Showing papers on "Wavelength published in 1985"

A Fifth‐Order Stokes Theory for Steady Waves

Abstract: An alternative Stokes theory for steady waves in water of constant depth is presented where the expansion parameter is the wave steepness itself. The first step in application requires the solution of one nonlinear equation, rather than two or three simultaneously as has been previously necessary. In addition to the usually specified design parameters of wave height, period and water depth, it is also necessary to specify the current or mass flux to apply any steady wave theory. The reason being that the waves almost always travel on some finite current and the apparent wave period is actually a Dopplershifted period. Most previous theories have ignored this, and their application has been indefinite, if not wrong, at first order. A numerical method for testing theoretical results is proposed, which shows that two existing theories are wrong at fifth order, while the present theory and that of Chappelear are correct. Comparisons with experiments and accurate numerical results show that the present theory ...

Refractive Index of Water and Its Dependence on Wavelength, Temperature, and Density

Abstract: A survey of the available experimental data and the existing equations for the refractive index of water is given. The dependence of the molar refraction on wavelength, temperature, and density is shown over an extended range. Based upon the electromagnetic theory of light an equation for the refractive index of water with wavelength, temperature, and density as independent variables is constructed. Its coefficients are directly deduced from all available experimental data by least‐squares fit. The range of validity of wavelength is restricted by the theory for normal dispersion to 182 nm≤λ≤2770 nm. The range of temperature and density is given by the available experimental data. Interpolations between the single measured points are possible and the following range of validity can be recommended: for temperature −10 °C≤T≤500 °C and for density 0.0028 kg/m3 ≤ρ≤1045 kg/m3. Good agreement exists between the new relation, the available experimental data, and several existing equations.

Multiple-wavelength phase-shifting interferometry

Abstract: This paper describes a method to enhance the capability of two-wavelength phase-shifting interferometry. By introducing the phase data of a third wavelength, one can measure the phase of a very steep wave front. Experiments have been performed using a linear detector array to measure surface height of an off-axis parabola. For the wave front being measured the optical path difference between adjacent detector pixels was as large as 3.3 waves. After temporal averaging of five sets of data, the repeatability of the measurement is better than 25-A rms (λ = 6328 A).

Plane waves in linear elastic materials with voids

Abstract: The behavior of plane harmonic waves in a linear elastic material with voids is analyzed. There are two dilational waves in this theory, one is predominantly the dilational wave of classical linear elasticity and the other is predominantly a wave carrying a change in the void volume fraction. Both waves are found to attenuate in their direction of propagation, to be dispersive and dissipative. At large frequencies the predominantly elastic wave propagates with the classical elastic dilational wave speed, but at low frequencies it propagates at a speed less than the classical speed. It makes a smooth but relatively distinct transition between these wave speeds in a relatively narrow range of frequency, the same range of frequency in which the specific loss has a relatively sharp peak. Dispersion curves and graphs of specific loss are given for four particular, but hypothetical, materials, corresponding to four cases of the solution.

Near-Infrared Spectroscopy of Organic Substances

Abstract: The near-infrared spectral region is generally defined as the wavelength range from 700 nm to about 2500 nm, although there is considerable variation in wavelength ranges of the different instrument types. The absorption bands in this region are due to overtones and combinations of the fundamental mid-IR molecular vibration bands. The energy transitions are between the ground state and the second or third excited vibrational states. Because higher energy transitions are successively less likely to occur, each overtone is successively weaker in intensity. Since the energy required to reach a second o r third level excited.

