The spectroscopy of surface vibrations by atom scattering

The recent progress in the production of highly monochromatic atomic beams is opening new perspectives in surface physics, having paved the way for a full determination of the surface vibrational structure. After a discussion on the possible determination of Rayleigh wave dispersion curves from angular distributions exploiting the kinematical focussing effect, a short review is presented on the direct measurement of surface phonon dispersion curves, first achieved by Brusdeylins, Doak and Toennies in alkali halides, from time-of-flight (TOF) spectra of scattered He atoms. A comparison is made with the existing theories of surface phonons in ionic crystals. The state of the art in the theory of inelastic processes is briefly illustrated in order to discuss the theoretical interpretation of TOF spectra. The one-phonon energy loss spectra of He scattering from LiF(001) calculated for a hard corrugated surface model are found to be in general good agreement with the experimental TOF spectra. From such a comparison evidence is obtained that: i) one-phonon processes are predominant, and ii) in addition to Rayleigh waves important contributions to the inelastic scattering come from the surface-projected density of bulk phonons. Important effects due to inelastic resonances with surface bound states are put in evidence and explained by simple kinematical arguments. The possible observation of surface optical modes in NaF(001) is finally discussed.     

A simple model for the surface energy of ionic crystals

The surface energy of ionic materials is empirically related to bulk properties (elastic constants, electronic dielectric constant and optical band gap) through an analysis of the cleavage force. This is evaluated at small and large separations of the two crystal halves from phonon dispersion curves and from van der Waals interactions, respectively, and these two limiting behaviours are connected by a scaling hypothesis introduced for metals by Kohn and Yaniv. The experimental data that are available for a few ionic crystals seem to satisfy the suggested relation, with an empirical universal parameter which has roughly the same value as determined for metals.     

Inversion of Rayleigh waves using a genetic algorithm in the presence of a low-velocity layer

The shear-wave velocity profile can be obtained by the velocity of Rayleigh waves through the back-calculation based on dispersion curves. However, the dispersion curves obtained in practical application are always discontinuous and correspond to different mode branches due to mode jumping, especially in the presence of low-velocity layer. Mode misidentification may be encountered in inversion based on these jumped dispersion curves. Mode analysis demonstrates that the mode jumping is caused by a different surface displacement distribution with frequency for each mode. This indicates that the surface displacement distribution of the modes should be taken into account for the case of a low-velocity layer. Shear-wave velocity profiles are inversed based on the (possibly discontinuous) dispersion curves of fundamental and/or higher modes using a genetic algorithm (GA). In addition to the dispersion characteristics, the surface displacement distribution is also taken into account for the case of a low-velocity layer; as a result, mode misidentification is avoided. Published in Russian in Akusticheskiĭ Zhurnal, 2006, Vol. 52, No. 6, pp 811–824. The text was submitted by the authors in English.     

Elastic and phonon properties of FeSi and CoSi in the B2 structure

First principles calculations of structural, electronic, elastic, and phonon properties of the intermetallic compounds FeSi and CoSi in the B2 (CsCl) structure are presented, using the pseudopotential plane-wave approach based on density functional theory, within the local density approximation. The optimized lattice constants, independent elastic constants, bulk modulus, and first-order pressure derivative of the bulk modulus are reported for the B2 structure and compared with earlier experimental and theoretical calculations. A linear-response approach to density functional theory is used to derive the phonon dispersion curves, and the vibrational partial and total density of states. Atomic displacement patterns for FeSi at the Γ, X, and R symmetry points are presented. The calculated zone-center optical phonon mode for FeSi is in good agreement with experimental and theoretical data.     

Virtual excitation type surface polaritons on anisotropic media

We discuss the nature of a new type of surface polariton which occurs on anisotropic media, involving a photon coupled to a surface virtual excitation. Dispersion curves are calculated for α-quartz, where both real excitation type and virtual excitation type surface polaritons are predicted. The dispersion curves for virtual excitation surface polaritons are found to remain at small wavevector, and the endpoints of the dispersion curves terminate on the bulk polariton dispersion curves in the two media. The virtual excitation surface polaritons which occur on gyromagnetic and gyrodielectric media are also noted.     

快速数值差分递推算法在偏振模色散作用下光脉冲传输中的应用研究

利用快速数值差分递推算法对非线性薛定谔方程进行推导分析,得到一个同时考虑群速色散效应、非线性效应以及偏振模色散效应的时域快速数值差分递推关系,并将该方法应用于研究偏振模色散作用下的光脉冲传输,得到的计算结果分别与解析结果和传统的分步傅里叶算法所得结果进行对比,表明这种快速数值差分递推算法拥有很高的计算准确度,并且物理模型更加合理,完全适合分析计算偏振模色散作用下的光脉冲传输问题.利用该方法研究了光脉冲的畸变以及脉冲展宽问题,获得的计算结果为光纤传输系统的设计提供了参考.     

