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Volume 70, Issue 8, 15 October 1991

Functional minimization and one‐dimensional profile inversion
View Description Hide DescriptionModern techniques of functional minimization are applied to the one‐dimensional profile inversion problem. The procedure is applied to profiles that can be represented as a series of linear ramps. A band‐limited knowledge of the transmission function is used to determine the parameters that describe the profile. It is found that simple profiles can be readily determined. For more involved profiles, the method of simulated annealing proves to be helpful in obtaining the correct profile.

The distribution of fluctuation measurements within the random‐phase model
View Description Hide DescriptionA variety of diagnostics measure fluctuating quantities at a small number of locations. A common method to estimate the wave‐number spectrum S(k) at a given frequency is to make many measurements of the ‘‘local’’ wave number k _{ l }, which is the phase difference between two locations divided by their separation. The random‐phase model allows the synthesis of a typical signal from a given S(k). We apply local wave‐number analysis to such synthetic signals and show that, in the limit of small separation, the power‐weighted mean of k _{ l } accurately reflects the mean of S(k), and the width of the distribution is exactly ■ times smaller than the width of S(k). We also show that no information on the shape of S(k) exists in the measurements. Finally, we generalize these results to finite separations, finite measurement volumes, and any number of locations.

Two‐point estimates of the spectral density function with finite separation and volume
View Description Hide DescriptionThe spatial and temporal variation of a fluctuating quantity can often be described with sufficient accuracy as a sum of independent modes, whose powers are given by a function S(k) for each frequency. Many diagnostics are restricted to making measurements at two points, so that a determination of S(k) by spatialFourier transformation is not possible. Nevertheless, in the limit of point measurements with infinitesimal separation, the mean wave number k̄ and the rms deviation σ about the mean can be exactly determined by repeated measurements of the phase difference between the tips. If the separation is finite, the method can be extended in such a way that the correct results are obtained for any separation as long as S(k) is Gaussian. For other spectral shapes, the error in the measurement of k̄ may be of the order of σ, and the fractional error in the measurement of σ may be substantial. A finite measurement volume reduces the sensitivity to short wavelength modes. Under certain assumptions, the measured values can be adjusted to yield better estimates of k̄ and σ.

Microscopic and macroscopic effects of electron irradiation on ferroelectric poly(vinylidene fluoride‐TrFe) copolymers
View Description Hide DescriptionThe effect of electron irradiation on ferroelectric poly(vinylidene‐trifluoroethylene) copolymers has been studied from both microscopic and macroscopic points of view. Microscopically, it is found by x‐ray photoemissionspectroscopyanalysis and ultraviolet absorption that the irradiation damaging is mainly through dehydrofluorination and leads to double‐bond production and crosslinking. On the other hand, dielectricpermittivity, internal friction, x‐ray diffraction, and differential scanning calorimetry experiments show that both the ferroelectric transition temperature T _{ c } and the melting temperature T _{ m } are lowered under irradiation. These various experimental features are consistently analyzed taking into account three main mechanisms resulting from the electron irradiation: (i) reduction of the crystallite mean size, (ii) changes in the internal pressure, and (iii) reduction of the dipolar energy.

Small‐hole coupling of radiation into a near‐field probe
View Description Hide DescriptionThe coupling of electromagnetic energy into a conical waveguide through an electrically small hole near the cone tip is considered. This problem is relevant to near‐field microscopy, where tapered metallic probes are used to either illuminate, or collect light from, the structure under investigation. The situation considered in detail here is simplified by assuming that the aperture is surrounded by a planar baffle, which approximates the flat ends of fabricated probes. An established formulation for small‐hole coupling into waveguides is used and the waveguide itself taken to be a truncated, perfectly conducting cone. As expected, the values obtained for the energy transmitted through an aperture with a diameter significantly less than that of the radiation being used are small. However, it is also found that the size of the waveguide at the hole position strongly affects the percentage of the incident energy transmitted.

A dc high‐current low‐energy electron beam gun
View Description Hide DescriptionA dc high‐current and low‐energy electron beam gun has been developed. The maximum electron beam current is 63 A for an accelerating energy of 140 eV. The maximum ratio of the beam current to the discharge current is 78%. The ion current, which is extracted from the helium plasma produced by the electron beam, is 12.3 A. This value corresponds to the current density of about 7 A/cm^{2}, which is the highest value among the ion sources in steady operation. The electron density of the plasma is estimated from the ion saturation current to be about 4.6×10^{13} cm^{−3}, which corresponds to the degree of ionization of 21%. This gun will open the way for many electron beam applications.