Elastic wave scattering by a random medium and the small‐scale inhomogeneities in the lithosphere

Abstract: In this paper we use Born approximations to derive the mean square amplitudes of the scattered field for P-P, P-S, S-P, and S-S scattering by an elastic random medium characterized by perturbations of elastic constants and density. We also obtain the total scattered power or the scattering coefficient for the case of an incident P wave. We find that, in both the spatial scattering pattern and the frequency dependence of the scattering coefficient, there are some significant differences between scalar wave scattering and elastic wave scattering. These differences are most striking when the wavelength is comparable to the size of inhomogeneities, which is often encountered in the study of short-period seismic body waves. Under certain conditions, the perturbations of the medium parameters can be decomposed into an impedance term and a velocity term. In the forward direction, scattered waves are primarily controlled by the velocity perturbations. For backscattering, scattered waves are generated mainly by impedance perturbations. We derive low- and high-frequency asymptotic forms of the directional and total scattering coefficients. In the low-frequency range, Rayleigh scattering with fourth-power frequency dependence occurs. For the high-frequency range the scattered power for common-mode scattering has a second-power frequency dependence, which is attributed to velocity perturbations. The scattered power of converted waves reaches a maximum, for the case of an exponential correlation function, in the high-frequency range. We find that the scalar wave theory can be only approximately used for the forward scattering problem in the high-frequency range, such as the phase and amplitude fluctuations in large seismic arrays. The case of coda wave excitation by local earthquakes, which is a backscattering or a large-angle-scattering problem, must be handled by the full elastic wave theory. A preliminary analysis of past observations using our theory suggests that the lithosphere may have multiple-scale inhomogeneities. Besides the 10–20 km scale velocity inhomogeneities revealed by the forward scattering observations at LASA and NORSAR, the lithosphere in tectonically active regions may be rich in small-scale (less than 1 km) inhomogeneities.

Acoustic radiation potential on a sphere in plane, cylindrical, and spherical standing wave fields

Abstract: The method of Gor'kov is applied for deriving the acoustic radiation potential on a sphere in an arbitrary sound field. Generalized potential and force expressions are derived for arbitrary standing wave modes in rectangular, cylindrical, and spherical geometries for the case where the sphere radius is much smaller than the wavelength. Criteria for determining radiation-potential minima are derived and examples of characteristic spatial radiation-potential profiles are presented. Single modes that can sustain stable positioning are discussed for each geometry. The localizing force strengths for representative standing wave modes in the three geometries are also compared. The positioning of samples due to acoustic forces only are considered. However, the method developed is general and is extended to include gravity or other external forces.

Numerical simulation of scattering from simple and composite random surfaces

Abstract: Numerical simulation studies of backscattering from one-dimensional, statistically known, perfectly conducting random surfaces are carried out to examine (1) the scattering characteristics in the intermediate-frequency region, where neither the low- nor the high-frequency approximation is applicable, (2) the validity of the two-scale concept in rough-surface scattering, and (3) applicability of the wavelength filtering concept to simple and composite surfaces. It is found that in the intermediate-frequency region the angular scattering curves for both the horizontal and vertical polarizations decrease at a slower rate than that predicted by a first-order small perturbation solution and that the Kirchhoff solution always lies between the two polarizations. In addition, the level difference between the horizontal and vertical polarization scattering coefficients is smaller than that of the perturbation solution. The two-scale concept has no general applicability. Its application is restricted to two-scale surfaces where one scale satisfies the Kirchhoff approximation and the other the small perturbation assumptions such that the two scales dominate scattering in different angular regions. The concept of wavelength filtering is applicable to simple surfaces or to each component of a composite surface in the low-frequency region where scattering is dominated by a narrow band of surface frequency components but loses its validity gradually as we approach the high-frequency limit where scattering is determined by the surface slope distribution. It is not the explanation of why the surface components of a composite surface may dominate scattering over different angular regions.

Synchronous cavity mode and feedback wavelength scanning in dye laser oscillators with gratings

Abstract: A simple result of scalar diffraction theory is used to derive the round trip phase accrual of a plane wave in dye laser oscillators containing gratings. This is used to determine configurations where the standing wave condition is satisfied at the feedback wavelength throughout an angle scan. We find that at least one such exactly synchronous configuration always exists regardless of oscillator type.

