Direction Of Wave Vector Research Articles

Light-induced diffraction in thermally reduced congruent and near-stoichiometric Er:LiNbO3 crystals

A polarization-isotropic two-colour light-induced diffraction (LID) phenomenon from thermally reduced congruent and near-stoichiometric Er:LiNbO3 crystals was observed when these crystals were exposed to superposed 632.8 nm probe and 488 nm pump beams. The LID is characterized by expansion of the probe beam spot and the appearance of alternate bright and dark diffraction rings at higher pump light intensities. This phenomenon is absent not only in all other Er-doped crystals which either were as grown or had experienced other post-growth treatments such as vapour transport equilibration (VTE), oxidation and strong annealing but also in a pure VTE-treated crystal even though the crystal was subjected to the same reduction procedure. The LID characteristics of five reduced crystals, which have different Li-to-Nb ratios and different doping levels of Er3+, were studied in detail by changing the light intensity, polarization state and wave vector direction of both the pump and the probe beams. The origin of the LID was investigated from the viewpoints of the red fluorescence of Er3+ excited by a 488 nm pump beam, light-induced scattering and light-induced thermal nonlinearity. The results have shown that the thermal nonlinearity mechanism is preferred as it can reasonably explain almost all the observed experimental phenomena.

Cascade of two-dimensional Fulde-Ferrell-Larkin-Ovchinnikov phases with anisotropy

For an isotropic two-dimensional system, when the temperature is lowered toward $T=0$, it has been found recently that, for the transition from the normal to the superfluid state in the paramagnetic limit, the order parameter describing the Fulde-Ferrell-Larkin-Ovchinnikov phase has an increasingly complex structure with contributions from an increasing number of wave vectors. This cascade of phase transitions, found while moving along the phase transition line from the normal to the superconducting phase, is directly linked to the fact that, due to the rotational invariance, all the wave vectors directions which can enter the order parameter are degenerate. Making use of Ginzburg-Landau analysis, we study how this cascade of phase transitions is modified when one takes into account the anisotropy arising in a real solid state compound. For a simple model of anisotropy with elliptical dispersion relation, we find surprisingly that the cascade of phase transitions is not modified and the degeneracy with respect to the wave vector direction is still present. When we take into account a deviation with respect to this elliptical model, which is treated to first order in perturbation, we find that the degeneracy is lifted and that, basically, a single wave vector is favored right at the transition. However when one enters the superfluid phase, additional wave vectors come in the order parameter and the cascade of transitions is still present, though in a modified form.

Spin of valence-band holes in wurtzite semiconductors

Spin polarization properties of a ballistic hole in wurtzite semiconductors are analyzed using the concept of spin surface. It is shown that, in general, the spin surface in a three-dimensional spin space has the shape of spheroid whose minor/major axis and orientation depend on a relative strength of the spin-orbit and crystal-field interactions as well as on the hole wave vector direction and length. Analytical expressions for the spin surfaces of heavy-mass, light-mass, and split-off bands were found for two experimentally important cases, when the hole wave vector is parallel and perpendicular to the hexagonal axis. For an arbitrary direction of the wave vector the numerical results are presented which show that the spin surface remains the spheroid in this case as well. However, the surface transforms to a line or sphere at small and large wave vectors. The properties of the spin surfaces are illustrated for valence band parameters of GaN, where the crystal field dominates in the band-edge splitting.

Enhanced tracer transport by the spiral defect chaos state of a convecting fluid

To understand how spatiotemporal chaos may modify material transport, we use direct numerical simulations of the three-dimensional Boussinesq equations and of an advection-diffusion equation to study the transport of a passive tracer by the spiral defect chaos state of a convecting fluid. The simulations show that the transport is diffusive and is enhanced by the spatiotemporal chaos. The enhancement in tracer diffusivity follows two regimes. For large Péclet numbers (that is, small molecular diffusivities of the tracer), we find that the enhancement is proportional to the Péclet number. For small Péclet numbers, the enhancement is proportional to the square root of the Péclet number. We explain the presence of these two regimes in terms of how the local transport depends on the local wave numbers of the convection rolls. For large Péclet numbers, we further find that defects cause the tracer diffusivity to be enhanced locally in the direction orthogonal to the local wave vector but suppressed in the direction of the local wave vector.

Semiconductor Spintronics: Role of the Valence-Band Holes

Two aspects related to valence-band hole spin are considered: spin surfaces in p-type semiconductors and flipping of the hole spin by an ultrashort electric field pulse. It is shown that heavy, light, and split-off holes have different spin surfaces. In general, the shape of the surface in real semiconductors may depend on the hole wave vector direction and magnitude. The concept of spin surface is used to explain very strong anisotropy of hole spin injection efficiency observed recently in ferromagnetic-semiconductor structures and in optimizing ultrafast spin switching. It was shown that, of all spin flipping mechanisms, the most effective one is associated with hole transfer between different spin surfaces in high electric fields. The less effective mechanisms are related to valence band warping and nonparabolicity. Examples of the hole spin flipping dynamics and the discussion on ultrafast control of spin in semiconductors by π-type electrical pulses are presented.

