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Volume 68, Issue 12, 15 December 1990

Canonical aberration theory in electron optics
View Description Hide DescriptionBy defining the Hamiltonian function in an electron optical system the canonical aberration theory has been developed in the up to fifth‐order approximation. Therefore, the canonical position and momentum aberrations can be expressed by eikonal functions and equivalently by Poisson brackets. Consequently, all fifth‐order canonical aberration coefficients for rotationally symmetrical electron optical systems have been derived at any arbitrary observation planes.

Canonical aberration theory in electromagnetic multipoles
View Description Hide DescriptionIn a 2N‐pole electromagnetic system, defining the electron optical Hamiltonian function, we have derived both general algebraic expressions (arbitrary N) and special numerical formulas (N=3,4,5,6,7) for different aberrations from lower to higher order (i.e., the order of N−1, N+1, 2N−3, 2N−1, 3N−5). The so‐called canonical aberrationtheory in electromagnetic multipoles has thus been developed, which allows us to deduce angular dependencies of different aberrations and to examine the possibility for spherical correction of a round lens by using multipoles.

Dependence of luminescence in five membered heterocyclic conducting polymers on molecular structure and temperature
View Description Hide DescriptionDependencies of photoluminescence in five membered heterocyclic conducting polymers on heteroatoms and temperature are studied. Luminescence intensity of poly(3‐alkylthiophene)s increases with temperature and luminescence intensity of poly(3‐alkylfuran)s is slightly enhanced with increasing temperature. However, luminescence intensity of poly(3‐hexylselenophene) is even suppressed with temperature. These difference of properties among heterocyclic conducting polymers with different heteroatoms can be interpreted in terms of the difference of steric hindrance effect between heteroatoms and alkyl side chain and the interchain interaction which influence on the dynamics of excited species and recombination.

Collision‐induced resonant amplification of electromagnetic waves by electrons in circular orbits
View Description Hide DescriptionElectrons moving in circular orbits and colliding with gas atoms interact with a circular electromagnetic mode. Applying the linearized Boltzmann equation, the known nonresonant‐stimulated bremsstrahlung and the near‐resonance Landau effect are obtained. We predict that resonant electrons moving with angular velocity equal to the azimuthal phase velocity of the electromagnetic wave can exchange energy with the wave if the momentum transfer cross section for an electron‐atom collision is velocity dependent. Amplification is obtained if the momentum transfer cross section has a positive slope.

Foil focusing of electron beams
View Description Hide DescriptionThin conducting foils focus charged particle beams through image charges induced on the foils. Such focusing has led to the suggestion that foils be used to transport intense, relativistic electron beams in high‐energy accelerators. This paper examines some of the limitations of foil focusing including sensitivity to the beam parameters, emittance growth from anharmonic focusing, and beam stability in multifoil transport. The analysis is based on a thin‐lens electrostatic treatment of paraxial beams.

Electromagnetic induction (eddy currents) in a conducting half‐space in the absence and presence of inhomogeneities: A new formalism
View Description Hide DescriptionTwo problems are studied. First, a new method is presented for calculating the electromagnetic field in two conjoined conducting half‐spaces in the presence of current sources in either or both half‐spaces. The method allows the two half‐spaces to differ in the conductivity, permeability, and permittivity. The full Maxwell’s equations are used; the quasistatic results may be derived as a particular limit. The method is unique in that it depends only on the solution of two variables; the components of the magnetic field B _{ z }, and the current J_{ z }, normal to the interface between the half‐spaces. The second problem involves the determination of the fields induced by a current source in one half‐space with an arbitrary 3D inhomogeneity in the other. New, coupled integral equations for the fields are written down strictly in terms of B _{ z }, J_{ z }, and the external current source. The same formalism, used to generate the new integral equations, is also shown to yield the standard dyadic volume integral representations. Finally, it is shown that the formalism is a useful way of deriving various asymptotic results. The weak scattering limit (the Born approximation) is derived as an example.

