Showing papers on "Group velocity published in 1968"

Excitation of nonradiative surface plasma waves in silver by the method of frustrated total reflection

Abstract: A new method of exciting nonradiative surface plasma waves (SPW) on smooth surfaces, causing also a new phenomena in total reflexion, is described. Since the phase velocity of the SPW at a metal-vacuum surface is smaller than the velocity of light in vacuum, these waves cannot be excited by light striking the surface, provided that this is perfectly smooth. However, if a prism is brought near to the metal vacuum-interface, the SPW can be excited optically by the evanescent wave present in total reflection. The excitation is seen as a strong decrease in reflection for the transverse magnetic light and for a special angle of incidence. The method allows of an accurate evaluation of the dispersion of these waves. The experimental results on a silver-vacuum surface are compared with the theory of metal optics and are found to agree within the errors of the optical constants.

Theory of hydromagnetic propagation in the ionospheric waveguide

Abstract: In this paper, we consider the propagation of low-frequency (Pc 1) hydromagnetic waves in the ionospheric duct, which results from the minimum in the Alfven speed near the F2 ionization peak. We consider an inhomogeneous (in the vertical direction) waveguide in the presence of a uniform static magnetic field and treat the case of horizontal propagation in the plane of the magnetic meridian. Propagation in the waveguide is governed by two coupled equations for the horizontal components of the electric field. For nighttime conditions, where the ionized region of interest starts at sufficiently high altitude that the collision frequency of ions with neutrals is small compared with the ion cyclotron frequency, the two components become uncoupled, and only the isotropic, or fast wave, need be considered. For daytime conditions, however, coupling between the fast and slow waves must be taken into account; to simplify the analysis, the static field is assumed uniform in this case. To obtain analytic solution of the waveguide equations, it is necessary to have analytic approximations to the height dependence of the relevant ionospheric parameters; such approximations are constructed to fit some representative tabulated ionospheric profiles for a variety of conditions of time of day and sunspot activity. Solution of the waveguide equations subject to the appropriate boundary conditions results in a rather complicated dispersion relation between complex (horizontal) wave number and angular frequency. The solutions of the dispersion relation prescribe the allowed bands of propagation in the guide. It is shown that each band, including the lowest, has a low-frequency cutoff, and that the existence of a low-frequency cutoff is a consequence of the boundary conditions and not of attenuation, as assumed in some theories. Numerical solutions of the dispersion equation are obtained for the two lowest bands for each of the conditions considered. From the dependence of the real part of the wave number on frequency, the cutoff frequencies and the phase and group velocities are determined, while the imaginary part provides the attenuation length. For nighttime conditions, attenuation is not large, and propagation can take place over distances of thousands of km, whereas daytime propagation is restricted by attenuation to distances of the order of hundreds of km. For nighttime minimum conditions, the calculated waveguide cutoff is about 0.4 cps, and the group velocity for the lowest band is about 720 km/sec, both in reasonable agreement with experiment. Finally, it is pointed out that there is an effective high-frequency ‘cutoff’ (in any band) as far as ground-level signals are concerned due to an exponential decrease of transmission coefficient with frequency at high frequencies.

An Optical Waveguide with the Optimum Distribution of the Refractive Index with Reference to Waveform Distortion

Abstract: The group velocities of different modes are not the same when a usual type of optical waveguide is considered. The envelope of an optical pulse is therefore broadened while the optical pulse travels. In the case of a two-dimensional waveguide, it is found that the group velocity of each mode can be made the same if an appropriate distribution of the refractive index in the guide is realized. When a waveguide with such an optimum distribution is considered, the group velocity is also independent of frequencies if the medium is dispersion free. The property mentioned above is closely related to the fact that such a waveguide has an ideal focusing property. In the case of a cylindrical optical waveguide in which the refractive index depends only on the radius, such an optimum distribution does not exist. A method of calculating the mean velocity of an arbitrary ray in the guide is described on the basis of the WKB approximation to the wave equation.

