Showing papers on "Wavelength published in 1970"

Optical phonons of small crystals

Abstract: The long wavelength optical phonons of ionic crystals give rise to dipole-dipole forces, whose long range nature causes the vibrations to depend on the size and shape of the crystal sample. This dependence affects significantly most spectral properties of all crystals whose dimensions are of the order of or shorter than the wavelength of reststrahlen (characteristically several tens of micrometres). In experimental work in which the infrared properties of ionic crystals were examined on small samples, in powder form or in colloidal suspension or in the shape of thin layers, the peculiarities due to size and shape were not always properly recognized. The infrared frequencies of the material which are derived with disregard to these peculiarities may be in error by some tens of wavenumbers. In the experimental section of the review we interpret the general characteristics of the experimental spectra and analyse in detail some representative infrared measurements in the light of the theory. The theory of optical vibrations which takes account of the finiteness of the specimen is formulated firstly in general terms and then by special reference to samples which have one, two or three dimensions short (slab, cylinder and sphere-like geometries). Synthetic spectra are drawn whose characteristic features are interpreted in terms of bulk and surface modes. In the theory retardation effects, i.e. the coupling between lattice and electromagnetic waves, are also included, and the quantized modes are combinations of these, i.e. polaritons. For tiny crystallites of such size that the characteristic infrared radiation wavelength is much larger than the sample size, retardation effects can be neglected. The theory becomes much simpler and the spectrum sharper. Some of the absorption peaks are due to optical surface modes, and their positions are simply related to the characteristic shapes of the crystallites. The theory is so presented as to provide a practical aid in the correlation of spectra with sample shape. The consequences on the spectra of other, less common variables of experiments, for example, the refractive index of the environments, are also calculated. The role of optical surface modes in Raman - and electron - scattering is then discussed. Simple geometrical arrangements of small sized crystals enable the spectra of surface modes to be scanned.

Edge‐, bottom‐, and Rossby waves in a rotating stratified fluid

Abstract: It is found that in a rotating stratified fluid bounded by a single rigid wall, edge waves may occur at all frequencies less than or equal to N sin a (a is the angle of the wall from the horizontal and N the Brunt‐Vaisala frequency). These decay exponentially away from the boundary, in a distance of O(S) wavelengths, for α = O(1), or O(S ‐1) wavelengths, for αS ≤ O(1), where S is the ratio of N to the Coriolis parameter f, taken for illustration to be large. The phase and energy both move with a component to the left, facing shallow water. The waves could, for example, appear as an internal tide at the continental rise or as baroclinic meandering of currents over a slope. The low‐frequency limit, αS ≪ 1, is studied in detail. To allow for large scales of motion other rigid boundaries and variations in f are included. The edge (actually “bottom") waves then merge with topographic‐planetary waves as the wavelengths increase; the familiar depth‐independent mode is found to be possible in the sea for...

Surface motion of a layered medium having an irregular interface due to incident plane SH waves

Abstract: A practical method is devised to calculate the elastic wave field in a layer-over-half-space medium with an irregular interface, when plane waves are incident from below. This method may be used for studying the interface shape of the M discontinuity, for example, using the observed spectral amplitude and phase-delay anomalies due to teleseismic body waves. The method is also useful for the engineering-seismological study of earthquake motions of soft superficial layers of various cross sections. The scattered field is described as a superposition of plane waves, and application of the continuity conditions at the interface yields coupled integral equations in the spectral coefficients. The equations are satisfied in the wave-number domain when the interface shape is made periodic and the equations are Fourier transformed and truncated. Frequency smoothing by using complex frequencies reduces lateral interferences associated with the periodic interface shape and permits comparison of computed results with those obtained from finite bandwidth observations. Analyses of the residuals in the interface stress and displacement, performed for each computed solution, provided estimates of the errors. The relative root-mean-square residual errors were generally less than 5% and often less than 1% for problems in which the amplitude of the interface irregularity and the shortest wavelength were comparable. The method is applied to several models of ‘soft basins’ ‘dented M discontinuity’ and ‘stepped M discontinuity’ The results are compared with those derived from the flat-layer theory and from the ray theory. In addition to vertical interference effects familiar in the flat-layer theory, we observe the effects of lateral interference as well as those of ray geometry on the motion at the surface.