Dispersion of surface polaritons in uniaxial CdS

The dispersion of ordinary and extraordinary surface polaritons in uniaxial CdS has been measured using the ATR technique. The results have been compared with theoretical dispersion curves based on a classical oscillator model. The dielectric dispersion has also been generated. Comparison is made between the bulk phonons derived from Raman, infrared and from the surface mode data. Infrared measurements of small crystallites of CdS are in good agreement with the frequencies predicted for surface modes of small isolated spheres.     

光子晶体表面光波导的特性研究

采用平面波展开法和时域有限差分法,研究了光子晶体表面光波导的色散及光传输特性。研究结果表明,表面模的出现及其色散特性与表面介质柱的半径相关,色散曲线的斜率保持单调变化,并在最低或最高频率附近展现低群速度频率区。由于光子带隙和全内反射的共同影响,光场将沿晶体表面高效率地传输。研究结果为探索在光子晶体外部控制光传输具有重要的理论意义。     

Theory of damped surface magnetoplasmons in n-type InSb

A theoretical investigation of surface magnetoplasmons in n-type InSb has been carried out with the effect of damping taken into account. Part of the investigation included surface magnetoplasmons interacting with surface optical phonons. The calculated dispersion curves show backbending, in contrast to the situation were damping is neglected. In addition, there are gaps in the dispersion curves for certain frequency ranges.     

Refractive-index dispersion measurement of bulk optical materials using a fiber raman laser widely tunable in the visible and near-infrared

We propose a simple, highly sensitive fiber-optic autocollimation method for refractive-index dispersion measurement of solid-state and liquid bulk optical materials using a double-pass fiber Raman laser with Littrow-prism-tuned emission. The optical fiber is a key element of the scheme and serves simultaneously as a point laser source for the test, as a highly sensitive point receiver (or spatial filter) of the autocollimation backreflectance signal and as a medium for nonlinear frequency conversion and generation of a broadband continuum spectrum. When the Raman medium is a graded-index multimode fiber with powerful pumping (over 100 kW) using the second harmonic of a Q-switched Nd:YAG laser (λ_p=532nm), we obtain widely tunable (0.54-1.01 μm) generation in both the visible and near-IR ranges. The results obtained in the refractive-index dispersion measurements are fitted to the Sellmeier dispersion equation and the standard deviation of the experimental data from the analytical curve does not exceed 5x10^-5.     

Thermal expansion and lattice dynamics under pressure of ZnS,ZnSe and ZnTe

The thermal expansion against temperature of ZnS, ZnSe and ZnTe is studied theoretically using the experimental pressure dependence of elastic stiffness constants and phonon frequencies. The mode Grüneisen parameters obtained from the high pressure effect on the one- and two- phonon Raman spectra at the metallic transition pressure by Weinstein are used originally, but do not reproduce the experimental linear expansion coefficient at high temperatures. The contributions from optical modes with large phonon frequency are important to the thermal expansion at high temperatures, and a set of mode Grüneisen parameters, which bring good agreement with the observed linear expansion coefficient not only at low temperatures, but also at high temperatures, are obtained. Then, the phonon dispersion curves of ZnS, ZnSe and ZnTe at their metallic transition pressures are quantitatively shown.     

Optical 3R regeneration of 40 Gbit/s degraded data signals

A 40 Gbit/s optical 3R regenerator is proposed and demonstrated. The 3R regenerator consists of a dual-ring injection mode-locked fiber ring laser as the clock recovery module and an electroabsorption modulator (EAM) as the decision gate. The clock recovery module extracts the optical short pulse clock with low timing jitter from degraded 40 Gbit/s optical data streams, while the decision gate restores their signal quality. A numerical model describing the cross-absorption modulation effect in a bulk EAM is developed to explore the operating conditions, such as bias voltage, pump signal power. The timing jitter tolerance for the EAM optical gate is also investigated. Significantly improvement of BER is obtained from 40 Gbit/s RZ signals which are degraded by polarization mode dispersion or chromatic dispersion.     

Accurate Jones matrix expansion for all orders of polarization mode dispersion

I present a simple method for extracting the dispersive elements from a general unitary Jones matrix in such a way that the parts comprising the phase delays and higher-order dispersion in the two principal states of polarization are separated from those describing the frequency-dependent coupling between them. I then rigorously expand these two parts into power series in relative optical frequency, wherein the coefficients are explicit functions of the polarization mode dispersion vectors of various orders. This accurate expansion of the Jones matrix reveals in particular the amplitudes and phases of the cross-coupled components of the principal states of polarization, which are incorrectly described in most polarization mode dispersion models.     

