Showing papers on "Wavelength published in 1972"

Super-resolution aperture scanning microscope.

Abstract: THE classical theory of the resolving power of optical instruments implies a limit to the observation of details in an object if these are significantly smaller than one wavelength, λ0, of the illuminating radiation. This Abee barrier is not entirely impenetrable. Lukosz1,2 has shown how an improvement by a factor of two can be made by the use of complementary spatial filters. Attempts to proceed further in this direction are soon frustrated, however, because the spatial frequencies one is seeking to transfer are such that the waves become evanescent in the direction in which one would like them to propagate. Nassenstein has developed an ingenious scheme3 in which evanescent waves are used to illuminate the object, and a magnified image is obtained using a holographic technique. The resolution capability is determined by the wavelength of the evanescent wave. This is less than λ0, but it is not easy to devise systems where it would be very much smaller.

Scattering of plane sh waves by a semi‐cylindrical canyon

Abstract: The two-dimensional scattering and diffraction of plane SH waves by a semi-cylindrical canyon is analysed for a general angle of wave incidence The closed-form solution of the problem shows that the surface topography can have prominent effects on incident waves only when the wavelengths of incident motion are short compared to the radius of a canyon The surface amplification of displacement amplitudes around and in the canyon changes rapidly from one point to another, but the amplification is always less than 2 The over-all trends of amplification pattern are determined by two principal parameters: (1) γ, the angle of incidence of plane SH waves, and (2) η, the ratio of radius of the canyon to one-half wave length of incident waves The higher η leads to greater complexity of the pattern of surface displacement amplitudes characterized by more abrupt changes of amplification from one point to another, while γ mainly determines the over-all trends of displacement amplitudes For grazing and nearly grazing incidences, for example, a strong shadow zone is developed behind the canyon The qualitative analysis of the topographic effects on the Pacoima Dam accelerogram,1 based on the semi-cylindrical canyon, suggests that this strong-motion record was not seriously affected by surface topography of the recording site

An Experimental and Theoretical Investigation of Elastic Wave Propagation in a Cylinder

Abstract: A high‐speed computer was used to investigate the problem of wave propagation in an isotropic elastic cylinder. Dispersion curves corresponding to real, imaginary, and complex propagation constants for the symmetric and the first four antisymmetric modes of propagation are given. The radial distributions of axial and radial displacements and of shear and normal stresses are given for the symmetric mode. By using a finite number of modes of propagation, an approximate solution is found for the problem of the L(0,1) mode impinging on a traction‐free interface. The reflection coefficient is determined in this way and the accompanying generation of higher order modes at the interface is shown to cause a high‐amplitude end resonance. Experimental results obtained by using the resonance method in conjunction with a long rod are presented to substantiate the calculated reflection coefficient and the frequency of end resonance. Phase velocities, based on measurements of the wavelength of standing waves and resonance frequencies, were obtained for the symmetric and first two antisymmetric modes. These measurements extend into the frequency range of more than one propagating mode. The rms deviation between theoretical and experimental results is in general less than 0.2% with the exception of the dispersion curve for the L(0,2) mode which deviates by 0.7%.

Analysis of the resistance increase in waves of a fast cargo ship

Abstract: A new method to calculate the added resistance of a ship in longitudinal waves is discussed. For the particular case of a fast cargo-ship the calculated values are compared with experimental results, and a satisfactory agreement is shown. In addition the experiments with the considered shipform confirm that added resistance varies as the squared wave height for constant speed and wave length.

Propagation and Amplification of Rayleigh Waves and Piezoelectric Leaky Surface Waves in LiNbO3

Abstract: Velocities and attenuations of piezoelectric leaky surface waves in LiNbO3 are analyzed. As a result, we have found that the effective electromechanical coupling coefficient of the leaky surface wave propagating along the X axis of a 64° rotated Y‐cut plane is very large, K2 = 0.113, and the attenuation of this wave, caused by radiation of the energy into the solid, is 0.036 dB/wavelength for a free surface and goes to zero for a metalized surface. Moreover, K2 of the elastic surface wave for a 130° rotated Y‐cut, X propagation, is found to be larger than that for a Y cut, Z propagation. The theory is verified experimentally. The theoretical analysis and experiments on amplification are performed for these types of waves. In an experiment utilizing the leaky surface wave, net terminal gain of 13 dB/cm is observed for the interaction between the carrier in 200‐Ω cm Si wafer (0.3×3×10 mm), separately mounted on a LiNbO3 surface, and the leaky surface wave. The air gap between the Si wafer and LiNbO3 single crystal is about 0.5 mμ.