Long‐wave instability at the interface between two viscous fluids: Thin layer effects

Abstract: The stability of the interface between two viscous fluids is considered when the depth of the lower fluid is much less than the depth of the upper fluid. A long wavelength perturbation scheme is used to solve the linear stability problem and the equation governing the nonlinear evolution of the interface is deduced. The exact dispersion relation is derived for arbitrary values of wavelength and then simplified for large wavelength values. It is found that the flow is always linearly unstable when the lower fluid is also the more viscous fluid.

Rough surface interferometry with a two-wavelength heterodyne speckle interferometer.

Abstract: If a rough surface is illuminated by a coherent lightwave of wavelength λ1, it is not possible to determine the surface profile from the phases of the speckle field formed by the scattered light. If the rough surface is illuminated, however, by an additional coherent wave of wavelength λ1, the phase differences between the two speckle fields do contain information about the macroscopic surface profile even if subject to a statistical error. It is shown that (1) the macroscopic surface profile may be determined from the phase differences if the effective wavelength Λ = λ1λ2/|λ1−λ2| is sufficiently larger than the standard deviation of the microscopic profile of the illuminated surface, and (2) the statistical error is reasonably small if the phase measurements are obtained from speckles of sufficient intensity. Using a heterodyne interferometer we demonstrate the feasibility of this technique. In the first experiment we determine the radius of curvature of a rough spherical surface. In the second experiment the macroscopic surface contour on two ophthalmic lenses of the same power variation, one with a grounded surface and the other with a polished surface, was determined.

Wavelength-dependent transmission of monomode optical fiber tapers.

Abstract: The transmission of light as a function of wavelength through biconical tapers formed in sections of monomode and low-mode number optical fibers is considered. It is found that in the monomode propagation regime the transmission varies sinusoidally with wavelength with a 50% peak loss and a 50-nm period, for tapers typical of those used in the manufacture of fused-biconical directional couplers. The observed dependence of transmission on wavelength can be understood using a coupled-mode formalism and leads to new insights into the operation of monomode fused-biconical directional couplers.

Contouring Aspheric Surfaces Using Two-wavelength Phase-shifting Interferometry

Abstract: Two-wavelength holography and phase-shifting interferometry are combined to measure the phase contours of deep wavefronts and surfaces, such as those produced by aspherics, with a variable sensitivity. When interference fringes are very closely spaced, the phase data contain high frequencies where 2 ~ ambiguities cannot be resolved. In this technique, the surface is tested at a synthesized longer equivalent wavelength. The phase of the wavefront is calculated modulo 2φ using phase-shifting techniques at each of two visible wavelengths. The difference between these two phase sets is the phase of the wavefront as it would be measured at λeq=λ1λ2/|λ1 − λ2 |, assuming that 2π ambiguities can be removed at λeq. This technique enables surfaces to be contoured to an accuracy of λeq/100.

Optical measuring device using a spectral modulation sensor having an optically resonant structure

Abstract: Physical changes induced in the spectral modulation sensor's optically resonant structure by the physical parameter being measured cause microshifts of its reflectivity and transmission curves, and of the selected operating segment(s) thereof being used, as a function of the physical parameter being measured. The operating segments have a maximum length and a maximum microshift of less than about one resonance cycle in length for unambiguous output from the sensor. The input measuring light wavelength(s) are selected to fall within the operating segment(s) over the range of values of interest for the physical parameter being measured. The output light from the sensor's optically resonant structure is spectrally modulated by the optically resonant structure as a function of the physical parameter being measured. The spectrally modulated output light is then converted into analog electrical measuring output signals by detection means. In one form, a single optical fiber carries both input light to and output light from the optically resonant structure. When more than one input measuring light wavelength is used, means may also be provided to divide the input light wavelengths into two portions and then take the ratio thereof. This provides several advantages simultaneously, such as enabling longer operating segments and microshifts to be used for greater sensitivity or detection range, and also eliminates certain errors caused by fluctuations in input light intensity or by changes in light intensity caused by optical fiber bending and optical fiber connectors.