Transmission through a Conducting Screen Perforated Periodically with Apertures

Abstract: A general solution to the problem of determining first the aperture field distribution and then the transmission and reflection coefficients of an infinite planar conducting sheet perforated periodically with apertures has been formulated. The excitation is considered to be a plane wave incident at any arbitrary angle. The aperture dimensions and array element spacings were assumed to be comparable with the wavelength of the incident electromagnetic field. The solution given can include the effect of a dielectric slab used to support the thin conducting sheet. The solution is obtained by matching the tangential field components at the surface of the screen. The resulting integral equation is solved by the method of moments which reduces the integral equation to a system of linear algebraic equations that can be solved with the use of a digital computer. Accurate results for both the magnitude and phase of the aperture field distribution and the transmission coefficients for the propagating modes are determined explicitly for a specific example of slots arranged in an equilateral triangular lattice. The balance of power flow between the reflected and the transmitted waves has been checked with satisfactory results. The solution can be applied to the problem of scattering from a conducting screen with periodic apertures and to the complementary problem of scattering from a set of conducting plates by the use of Babinet's principle.

Wave flow regimes of a thin layer of viscous fluid subject to gravity

Abstract: The studies of Kapitsa initiated the detailed experimental and theoretical study of the flow of a thin layer of viscous liquid (liquid film) over a solid surface [1–2]. Extensive experimental data on this question have now been accumulated. As a rule, the existing theories are based on linearization of the problem and diverge considerably from the experimental results. The present paper is also addressed to the theoretical solution of this problem. The solution method used enables consideration of the wave flow of the liquid as a nonlinear problem and on this basis permits determining all the parameters of the wave regime-amplitude, wavelength, wave propagation speed, frequency.

Occurrence of Finite‐Amplitude Surface Waves on Falling Liquid Films

Abstract: The linearized stability problem for a steady parallel flow of a thin viscous fluid layer flowing down an inclined plane has been investigated by several authors. When the volume flux exceeds a critical value, the steady parallel flow is known to be unstable. In order to explain the development of steady surface waves on such a flow, finite‐amplitude effects must be considered. The growth of a linear unstable periodic perturbation and its nonlinear interaction with higher harmonics are studied. For small volume fluxes and fluids with sufficiently strong surface tension, such as water and alcohol, it is shown that for a flow down a vertical plane a steady finite‐amplitude surface wave will develop. The transient development of the finite‐amplitude waves is investigated by numerical integration. Numerical values for wave velocities and amplitudes are given. The dependence of the wave form on the wavelength of the initial perturbation is also discussed.

Ultrashort-Pulse Generation by Q -Switched Lasers

Abstract: We have undertaken the complete temporal description of pulsed emission by a homogeneously broadened laser, including the effects of spontaneous emission, the detailed geometry of the laser cavity, and the variation of atomic polarization and level populations over wavelength distances. The model is based on traveling-wave equations which are derived from Maxwell's equations and solved in conjunction with boundary conditions imposed at the cavity mirrors. Thus, any direct assumptions concerning the nature of the laser's longitudinal mode structure is avoided. Variations in polarization and population over wavelength distances are treated by means of expansions in spatial Fourier series, having as fundamental a half optical wavelength. The Fourier series are truncated after the first harmonic. The treatment differs from earlier work in that the dephasing of the dipole moment is treated exactly without a rate-equation approximation. Spontaneous emission is simulated both as to spectrum and Gaussian character by including in the dipole equations stochastic shot-noise sources. The model equations are solved numerically, and results include the details of $Q$-switched pulse evolution from noise for both passive and active switching. In the case of an actively switched laser, the two-photon fluorescence intensity pattern has been calculated. It reveals a well-defined structure of subsidiary intensity maxima, even though subcavities are not assumed in the calculation. The pattern can be correlated directly with the emission pulse structure, and should vary from shot to shot. No single point in the pattern is suitable for a peak-to-background ratio determination. However, if the background is averaged over a distance in the fluorescing medium equal to twice the separation between cavity mirrors, the peak-to-background ratio would be \ensuremath{\approx} 1.6, indicating a highly uncorrelated spectrum.