Thickness dependence of the soft ferroelectric mode in SrTiO3 thin films deposited on MgO

We have measured the complex dielectric constants of SrTiO₃ thin films deposited on MgO substrate, by using the broadband terahertz time-domain spectroscopy. The dielectric dispersion of SrTiO₃ thin films with thickness of 1046, 460 and 55 nm has been observed in the frequency range from 0.1 to 8 THz. The dispersion mainly consists of the TO1 ferroelectric soft mode with a slight absorption of the TO2 phonon mode. From the analysis of the obtained dispersion, we found that the soft mode frequency hardens as the thickness of the film becomes thinner, and is extremely large compared with the bulk crystals. The damping of the soft mode is also larger than that of bulk SrTiO₃, which suggests the extrinsic nature of the broadening of the soft mode dispersion. In the thinnest film of 55 nm, even the shape of the dielectric dispersion changes, which may be related to integrated defects near the interface.     

Plasma modes in low-dimensional electron system over surface of liquid helium

The collective plasma modes in a quasi-two-dimensional (Q2D) electron system located over the free surface of liquid helium are studied theoretically within many-body dielectric formalism. The dispersion of modes is considered both over bulk liquid and over helium film where the essential modification of interelectron interaction occurs due to screening effects in the substrate with a large value of dielectric constant. It is shown that the plasma spectrum consists of longitudinal and transverse branches which dispersion laws depend on the values of the dielectric constant of helium and the film thickness. For the helium film covering metal, the longitudinal mode is acoustic differing of that for the surface electron (SE) system over bulk helium.     

Guided wave topological imaging of isotropic plates

Topological imaging is a recent method. So far, it has been applied to bulk waves, and high resolution has been demonstrated for imaging scatterers even with a single ultrasonic insonification of the inspected medium. This method consists of (i) emitting waves and measuring the response of the medium; (ii) solving two propagation problems: the direct problem, where the experimental source is simulated, and the adjoint problem, where the source is the time-reversed difference between the measured wave field and that obtained from the direct problem; (iii) computing the image by simply multiplying both wave fields together in the frequency domain, and integrating over the frequency. The speed of the method depends only on the cost of the field computations that are performed in the defect-free medium. The present work deals with the application of topological imaging to plate guided waves. Combining modal theory and Fourier analysis, the computations are performed in a very short time. In the investigated cases, two-dimensional in-plane imaging is based on propagation of the single S0 Lamb mode. Despite very high dispersion of that mode, scatterers are accurately located and the spatial resolution is equal to about one wavelength.     

Anomalous dispersion and group velocity properties in subwavelength uniaxial metamaterial waveguide with metal cladding

We investigate propagation behavior of electromagnetic waves in a slab uniaxial metamaterial waveguide with metal cladding and discuss the dispersion relation, group velocity and energy flux distribution of transverse electric guided modes in two kinds of uniaxial metamaterial waveguides with different orientations of optical axis in detail. The numerical results show that there exist anomalous dispersion properties such as backward modes existing in low-frequency range, and the group velocity can be negative or approach zero. If the orientation of optical axis is selected properly, each guided mode has two dispersion curves—one is normal dispersion and another belongs to anomalous dispersion and shows a transition from a backward mode to a forward one with the angular frequency increasing. In addition, the condition of the existence of cutoff frequency is clarified. These properties may have potential applications in optical information storage, optical communication, integrated optics and nanophotonic devices.     

Surface phonons of LaB6(100): deformation of boron octahedra at the surface

The surface phonon dispersion of clean LaB₆(100) surface has been measured by means of high resolution electron energy loss spectroscopy. Eight vibrational modes, of which most are located in the energy gaps between the bulk phonon bands, have been detected. The lattice dynamical calculation of a slab-shaped crystal based on a force constant model has reproduced these experimental dispersion curves, which indicates the large increase in the force constant of interoctahedral boron-boron bond at the surface by 25%, and the large decrease in the force constants of intraoctahedral boron-boron bonds at the surface by 25–50%. These changes together with the analysis of the bulk phonon structure of metal hexaborides strongly suggest that the boron octahedra at the surface are expanded by about 0.004 nm parallel to the surface.     

Analytical solution of the scalar wave equation for slightly deformed optical Bragg waveguide

Using a simple analytical method, we study the electromagnetic-wave propagation in an optical Bragg waveguide which is slightly deformed at one side. We show the results of computations in the form of dispersion curves and provide a comparison with standard circular Bragg waveguides and step-index circular waveguides. We show that the correspondence between the cutoff V values for the standard step-index fiber and the new Bragg waveguide, which is slightly flattened on one side, is quite close for the lowest mode under the weak guidance condition.