Radiation from a disk and loop of charge in a cylindrical pipe with multiple step changes in wall radius
View Description Hide DescriptionA theory is developed to model diffraction and Bremsstrahlung radiation from a loop and a disk of charge in a cylindrical pipe with multiple step changes in wall radius supporting all azimuthally symmetric transverse magnetic modes. The beam kinetics are assumed a p r i o r i. A correction in phase due to the abrupt change in beam velocity is incorporated at each step change in wall radius. A longitudinal coupling impedance based on energy and power considerations is employed. Loop charge radiation from cavity and collimator geometries is examined. By suitably choosing the loop charge radius, the energy backscattered in the beam tunnel problem can be minimized. The loading effects of the cavity onto the beam is sensitive to its length.

Second‐order nonlinearity of a novel diazo‐dye‐attached polymer
View Description Hide DescriptionSecond‐order nonlinear optical properties of a newly synthesized dye‐attached polymer (3R) were investigated. The dye has a conjugated diazo structure, and the βμ_{ g } (β: second‐order molecular hyperpolarizability, μ_{ g }: dipole moment in the ground state) is larger than five times that of a monoazo dye (2R). The second‐order nonlinear coefficient (χ^{(2)}) of a 3R polymer is also greater than that of a 2R polymer throughout the fundamental wavelength of 1.06 μm and between from 1.50 to 1.70 μm when the polymers are electrically poled. For both polymers, the χ^{(2)} dependence on the fundamental wavelength corresponds to the absorptionspectrum, which is explained by two‐photon resonance near the absorption maxima. The attainable χ^{(2)} of the polymers deviates from the theoretical linear relationship with the dye content when it is high. This indicates that the dipolar interaction increases as the dye content rises.

First design and characterization of HgZnTe optical waveguides
View Description Hide DescriptionInfrared waveguides have been made by isothermal evaporation diffusion of HgTe on a ZnTe substrate and characterized at 10.6 μm by m‐lines analysis. Refractive index profiles deduced from this analysis are correlated to the composition ones measured with a microprobe. As a result, we obtain the refractive index of the alloy as a function of the zinc concentration ranging from 0.2 to 1. Direct measurement of the substrate refractive index gives a value 2.60 to 2.65, results in slight disagreement with the previous data.

Field analysis of the Cerenkov doubling of infrared coherent radiation utilizing an organic crystal core bounded by a glass capillary
View Description Hide DescriptionWe present a mode field analysis of the second‐harmonic electromagnetic wave that radiates from a nonlinear core bounded by a dielectriccladding. With this analysis the ultimate performance of the organic crystal‐cored single‐mode optical fiberwaveguide as a guided‐wave frequency doubler is evaluated through the solution of nonlinear parametric equations derived from Maxwell’sequations under some assumptions. As a phase‐matching scheme we consider a Cerenkov approach because of advantages in actual device applications, in which the phase matching is achievable between the fundamental guided LP_{0} _{1} mode and the second‐harmonic radiation (leaky) mode. Calculated results for organic cores made of benzil, 4‐(N, N‐dimethyl‐amino)‐3‐acetamidonitrobenzen, 2‐methyl‐4‐nitroaniline, and 4’‐nitrobenzilidene‐3‐acetoamino‐4‐metxianiline provide useful data for designing an efficient fiber‐optic wavelength converter utilizing nonlinear parametric processes. A detailed comparison is made between results for infinite and finite cladding thicknesses.