Stability of a sand bed subjected to a shear flow of low Froude number

Abstract: The problem of sand bed stability is formulated and solved for a model in which the local slope of the free surface is small relative to the slope of the perturbed lower boundary The solution shows the bed to be unstable to perturbations of wavelength greater than the wavelengths for which the inertia of the sediment grains is important Wave speeds and growth rates from numerical calculations are presented and compared with long- and short-wave asymptotic expressions Although the fluctuating velocity field in the nonuniform flow is approximated by a constant eddy viscosity, a general picture of the relationship between the flow over a perturbed boundary and the observed geometrical and dynamical parameters of the resulting boundary waves can be developed It is shown that the sand bed instability is due to local accelerations of a shear flow caused by the nonuniform boundary If either the shear or the acceleration is eliminated from the analysis, the instability cannot be found On the other hand, no wavelength is defined by such an analysis, and it is shown that the wavelength is determined by spatial adjustments in the turbulent velocity field

Ice flow over bedrock perturbations

Abstract: The use of well known simple periodic solutions of the two-dimensional biharmonic stress equation for studying the flow over undulations of an ice mass of small surface slope is examined. The model considered is one in which most of the shear (deformation or. sliding) takes place near the base and the upper part moves largely as a block, with longitudinal strain-rates varying linearly with the longitudinal stress deviations. For bedrock perturbations of a given wavelength the steady-state surface shape consists of similar waves but out of phase by ½π, such that the steepest slope occurs over the highest bedrock; and the amplitude is reduced by a “damping factor”, depending on the speed, viscosity, ice thickness and wavelength. Minimum damping occurs for λ m ≈ 3.3 times the ice thickness, while waves much longer or much shorter than this are almost completely damped out. The energy dissipation and the resistance to the ice flow is also a maximum for an undulation scale of several times the ice thickness, whereas the effects of small basal irregularities die out exponentially with distance into the ice, and only have an effect in so far as the average basal stress is related to the average surface slope. As a result of this a revision of present glacier sliding theories becomes possible. Various predictions of the theory have been confirmed from spectral analysis of surface and bedrock profiles of ice caps.

Absolute spectral energy distribution of quasi-stellar objects from 0.3 to 2.2 microns.

Abstract: The absolute spectral energy distribution from 0.32 to 2.2 μ, has been obtained for twenty-eight quasi-stellar sources. Photometry at 2.2 μ, has been obtained for an additional fifteen objects. The data show that the continua over this wavelength range generally can be described with a power-law spectrum; the index varies from -0.2 to -1.6, with the entire range being populated. For quasi-stellar objects which are known to have large-amplitude variations in visual magnitude, the energy distributions remain sensibly unchanged during the variations. No characteristic of the energy distribution in the observed range of wavelengths which distinguishes between radio-quiet and radio-active quasi-stellar objects is found. The near constancy of the observed ratio of the line intensities of Lɑ to the C IV line can be interpreted as implying an electron temperature of 20000° K. The range of equivalent widths of both (Hɑ + [N II]) and Lɑ is small. The ratio of the number of photons in the Lyman continuum with respect to the number in the Lɑ line is not consistent with radiative recombination from an opaque source.

