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Topic: Wavevector

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	Piezoelectric Contributions to Pulsed Degenerate Four-Wave Mixing
		strain-free value [5] when the wavevector of the rectified polarization increases to a magnitude that allows for elastic relaxation during the pulse duration.
		The effect of acoustic phonons for longer wavevectors can clearly be seen as the increase of the third-order susceptibility when the angle between the beams increases.
		measured at short wavevectors is somewhat lower than what is expected from the calculated values of the second order contributions [5] but this small discrepancy is also within the experimental error.
	www.lehigh.edu /~ivb2/acoustic.html (2053 words)

	Bloch wave - Wikipedia, the free encyclopedia
		The plane wave wavevector (or Bloch wavevector) k (multiplied by the reduced Planck's constant, this is the particle's crystal momentum) is unique only up to a reciprocal lattice vector, so one only needs to consider the wavevectors inside the first Brillouin zone.
		For a given wavevector and potential, there are a number of solutions, indexed by n, to Schrödinger's equation for a Bloch electron.
		A corollary of this result is that the Bloch wavevector k is a conserved quantity in a crystalline system (modulo addition of reciprocal lattice vectors), and hence the group velocity of the wave is conserved.
	en.wikipedia.org /wiki/Bloch_wave (576 words)

	Diffraction from a Bravais lattice (Site not responding. Last check: 2007-09-02)
		Let theta be the angle between the incident wavevector and the layer and (for now) assume that the reflected wave will have the same magnitude wavevector (equivalent to assuming elastic scattering).
		Evidently, the plane that contains the incoming and outgoing wavevectors must be perpendicular to one of the families of planes for Bravais lattice.
		The change in wavevector must be in the direction of one of the reciprocal lattice vectors (say ).
	carini.physics.indiana.edu /p615/scattering-lattices.html (675 words)

	[No title] (Site not responding. Last check: 2007-09-02)
		The second substitution results in a complete quartic equation specifying the normal components k j of the wavevectors, provided that the tangential component t is given, so that one obtains a parametric representation k j = t+ k j (t)q, j=1,2,3,4.
		In the paper we present new types of parametric representation k = k(u v) of the wavevector surface in a biaxial crystal, which are based on the use of orthogonal curvilinear coordinates u v making possible to obviate the need for solving algebraic equations.
		The second one describes the whole wavevector surface as a two-sheeted surface with different coordinate systems for the inner and outer sheets.
	www.maths.gla.ac.uk /events/tropics/abstracts/asc/A10_BOR3.ASC (349 words)

	[No title]
		It is based on a linear analysis in which the wavevector is extended to the complex space.
		In particular, we first determine the wavevector of the most unstable modes by calculating the complex saddle point ${\vec k_s}=(k^s_x,k^s_y)$ \begin{eqnarray} \label{saddle0} \nabla_{\vec k} \lambda({\vec k}) _{\vec k_s} =0 \;, \; \Re[\nabla_{\vec k}^2 \lambda({\vec k}) _{\vec k_s}] \geq 0 \end{eqnarray} where $\lambda({\vec k})$, the eigenvalue which results from the linearization of eqs.
		The characteristic wavevector observed in the numerical solutions is in agreement with the theory for the whole range of parameters.
	www.imedea.uib.es /physdept/publications/downfile.php?fid=2165 (2019 words)

	KLUEDO - Lateral quantization of spin waves in micron size magnetic wires
		At small wavevectors (q_1 = 0 - 0.9100000 cm^-1) several discrete, dispersionless modes with a frequency splitting of up to 0.9 GHz were observed for the wavevector* oriented perpendicular to the wires.
		From the frequencies of the modes and the wavevector interval, where each mode is observed, the modes are identified as dipole-exchange surface spin wave modes of the film with quantized wavevector values determined by the boundary conditions at the lateral edges of the wires.
		With increasing wavevector the separation of the modes becomes smaller, and the frequencies of the discrete modes converge to the dispersion of the dipole-exchange surface mode of a continuous film.
	kluedo.ub.uni-kl.de /volltexte/2001/899 (177 words)