Coherence and band structure of inertial motion in the sea

Abstract: It is now well established by observation that a peak in the spectrum of horizontal motion should be anticipated everywhere in the ocean near the local inertia frequency, 2ω sine (latitude). The theory of wave motion in a weakly stratified, rotating ocean of constant depth explains this observation either by the existence of a frequency condensation point in wave-number space or, alternatively, by the vanishing of the meridional group velocity. This explanation is independent of a specific generating mechanism, such as tidal forcing. The details of the wave structure and dispersion relation are readily obtained when, as seems both likely and desirable, it is permissible to ignore the discrete normal-mode-producing effects of distant lateral boundaries. This theory predicts a spectral peak slightly above the inertia frequency, and this displacement depends on the zonal and vertical wave numbers. The peak frequency in the North Atlantic measurements by Fofonoff and Webster implies vertical modes of O(10) and a zonal wave number of O (several hundred cycles per earth circumference). When these numbers are applied to a simple coherence model, assuming phase independence between different wave numbers, one can account for the observed lack of coherence between stations separated in depth or longitude. This theory also defines a latitudinal scale; for vertical wave number 10 this is, typically, of O(25 km), which is in qualitative agreement with Hendershott's observations in the eastern North Pacific. The present theoretical model is appropriate for random distributed sources. The observations, however, indicate a higher degree of intermittency than is implied by this model. We conclude that both random distributed sources and intermittent discrete sources must be taken into account for a satisfactory description of the phenomena.

Observation of electrostatic resonances of the ionospheric plasma

Abstract: THE theory of electrostatic waves is highly developed1–3. The propagation of electrostatic waves has been observed in laboratory plasmas by measuring the time required for a pulse of these waves to travel between antennae imbedded in the plasma4. Resonance phenomena have been expected to appear in a plasma irradiated with radio waves at frequencies for which the group velocity of the electrostatic waves is zero or small. This concept has been used5 to explain certain previously observed resonances. Bernstein's theory, however, also predicts zero group velocity at frequencies for which resonances have not previously been observed. A simplified approximate equation has been developed by Stix6 and improved by Dougherty and Monaghan7 to predict the frequencies at which these electrostatic resonances should appear. The resonances observed by instruments carried on satellites may correspond to a finite group velocity that matches the velocity of the satellites.

Measurement of the Interstellar Magnetic Field

Abstract: The discovery of linear polarization of the radio emission from the pulsating radio stars1 provides an opportunity for the first direct measurement of the average magnetic field over distances of up to 100 pc from the Sun. It has already been shown2,3 that the frequency dispersion in arrival time of the pulses can be entirely explained by a dispersion in group velocity in ionized interstellar gas, and for the pulsating star CP 1919 the integrated electron density ∫N dl along the line of sight has been found3 to be 12·55 cm-3 pc. If a magnetic field has a component H 11 along the line of sight, then the Faraday rotation of the plane of polarization is a measure of ∫N H 11 dl; the ratio of the two integrals then gives H 11, the average value of H 11 along the line of sight, weighted according to the electron density.

Ray‐Theory Analysis of Magnetoelastic Delay Lines

Abstract: Magnetoelastic wave propagation at microwave frequencies in single‐crystal yttrium iron garnet, of various nonellipsoidal geometries, has been intensively investigated experimentally in recent years in connection with delay‐line applications. However, two important features, namely the detailed nature of the energy paths and the magnetic excitation mechanisms, have received scant attention. This paper examines these features from the viewpoint of geometrical ray theory. Attention is first directed to two basic phenomena: magnetoelastic wave anisotropy, which gives rise to deflection of the group velocity from the phase velocity vector, and refraction, which arises from the inhomogeneous internal magnetic field. Consideration is then given to justifiable approximations for the wave behavior and magnetic field, and guidelines which enable a specification of the launching surface to be made. Ray plots are presented for the axially magnetized rod, which is found to be strongly focusing, and for the complement...

Universal dispersion tables: II. Variational parameters for amplitudes, phase velocity and group velocity for first four Love modes for an oceanic and a continental earth model

Abstract: The universal dispersion theory, presented in Part I, is extended to allow computation of group velocity and amplitude partial derivatives. Tables giving the effect of a change in any parameter on phase velocity, group velocity and amplitude are given for two earth models, one oceanic and one continental shield. Tables are given for the fundamental and first three higher Love modes. These tables make it possible to compute dispersion parameters for the first four Love modes for any realistic earth model or to invert observations to an earth model. Attenuation of Love waves for an arbitrary distribution of Q versus depth can also be computed by using techniques previously described.

Speed of Light

Abstract: Extinction considerations are used to evaluate the instantaneous velocity of light as it traverses a moving medium in a series of discrete steps, each step defined by extinction and re-emission of the photon. The analytical results agree with the experimental values obtained by Fizeau if the instantaneous velocity between extinctions is C relative to the laboratory, and C ∓ v relative to the fluid moving at velocity ± v. It is shown that this implies a verification of the convective ether hypothesis of D. C. Miller. Further testing of this hypothesis is suggested, using modified arrangements for the Fizeau experiment.

Observation of growing carrier waves in indium antimonide

Abstract: Measurements of the phase velocity and growth rate of carrier waves in near‐intrinsic InSb are presented. The frequency range is from 10 to 40 MHz and a transverse magnetic of about 2 kG is required. The phase velocity of the wave agrees with predictions of previous theories, but the large growth rates suggest a new type of two‐stream interaction involving surface waves suggested by Kino.