On the saturation of Tb phosphors under cathode‐ray excitation. I. Excited‐state absorption in Tb‐activated phosphor powders
View Description Hide DescriptionOptical transitions between the ^{5} D _{4}excited state of the Tb^{3+} (4f)^{8} configuration and the crystal‐field split components of the (4f)^{7}(5d) configuration are observed using high‐resolution laser excitation of Tb‐doped powder samples at room temperature. Excited‐state absorption spectra of Tb^{3+} in YAG, YAGaG, Y_{2}SiO_{5}, and LaOBr are presented. Superimposed on the broadband excitation spectrum of these transitions we find the relatively narrow 4f→4f lines. We present a theoretical model for interpreting the 4f→5d transitions, which predicts a strict proportionality between the (4f)^{8} ^{5} D _{4}→(4f)^{7}(5d) and the (4f)^{8} ^{7} F _{6}→(4f)^{7}(5d) transitions. This model is used to estimate the optical‐absorption cross section for the former transitions. Although the terminating 4f levels lie at the same energy as the 5d bands, the 4f→4f transitions can be interpreted on the basis of the Judd‐Ofelt theory. We derived a method for calibration of the Tb^{3+} 4f→5d fluorescence‐excitation spectra from powder samples. For YAG:Tb, the resulting optical cross sections were confirmed by direct‐absorption measurements on a Tb^{3+} ‐doped epitaxial YAG layer. To our knowledge, this is the first time that the probabilities for excited‐state absorption to highly excited 5d and 4f states in Tb^{3+} have been obtained theoretically and experimentally from Tb‐doped powder materials.

On the saturation of Tb phosphors under cathode‐ray excitation. II. Upconversion processes in the excited‐activator bath
View Description Hide DescriptionA physical model based on resonant electric dipole interaction between excited activators is presented that may be used for gaining insight into the second‐order energy‐loss process in cathode‐ray‐irradiated Tb phosphors. It is shown that resonant up‐conversion of the ^{5} D _{ J }excitons (J=3,4) to highly excited 4f and 5d states may be of equal importance. The derivation of the rate constants for this second‐order energy‐loss process is given and experimental values for the ^{5} D _{4} ‐^{5} D _{4} and ^{5} D _{3} ‐^{5} D _{4} interaction are presented for Tb‐doped YAG, YAGaG, LaOBr, and Y_{2}SiO_{5}. The values depend on previously determined optical cross sections for excited‐state absorption. Based on this model we explain well‐known differences in saturation behavior between these Tb‐doped phosphors under cathode‐ray excitation.

Effect of magnetostatic field on the second‐order optical susceptibility of III‐V semiconductors
View Description Hide DescriptionAn analytical investigation of the application of a large magnetostatic field on the second‐order optical susceptibility χ^{(2)} in III‐V semiconductors like GaAs and InSb is reported. The model is based upon the parity indefiniteness of the electron wave functions in crystals lacking inversion symmetry. The generalized force and the electronic dipole moment operators are accordingly taken to be 2×2 matrices with all elements being finite. We have followed perturbation technique for the density matrix. The magnetostatic field renormalizes the transition frequency and sharpens the density of states. Both the resonant as well as nonresonant three‐wave parametric interactions have been discussed. Numerical estimates made for InSb crystal under resonant regime reveal considerable enhancement in the real part of χ^{(2)} even at moderately low magnetic field while the imaginary part exhibits a near saturation behavior. Under nonresonant laser excitation, both χ^{(2)} _{ r } and χ^{(2)} _{ i } rise very sharply with magnetic field for effective cyclotron frequency ω_{ c }≤ω_{0}−ω_{ g }, ω_{0} and ω_{ g } being the pump and crystal band‐gap frequencies, respectively. Quite interestingly, χ^{(2)} _{ r } and χ^{(2)} _{ i } decay almost exponentially to very low values at ω_{ c }>2(ω_{0}−ω_{ g }).

Evaluation of friction‐welded aluminum‐steel bonds using dispersive guided modes of a layered substrate
View Description Hide DescriptionIn nondestructive evaluation the inspection of bond quality is a very important problem. In this paper we suggest an experimental method based on dispersion curve measurements for evaluating the quality of the bond between a layer and a substrate bonded by the inertia‐friction welding process. The experimental results are in good agreement with theoretical calculations which show that the behavior of the lowest velocity modes is very sensitive to the interface conditions and to the quality of the bond.

Laser ultrasonic monitoring of ceramic sintering
View Description Hide DescriptionNoncontacting laser‐ultrasonic measurements of the sintering of ceramics in real‐time are described. Lasers are used for both generation and detection of ultrasonicwaves propagating through the material. A pulsed laser generates the ultrasonicwave from thermoelastic absorption at the material surface. Detection is accomplished by a confocal Fabry–Perot interferometer, which is insensitive to the speckle nature of the scattered light from the sample surface and can obtain measurements from samples with rough or diffusely reflecting surfaces. The densification of the ceramic sample is determined by changes in the bulk longitudinal wave velocity and the sample shrinkage.