Backscattering of an electromagnetic missile by a perfectly conducting sphere
View Description Hide DescriptionIt has been shown recently that when an electromagnetic (EM) missile with an energy decreasing as r ^{−ε} is incident upon a perfectly conducting plate, the reflected energy will decrease as r ^{−ε} with the same exponent as the EM missile. The question of studying the backscattering properties of an EM missile by other objects is then left open to further investigation. In this paper we make a study of backscattering of an EM missile with an energy decreasing as r ^{−ε} by a perfectly conducting sphere, and the analysis indicates that the rate of energy decay for the backscattered field far from the sphere is proportional to r ^{−(2+ε)} (0<ε<2), which is faster than r ^{−ε} for plate scattering but slower than the usual energy decay r ^{−4} for a three‐dimensional backscattered field.

Laser‐induced damage threshold measurements of optical dielectric coatings at λ=1.06 μm
View Description Hide DescriptionThe laser‐induced damage thresholds for λ=1.06 μm of commercially available (produced at Institute of Optics) dielectricoptical coatings, both antireflective and high reflectance, have been determined. The dependence of the optical coatings stability on design and selection of materials has been investigated. An improvement of the coatings durability by using nonquarterwave layers in addition to the basic design of the mirrors has been obtained. The choice of the coatingmaterials is also discussed.

Short‐optical‐pulse generation from gain‐switched laser diodes with two oscillation modes
View Description Hide DescriptionThe effect of two‐wavelength oscillation for short‐optical‐pulse generation in laser diodes by sinusoidal current modulation has been investigated using a rate equation analysis. A high peak power and short pulse without a tail can be generated at the shorter wavelength λ_{2} with the help of carrier damping through carrier‐photon conversion at the longer wavelength λ_{1}. This can be obtained provided that the cw threshold current for λ_{1} is lower than that for λ_{2} and the gain g _{2} larger than g _{1} at the high carrier excitation levels that occur under the conditions of gain switching.

Crystal structures and light absorption spectra of 1,4‐dithioketo‐3,6‐diphenyl‐pyrrolo‐[3,4‐c]‐pyrrole
View Description Hide Description1,4‐dithioketo‐3,6‐diphenyl‐pyrrolo‐[3,4‐c]‐pyrrole, which is a good charge generation material for a near‐infrared electrophotographic photoreceptor, has three polymorphs called the I, II, and III forms. The I and II forms are transformed into the III form after having been kept in suitable organic solvents. On the other hand, the III form is changed to the I and/or II forms by heat treatment above 320 °C. Among the three polymorphs, only the highly ordered III form shows the necessary and characteristic absorption in the near‐infrared region.

Narrow linewidth gain measurements in KrF and ArF excimer amplifiers pumped longitudinally by high‐power electrons
View Description Hide DescriptionSingle‐pulse KrF and ArF gain measurements have been conducted with an excimer amplifier longitudinally pumped by a high‐power (∼5‐MW/cm^{3}deposition)electron beam. This amplifier has preserved the narrow linewidth (∼10 GHz) exhibited by the probe laser beam generated by a grating‐tuned, discharge pumped excimer laser. Single‐pass gain was measured at 248.45 nm, the peak of the KrF laser gain profile, for a laser pulse with full width half maximum (FWHM) of 20 ns. Analysis of the gain data by a modified Rigrod steady‐state formulation yielded values for the small‐signal gain, the nonsaturable absorption, and saturation intensity of g _{0} = 12.6%/cm, α∼0.45%/cm, and I _{ s } = 4.1 MW/cm^{2}, respectively, for a 750‐Torr laser mix. The corresponding gain peak measurement for an ArF beam at 193.31 nm with FWHM of 15 ns produced g _{0} = 12.1%/cm, α∼0.70%/cm, and I _{ s } = 6.7 MW/cm^{2} for a 963‐Torr laser mix with the same stopping power as the KrF mix. Measurement of gain at 193.68 nm, well away from gain peak, resulted in g _{0}= 10.8%/cm, α∼0.70%/cm, and I _{ s } = 7.9 MW/cm^{2} for the same ArF mixture. Several amplified spontaneous emission and oscillator measurements have also been performed. Indications of laser gain saturation at high‐power electron‐beam deposition have been deduced.