Vibrations of an Infinite Beam on an Elastic Foundation with Consideration of Mass of a Foundation

Abstract: An analysis of wave propagation in an infinite elastic beam on an elastic foundation is presented, considering the effect of the mass of a foundation. The foundation is represented as a base consisting of closely spaced, independent bars or linear springs. The frequency equation is derived and the spectrum of frequencies for real, imaginary, and complex wave numbers is investigated. The phase velocity and group velocity versus wave number are also calculated for various ratios of the mass of a foundation to that of a beam. Results from the present method of solution are compared with those obtained under the assumption that a beam is supported by a massless elastic foundation whose local restoring force per unit length depends only on the local deflection.

Acoustic-Gravity Wave Propagation in a Temperature- and Wind-Stratified Atmosphere

Abstract: A theory of propagation of acoustic-gravity waves in a temperature- and wind-stratified atmosphere is developed. It is shown by using suitable wind structure in a COSPAR standard atmosphere that both the normal dispersion (group velocity increasing with period) and the inverse dispersion (group velocity decreasing as the period increases) of acoustic-gravity waves can be explained. It is found that winds of the order of 100 m sec−1 at about 100 km altitude are needed to account for inverse dispersion in the period range of about 5–15 min.

Sampling system utilizing electrooptic techniques

Abstract: A sampling system is described which utilizes electrooptic techniques for sampling an electrical signal. Short duration light pulses are polarized and directed through a crystal exhibiting either a linear or longitudinal electrooptic effect or through a liquid showing a large Kerr effect, located in traveling wave relationship with a terminated transmission line structure. The group velocity of the polarized light, that is, the velocity of a light pulse, or the velocity, of the modulation envelope of a modulated light beam, along the electrooptic crystal and the phase velocity of the electrical signal along the transmission line structure are in synchronism. Due to electrically induced birefringence, the state of polarization of the light pulse is altered according to the electrical field intensity to which the electrooptic crystal is subjected by that portion of the electrical signal traveling coincidentally along the transmission line structure. Consequently, the transmission of the light pulse by a crossed analyzer placed at the output of the electrooptic crystal varies in response to the coincidental portion of the electrical signal. The energy of the light pulse emanating from the analyzer is detected and directed to a utilization of circuit, for example, the hold and display circuitry of a sampling oscilloscope.

Scattering of Velocity‐Filtered Atomic Beams of Ar and Xe from the (111) Plane of Silver

Abstract: The scattering of nearly monoenergetic atomic beams of Ar and Xe from the (111) plane of silver has been studied as a function of the nominal velocity υ0 transmitted by a slotted‐disk velocity selector (SDVS) used as a velocity filter on the incident thermal‐energy (Maxwellian) beam. The selector has a velocity spread of ±0.19 υ0 and studies were carried out over a range of υ0 from 2.2 × 104 to 5.3 × 104 cm/sec. The scattered beam distributions were found to be directed, corresponding closely to those of Maxwellian beams when υ0 = ῡ = 34(2πkTB / M)1 / 2, the average velocity of the corresponding Maxwellian beam of temperature TB. These results, together with the results of earlier scattering studies, imply that the thermal motion of the lattice is the dominant factor in producing the spatial dispersion as well as the velocity dispersion in the scattered beam that has been observed by other investigators. The most likely origin of these dispersive effects is the languidness of the collision in the sense us...

Dispersion in developing velocity fields

Abstract: Convective diffusion in laminar flows which develop from rest and in the velocity entrance region of tubes, is studied. Criteria for the validity of the simple dispersion model are established by comparison of analytical results with numerical experiments. It is found that the extent of dispersion is less in developing velocity fields than in those which are fully developed. This occurs because dispersion is enhanced by differences in the velocity of the fluid particles on a plane perpendicular to the main direction of flow. Such differences are greatest when the flow is fully developed.

Velocity and turbulent fluctuation fields in water containing low concentrations of high-molecular substances

Abstract: The stroboscopic visualization method has been used to measure velocity profiles and RMS values of the longitudinal and transverse components of the velocity fluctuations in weak solutions of DNA.