Collective magnon modes for magnetic dot arrays

Both static and dynamic properties of the magnetic dot array with the uniform in-plane magnetization with the most symmetric configuration (round dots placed in a square lattice) have been investigated. Due to the long distance dipole coupling physical properties, such system has a strong four-fold anisotropy with respect both to orientation of the total array magnetization regarding the lattice symmetry axis and to the wave vector direction of a collective oscillations wave. The ferromagnetic state is stable only in the presence of the magnetic field; however, it can also be stable against small perturbations for some orientations of the total magnetization.

Polar Oscillation of Interface and Surface Optical Phonons in Free-Standing Cylindrical Quantum-Well Wires**The project supported partly by Natural Science Foundation of Guangdong Province of China

Under dielectric continuum approximation, interface optical (IO) and surface optical (SO) phonon modes as well as the corresponding Fröhlich electron-phonon interaction Hamiltonian in a free-standing cylindrical quantum-well wire (QWW) are derived and studied. Numerical calculations on As cylindrical QWW are performed. Results reveal that there are two branches of IO phonon modes and one branch of SO phonon mode, and the dispersion frequencies of IO or SO phonon modes sensitively depend on the Al mole fraction in As material and the wave-vector in direction, . With the increasing of and quantum number , the frequency of each IO mode approaches one of the two frequency values of the single As heterostructure, and the electrostatic potential distribution of the phonon mode tends to be more and more localized at a certain interface or surface, meanwhile, the coupling between the electron-IO and -SO phonons becomes weaker.

Two‐point studies of fast Z‐mode waves with dipoles in the ionosphere

An HF transmitter and synchronized receiver, both connected to dipoles, were operated during the tethered rocket experiment OEDIPUS C. On the flight downleg after the tether had been cut, direct bistatic propagation experiments were carried out with the transmitter in one subpayload and the receiver in the other subpayload. Medium‐frequency Z‐mode transmissions were observed to be strong compared with the adjoining wave modes. This fast Z mode is the left‐hand polarized mode propagating between its cutoff frequency fZ and the local plasma frequency fp. The Z mode is of particular theoretical interest because its refractive index surface evolves from a simple ellipsoid to an ellipsoid with inflections as the frequency is swept through the band. The Z‐mode signal was strongest at frequencies just below fp, at relatively low fp values. At higher values of fp, the Z‐mode signals were strongest at frequencies just above fZ. Details of these characteristics and of the measurements are presented. The magnitudes of transmitted signals predicted by a cold‐plasma theory for short dipoles are found generally to be in good agreement with the measurements. The exceptions were at the highest frequencies where the inflected shape of the refractive index surface leads to three separate wave vector directions for a single group direction. A possible explanation for the relatively strong Z‐mode signal is that the transmitting dipole impedance in the fZ − fp frequency range provides a better match to the output of the transmitter than in the bands of other wave modes swept.

Spectroscopy of the photonic stop band in synthetic opals

The photonic band gap of opals has been studied experimentally from their optical transmission spectra as a function of the incident beam orientation in the opal crystal lattice. The measurements were carried out for all high-symmetry points on the surface of the Brillouin zone of an fcc lattice. The experimental dependence of the energy position of the photonic band gap on the light wave vector direction is well described by the set of theoretical relations developed for the stop bands originating from the Bragg diffraction of light on {111}-type planes of the twinned fcc lattice of synthetic opals.

Novel properties of wave propagation in biaxially anisotropic left-handed materials

Some physically interesting properties and effects of wave propagation in biaxially anisotropic left-handed materials are investigated in this paper. We show that in the biaxially gyrotropic left-handed material, the left-right coupling of circularly polarized light arises due to the negative indices in permittivity and permeability tensors of gyrotropic media. It is well known that the geometric phases of photons inside a curved fiber in previous experiments often depend on the cone angles of solid angles subtended by a curve traced by the direction of wave vector of light, at the center of photon momentum space. Here, however, for the light propagating inside certain anisotropic left-handed media we will present a different geometric phase that is independent of the cone angles. The extra phases of electromagnetic wave resulting from the instantaneous helicity inversion at the interfaces between left- and right- handed (LRH) media is also studied in detail by using the Lewis-Riesenfeld invariant theory. Some interesting applications (e.g., controllable position-dependent frequency shift, detection of quantum-vacuum geometric phases and helicity reversals at the LRH interfaces etc.) of above effects and phenomena in left-handed media is briefly discussed.