The effect of shallow traps on the dark storage of photorefractive grating in Bi_{12}SiO_{20}
View Description Hide DescriptionDark decay of photorefractive gratings and persistent photocurrents in Bi_{12}SiO_{20} are interpreted using a model of the photorefractive effect which includes shallow traps as well as deep traps. The model explains the grating spacing dependence of the coasting and initial decay rate quite well. The intensity dependence of the initial decay rate and coasting, however, suggest large optical absorption contradicting the results of direct measurements. It is suggested that the recombination of holes to the shallow traps as a possible explanation of the discrepancy. It is demonstrated, for the first time to our knowledge, that the photorefractive grating dark decay experiments can be used to determine the densities of ionized donors in dark (N _{ A }) in addition to the effective trap density (N _{ E }). We also report, for the first time to our knowledge, the observation of oscillatory dark decays of photorefractive grating in three Bi_{12}SiO_{20} crystals and explain them in terms of the dynamics of coupled chargegratings.

Spectroscopic properties, energy transfer, and laser operation of pulsed holmium lasers
View Description Hide DescriptionSpectroscopic studies of Er:Tm:Ho:LiYF_{4} (YLF) and Cr:Tm:Ho:Y_{3}Al_{5}O_{12}(YAG) crystals were performed, with a detailed analysis of the absorption spectra of Er:Tm:Ho:YLF at 4 K. The dynamics of energy transfer Cr^{3+}→Tm^{3+}→Ho^{3+} (in YAG) and Tm^{3+}→Ho^{3+} (in YAG and YLF) were studied utilizing laser‐induced fluorescence. Pulsed, free‐running laser performance of a freon‐cooled Er:Tm:Ho:YLF at −10 and −50 °C, at different current densities with maximum laser energies of 1.5 and 2.25 J/pulse, respectively, was performed.

A numerical technique to describe acoustical scattering and propagation from an object in a waveguide
View Description Hide DescriptionThe treatment of scattering from submerged objects in an unbounded environment is of considerable interest to both the academic and technological communities. Several approaches have yielded results for different classes of problems and have proven manageable for the free‐environment case. Scattering in a confined environment is difficult to express in a form useful for calculation because the effects from the scattered object couple with the boundary effects. The purpose of this work is to propose a numerical scheme that will adequately describe scattering from realistic objects in a confined environment. Some realistic objects of interest are elongated spheroids and cylinders with rounded end caps. Boundary conditions of interest range from those associated with rigid objects to those associated with elastic shells. The object in a waveguide problem is examined in approximate numerical schemes rather than with attempts at exact solutions. The starting point will be the solution of the incident field in terms of normal modes. Next, transition matrix is used that relates the incident field to the scattered field. The transition matrix, which is obtained from Waterman’s extended boundary condition method, does not account for boundaries other than that of the object. The solution is then coupled with a waveguide solution to satisfy all boundary conditions. The method, an application of Huygens’ principle, couples the solutions and leads to a manageable solution of the problem. This method also satisfies all appropriate boundary conditions and yields a continuous solution throughout space. Details and examples of this method are presented.

Propagation of ultrasonic Lamb waves in piezoelectric plates
View Description Hide DescriptionThe propagation of the lowest‐order symmetric (S _{0}) and antisymmetric (A _{0}) Lamb wave modes in a piezoelectric plate is investigated both theoretically as well as experimentally. The characteristics of the modes and their relation to the surface acoustic wave is modified by electrical boundary conditions on the plate surfaces. It is found that when both surfaces are either metallized or unmetallized, the surface acoustic wave is obtained by a linear superposition of the A _{0} and S _{0} modes. On the other hand, if only one surface is metallized, then the surface acoustic wave is equivalent to just one of modes (either the A _{0} or S _{0} mode, depending on which surface is metallized). The beating phenomenon, whereby waveenergy launched on one surface transfers periodically back and forth between opposite plate surfaces, is present when both surfaces are either metallized or unmetallized, but is absent if only one surface is metallized. Experimental measurements performed on Lamb wave devices fabricated on Y‐cut, Z‐propagating lithium niobate plates are found to be in good agreement with theoretical calculations.