Wavelength‐selective voltage‐tunable photodetector made from multiple quantum wells

Abstract: We show that a pin‐doped multiple quantum well (MQW) diode can be used as a photodetector whose voltage of maximum photocurrent is wavelength dependent. The voltage of maximum photocurrent can be located accurately and related to the wavelength of the incident light, allowing measurements of the wavelength with a precision of 0.03 A=1.2 GHz. This provides a simple, compact, solid‐state device that can be simultaneously used to measure the intensity and wavelength of an optical beam. Furthermore, the device shows high responsivity, low dark current, and fast response.

Investigation of a surface field phase perturbation technique for scattering from rough surfaces

Abstract: We present initial results from the investigation of a surface field phase perturbation method for the calculation of the wave field scattered by a rough surface. This technique is based on the extinction theorem and uses a perturbation expansion of a function closely related to the complex phase of the surface field. This approach was suggested earlier, but we use the expansion in a different way. In the present work we consider only deterministic periodic surfaces, rough in one dimension, on which the total field is zero. We find that, for surfaces with modest slope and curvature, this technique can be used to calculate scattered fields even when surface relief is significant compared to the wavelength of the incident radiation.

On the Theory of Sound Scattering and Viscous Absorption in Aqueous Suspensions at Medium and Short Wavelengths

Abstract: An explicit expression is derived for the phase shifts of the partial waves scattered by a solid elastic sphere, incorporating the effects of the viscosity of the ambient fluid. The solution is applicable to frequencies and scatterer sizes for which the viscous boundary layer thickness is much less than the radius of the sphere. For particle sizes in the sand‐size range (30 μm

Microphysical Interpretation of Multiparameter Radar Measurements in Rain. Part III: Interpretation and Measurement of Propagation Differential Phase Shift between Orthogonal Linear Polarizations

Abstract: As radar waves having different polarizations propagate through a collection of nonspherical oriented hydrometeors, a phase difference between the waves appears. In a collection of uniformly horizontally oriented quiescent water drops, the rate of change of the propagation differential phase shift with increasing distance from the radar is proportional to the product of the liquid water content and the departure from unity of the mass-weighted mean axis ratio of the drops provided the radar wavelength is much larger than the drops. The appropriateness however, of such a simple relation to natural rain 'in which some drops assume complex shapes and a variety of orientations through the processes of collision, coalescence, break-up and oscillation remains to be determined.

VI Wave Propagation in Random Media: A System Approach

Abstract: Publisher Summary This chapter discusses a system approach of wave propagation in random media. The chapter presents the review of the properties of electromagnetic wave propagation in a random medium in the limit when the random spatial inhomogeneities in the medium are large in comparison with the wavelength of the radiation and the magnitude of the index of refraction fluctuations (produced by these random inhomogeneities) is small in comparison with unity. It is also being assumed that the electromagnetic field is sufficiently weak, so, non-linear effects can be ignored, and that the propagation path is not so long that there is a saturation of the scintillations. The treatment begins with the vector form of the Maxwell wave equation, which is used to derive a generalized version of the Huygens-Fresnel Principle. This serves as the basis of all of the important results to be obtained.

The spin‐wave spectrum of layered magnetic thin films

Abstract: The ferromagnetic resonance spectrum of a layered magnetic thin film is expected to show a number of standing spin‐wave resonances with a wavelength that matches the thickness of the film. For the case of perpendicular resonance such spectra were calculated for some typical films in which magnetic layers are alternated with weaker magnetic layers. Some useful approximations are discussed. The results of the calculations are compared with experimental perpendicular spectra measured on films in which fifty Permalloy layers alternate with Ni layers.