Acousto‐optic light deflectors using optical activity in paratellurite

Abstract: Light deflector designs which use the anomalously low shear wave acoustic velocity and high acousto‐optic figure of merit in single‐crystal paratellurite, first proposed by Uchida and Ohmachi, have been made practical by exploiting this material's birefringence to circularly polarized light. Dixon's equations for Bragg interaction in birefringent materials are found to be equally applicable to optically active materials when linearly polarized propagation modes are replaced by circularly polarized modes. For specific ratios of sound‐to‐light wavelengths, there is a substantially expanded angular range over which Bragg interaction can take place. One effect of this increased range is to permit longer interaction lengths between light and sound, which greatly reduces the acoustic power required. In paratellurite, for visible light, this expanded range occurs for sound frequencies below 100 MHz, in the region of acceptable acoustic loss. Examples of possible designs include a deflector only 3×5×7 mm having a capacity of 500 linearly resolvable spots with a random access time of 10 μsec, with 50% of the incident light being deflected at 35‐mW acoustic power.

Shallow Water Waves on a Viscous Fluid—The Undular Bore

Abstract: A theory is presented for the surface profile above a fully developed Poiseuille channel flow. Small disturbances to this flow are examined, and it is shown that if the (channel depth)/(wavelength) ratio is small (shallow waves), and the Reynolds number large enough, these disturbances initially travel at the classical dynamic (Burns) wave speeds. However, by introducing appropriate far‐field coordinates it follows that the disturbance eventually travels at a different wave speed—the kinematic wave speed. To confirm this, the dynamic waves are shown to decay by using standard boundary layer techniques. This general result (of decay) agrees with previous one‐dimensional theories. The profile close to the kinematic wave front is examined and shown to satisfy an equation of the form ηT + ηηX + ηXXX = ΔηXX, where η(X, T) is the surface profile. This equation is called the Korteweg‐de Vries‐Burgers equation. The form of the steady solution of this equation exhibits all the characteristics of the undular bore. A bound on Δ agrees with stability requirements found by other authors using different methods.

Light scattering from fused polycrystalline aluminum oxide surfaces

Abstract: The results of a study of the topography of fused polycrystalline aluminum oxide surfaces using reflected coherent light of 6328-A wavelength are reported. It is shown that the wavelength and angular dependences of the specular intensity can be understood in terms of optical scattering theory in the Kirchhoff approximation for a surface with a Gaussian roughness distribution. The values of the rms roughness obtained optically by fitting the experimental observations to the theory agree well with those obtained from Talysurf measurements. Estimates of the rms slope and correlation distance of the surface structure are obtained from a treatment of the specular and diffuse components of the reflected light intensity using the Beckmann model. An empirical relationship is shown to exist between the mean surface grain size as determined by microscopic observation using the line intercept method and the rms surface roughness. These results have formed the basis of an optical technique for rapidly estimating the mean surface grain size on high alumina substrates used in the microelectronics industry.

Interactions between Steady Won-Uniform Currents and Gravity Waves with Applications for Current Measurements

Abstract: Interactions between steady non-uniform currents and gravity waves are generalized to include the case of a random gravity wave field. The Kitaigorodskii-Pierson-Moskowitz frequency spectrum is used as the basic spectral form for zero current condition. Modified spectral functions in both wavenumber and frequency spaces under the influence of current are found by using energy conservation and kinematic wave conservation laws. The relative importance of the current-wave interaction was measured by the nondimensional parameter U/C0, with U as the current speed and C0 the phase speed of a wave under no current. As a result of the current-wave interaction, the magnitude and the location of the energy peak in the spectrum is altered. Since the phase speed of gravity waves is a monotonically decreasing function of wavenumber and frequency, the influence of current will be predominant at the higher wavenumber range. Furthermore, the contribution from the higher wavenumber range dominates the surface slo...

Refractive indices and electro‐optic coefficients of the eulitities Bi4Ge3O12 and Bi4Si3O12

Abstract: Measurements are reported on the refractive index n and of the static electro‐optic coefficient r41 as a function of wavelength throughout the visible for Bi4Ge3O12 and Bi4Si3O12. Both materials exhibit large dispersion. At 633 nm, n=2.0975 for the germanate and 2.0211 for the silicate. The corresponding values for r41 are 0.95×10−10 cm/V and 0.54×10−10 cm/V, respectively.

Spectral Response of Low-Loss Optical Waveguides

Abstract: The attainment of 20-dB/km attenuation in experimental single-mode glass optical waveguides has spurred interest in their use for optical communications. The primary wavelength region of interest is in the red or near-infrared region of the spectrum. In this work independent attenuation measurements from 600 nm to 1060 nm have been made on low-loss waveguides and bulk cladding glass, using both laser and scanning-prism monochromator sources. Three bands were observed in the waveguides, at 725 nm, 875 nm, and 950 nm, and identified as due to OH in the glass. Absorptions too small to be precisely measured in the bulk glass are seen to be exceedingly important in the waveguides and easily measured in them.