Influence of viscosity variation on salt‐finger instability in a fluid layer, a porous layer, and their superposition
View Description Hide DescriptionWe consider the effect of temperature‐dependent viscosity on the onset of buoyancy‐driven salt‐finger convection (stratifications of salt and temperature being destabilizing and stabilizing, respectively) in a horizontal fluid layer, a horizontal layer of a stratified porous medium, and in a horizontal fluid layer overlying a saturated porous medium. It is found that the viscosity variation affects the stability characteristics through two mechanisms. One is the formation of a relatively viscous sublayer which leads to multicellular convection and stabilizing; the other is the decrease of viscosity which favors the onset of convection. In a horizontal porous layer, the destabilizing mechanism prevails so that the motionless state becomes less stable as γ=ln(ν_{max}/ν_{min}), where ν is kinematic viscosity of the fluid, increases, and a general relation between critical solute (R ^{ c } _{ sm }) and thermal (R _{ m }) Rayleigh numbers is found as R ^{ c } _{ sm } = R _{ m } + 4π^{2} H(γ), where H(γ) is determined by curve fitting on the basis of calculated results.
In a horizontal fluid layer, the first mechanism predominates the convection when γ<6.86 and the second mechanism prevails when γ≳6.86; the motionless state is most stable at approximately γ=6.86. Another general relation between critical solute (R ^{ c } _{ s }) and thermal (R) Rayleigh numbers is also determined based on the calculated results as R ^{ c } _{ s } = R + 1070.76 G(γ). For superposed fluid and porous configuration, the stability characteristics become more complex and depend on the variations of γ,ζ (ratio of fluid layer depth to porous layer depth), and R _{ m }, and so on. In general, the unicellular convection occurs for ζ=0.1 and the multicellular convection is observed for ζ≥ (R18)0.2; for R _{ m } = 1, the stabilizing mechanism and destabilizing mechanism compete with each other; for R _{ m } = 50, nevertheless, the stabilizing mechanism prevails so that increasing γ leads to stabilization; the fluid layer dominates the superposed system by convection at large γ for all ζ considered. The current results would provide valuable information for understanding the double‐diffusive convection during the directional solidification of binary alloys.

Extended two‐dimensional analysis of electrical breakdown between a wire and a plane
View Description Hide DescriptionThe formation of a discharge between a wire and a plane has been simulated numerically through the development of large electron and positive ion number densities. When the number densities grow sufficiently large and equal a new region within the computational model is formed, within which the governing equations of the quasi‐neutral region are solved for the common ion and electron number density and electric potential. Results for the temporal development of the quasi‐neutral region, radial profiles of charged particle number density, electric potential, and electric field strength from discharge initiation to program termination are described. The quasi‐neutral region is shown to develop first off of the discharge axis, above the wire‐to‐plane gap. Near the quasi‐neutral region the electric field strength and electric potential are highly distorted and within the quasi‐neutral region are greatly diminished.

A model of a dc silane discharge
View Description Hide DescriptionThis paper describes a novel approach to modeling chemically active dc discharges, and its application to silane. An appropriate electric field was determined from a combination of experimental results and classical dc discharge theory. Utilizing this electric field, a kinetic description of the electron motion was used to calculate the ionization rate and the electron distribution function throughout the discharge. From the calculated rate of ionization and the assumed electric field and allowing for chemical reactions, steady‐state fluxes of ions to the anode were calculated. These results compared favorably to the experimental results of Weakleim et al. [J. Vac. Sci. Technol. A 1, 29 (1987)]. A proposed model for the observed variations in the fractional ion currents is given.

Self‐consistent modeling of surface wave produced discharges at low pressures
View Description Hide DescriptionA self‐consistent theory of a low‐pressure gas discharge sustained by a surface wave (SW) is presented which provides a complete description of the plasma density (n _{ e }) and SW‐field distribution both in the radial (r) and the axial (z) directions. The theory is based on a complete set of equations including Maxwell’sequations and the boundary conditions for the SW‐field, the electron Boltzmann equation which yields local collisional and transport data versus the SW‐electric field E, and the continuity and momentum transfer equations for the electrons and the ions. For given operating frequency, gas density, setup dimensions and total incident power P _{ i }(0), the theory enables the determination of: (i) the SW‐dispersion relation; (ii) n _{ e }(r,z) and E(r,z); (iii) P _{ i }(z); and (iv) θ(z), the radially averaged mean absorbed power per electron. It is shown that Ē(z), the radially averaged field in the plasma, and θ(z) are practically constant along z, in spite of the fact that P _{ i }(z) steadily decreases. Comparison with experiment is made for SW discharges in Ar operated at the frequencies of 433 MHz and 2.45 GHz.

Measurement of breakdown voltages and V‐I characteristics of sodium, potassium, cadmium, and zinc vapors using coaxial cylindrical electrodes
View Description Hide DescriptionExperimental results of breakdown voltages and V‐Icharacteristicsmeasured for the first time using coaxial cylindrical electrodes over the pressure range 0.006–0.72 kPa in sodium,potassium,cadmium, and zinc vapors are reported. The breakdown voltages in all the vapors are found to obey Paschen’s Law. The breakdown voltages in cadmium and zinc are substantially higher than those in alkaline sodium and potassium, directly in relation to their ionization potentials. The investigations also reveal that the V‐Icharacteristics are pressure dependent and do not exhibit any negative current growth.