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Volume 54, Issue 2, 01 February 1983

Diffraction of horizontally polarized shear waves by normal edge cracks in a plate
View Description Hide DescriptionA combined finite element and analytical method is presented here for analyzingscattering of time harmonic horizontally polarized shear (SH) waves by material and geometric irregularities in an isotropic linearly elastic infinite plate. All the irregularities are assumed to be contained in a bounded region. The problem of scattering is solved by replacing this region with a finite element mesh. A nodal force‐displacement relation is developed to satisfy the continuity conditions along the boundaries separating the inner finite‐element region from the exterior regular region. The method is illustrated by solving the problem of scattering of SH waves by a surface breaking crack. The crack is taken to be normal to the surface of the plate. The reflection and transmission coefficients are computed for zeroeth, first, and second incident wave modes. The validity and accuracy of the results are checked by satisfaction of the energy conservation principle and the reciprocity relations.

Multidetector intensity interferometers
View Description Hide DescriptionThe intensity fluctuations of incoherent radiation are used to determine the position of sources with respect to a detector system. For electromagnetic radiation the system uses square‐law detectors and for acoustic waves the detector output is squared before being processed. The theory is developed for ndetectors and the results are applied to two‐, three‐, and four‐detector arrangements. The two‐detector intensity inteferometer measures the square of the first‐order correlation function and can determine the angular size of a source. The three‐detector intensity interferometer yields two coordinates of the location of a source, and a modified version involving only one detector functions as a Fourier transform spectrometer. It measures the first‐order correlation function and thus can be used to obtain the spectrum of the source. The four‐detector intensity interferometer can simultaneously determine the three‐dimensional coordinates of several sources. The operation of several acoustic multidetector intensity interferometers are described and a number of applications are discussed.

Statistical investigations of signals detected by nonideal detectors
View Description Hide DescriptionWe analyze the statistical properties of Gaussian and non‐Gaussian signals detected by a nonideal photon detector. Such a detector is assigned a realistic response function, and parameters like average intensity and bunching property are evaluated. We show that there is a significant difference between the signal detected by an ideal and a nonideal detector.

Magnetostatic field calculations in the presence of iron using a Green’s function approach
View Description Hide DescriptionAn alternative method to that of Caldwell [J. Phys. D 1 2, 1653 (1979)] is used to calculate the effects of iron on the magnetic field produced by a current‐carrying axisymmetric conductor. In this way a neater solution is obtained by constructing the Green’s function from an eigenfunction expansion. Good agreement with the previous results is achieved and an indication is given of the advantages of this Green’s function approach.

Magnetostatic energy of a ferromagnetic cylinder
View Description Hide DescriptionThe magnetostatic self‐energy is expressed in terms of integrals which are easier to manipulate than the conventional Green function of the potential. Specific expressions are derived for a finite ferromagnetic particle, in the form of a right‐circular cylinder, which has no volume charge.

Impedance parameters and radiation pattern of two coupled circular microstrip disk antennas
View Description Hide DescriptionThe current distribution on a two‐coupled circular microstrip disk antenna fed by two probes is rigorously derived using the Vector Hankel Transform. It is shown that the current on the two disks is governed by a set of vector integral equations. These equations are solved approximately for the amplitudes of the currents on the two disks, in the limit of thin substrate. Expressions for the self, mutual, and input impedances are then rigorously derived. It is shown that excitation of the odd symmetric TM_{1} _{1} mode can cause the two‐disk antennas to act as a better radiator than the single‐disk antenna, while the odd antisymmetric modes can cause the two‐coupled disk structures to act as a better resonator than the single‐disk structure. Expressions for the radiation pattern are then derived, and the impedance parameters and the radiation patterns plotted.

Lateral waves: Formulas for the magnetic field
View Description Hide DescriptionNew simple formulas are obtained as an approximation of the exact general integrals for the components of the magnetic field generated by a horizontal electric dipole in a half‐space of water or earth near its boundary with air. These formulas supplement the earlier derivation of the three components of the electric field which are repeated here for completeness. The formulas for the transverse and vertical components are needed in treating the reflection of lateral waves from plane or cylindrical boundaries.

Electron‐beam uniformity of a large‐area high‐current accelerator diode
View Description Hide DescriptionTime‐resolved photography of Cherenkov emission has been used to study large‐area electron‐beam uniformity and electron‐beam propagation in air. For the 50‐ns pulse widths used, we show that the time‐dependent electron emission from large‐area cathodes is typically very nonuniform. Pinching of the electron beam by its self‐magnetic field can be prevented by the use of an applied axial magnetic field approximately equal to the self‐magnetic field generated by the electron beam. When an applied field is used, beam nonuniformities introduced by the anode support structure persist through tens of centimeters of air outside the diode. These nonuniformities can reduce efficiency and beam quality of the laser. Beam rotation in the diode caused by the applied magnetic fields can result in significant loss of electron‐beam energy to the anode chamber and foil‐support structure. However, we have shown that emission can be reduced on areas of the cathode which map onto obstructions on the anode so the electron energy loss can be reduced.