Measurement of an optical frequency and the speed of light.

Abstract: We report the measurement of the frequency of the 633-nm red laser line. This is the first measurement of an optical frequency in the visible range without reference to the speed of light or to a measured wavelength. Combination of the optical frequency with the known wavelength yields $c$ to an accuracy higher than previously known. This method demonstrates the practicability of a single-standard time-length measurement system unified via a defined value of the speed of light.

Electromagnetic scattering by arbitrarily oriented ice cylinders.

Abstract: The scattering of electromagnetic waves by arbitrarily oriented, infinitely long circular cylinders is solved by following the procedures outlined by van de Hulst. The far-field intensities for two cases of a linearly polarized incident wave are derived. The scattering coefficients involve the Bessel functions of the first kind, the Hankel functions of the second kind, and their first derivatives. Calculations are made for ice cylinders at three wavelengths: 0.7, 3, and 10 microns. The numerical results of intensity coefficients are presented as functions of the observation angle. A significant cross-polarized component for the scattered field, which vanishes only at normal incidence, is obtained. It is also shown that the numerous interference maxima and minima of the intensity coefficients due to single-particle effects depend on the size parameter as well as on the oblique incident angle.

Nonlinear energy transfer in gravity–capillary wave spectra, with applications

Abstract: The energy flux in gravity-capillary wave spectra has been obtained using Hasselmann's (1962) perturbation analysis for a homogeneous Gaussian sea. As expected, resonant interactions now appear at second order, and a third-order perturbation analysis shows that energy is redistributed from waves with intermediate wavelengths (in the neighbourhood of 1·7 cm) toward gravity and capillary waves. Numerical computations are also obtained for the energy flux and the interaction time of a sharply peaked spectrum consisting of wavenumbers concentrated around a single wavenumber, superposed on a smooth background spectrum. The range of validity of the inviscid results is discussed.

Efficient GaAs–AlxGa1−xAs Double‐Heterostructure Light Modulators

Abstract: Properly designed GaAs–AlxGa1−xAs double heterostructures produce strong optical waveguides The propagation constants of the waveguide modes can be readily modulated by the linear electro‐optic effect Measurements at a wavelength λ = 1153 μm have yielded a phase modulation of 180° with ‐10 V applied bias to a device only 1 mm long The power necessary to phase modulate light at λ ≈ 1 μm by 1 rad is of the order of 01 mW per 1‐MHz band‐width The power dissipation is very strongly dependent on wavelength At present, the high‐frequency modulation is limited by the series resistance and capacitance of the device The highest cutoff frequency determined thus far, ≈ 4 GHz, is considerably lower than that calculated based on the geometry and material properties

Elastic surface waves

Abstract: Devices that exploit the properties of elastic surface waves can perform very complex signal‐processing functions, identical to those carried out by conventional electromagnetic devices. The great advantage to using surface waves instead of electromagnetic waves is the tremendous reduction in size of surface‐wave devices compared to their electromagnetic counterparts. This great reduction in size is the result of the great difference between the elastic and electromagnetic velocities. Surface waves propagate at velocities approximately 105 times slower than electromagnetic velocities; thus, at the same frequency, the elastic wavelength is 105 times shorter than the electromagnetic wavelength. A further advantage is that the energy in the elastic surface wave can readily be sensed anywhere along its path.

Wave propagation and dispersion in space-time periodic media

Abstract: The dispersion characteristics of electromagnetic fields are examined for waves propagating in a medium with a permittivity which is modulated periodically with respect to time and one spatial co-ordinate. By taking a guided-wave approach, which expresses the fields of arbitrary sources in terms of a superposition of modal solutions, it is shown that many properties of the individual modes may be inferred by means of wavenumber diagrams. These diagrams are easily constructed for the special case of a vanishingly small periodic modulation. By using coupled-mode consideration, this special case is extended to serve as a good approximation for finite modulation amplitudes. In addition to yielding information on the dispersion character of modal fields, it is shown that the wavenumber diagrams may be employed to extract the modal constituents of a plane wave scattered by a layer containing a space-time periodic medium. The principal far-field components of waves excited by a localised arbitrary source embedded in such a medium may also easily be obtained from the wavenumber diagrams. The guided-wave approach, together with its associated wavenumber diagrams, is thus shown to serve as a powerful tool in analysing and understanding a large class of phenomena, which includes the diffraction of light by sound and parametric effects in nonlinear media, as well as other aspects of wave interactions in material bodies.