Surface‐Wave Modes in Dielectric‐Lined Coaxial Cables

Abstract: An analysis is given for hybrid, TM, and TE surface-wave modes in coaxial cables with homogeneous dielectric linings on either or both conductors The characteristic equations and expressions for the group velocity are derived using the field components in the loss-free cases A perturbation technique is then used to derive expressions for the attenuation coefficients of all slow-wave modes For the dominant mode, these are shown to reduce to expressions which can be obtained by a quasi-TEM approach

The influence of neutral gas temperature on the parameters of ionization waves in neon

Abstract: In the present paper, the influence of cooling down the neutral gas to a temperature of 77°K on the parameters of ionization waves excited in the positive column of a d. c. glow discharge in neon is studied. After the cooling, the group velocity, phase velocity, frequency and relaxation time of the waves of varietyp decreased and they increased in case of varietiesr ands. The results of measurements were compared to the lifetime of metastable atoms in the case of thep-wave, and to that of atomic ions in the case of ther-wave. The variations of lifetime with temperature correspond to the variations of relaxation times of the waves; the lifetime of metastable atoms is 5 to 7 times longer, the lifetime of atomic ions agrees with the relaxation time fairly well.

Radiation From an Oscillating Source Moving Through a Dispersive Medium With Particular Reference to the Complex Doppler Effect

Abstract: The complex Doppler effect is analyzed from the time behavior of the radiation field of an oscillating source traversing a dispersive medium. The effect is calculated for the case where an oscillating electric dipole is moving uniformly through an ionized gas permeated by an infinitely large magnetostatic field. It is found that the radiation field can be split into a number of waves, each having characteristics of its own, and that the number of waves changes with time. The group velocity of each individual wave is shown to play an important role in the physical mechanism of the effect.

Diffraction of light by magnetoelastic waves

Abstract: The diffraction of light at 1.15 microns has been observed from transverse magnetoelastic (ME) waves at a frequency of 1.1 GHz in a YIG bar. A shift in the Bragg diffraction angle was observed when the external magnetic field along the bar axis was varied in order to change the elastic and spin wave admixture. The waves were excited by a shear wave transducer, and were on the upper branch of the ME dispersion curves. The largest shift obtained experimentally was -3°, measured from the elastic limit of 9.5°. This required a field change of about 20 Oe. The shift was accompanied by a delay in the diffracted pulse of about 1μs, due to the change in the group velocity. The optical polarization properties indicate that both the elastic and spin wave parts of the ME wave were contributing to the diffraction through the photo-elastic effect and optical Faraday rotation, respectively. The diffracted signal in the magnetically shifted region was transient in nature, and showed strong saturation effects due to saturation of the ME wave.

Highly efficient raman emission device

Abstract: The invention includes an elongated Raman active medium having total internal reflection means along its longitudinal dimension. Optical pumping is by pulses of duration of the order of several picoseconds or less made incident upon one end of the medium and direction along the longitudinal axis thereof. The Raman emission inherently traverses a zigzag path within the medium at an angle such that the group velocity of the Raman and pump pulses is matched, i.e., differences in group velocity of the pump and Raman radiation due to the dispersion of the medium are compensated for.

Dispersion relations, stored energy and group velocity for anisotropic electromagnetic media

Abstract: The Hermitian and skew-Hermitian components of the susceptibility matrix of a general linear electromagnetic medium are represented as Hilbert transforms of each other. These so-called dispersion relations lead to a priori inequalities which must be satisfied by the susceptibility of a passive medium in a frequency interval in which the medium is lossless. One such inequality states that the stored energy density for a given E(«) and H(ai) is always greater than in free space. This is also verified directly from the usual gyrotropic susceptibilities of ferrites and plasmas. The group velocity for an eigenwave or mode of a structure with one, two or three independent translational symmetry vectors is shown to be, in general, an average Poynting vector divided by an average stored energy density. This formula is then combined with the above inequality for the stored energy density to show that the magnitude of the group velocity is less than c, the velocity of light in free space.

Wind velocity profile above progressive water waves

Abstract: An investigation of the air velocity profile above progressive, mechanically-generated waves was made m the wind and wave facility at Stanford University. The influence of propagating waves on the mean velocity profile was sought especially. Both the instantaneous and mean velocity profiles were obtained with the use of high response total head and static pressure probes, m conjunction with a wave height gage. Experimental evidence is presented which suggests that the air velocity field responds to the wave motion. The dependence of the mean velocity profile on wave frequency was investigated experimentally over mechanically generated waves having a constant amplitude. Also, the dependence of the mean velocity profile on wave amplitude was investigated over mechanically generated waves with a specified frequency. The theoretical results suggest that the wave influence is threefold. The first is due to the fact that a velocity-measuring instrument continuously shifts streamlines when measuring the air velocity above a perturbed water surface. The second is due to the wave-induced perturbation in the air velocity. The third is due to the interaction between the two effects just described. The results contribute towards explaining the lack of consistency in the existing data.

Group velocity of dielectric waveguide modes

Abstract: The group velocity and dispersion of surface-wave modes propagating along a circular dielectric rod are computed and presented graphically in normalised form. The group velocity as each mode approaches the cutoff frequency is calculated approximately.