Surface Waves on a Plasma Half‐Space

Abstract: The effect of density gradients and a finite temperature on the dispersion relation for surface waves on a plasma half‐space has been investigated analytically. The full set of Maxwell's equations is used to obtain the dispersion of surface waves on a warm homogeneous plasma, thus complementing earlier work on the electrostatic mode. The full surface‐wave dispersion relation is then derived for a cold plasma with arbitrary but weak density profile in the WKB limit. Finally, the dispersion of electrostatic surface modes on a cold plasma with a linear density profile of arbitrary strength is obtained. It is shown that when the density variation over a wavelength is very large, a new type of damped surface wave with a frequency higher than the surface plasma frequency is possible.

Optically Induced Refractive Index Changes in BaTiO3

Abstract: The phenomenon of ``optical damage,'' that is, optically induced changes in the index of refraction, can be used as a form of holographic storage in transparent ferroelectric crystals. In this paper we describe a series of experiments which characterize the optical damage in ferroelectric BaTiO3. This is done by recording in a single crystal of the material a plane wave hologram, i.e., a diffraction grating, with a laser at one wavelength and reconstructing the hologram with a laser at another wavelength. The time‐dependence and steady‐state value of the diffracted light is studied with respect to variations in incident light intensity, temperature, writing wavelength, and grating spacing. A model describing the optical damage, based on the work of Chen [F. S. Chen, J. Appl. Phys. 40, 3389 (1969)] and Johnston [W. D. Johnston, Jr., J. Appl. Phys. 41, 3279 (1970)] is presented and the results explained in terms of this model.

Development of a Rossby Wave Critical Level

Abstract: We discuss the time-dependent behavior of a Rossby wave on a latitudinally varying flow, near the point where the steady-state wave equation is singular. The wave is forced by the switch-on of a steady forcing. Analytic solutions are obtained for the latitudinal propagation of nondivergent Rossby waves in a linear shear flow and for a large longitudinal wavelength. It is shown that the north–south eddy velocity v′ approaches the steady-state solution everywhere when nondimensional time >1, this time being a few days or less for atmospheric planetary waves. The east–west eddy velocity u′ takes much longer to approach a steady state near the singularity. One-half the steady-state amplitude of u′ is approached in a time inversely proportional to the square root of the distance from the singularity. The solution for u′ near the singularity settles down to the steady solution only after a time large compared to the inverse of the distance from the singularity. The steady-state solution for u′ is logar...

Computed transmission through rain at microwave and visible frequencies

Abstract: In this paper we present tables which contain the Mie scattering coefficient, absorption coefficient, extinction coefficient, equivalent medium index of refraction and phase delay for rains conforming to the Laws and Parsons drop-size distribution. These transmission characteristics have been calculated for microwave frequencies of interest in common carrier radio relay systems, 300 to 1.43 GHz, that is, 0.1 to 21.0 cm, at rain rates from 0.25 to 150.0 mm/hr. We also include the extinction coefficients for the visible wavelength 0.6328 μ. The microwave tables were generated by using a Mie scattering computer program similar to that designed and previously reported by Deirmendjian. The calculations at 0.6328 μ were made separately by employing the usual assumptions for droplets with very large circumference to wavelength ratios.

Experimental investigations of the stability of channel flows. Part 1. Flow of a single liquid in a rectangular channel

Abstract: The stability of the laminar flow in a rectangular channel with aspect ratio 1:8 was investigated experimentally, with and without artificial excitation. The critical Reynolds number based on the hydraulic diameter and the average velocity was found to be 2600. Behaviour of damped and growing waves, using artificial excitation, was examined in detail. In particular the progress of growing disturbances was followed. Breaking was found to be the ultimate fate of a growing wave. Spectra of growing and damped waves were also obtained. Measurements were made for wavelengths, wave speeds and amplification or damping rates. The neutral stability boundary in the αr, R plane was determined. In the damped region, comparison of several aspects of the behaviour of the measured disturbances with the plane Poiseuille theory for spatial decay yielded good agreement.Three-dimensionality and non-linear subcritical instability were briefly examined. Neutral subcritical waves at low Reynolds numbers appeared possible when the exciter amplitude was quadrupled.The possible bearings of the present study on the stability of plane Poiseuille flow are suggested.