The field distribution of a focused Gaussian beam reflected at 45° from a conducting plane and its effects in plasma‐ignition experiments
View Description Hide DescriptionThe electrical field distribution over the focal region of a Gaussian beam, incident at 45° and focused onto a perfectly conducting infinite plane, is calculated numerically by summing the plane waves in an angular spectrum representation. The beam is plane‐polarized with the transverse electric field perpendicular to the plane of incidence. The configuration and parameters were chosen to agree with our experiments on plasma initiation near a metallic conductor by 35‐GHz/8.6‐mm microwave radiation. The results of the calculation show that the field distribution determines the ignition threshold, spatial location, and initial development of the microwave plasma at a metal surface.

Reflection of electromagnetic waves at a biaxial–isotropic interface
View Description Hide DescriptionThe reflection of electromagnetic waves at a plane boundary between isotropic and biaxial media has been investigated using the k D B approach. The general case has been considered in which the principal dielectric axes of the biaxial medium are oriented at an arbitary angle to the normal of the plane boundary. In general, two characteristic waves propagate in the biaxial medium, leading to coupling of vertical and horizontal polarizations in the reflected waves. Some special cases are illustrated. The results have applications to problems in remote sensing and integrated optics.

Effects of iodine saturation dispersion on the ^{1} ^{2} ^{7}I_{2} stabilized He‐Ne laser
View Description Hide DescriptionIn a ^{1} ^{2} ^{7}I_{2} stabilized 633‐nm He‐Ne laser, the effects of saturation dispersion in iodine on the inverted Lamb dips of the iodine hyperfine components are discussed. Analytical expressions for the second and third harmonic of the frequency modulated dips are derived. Dispersion is found to influence strongly the modulation dependent frequency shifts of the absorption line centers and also introduce asymmetry in the second harmonic.

Enhanced indium phosphide substrate protection for liquid phase epitaxy growth of indium‐gallium‐arsenide‐phosphide double heterostructure lasers
View Description Hide DescriptionThermal degradation of indium phosphide (InP)single crystal substrates prior to liquid phase epitaxygrowth has been virtually eliminated by using an improved protection technique. The phosphorus partial pressure provided by a Sn‐In‐P solution localized inside an external chamber surrounding the InP substrate prior to growth prevents thermal damage to the surface. Nomarski contrast photomicrographs, as well as photoluminescence and x‐ray diffractometric measurements indicate that InP substrates protected by this method suffer a negligible deterioration, in contrast to the results of the more commonly used cover‐wafer method.

Prediction of transverse‐mode selection in double heterojunction lasers by an ambipolar excess carrier diffusion solution
View Description Hide DescriptionTransverse‐mode selection is characterized for GaAs/AlGaAs double heterojunction lasers from optical field and electron/hole interaction. The electron/hole distribution determined from a solution of the ambipolar diffusion equation provides the necessary information about gain/mode coupling to predict the current at threshold. Lasing power out versus current solutions provide information about internal differential quantum efficiency.Theory is matched to experiment for a multimode laser with one heterojunction having a very small index step. It is found that the laser’s characteristics over a temperature and current range are predicted by adjusting the active‐layer refractive index as determined from far‐field measurements.

Design of double passive modulated mode‐locked lasers
View Description Hide DescriptionA set of equations is obtained that allow the determination of the optimum values for the laser parameters in order to obtain perfect mode‐locking by double passive modulation. The double modulation consists of a fast saturable absorber and a passive loss proportional to the mean intensity in the cavity provided by a passively driven electro‐optic modulator. The stochastic nature of the emission of conventional passive modulated systems is eliminated if the correct values of the modulation parameters are chosen as predicted by the equations presented here. The predictions given by the equations were compared with previous numerical computations in order to check the validity of certain approximations used. Experimental results obtained confirm the predictions given by said equations.

Use of neutron diffraction texture measurements to establish a model for calculation of ultrasonic velocities in highly oriented austenitic weld material
View Description Hide DescriptionNeutron diffraction has been used to measure the crystallite orientation distribution function for a cubic test sample of highly textured austenitic weld material. The longitudinal and transverse ultrasonic velocities in three orthogonal directions in the sample have been calculated from this function and compared with measured values for the sample. The Voigt approximation is found to give good agreement with experiment and appears to be the most useful approach for the calculation of ultrasonic velocities in highly textured materials.

Surface acoustic wave resonators on a ZnO‐on‐Si layered medium
View Description Hide DescriptionThe adaptation of surface acoustic wave resonator technology to a ZnO‐on‐Si layered medium is presented. Several distributed reflector schemes are considered, including shorted and isolated metallic strips, as well as grooves etched in the ZnO layer. In the case of etched groove reflectors, a first‐order velocity perturbation arises due to the dispersive nature of the layered medium. Unique resonator design considerations result from the reflector array velocity and reflectivity characteristics. Transverse mode resonances are characterized and their effect on resonator response eliminated by a novel transducer design. A technique for temperature compensating the devices by use of a thermal SiO_{2} layer is discussed.