Analytical model for the thermal conductivity of nanostructures

We present an analytical expression for the thermal conductivity in nanostructures which takes into account all phonon properties: the number of modes, the group velocity, the relaxation time due to the Umklapp process and the boundary surface scattering and their variation with the wave vector directions. Phonon properties can be determined from the known dispersion curves and the bulk thermal conductivity. For the example of a cube made of solid argon, the variations of the thermal conductivity with the system size obtained using the analytical model and nonequilibrium molecular dynamics (NEMD) are in good agreement. The model is also used to calculate the thermal conductivity of a single graphite sheet and carbon nanotubes as a function of their characteristic lengths. The variations of the thermal conductivity with size are compared with the theoretical predictions for one and two dimensional systems. Good agreement is obtained for the single graphite sheet, but not for carbon nanotubes, which reveals the limitation of the analytical model.

Interpretation of Cluster data on chorus emissions using the backward wave oscillator model

The measurements of chorus emissions by four closely separated Cluster spacecraft provide important information concerning the chorus generation mechanism. They confirm such properties of the wave source as their strong localization near the equatorial cross section of a magnetic flux tube, an almost parallel average wave-vector direction with respect to the geomagnetic field, and an energy flux direction pointing outward from the generation region. Inside this region, Cluster discovered strong temporal and spatial variations in the amplitude with correlation scale lengths of the order of 100 km across the magnetic flux. The wave electric field reached 30 mV/m, and the maximum growth and damping rates are of the order of a few hundreds of s−1. These and other properties of the detected chorus emissions are discussed here in relation with the backward wave oscillator mechanism. According to this mechanism, a succession of whistler wave packets is generated in a small near-equatorial region with temporal and spatial characteristics close to the Cluster data. Amplitudes and frequency spectra, as well as dynamical features of the Poynting flux of chorus are estimated and compared with the Cluster measurements.

Analytical model for the thermal conductivity of nanostructures

We present an analytical expression for the thermal conductivity in nanostructures which takes into account all phonon properties: the number of modes, the group velocity, the relaxation time due to the Umklapp process and the boundary surface scattering and their variation with the wave vector directions. Phonon properties can be determined from the known dispersion curves and the bulk thermal conductivity. For the example of a cube made of solid argon, the variations of the thermal conductivity with the system size obtained using the analytical model and nonequilibrium molecular dynamics (NEMD) are in good agreement. The model is also used to calculate the thermal conductivity of a single graphite sheet and carbon nanotubes as a function of their characteristic lengths. The variations of the thermal conductivity with size are compared with the theoretical predictions for one and two dimensional systems. Good agreement is obtained for the single graphite sheet, but not for carbon nanotubes, which reveals the limitation of the analytical model.

Torque on an ideal plasma.

Ripples in the confining field may exert a torque on a rotating plasma. Time reversal symmetry implies that this torque should vanish for an ideal plasma. However, even in an apparently ideal plasma, singularities can give rise to a nonzero torque. This torque is evaluated for a simple configuration. Although the primary force is magnetic, an essential contribution arises from other nonlinear terms in the equations of motion. The net force is confined to the singular layer, in the direction of the ripple wave vector and related to the energy absorbed in the layer.

Double refraction and reflection of sequential interfaces in a crystal and application to integration of 1 × N optical switch

The general formulation of double refraction or internal double reflection with different directions of propagation vector and wave vector in a uniaxial crystal is analysed in terms of Huygens' principle. Then double refraction and double reflection along the sequential interfaces in a crystal are discussed. On this basis, a configuration of electro-optic 1 x N optical switch with modulators and birefringent crystal slabs integrated in a single block of crystal is suggested, which is simple and compact in construction, low in loss and insensitive to environment. Finally, calculations are given which lead to a proposed design of a 1 × 4 switch.

Spatio‐temporal structure of storm‐time chorus

We discuss chorus emissions measured by the four Cluster spacecraft at close separations during a geomagnetically disturbed period on 18 April 2002. We analyze the lower band of chorus below one half of the electron cyclotron frequency, measured at a radial distance of 4.4 Earth's radii, within a 2000 km long source region located close to the equator. The characteristic wave vector directions in this region are nearly parallel to the field lines and the multipoint measurement demonstrates the dynamic character of the chorus source region, changing the Poynting flux direction at time scales shorter than a few seconds. The electric field waveforms of the chorus wave packets (forming separate chorus elements on power spectrograms) show a fine structure consisting of subpackets with a maximum amplitude above 30 mV/m. To study this fine structure we have used a sine‐wave parametric model with a variable amplitude. The subpackets typically start with an exponential growth phase, and after reaching the saturation amplitude they often show an exponential decay phase. The duration of subpackets is variable from a few milliseconds to a few tens of milliseconds, and they appear in the waveform randomly, with no clear periodicity. The obtained growth rate (ratio of the imaginary part to the real part of the wave frequency) is highly variable from case to case with values obtained between a few thousandths and a few hundredths. The same chorus wave packets simultaneously observed on the different closely separated spacecraft appear to have a different internal subpacket structure. The characteristic scale of the subpackets can thus be lower than tens of kilometers in the plane perpendicular to the field line, or hundreds of kilometers parallel to the field line (corresponding to a characteristic time scale of few milliseconds during the propagation of the entire wave packet). Using delays of time‐frequency curves obtained on different spacecraft, we have found the same propagation direction as obtained from the simultaneous Poynting flux calculations. The delays roughly correspond to the whistler‐mode group velocity estimated from the cold plasma theory. We have also observed delays corresponding to antiparallel propagation directions for two neighboring chorus wave packets, less than 0.1 s apart.