On the non-separable baroclinic parallel flow instability problem

Abstract: Perturbation series are developed and mathematically justified, using a straightforward perturbation formalism (that is more widely applicable than those given in standard textbooks), for the case of the two-dimensional inviscid Orr-Sommerfeld-like eigenvalue problem describing quasi-geostrophic wave instabilities of parallel flows in rotating stratified fluids. The results are first used to examine the instability properties of the perturbed Eady problem, in which the zonal velocity profile has the form u = z + μ u 1 ( y , z ) where, formally, μ [Lt ] 1. The connexion between baroclinic instability theories with and without short wave cutoffs is clarified. In particular, it is established rigorously that there is instability at short wavelengths in all cases for which such instability would be expected from the ‘critical layer’ argument of Bretherton. (Therefore the apparently conflicting results obtained earlier by Pedlosky are in error.) For the class of profiles of form u = z + μ u 1 ( y ) it is then shown from an examination of the O (μ) eigenfunction correction why, under certain conditions, growing baroclinic waves will always produce a counter-gradient horizontal eddy flux of zonal momentum tending to reinforce the horizontal shear of such profiles. Finally, by computing a sufficient number of the higher corrections, this first-order result is shown to remain true, and its relationship to the actual rate of change of the mean flow is also displayed, for a particular jet-like form of profile with finite horizontal shear. The latter detailed results may help to explain at least one interesting feature of the mean flow found in a recent numerical solution for the wave regime in a heated rotating annulus.

Dispersion of surface plasmons in dielectric-metal coatings on concave diffraction gratings

Abstract: Anomalies in the intensity ofp-polarized light from concave diffraction gratings (Wood's anomalies) have been used to obtain surface plasmon dispersion curves for dielectric-metal layers on the grating surface. These include a 350 A MgF2 layer and Al2O3 layers varying from a few angstroms to over 800 A on an Al substrate. The wavelength range of the incident and diffracted light is from the visible to the vacuum ultraviolet (7,500−500 A). Anomalous polarization peaks for Al2O3 layers in the vacuum ultraviolet (at ∼ 1,600 A) are shown to shift significantly to longer wavelengths for only a few angstroms (up to 50 A) of oxide thickness, while for thicknesses greater than ∼ 50 A any further shift is small. In the visible region (> 4,000 A), on the other hand, the wavelength shifts are small for dielectric thicknesses up to ∼ 50 A, but are large for thicknesses of several hundred angstroms. These results are in substantial agreement with the theoretical dispersion curves for these cases. Also considered are some of the effects of diffusion pump oil.

The Measurement of Water Depth by Remote Sensing Techniques

Abstract: : The study demonstrates successful remote determination of shallow water depth by measuring wave refraction changes and using the Fourier transform plane for wavelength measurements with data obtained at a Lake Michigan test site. The study shows that the technique is suitable for use from spacecraft altitudes, provided that water waves of suitable length occur in the region of interest.

Ii. the mechanical scanner of cydac, the theory of scanning photometry and the magnitude of residual errors'

Abstract: The mechanical scanner of CYDAC is a dual beam cytophotometer with a Nipkow scanning disc, analogue photometric circuits, digital conversion and accumulation of the photometric values and digital control of the scanning procedure. A measuring sequence involves object and clear field scans, and the final readout is virtually independent of fluctuations and heterogeneities in illumination and of variations in the size of the scanning apertures. Optical sources of error are analyzed both theoretically and experimentally as they apply to scanning cytophotometers The effects of conical and polychromatic illumination, stray light and heterogeneous distribution of chromophore lead to negative averaging errors that are a function of optical density. The role of scan aperture size and optical resolution on distributional error is discussed and calculated in terms of three possible models. Nonabsorptive phenomena, such as scattering and diffraction, lead to positive errors that are complementary, in a qualitative sense, to distributional error. In attempting to isolate these different errors experimentally, we show that measurements of the relative deoxyribonucleic acid stain content of human leukocytes are independent, within wide limits, of condenser and objective numerical aperture and of changes in absorptivity secondary to changes in wavelength. Where an adequate theory exists, these experimental results agree well with the theoretical predictions and, in any case, they indicate that for stained leukocytes the net effect of all optical errors must be less than 2%. Random measuring errors include both photon shot noise and errors associated with the geometry of the scanning disc. These errors contribute to an error of 1.2% among replicate measurements of leukocytes made under standard conditions. The previously reported differences in stain content among leukocyte types and among individual cells within types cannot be ascribed to either optical or instrumentation errors. Thus, the measured differences must reflect actual differences either in the amount or in the absorptivity of the stain.

