temperature. Over the temperature range from 20° to 100°C the slope of λ_co, with temperature for all materials was fairly constant, but below 20°C it decreased, approaching zero as the temperature approached 20°-10°K. In the case of synthetic crystal quartz, for example, the slope changed from about 0.28 Å/°K at room temperature to about 0.055 Å/°K at 80°K.     

Determination of the optical constants of metals and semiconductors by combining ellipsometry with electron spectroscopy microscopy and X-ray specular reflection analysis

The optical constants n(λ) and k(λ) of metals and semiconductors can be determined by spectroellipsometry, however, their apparent values are considerably affected by the roughness and oxide overlayer thickness dof the sample. Aluminium thin film samples of high perfection and very low roughness (<1 nm) have been studied by cross-disciplinary experimental methods: X-ray specular reflection analysis for determining the structure and thickness of the natural (hydrated) oxide overlayer and roughness of the substrate; plasmon electron energy loss spectroscopy supplied d. For calibration of the d measurements a special thin film multilayer system was developed, suitable for preparing cross-sectional samples for resolution transmission electron microscopy. Knowing the roughness and d-data, the optical constants n(λ) and k(λ) of aluminium were determined by spectroellipsometry in the spectral range λ=365–633 nm. Experimental results and a nomogram are presented for evaluating n(λ) and k(λ). The dependence of the ellipsometric optical constants on roughness and d is discussed. Very good agreement of the optical constants with the corrected ellipsometric results of Blanco and the synchrotron spectroscopy data of Hagemann was found. The cross-disciplinary methods can be applied to metals and semiconductors covered with an overlayer.     

Polarization instability in lasers with weakly anisotropic cavities

A theoretical study is made of the influence of the active medium and the cavity parameters, as well as that of an external magnetic field, on the properties of spontaneous pulsation regimes of lasers with weakly anisotropic cavities. Our results provide a physical interpretation of recently reported experimental data for spontaneous intensity pulsations of orthogonal components of the electromagnetic field generated by a single-mode, Fabry-Perot, HeNe gas laser at λ = 3.3922 μm and by a HeXe laser at λ = 3.51 μm.     

Numerical evaluation of the impulse response of multimode optical fibers

A numerical technique based on ray optics is presented that provides the impulse response of multimode optical fibers having arbitrary smooth index profiles and arbitrary material dispersion. The variation of dn/dλ₀ as a function of n when the dopant concentration varies is obtained from Fleming⁽¹⁾ measurements on bulk samples. This technique is applied to germania-doped multimode fibers with power-law profiles and various values of Δ ≡ Δn/n Previous results⁽²⁾ are shown to be invalid when Δ ≳ 0.005. By successive approximations, optimum profiles that minimize the impulse response widths for quasi-monochromatic sources are found. For these optimum profiles, the quasi-monochromatic root-mean-square (rms) impulse response width is found to be of the order of 150 Δ²nsec/km, in agreement with a recent analytical result.⁽³⁾     

Surface mass transport of Ag and In on vicinal Si(111)

Mass transport of Ag and In on vicinal Si(111) has been investigated by scanning Auger microscopy (SAM). Highly anisotropic surface diffusion and surface electromigration due to direct current were observed for Ag and In adatoms on 0°−, 0.5°−, 3°− and 6°−off vicinal Si(111) surfaces. The diffusion on the intermediate layer is strongly enhanced in the direction parallel to the step edge for Ag adatoms, while it is remarkably suppressed in the direction perpendicular to the step edge for In adatoms. The activation energy of the diffusion for the Ag adatoms ranged between 0.81 and 1.3 eV, while that for In adatoms increased from 0.31 to 0.66 eV with increasing the vicinal angle. The anisotropic diffusion transport is explained in terms of the step structure and the difference in the binding energy at the step site and the terrace site.     

Magnetic phase transition in (Ba, Sr)Fe12O19 single crystals

The critical exponents β, γ and δ of single crystals of hexagonal ferrites BaFe₁₂O₁₉ and SrFe₁₂O₁₉ were determined from modified Arrott plots, scaling plots, ln(J) versus ln(μ₀H) plots and the method of Kouvel and Fisher. The results resemble those of the strong anisotropic ferromagnet Nd₂Fe₁₄B. Crossover effects are discussed by estimating the ranges within which dipolar and anisotropic interactions dominate, and by analyzing the temperature-dependent exponents β(T) and γ(T). In addition, the λ-line was determined from measurements in the hard direction, and the critical exponent ω was fitted.     

Frequency, field, and temperature dependence of the AC penetration depth of a GdBa2Cu3O7−δ film in the mixed state

We report on a systematic mutual induction measurement of the complex AC penetration depth λ of a sputtered high-quality GdBa₂Cu₃O_7−δ film in the mixed state by a very small coil system arranged near the sample surface. The complex penetration depth λ(B, T, ω) for DC inductions B 0.65 T (perpendicular to the film), for temperatures 36 K T 81 K, and for frequencies 1 kHz ω/2π 500 kHz was determined from the measured signal by a novel inversion scheme. The results are consistent with theoretical predictions based upon single vortex pinning. The Labusch parameter , the flux creep relaxation time τ, as well as the effective activation energy U are simulateneously determined.     

A new ultrasonic lens

There is an increasing need for good ultrasonic lenses in nondestructive testing, medical diagnostics and short range underwater applications. The difficulties encountered are material problems in nature; optical design techniques are well developed.