Interference of atoms in separated optical fields

Abstract: We consider the interference of atoms caused by the wave nature of their motion. Coherently interfering beams of particles may be obtained by using the diffraction of atoms from separated standing waves resonant with the transition between the ground and excited states of the atoms. Interference arises with and without spatial separation of the diffracted atomic beams. A problem concerning two-quantum perturbation of the wave function of an atom in the ground state by a standing-wave field has been solved. Both amplitude and phase perturbation are taken into account. We show that in spite of the absence of coherence in the incident beam and a rapid decay of the coherence induced by the standing wave for scattered spatially overlapping beams, the interference can be observed for the conditions of an echo. We first consider the phenomenon of an echo under the quantum-mechanical action of light on the translational degrees of freedom. We show that owing to this phenomenon phase memory can be transferred through the ground state over unlimitedly large distances. Owing to the interference of the density harmonics, a periodic structure in the spatial distribution of the atomic density with a period of less than one wavelength of the light is localized at distances of the order of the distance between the fields. The harmonic amplitude is calculated for instantaneous excitation in the case in which the duration of the excitation is comparable with the backward Doppler linewidth in the beam and for scattering under Bragg conditions. In the latter case we show that the effective temperature of the atoms participating in the interference is less than one recoil energy.

A Double Wavelength Laser Doppler System to Investigate Skin Microcirculation

Abstract: A new experimental laser Doppler setup has been designed to discriminate between total and superficial skin blood flow. This selectivity is based on the use of two wavelengths with different penetration depths into the skin. An argon ion and helium-neon laser are mounted on the same optical bench and are stabilized by an optical feedback loop. A single optical fiber directs the beams to the skin and collects the reflected light back to a photodetector, the signal of which is sampled and Fourier transformed to give a frequency power spectrum. Several models of light scattering by the skin are examined, and a single Lorentzian function is found to be the best fit for our experimental power spectra. Flow parameters have been thus measured for several in vitro and in vivo situations. In vitro calibration indicates that there is a constant ratio between the frequency responses at both wavelengths used. The decrease of this ratio encountered in in vivo measurements is attributed to different depths of investigated skin microcirculation according to the incoming wavelengths.

Method of and an apparatus for ultrasonic measuring of the solids concentration and particle size distribution in a suspension

Abstract: Simultaneous measuring of the concentration of solids and particle size distribution in a suspension is effected by exciting the suspension by ultrasonic waves of a plurality of frequencies, the wavelength at the lowest frequency being greater than the diameter of the largest particles to be expected and the wavelength of the highest frequency being smaller than the diameter of the smallest particles to be expected. The dimensional spectrum of the solid particles is divided into a plurality of dimensional intervals for which the respective solids concentrations are determined by measuring the radiation absorption of each frequency used for irradiation and representing the same as the sum of the products of the absorption coefficients which are specific of the frequency and dimensional interval with the unknown particle concentrations. This results in a linear system of equations which is solved with respect to the unknown concentrations.

Analysis and computation for nonlinear elastic surface waves of permanent form

Abstract: Linear elastic surface waves are nondispersive. All wavelengths travel at the Rayleigh wave speed c R. This absence of frequency dispersion means that nonlinear waves of permanent form cannot be determined as a small perturbation from a sinusoidal wavetrain. By representing the general Rayleigh wave of the linear theory in terms of a pair of conjugate harmonic functions, waves which propagate without distortion are characterized as those having surface elevation profiles which satisfy a certain nonlinear functional equation. In the small-strain limit, this reduces to a quadratic functional equation. Methods for the analysis of this equation are presented for both periodic and nonperiodic waveforms. For periodic waveforms, the infinite system of quadratic equations for the Fourier coefficients of the profile is solved numerically in the case of a certain ‘harmonic’ elastic material. Two distinct families of profiles having phase speed differing from the linearized Rayleigh wave speed are found. Additionally, two families of exceptional waveforms are found, describing profiles which travel at the Rayleigh wave speed.