Wavelength discrimination measured with square-wave gratings.

Abstract: Wavelength discrimination was measured from 480 to 660 nm using wavelength-modulated square-wave gratings. When adjacent grating bars are matched in brightness, wavelength-difference thresholds in all regions of the spectrum increase with spatial frequency within the range of 2.4–19.9 cycles per degree (cpd). Unlike luminance-modulated gratings, no sign of low-frequency attenuation was found. Wavelength differences alone do not yield good visual acuity. Small brightness mismatches between adjacent grating bars generally improve wavelength discrimination and cause low-frequency attenuation in the wavelength modulation vs spatial-frequency function so that it resembles conventional luminance modulation vs spatial-frequency functions.

Effects of an artificial sea slick upon the atmosphere and the ocean

Abstract: Vertical mean wind profiles, hot-film data, and wave height data measured during the passage of an artificial sea slick are compared with similar measurements without a sea slick. The effects of the slick are modifications of profile roughness length z0, and a possible increase in mean wind speed. Power spectral density plots of wave records obtained before, during and after the slick show wave energy modifications for wavelengths up to 10 m. Coherence values computed from a cross-spectral density of the wind field and simultaneously measured wave field both during and after the slick demonstrate the importance of small waves to air-sea interaction processes. Phase angles indicate the maximum horizontal velocity occurs over the wave trough for all spectral components, some of which are above and some below the wind-wave “matched layer.” During a stick, however, the horizontal velocity maximum occurs over the wave crest for those waves remaining coherent with the wind field.

Analysis of combined gravity and magnetic fields in wave number domain

Abstract: Potential field data has been analyzed in the two-dimensional wave number domain to obtain the ratio of intensity of magnetization to the density (J/ρ). A two-dimensional fast Fourier transform is used to obtain convolution, upward continuation, vertical and horizontal derivatives, and reduction of the total field to the pole. A coherency test is used on the two sets of data to evaluate the validity of the calculated J/ρ ratio for each wavelength. A high-coherency value is assumed to arise if the gravity and magnetic anomalies are caused by the same body. A theoretical prismatic model and a field example from northern Saskatchewan illustrate the techniques.

Determination of Surface-Film Thickness from Shift of Optically Excited Surface Plasma Resonance

Abstract: The strong coupling between photons and surface plasmons that occur on rough metal surfaces permits optical measurements of the shift of the surface plasma resonance frequency when the metal surface is covered with a thin film Thin, discontinuous silver sulfide tarnish films on silver shift the resonance to lower frequencies and also damp the resonance, in agreement with surface plasmon dispersion theory The wavelength of the dominant surface plasma wave is large compared to the size of the discontinuities, so the effect of the thin film should be the same as that of a continuous film whose thickness is the average thickness of the discontinuous film On this basis, the thicknesses of several silver sulfide films are calculated from the measured frequency shift of the resonance peak and are found to be in excellent agreement with values determined from independent ellipsometric measurements

The term systems of C V

Abstract: Term values of the He I-like spectrum of carbon, C V, are derived by using new measurements in the region below 300 AA and some previous observations at longer wavelengths. Ritz formulae and other relationships are established, permitting an arbitrary extension of the term system. The results are compared with available theoretical calculations of ionization energies. Part of the discussion includes He I and Li II.