	THREE-DIMENSIONAL IMAGING OF COHERENT AND INCOHERENT SOURCES UTILIZING WAVEVECTOR DIVERSITY
		This dissertation unifies the class of imaging techniques which use spectral degrees of freedom to obtain high resolution three-dimensional images of spatially coherent and incoherent broadband sources.
		Three-dimensional images are presented in the form of tomographic parallel slices of the object, obtained from actual wavevector diversity data.
		Verification of the aperture synthesis by wavevector diversity for spatially incoherent sources leads to practical applications in 3-D radiometry, thermography, sonar, and noise analysis of machinery and has implications in remote sensing, surveillance, and emitter identification.
	repository.upenn.edu /dissertations/AAI8714150 (365 words)

	Raman Spectroscopy
		For visible light, Raman phonons live near the center of the Brillouin zone (zero wavevector) because the wavelength of visible light is large compared to the lattice spacing.
		For this subgroup, the representation of all zero-wavevector phonons is the one which simultaneously depicts the vector displacements of all of the atoms in the unit cell--it is 3N dimensional, if N is the number of atoms in the unit cell.
		For example, if the phonon wavevector occurs along one of the fourfold-symmetric directions in a tetragonal crystal, then the point P in the Brillouin zone corresponding to the phonon momentum has only twofold symmetry corresponding to reflection across the line between P and the zone center.
	physics.nist.gov /Divisions/Div844/facilities/raman/Ramanhome.html (3333 words)

	I. TITRE DU CHAPITRE
		For a wavelength lambda, the wavevector is defined by :
		The wavevector in the medium of indices n is defined by :
		For a homogeneous medium, the refractive indices n is defined by the ratio of the wavevector in the material to the wavevector in the vacuum :
	www-llb.cea.fr /menl/ref/reflecto/reflecto1.html (697 words)

	Spin Waves
		Since it has not, this means (a) your browser is not capable of viewing Java applets (In which case you should consider downloading a new browser from Netscape or Microsoft) or (b) you need to check your browser settings to enable Java.
		When the wavevector magnitude becomes small, the wavelength becomes large, and the phase difference becomes negligible.
		A well known property of spin waves is that the frequency depends on the wavevector magnitude and direction.
	www.angelfire.com /wa/hurben/swaves.html (412 words)

	Citebase - Wavevector resonance in a nonlinear multi-wavespeed chaotic billiard
		Citebase - Wavevector resonance in a nonlinear multi-wavespeed chaotic billiard
		Wavevector resonance in a nonlinear multi-wavespeed chaotic billiard
		The phenomenon is investigated numerically for an ensemble of 2D square two-wavespeed billiards with rough boundaries and quadratic nonlinearity representative of elastodynamic waves.
	citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:nlin/0601018 (429 words)

	4 Bloch wave method. (Site not responding. Last check: 2007-09-02)
		The unknown are the ch(j) and the wavevector k(j) of the Bloch wave (j).
		where n is the outward pointing normal to the entrance surface and k0 the wavevector of the refracted plane wave (figure 4).
		This definition is compatible with the continuity of wave function at the entrance surface of the crystal slab.
	cimesg1.epfl.ch /CIOL/asu94/ICT_5.html (842 words)

	[No title] (Site not responding. Last check: 2007-09-02)
		The method is based on the fact that mirror mode waves are linearly polarized and have zero frequency in the plasma rest frame.
		The wavevectors estimated during the event are highly oblique to the ambient magnetic field direction as is expected from mirror wave theory.
		The application of the wavevector determination technique to further studies, such as studying the effect of finite electron temperature on mirror wave characteristics, is discussed.
	www.agu.org /pubs/abs/ja/1998JA900044/tmp.html (203 words)

	The Keith Nelson Group - 2D Pulse Shaping
		The 2D SLM is easily reconfigured from real space shaping (RSS) to wavevector shaping (WVS) by changing the cylindrical lens.
		The real space shaping and wavevector shaping waveforms shown on the right were both generated with the same phase pattern applied to the SLM.
		Using wavevector shaping, a single pulse, originally centered in space and time, has been steered around to different positions all located on a circle in space-time.
	web.mit.edu /nelsongroup/research/2DPS/2DPS_wavevector.shtml (149 words)