Verification of the localized‐wave transmission effect
View Description Hide DescriptionAn acoustic array driven with a designed set of localized‐wave (LW) solutions of the scalar‐wave equation generates a robust, well‐behaved, transient pencil beam of ultrasound in water. The performance of the LW‐pulse‐driven array theoretically and experimentally exceeds a tenfold improvement over related continuous‐wave excitations of the same array.

Analysis of characteristic thermal transit times for time‐resolved infrared radiometry studies of multilayered coatings
View Description Hide DescriptionTime‐resolved infrared radiometry (TRIR) has been shown to be a valuable thermal characterization technique for the nondestructive evaluation of layered coatings. In this method an external step heating pulse is applied to the coating system and the resulting change in surface temperature is monitored as a function of time. Characteristic times and amplitudes can be ascribed to internal thermal reflections that return heat to the coating surface. A full description of the time dependence of the coating surface temperature can be obtained from these quantities. This paper describes a method for determining these characteristic times and amplitudes and shows their relationship to internal heat‐flow patterns. Uses and limitations of the method are discussed, and comparison of the theory with experimental TRIR results is presented.

Particle size statistics in dynamic fragmentation
View Description Hide DescriptionCondensed matter, when subjected to intense disrupting forces through impact or radiation deposition, will break up into a randomly distributed array of fragments. An earlier analysis of random fragmentation is extended to account for fragmentation in bodies which are finite in extent and for bodies within which the minimum fragment size is bounded. The statistical fragment size relations are compared with molecular dynamic simulations of dynamic fragmentation, with fragmentation caused by the high‐energy collision of nuclear particles, and with the distribution of galaxies in the universe which are assumed to be fragment debris from the primordial Big Bang.

Boundary‐condition refinement of the Child–Langmuir law for collisionless dc plasma sheaths
View Description Hide DescriptionAn exact solution to the problem of collisionless, space‐charge‐limited flow of cold ions across a one‐dimensional (planar) dcplasma sheath of negligible electron density is derived for general values of the presheath ion velocity v _{0} and electric fieldE _{0}. For a given ion current densityJ and sheath thickness d, the exact solution reduces to the classical Child–Langmuir model in the case that v _{0}=0 and E _{0}=0. When either v _{0} or E _{0} is sufficiently large, however, the exact solution may differ appreciably from the Child–Langmuir law. The existence of a closed‐form expression for the spatial variation of the sheath potential is shown to be contingent upon the satisfaction of a simple inequality relating v _{0} and E _{0} to J. When v _{0} obeys the Bohm criterion and the magnitude of E _{0} suggests that the Bohm energy is acquired over a distance not less than one Debye length, this inequality is indeed satisfied.

Electron‐beam probe measurements of electric fields in rf discharges
View Description Hide DescriptionAn electron‐beam probe has been used to make time‐ and space‐resolved measurements of the electric field in a parallel plate rf discharge.Measurements were taken at a time resolution of 5 ns and a field resolution ±1 V/cm at increments of 0.32 cm from the powered electrode. The detection method provides the weighted average of the electric field along the beam trajectory. Measurements of fields less than 20 V/cm were made throughout the entire discharge. Data were obtained for 13.6‐MHz argon discharges at 2.3 and 20 mTorr, and at rf voltage amplitudes of 100 and 600 V at each pressure. The data for the 2.3‐mTorr, 600‐V case show (1) that a propagating double layer forms during the collapse of the sheath, (2) that the field near the electrode points in toward the plasma at the extreme collapse of the sheath, (3) that the collapse and expansion of the sheath proceeds asymmetrically for measurable field values, and (4) that the trajectory averaged electric field in the plasma has an anomalous phase shift and magnitude. Similar phenomena are observed for the remaining three discharge cases.