Excitation of Parametric Instabilities by Radio Waves in the Ionosphere

Abstract: The excitation of parametric instabilities by radio waves in a magnetoplasma is discussed. A uniform medium is assumed and linear approximations are used. Excitation by a pump wave of ordinary polarization is hardly affected by the magnetic field. Low or zero frequency ion waves and high frequency Langmuir waves are excited simultaneously. For an extraordinary pump wave, the excited high frequency electrostatic waves are in the Bernstein mode. The threshold is slightly higher and excitation can occur only within certain 'allowed' frequency bands. A new type of parametric instability in which the excited waves are electromagnetic in nature and which is more strongly affected by the inhomogeneous nature of the medium is discussed qualitatively.

Hypersonic absorption in amorphous polymers by light scattering

Abstract: Brillouin lines have been observed in the spectrum of light scattered by poly(methylmethacrylate) and, for the first time, for poly(vinylchloride). The line widths have been measured, by a special technique, as a function of temperature. The attenuation per wavelength of thermal phonons below the glass transition temperature is almost constant over a wide frequency range (5 MHz to 10 GHz). The attentuation is ascribed to the mechanical strain field round static imperfections. Above the glass transition temperature the attenuation is associated with the well-known mechanical ∝ process. The Rayleigh light scattered by these polymers and their transparency is also discussed.

Instability of the Stratified Ekman Boundary Layer and the Generation of Internal Waves.

Abstract: With stable density stratification the shear-flow instability of the Ekman boundary layer exhibits two distinct regimes. At low values of a Richardson number the growth rate of instability, at specified Reynolds number, wavelength and angle, decreases linearly with Ri. At higher values of Ri the growth rate may decrease more slowly or may increase with Ri. The peculiar effects at the large values of Ri are interpreted as a resonance of the shear-flow instability with internal gravity waves. This resonance occurs when the speed of the shear-flow instability relative to the basic flow lies within the range of speeds of internal gravity waves relative to the basic flow, as determined by the Brunt-Vaisala frequency. Under these conditions the growth of waves appears to be dominated by the Type II mechanism of energy exchange for Ekman layer instability. Internal gravity waves generated by the shear-flow instability have their crests nearly parallel to the geostrophic flow above the boundary layer and...

Nonlinear theory of frequency shifts and broadening of plasma waves.

Abstract: It is shown that the linear dispersion relation for plasma waves is converted into a nonlinear one by making the replacement ω→ω+δω+idw. Here, ω is the wave frequency, and δω and dw are real nonlinear wave quantities that are explicitly calculated. The wave damping decrement dw has been determined in previous investigations, and shown to increase wave damping. Here, the nonlinear frequency shift δω is determined for a wide class of conditions. It is shown to have a direct and calculable influence on the frequencies of general electrostatic waves in magnetoplasmas. It is further shown that δω implies a splitting and broadening of frequency spectra of low‐frequency waves. The calculated value of such broadening is in good agreement with observations by Sheffield, and Halseth and Pyle. The present method is based on the use of an averaging operator to express the nonlinear dispersion relation in terms of perturbed orbit function. Cumulant expansions are then used to express the orbit function in terms of δω,...

System for performing spectral analyses under computer control

Abstract: Measurements of physical attributes such as dielectric film thickness that are susceptible to spectral analysis are accomplished rapidly and accurately by a spectrophotometric system in which a programmed digital computer operating concurrently with the optical scanning means automatically performs the calibrating, normalizing and data reducing functions that otherwise must be carried out as time-consuming human, mechanical or analog electronic operations. The control over the optical data handling operations exercised by the computer eliminates the need for mechanically or electronically adjusting the optical apparatus to meet changing system conditions, whether periodic or aperiodic. Source light is transmitted through a rotating variable-wavelength interference filter which acts during one-half of its cycle to transmit light of varying wavelength through a fiber-optic reference path directly to the optical data acquisition apparatus, while acting in the next half-cycle to transmit light of such varying wavelength indirectly to said data acquisition apparatus through a measurement path. In the present example, where film thickness is the attribute being measured, the measurement path comprises a bifurcated fiber-optic bundle, one branch of which is used to carry the light of variable wavelength to the sample, and the other branch of which carries light reflected from the sample to the aforesaid data acquisition apparatus. A computer program enables light passed through the reference path in one half-cyle to calibrate the system for measuring optical transmission or reflectance in the next half-cycle. Reduction of relative reflectance data to absolute reflectance data (needed for the accurate determination of film thickness) is accomplished by additional computer programs whose algorithms are based upon the discovery that all graphs of absolute reflectance versus wavelength for film samples of a given material having different thicknesses are bounded by a common pair of wave envelopes.