	[No title]
		Electrons near the surface of the Fermi sphere in the direction of the force will be able to move outside the Fermi sphere in the direction of the force.
		Thus the entire Fermi sphere should be displaced by the force, and hence the net velocity, momentum and wavevector should be changed from zero to a value in the direction of the applied force.
		The net change in wavevector would be:Ð4´Ð Á((ÁÁÁ ÀÀ ÀÀÐ´ÍÐ Ô ?(ÔÐÍ´ÐÁ((ÁÁÁÀ Àk = (©eE/À2À)ÃÃ ÄÄÀ)À, Ð´4Ðwhere À)À is the average time between collisions (of electrons with phonons © or with lattice defects).
	www.cbu.edu /~jholmes/P353/N304ElecCond.doc (965 words)

	Choice of the After-Scattering Electron Wavevector
		The scattering processes change the wavevector of the electron and it is necessary to have a method of choosing the wavevector after each scattering event.
		are the polar and azimuthal angles relative to the after-scattering wavevector
		If a self-scattering event is selected, then the energy and wavevector of the electron are not changed; the electron commences its next phase of ballistic motion occupying exactly the same state.
	www.dur.ac.uk /3h.physics/projects/montecarlo/node10.html (257 words)

	Behaviour of collective volume excitations in aluminium near the 'critical wavevector': transition into single-particle ...
		From energy loss measurements with 51 keV electrons the dependency of the aluminium plasmon energy has been derived as a function of the wavevector q.
		is the critical wavevector at which Landau damping sets in).
		The results are compared with calculations of the loss function Im(-1/ epsilon (omega,q)), using a dielectric function epsilon that takes into account finite electron lifetime and local field corrections.
	stacks.iop.org /0022-3719/7/L26 (247 words)

	Non-Local Contributions to Degenerate Four Wave Mixing in Noncentrosymmetric Materials
		In case of pulsed experiments, (1) describes the field in a time interval much shorter than the laser pulses, which we consider so long that the an "instantaneous" response can be safely assumed.
		The interacting beams and the sample are drawn in the x-y plane in the first line, and the coordinates of the beam wavevectors are plotted in the second line.
		All other cascaded contributions were calculated using the clamped (strain-free) coefficients, and are valid up to laser pulse lengths of several nanoseconds, depending on the angle between the beams.
	www.lehigh.edu /~ivb2/DFWMcasc.html (2313 words)

	More on surface plasmons (Site not responding. Last check: 2007-09-02)
		We currently use this resonant effect as a means of probing the optical properties of materials (high temperature superconductors, niobium and platinum silicide are on the agenda at present) and of enhancing the response of photodetectors and the effects of laser ablation.
		Surface Plasmons cannot couple directly to free-space electromagnetic radiation of the same energy because they travel too slowly, their associated wavevector being too large to satisify conservation of energy and momentum.
		The evenscent modes have wavevectors parallel to the interface similar to the incident radiation but with integer 'quanta' of the grating wavevector added or subtracted from it.
	www.qub.ac.uk /mp/con/plasmon/sp1.html (400 words)

	Optoelectronic devices
		Light absorption and emission in a semiconductor is known to be heavily dependent on the detailed band structure of the semiconductor.
		Direct bandgap semiconductors, i.e semiconductors for which the minimum of the conduction band occurs at the same wavevector, k, as the maximum of the valence band, have a stronger absorption of light as characterized by a larger absorption coefficient.
		semiconductors for which the minimum of the conduction band does not occur at the same wavevector as the maximum of the valence band, are known to have a smaller absorption coefficient and are rarely used in light emitting devices.
	ece-www.colorado.edu /~bart/book/book/chapter4/ch4_6.htm (2349 words)

	Behaviour of collective volume excitations in aluminum near the 'critical wavevector' (transition into single particle ...
		From energy loss experiments with 51 keV electrons the dependence of the aluminum plasmon energy on the wavevector q has been derived.
		The halfwidth of the loss peak has also been obtained as a function of q.
		It shows a nearly steplike increase near the critical wavevector.
	stacks.iop.org /0305-4608/5/645 (276 words)

	cCrankNicolsonSolver Class Reference
		bool to check whether we have loaded a wavevector from file or are using a hardcoded potential.
		You have to use the linSpace forms if you are using your own hardcoded functions for the potential and/or the wavevector.
		Then the new wavevector is saved to the file specified before.
	www.dd.chalmers.se /~f00masc/exjobb/classcCrankNicolsonSolver.html (967 words)