Radial source flows in porous media: Linear stability analysis of axial and helical perturbations in miscible displacements

Linear stability results are presented for axial and helical perturbation waves in radial porous media displacements involving miscible fluids of constant density. A numerical eigenvalue problem is formulated and solved in order to evaluate the relevant dispersion relations as functions of the Peclet number and the viscosity ratio. In contrast to the constant algebraic growth rates of purely azimuthal perturbations [C. T. Tan and G. M. Homsy, Phys. Fluids 30, 1239 (1987)], axial perturbations are seen to grow with a time-dependent growth rate. As a result, there exists a critical time up to which the most dangerous axial wavenumbers are larger, and beyond which the most dangerous azimuthal wavenumbers have higher values. This raises the possibility that early on, the smaller flow scales appear in the axial direction, whereas the later flow stages are dominated by smaller azimuthal features. By rescaling the axial wavenumber, the explicit appearance of time can be eliminated. The maximum growth rate of axial perturbations, as well as their most dangerous and cutoff wavenumbers, are seen to increase with the Peclet number and the viscosity ratio. The most dangerous wavenumber is observed to shift towards the lower end of the spectrum as the Peclet number increases. With increasing viscosity contrast, it first moves towards the lower part of the spectrum, only to shift towards the higher end later on. In the limit of large Pe, asymptotic solutions are obtained for the growth of axial disturbances. Numerical solutions of the full eigenvalue problem generally show good agreement with these asymptotic solutions for large Peclet numbers. Over the entire range of wave vector directions between the purely axial and azimuthal extrema, helical waves display an approximately constant maximum growth rate. The wavenumber of maximum growth as well the maximum growth rate of helical waves can be evaluated from the corresponding purely azimuthal and axial problems. This suggests that in three-dimensional flows the nature of the initial conditions plays an important role.

Singular value decomposition methods for wave propagation analysis

We describe several newly developed methods for propagation analysis of electromagnetic plasma waves. We make use of singular value decomposition (SVD) technique and we determine the wave vector direction, ellipticity and directions of axes of the polarization ellipse, wave refractive index, transfer function of electric antennas, estimators of the planarity of polarization, and electromagnetic planarity. Simulations of Z‐mode waves, which simultaneously propagate with different wave vectors, indicate that the SVD methods give reasonable results even if the assumption on the presence of a single plane wave is invalid. Simulations of whistler mode waves show that these methods can be used to recognize cases when the waves simultaneously propagate with wave vectors in two opposite hemispheres. Finally, we show an example of analysis of natural whistler mode and Z‐mode emissions measured in the high‐altitude auroral region by the MEMO experiment onboard the INTERBALL spacecraft.

Phonon trigonal warping effect in graphite and carbon nanotubes.

The one-dimensional structure of carbon nanotubes leads to quantum confinement of the wave vectors for the electronic states, thus making the double resonance Raman process selective, not only of the magnitude, but also of the direction of the phonon wave vectors. This additional selectivity allows us to reconstruct the phonon dispersion relations of 2D graphite, by probing individual single wall carbon nanotubes of different chiralities by resonance Raman spectroscopy, and using different laser excitation energies. In particular, we are able to measure the anisotropy, or the trigonal warping effect, in the phonon dispersion relations around the hexagonal corner of the Brillouin zone of graphite.

Anisotropic Delamination Energy of Bonded Rippled Silicon Surfaces Created by Ar+ Bombardment

AbstractThe surface topography of Si(100) modified by low energy Ar+ bombardment was characterized by Atomic Force Microscopy (AFM). AFM images show that ripples can be formed by 500eV Ar+ at incidence angle 40°. The spacing wavelength of ripples is around 70nm with wave vector parallel to the projected direction of ion beam. Direct bonding and mechanical delamination of Si wafer pairs with ripples are investigated. Delamination energy measured by crack-opening method along the direction perpendicular to the wave vector,γ⊥, is always smaller than that along the wave vector direction,γ„; Both γ⊥ and γ„ are found to decrease with sputtering time. The AFM images after delamination indicate that the bonding and delamination process do not eliminate the ripples on the wafer surface.