Scattering from thin dielectric disks

Abstract: A solution for scattering from thin dielectric disks has been obtained by approximating the currents induced inside the disk with the currents which would exist inside a dielectric slab of the same thickness, orientation and dielectric properties. This procedure yields an electrostatic approximation when the disk thickness T is small compared to the wavelength of the incident radiation and yields a conventional physical optics approximation when the dimension A , characteristic of the geometrical cross section of the disk, is large compared to wavelength. When the ratio A/T is sufficiently large one or the other of these approximations applies, regardless of the frequency of the incident radiation. Consequently, the solution provides a conventional approximation for the scattered fields at all kA . As a check on this conclusion, a comparison has been made between measurements of the radar cross section of thin dielectric disks and the cross sections predicted using this theory. Agreement was found for thin disks with both large and small values of kA .

Integrated semiconductor light emitting element with oscillation wavelength and phase modulated light output

Abstract: A semiconductor light emitting element is disclosed, which is provided with a light emitting region having a diffraction grating formed by periodic corrugations, a modulation region having an external waveguide layer optically connected directly to the light emitting region and a pn junction separated from a pn junction of the light emitting region and a window region formed of a semiconductor having a larger energy gap than that of a light emitting layer of the light emitting region and extending from at least one end of the light emitting region and the external waveguide layer. The refractive index of the external waveguide is varied through utilization of the electrooptic effect so that the frequency or phase of light stably oscillating at a single wavelength is precisely controlled or modulated. In particular, when the window region is formed only outside the light emitting region, frequency modulation is carried out, and when the window region is formed at least outside the modulation region, phase modulation takes place.

Temperature independent Faraday rotation near the band gap in Cd1-xMnxTe

Abstract: Faraday rotation spectra have been measured for Cd1−xMnxTe, 0.10≤x≤0.20, for temperatures from 213 to 373 K. At wavelengths well above the fundamental absorption edge the rotation decreases with increasing temperature. The opposite temperature dependence is found for shorter wavelengths since the rotation increases strongly when the wavelength approaches the edge and the edge moves towards longer wavelengths with increasing temperature. For each x a wavelength with temperature independent rotation can be found due to a cancellation of these effects. The large and temperature independent rotation is of great interest for optical devices such as magnetic field sensors, isolators, and modulators. By choosing 0.10≤x≤0.25 these devices would be compatible with GaAlAs emitting diodes and lasers. Optical transmission was also measured and was found to be fairly high at wavelengths of interest. A sensor design is presented, allowing dc response and very small physical dimensions.

Nonlinear Kelvin–Helmholtz instability of a finite vortex layer

Abstract: The nonlinear growth of periodic disturbances on a finite vortex layer is examined. Under the assumption of constant vorticity, the evolution of the layer may be analysed by following the contour of the vortex region. A numerical procedure is introduced which leads to higher-order accuracy than previous methods with negligible increase in computational effort. The response of the vortex layer is studied as a function of layer thickness and the amplitude and form of the initial disturbance. For small initial disturbances, all unstable layers form a large rotating vortex core of nearly elliptical shape. The growth rate of the disturbances is strongly affected by the layer thickness; however, the final amplitude of the disturbance is relatively insensitive to the thickness and reaches a maximum value of approximately 20% of the wavelength. In the fully developed layers, the amplitude shows a small oscillation owing to the rotation of the vortex core. For finite-amplitude initial disturbances, the evolution of the layer is a function of the initial amplitude. For thin layers with thickness less than 3% of the wavelength, three different patterns were observed in the vortex-core region: a compact elliptic core, an elongated S -shaped core and a bifurcation into two orbiting cores. For thicker layers, stationary elliptic cores may develop if the thickness exceeds 15% of the wavelength. The spacing and eccentricity of these cores is in good agreement with previously discovered steady-state solutions. The growth rate of interfacial area (or length of the vortex contour) is calculated and is found to approach a constant value in well-developed vortex layers.