	Abinis help file (response function part) (Site not responding. Last check: 2007-09-02)
		The wavevector to be considered in one dataset of ABINIT is determined by the input variables nqpt, qpt, and qptnrm.
		The perturbation is the change of wavevector by dk in the Hamiltonian, hence the perturbation is refered to as the derivative dk perturbation ("ddk" perturbation).
		To summarize, the perturbations are characterized by two numbers, "ipert" from 1 to natom+4, and "idir", from 1 to 3, as well as one wavevector (that is gamma when a non-phonon perturbation is considered); a number called "pertcase" combines "ipert" and "idir", and runs from 1 to 3*(natom+4).
	www.abinit.org /Infos_v5.1/users/respfn_help.html (4376 words)

	1.2 Molecular Aspects of Solid C60 Compounds (Site not responding. Last check: 2007-09-02)
		The nesting wavevector is just a wavevector that maps one part of the Fermi Surface into another.
		For a spherical (3d free electron) Fermi Surface such a wavevector exists for any state; however, that wavevector only maps a single state into a state on the opposite side of the Fermi Surface.
		The SDW wavevector will not, in general, be commensurate with the underlying lattice.
	musr.physics.ubc.ca /theses/MacFarlane/node6.html (1095 words)

	[No title]
		k is called the wavevector of the system, or sometimes it is called the momentum vector of the system.
		Each point represents a different quantum number m: Eventually, for large "N", we can consider the wavevector "k" to be a continuous variable, and represent the electronic structure as a continuous line, instead of a set of discrete points.: Each point along the line on the band structure diagram represents an energy level.
		The wavevector (sometimes called the "crystal momentum") is proportional to the quantum number m.
	hamers.chem.wisc.edu /chem630/band_structure/atoms_on_ring.doc (1752 words)

	SF Signal: December 2003 Archives
		This being, who goes by the name Wavevector, has bestowed upon Stellar Research a groundbreaking formula for controlling and producing energy that is to be shared by all humanity.
		Wavevector?s motive is not altruistic; he merely wants to observe how biological life forms go about investigating such discoveries.
		Wavevector could just as easily have been Good Guy Scientist out to share this groundbreaking discovery with humanity.
	www.sfsignal.com /archives/2003_12.html (3619 words)

	DAMOCLES: The physics -- band structure and scattering rates
		Instead of velocity, physicists use "momentum" (the product of velocity times mass, provided a mass can be defined!) or a quantity called "wavevector" (denoted by k and denoting the inverse of the wavelength associated with a particle of a particular momentum).
		The wavevector runs along some particular symmetry directions in the unit cell of the Si (cubic) lattice, directions labeled by capital Greek and Roman letters.
		The 'bottom' of the conduction band, where "thermal", "cold" electrons reside, is close to the symmetry point labeled X. The zero of the energy - an arbitrary quantity - has been made to coincide with the top of the valence band, at the symmetry point labeled Gamma.
	www.research.ibm.com /DAMOCLES/html_files/phys.html (883 words)

	Dynamical properties
		The current correlation spectra for water are shown in Fig.
		At the lengthscales probed by this wavevector the discrete nature of the fluid becomes not negligible, and the dispersion relation is not linear anymore.
		We notice that the effective sound velocity raises with increasing wavevector from the hydrodynamic value
	puccini.che.pitt.edu /~gio/PhD_thesis/node55.html (236 words)

	ex15
		It is important to note that in the above Fourier expansion, due to periodicity of the lattice,
		Note that, since the Coulomb potential does not have the periodicity of the lattice, wavevector
		Using equations (10) and (12), we find that the frequency of the long wavelength transverse phonons is proportional to the wavevector, and is given by
	www.physics.rutgers.edu /~kotliar/course/exe/sol/sl_015 (644 words)

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