A symmetrical doublet has been designed with an aperture of F 1 and with aberrations much less than λ/4 at 2 MHz. The calculated resolution is 4λ per line pair. Details of the construction and the first test results, which agree well with predictions, are reported.     

Vibrationally resolved band profiles for autoionisation of NO (cΠ) nℓλ (vR=0) Rydberg states into NO AΠ (vi=0, 1, 2) vibronic levels

Excitation spectra for dispersed VUV-fluorescence of NO (λ_fl=134–152 nm) were measured in the exciting-photon energy range between 16.9 and 24.8 eV using monochromatised synchrotron radiation at medium bandwidth of 29 meV. Fluorescence from A¹Π (v_i=0, 1, 2) vibronic NO⁺-levels and fluorescence from excited dissociation fragments NI (3s ²P_J) was observed simultaneously by recording the dispersed fluorescence with a monochromator–position-sensitive detector combination. The autoionisation of NO (c³Π) nℓλ (v_R=0) Rydberg levels into the NO⁺ A¹Π (v_i=0, 1, 2) vibronic levels was observed vibrationally resolved. Different Beutler–Fano profiles for autoionisation of one Rydberg level NO (c³Π) nℓλ (v_R=0) into the different vibronic NO⁺ A¹Π (v_i=0, 1, 2) levels are clearly visible. The dependence of the Beutler–Fano profiles on the quantum numbers n, ℓ, and λ of the Rydberg electron is discussed. For the direct photoionisation into the NO⁺ A¹Π (v_i=0, 1, 2) vibronic levels a non-Franck–Condon behaviour was observed.     

Photorefractive effect applied to flatten Gaussian beam profiles of near infrared lasers

The resonant behaviour of the two-wave mixing gain as a function of the intensity in photorefractive InP:Fe crystals is applied to flatten the Gaussian profiles of a beam emitted by a Nd:YAG laser at λ=1.06 μm. This can be extended efficiently to other wavelengths in the spectral range where InP:Fe is photosensitive.     

Fluctuation-induced attraction of vortices in anisotropic superconductors

We study the fluctuation-induced attraction of vortices for continuous anisotropic superconductors by using quantum statistical physics. In the low temperature or quantum limit, only the low-lying modes are relevant, the induced short-range attractive potential is proportional to (k_BT)³K₁(ΓR/λ), while in high temperature or classical limit, the induced attractive potential reduced to long-range van der Waals type k_BT/R⁴ for two vortices separated by a distance R.     

Thermal fluctuations in d-wave layered superconductors

We study the thermal fluctuations of anisotropic order parameters (OP) in layered superconductors. In particular, for copper oxides and a d-wave OP, we present some experimental consequences of fluctuations in the direction normal to the layers. It is shown that the c-axis penetration depth λ_c can have a “disorder-like” quadratic temperature dependence at low temperature. The fluctuations are analyzed in the framework of a Lawrence-Doniach model with an isotropic Fermi surface. Anisotropies pin the orientation of the OP to the crystallographic axes of the lattice. Then we study an extended t-J model that fits Fermi surface data of bilayers YBCO and BSCCO. This leads to a d-wave OP with two possible orientations and, including the thermal fluctuations, yields the announced temperature dependence of λ_c. Furthermore a reservoir layer is introduced. It implies a finite density of states at the Fermi energy which is successfully compared to conductance and specific heat measurements.     

A note on the angular distribution of the characteristic surface loss intensity of electrons with non-normal incidence to the foils

By using a quantized theory of non-radiative surface plasmon in a semi-infinite electron gas, where retardation is taken into account, the differential surface loss intensity of electrons in a metal foil is calculated for the case of non-normal incidence of electron to the metal surface. The result shows that the differential surface loss intensity neither has a zero at θ = 0 for the case of normal incidence nor has a zero at a forward direction (θ ≠ 0, φ = 0) for the case of non-normal incidence, whose existences were predicted by electrostatic theories, but diverges as 1/θ at θ = 0 for both cases. It is also shown that, when the angle of incidence is greater than a certain critical value, there is a region of direction to which incident electrons can be scattered by exciting any one of surface plasmons with three different wave vectors.     

Carrier relaxation in InGaAs

A modelocked Nd: YAG pumped optical parametric amplifier providing 35 ps pulses in the wavelength range λ = 1.45−2.1 μm has been used to study photoexcited carrier recombination in InGaAs. At carrier densities in excess of 10¹⁸ cm^-3 Auger processes are found to dominate the carrier recombination. An Auger rate of 2.5±0.5×10^-28 cm⁶ s^-1 is determined.     

Change of the surface induced optical anisotropy of the clean Si(110) surface by oxidation

Normal incidence ellipsometry has been used to measure the change in the complex anisotropic reflectance ratio γ upon oxidation of the clean Si(110)16 × 2 surface. The spectroscopic change in the amplitude of γ (tan(Ψ)) shows a broad maximum of height 1.4 × 10⁻³ in the high energy region above 2.5 eV. No phase shift difference for the reflectance coefficients belonging to the surface principal optical axes has been measured. A Kramers-Kronig transformation of the amplitude ratio showed that a change in the phase is not expected. The change in tan(Ψ) indicates that the change in reflection upon oxidation in the optical region ismainly in the ( 10) direction.