Signal and systems analysis for unsteady heat conduction problems
View Description Hide DescriptionA general formulation of heat transfer phenomena based on signal analysis is developed in this article. Starting from the classical matrix formulation of heat transfer through a slab, normal modes are defined. The thermal normal modes are linear combinations of heat flow and temperature variations measured on the external surfaces of the slab. Although normal modes fit to a superposition principle, they do not define thermal signals since the scalar product of heat flow and temperature has no physical meaning. Starting from this classical description, a new formulation of heat transfer based on entropy concept is then stated. The ‘‘entropy production’’ and ‘‘entropy exchanged with outside’’ are expressed in terms of normal coordinates. It is shown how the time distribution of entropy production for the quasi‐steady‐state of flow can be characterized by a cross‐correlation function between the space‐average heat flow and its entropy conjugated coordinate. In the same way, the time distribution of entropy exchanged with outside results from a cross‐correlation function between a normal coordinate and the corresponding entropy conjugated coordinate. Under unsteady‐state conditions, the entropy exchanged with outside can be computed by convoluting the cross‐correlation function representative of entropy production and the impulse response of heat transfer through the slab. This new formulation yields to consider thermal signal independently of their actual waveforms, but of their correlation function (i.e., their frequency content). In the experimental part, the theoretical results are extended to include practical problems of heat transfer in building sections exposed to natural weather conditions and internal heating.

Thermal effects in photothermal spectroscopy and photothermal imaging
View Description Hide DescriptionThe effect of thermal parameters on photothermal spectroscopy and photothermalimaging for certain types of spatially heterogeneous samples has been studied. Results have been obtained for both photoacoustic and photothermal deflection modes of detection. Specific attention has been paid to optical saturation in samples whose properties exhibit gradual spatial changes and to the dependence of the photothermal signal on the individual thermal parameters. Most photothermal spectroscopy has been done using thermally homogeneous samples, and most photothermalimaging using optically saturated samples. In this paper, these limitations are relaxed, and the photothermal signal is assumed to depend simultaneously on gradual spatial variations in the optical absorption coefficient, thermal conductivity, and thermal capacity of the sample.

Model of the anode region in a uniform multi‐cathode‐spot vacuum arc
View Description Hide DescriptionA model is developed for the anode region of a uniform multi‐cathode‐spot vacuum arc. A first‐order approach is used, in which the plasma up until the anodesheath is assumed to be produced solely by a multitude of cathode spots and is described by a zero‐order plasma model previously developed, and the influence of the anodic emissions on this plasma is assumed initially to be negligible. Calculations of the electron mean‐free‐path and the Debye length indicate that the anodesheath may be modelled as collisionless. The anode potential is calculated by imposing the requirement of current continuity, and it is found that the overabundant supply of random electron current forces the anode to assume a negative potential with respect to the adjacent neutral plasma with a magnitude of approximately (1/3)(k T _{ e }/e)(v _{ T }/v _{ d }), where T _{ e } is the electron temperature,v _{ d } is the electron drift velocity, and the thermal velocity v _{ T } is defined by (k T _{ e }/2πm _{ e })^{1} ^{/} ^{2}. The magnitude of the electric field at the anodesurface is also calculated, and it is found that under certain circumstances, its value may approach the value of 10^{7} V/m known to produce cathode spots. The possibility of ‘‘cathode spot’’ formation on the negatively charged anode is discussed. The energy flux incident on the anodesurface is analyzed and is found to contain both a component originating from the electron flux, and a component originating from the ion flux. The two components are of the same order of magnitude, with the ion flux dominant at lower values of T _{ e }, and the electron flux dominant at higher values of T _{ e }. The overall energy flux is given by Jφ_{ E }, where J is the current density and φ_{ E } is an effective anode drop whose value in a Cu arc ranges from 13 V for T _{ e }=1 eV to 33 V for T _{ e }=9 eV. Neutral atom emission from the anodesurface by evaporation and by sputtering is analyzed. Evaporation will be significant after a sufficient heating time has elapsed, on the order of 64 ms for a 3 eV, 10^{7} A/m^{2}Cu arc, for example. Sputtering, in the case of a Cu arc, may produce a local neutral density equal to 37% of the ambient ion density. All of the neutrals emitted from the anodesurface are eventually ionized by electron impact. Extension of the model to cover arcs where macroparticle‐produced plasma is significant, and where nonuniformities are produced by the electrode geometry or magnetic constriction, is discussed qualitatively.

Validity of spherical quantitative refractometry: Application to laser‐produced plasmas
View Description Hide DescriptionWe report an experimental laser technique of quantitative Schlieren imaging of spherical plasmas combined with streak camera recording. We show that quantitative refractometry applies for small values of refraction angles, i.e., when the law giving the refraction angle versus the impact parameter of rays passing through the plasma is a linearly decreasing function.