Radial Phase Shift Research Articles

Generation of optical vortices by flat-topped beam diffracted with a radial phase shift spiral zone plate

Generation of optical vortices by flat-topped beam diffracted with a radial phase shift spiral zone plate

Comprehensive focusing analysis of bi-segment spiral zone plate in producing a variety of structured light beams

This study introduces and demonstrates the diffractive feature of a bi-segment spiral zone plate, so that each segment has its own width, topological charge, and radial phase shift. We show that the focusing behavior of this element depends strongly on these parameters. We demonstrate how these features can handle the focused intensity and structure of an incident plane beam. A variety of beam shapes and structures are generated at the focal plane. Theoretical and simulation results are verified by the corresponding experiments.

Verification and validation of integrated simulation of energetic particles in fusion plasmas

This paper reports verification and validation of linear simulations of Alfvén eigenmodes in the current ramp phase of DIII-D L-mode discharge #159243 using gyrokinetic, gyrokinetic-MHD hybrid, and eigenvalue codes. Using a classical fast ion profile, all simulation codes find that reversed shear Alfvén eigenmodes (RSAE) are the dominant instability. The real frequencies from all codes have a coefficient of variation of less than 5% for the most unstable modes with toroidal mode number n = 4 and 5. The simulated RSAE frequencies agree with experimental measurements if the minimum safety factor is adjusted, within experimental errors. The simulated growth rates exhibit greater variation, and simulations find that pressure gradients of thermal plasmas make a significant contribution to the growth rates. Mode structures of the dominant modes agree well among all codes. Moreover, using a calculated fast ion profile that takes into account the diffusion by multiple unstable modes, a toroidal Alfvén eigenmode (TAE) with n = 6 is found to be unstable in the outer edge, consistent with the experimental observations. Variations of the real frequencies and growth rates of the TAE are slightly larger than those of the RSAE. Finally, electron temperature fluctuations and radial phase shifts from simulations show no significant differences with the experimental data for the strong n = 4 RSAE, but significant differences for the weak n = 6 TAE. The verification and validation for the linear Alfvén eigenmodes is the first step to develop an integrated simulation of energetic particles confinement in burning plasmas incorporating multiple physical processes.

Diffraction by a radial phase modulated spiral zone plate of abruptly autofocusing beams generated with multiple Bessel-like beams

In this paper, we present the generation of optical vortices using an abruptly autofocusing beam that is combined from multiple Bessel-like beams, diffracted by a radial phase shift modulated spiral zone plate (RSSZP). The analytical formula for the diffracted wave field amplitude of the produced beam is derived based on the Fresnel diffraction integral formula. The results show that the intensity distributions of the produced output beam in radial direction are determined by the initial beam parameters and the RSSZP parameters, such as shifting parameter and topological charge. The present work gives also the diffraction by a RSSZP of a fundamental Gaussian beam which is deduced as a particular case in this investigation.

Rotating waves in simple scalar excitable media: approximations and numerical solutions.

Rotating waves, in a two-dimensional annular region, are studied using a number of semi-analytical methods. For our kinetics, we use a simple one-variable phase model that arises as the normal form in the transition between excitability and oscillation at a saddle-node invariant circle (SNIC) bifurcation. After deriving asymptotic expressions for the scalar dispersion relationship, we use this to compare the approximations to a direct numerical simulation of the governing nonlinear partial differential equation. All of the approximation methods are based on writing the full solution [Formula: see text] as [Formula: see text] + "perturbation" terms where V is some function and [Formula: see text] is the radial phase shift. Finding an expression for the radial phase shift is the main aim of this paper. It is found that the total twist of the spiral is not a monotone function of the excitability. The largest twist occurs in the vicinity of the transition from excitable to oscillatory behavior.

Concentration tuned bandgap and corresponding nonlinear refractive index dispersion in Ga-Ge-Se nanocolloids

Solution-processing of chalcogenide glass materials has attracted attention for the fabrication of photonic devices. We have carried out linear and nonlinear optical studies on Ga9Ge27Se64 nanocolloidal solutions with varying concentrations and witnessed the opportunity for engineering the optical properties of the material by simply changing the concentration of solute in the solvent. An enhancement of bandgap, deterioration, and blue shift in the band tail states with decrease in concentration were observed from the absorption spectra. Open and closed aperture Z-scan studies reveal tunability of nonlinear absorption coefficient (β) and nonlinear refractive index (n2). As the bandgap approaches the one photon absorption edge, the material shows very large negative nonlinear refraction and also “two step photon absorption” due to the presence of intermediate tail states. The radial phase shift (Δφ0) induced after travelling through the nanocolloidal solution with respect to bandgap is plotted and we predict that the variation of Δφ0 is governed by a quadratic polynomial of Eg.

Rossby waves and α-effect

Rossby waves drifting in the azimuthal direction are a common feature at the onset of thermal convective instability in a rapidly rotating spherical shell. They can also result from the destabilization of a Stewartson shear layer produced by differential rotation as expected in the liquid sodium experiment (Derviche Tourner Sodium) working in Grenoble, France. A usual way to explain why Rossby waves can contribute to the dynamo process goes back to Busse [A model of the Geodynamo. Geophys. J. R. Astron. Soc. 1975, 42, 437–459]. In his picture, the flow geometry is a cylindrical array of parallel rolls aligned with the rotation axis. The axial flow component (parallel to the rotation axis) is maximum in the middle of each roll and changes its sign from one roll to the next (case (i)). It is produced by the Ekman pumping at the fluid containing shell boundary. The corresponding dynamo mechanism can be explained in terms of an α-tensor with non-zero diagonal coefficients. It corresponds to the heuristic picture given by Busse (1975). In rapidly rotating objects like the Earth's core (or in a fast rotating experiment), Rossby waves occur in the limit of small Ekman number (). In that case, the main source of the axial flow component is not the Ekman pumping but rather the “geometrical slope effect” due to the spherical shape of the fluid containing shell. This implies that the axial flow component is maximum at the borders of the rolls and not at the centres (case (ii)). If assumed to be stationary, such rolls would lead to zero coefficients on the diagonal of the α-tensor, making the dynamo probably less efficient if possible at all. Actually, the rolls are drifting as a wave, and we show that this drift implies non-zero coefficients on the diagonal of the α-tensor. These new coefficients are, in essence, very different from the ones obtained in case (i) and cannot be interpreted in terms of the heuristic picture of Busse (1975). They were interpreted as higher-order effects in Busse (1975). In addition, we consider rolls not only drifting but also having an arbitrary radial phase shift as expected in real objects.

Observation of radial phase shift of the edge harmonic oscillation in the edge transport barrier discharges in the Compact Helical System using beam emission spectroscopy

In the present study, a coherent density fluctuation similar to the edge harmonic oscillation (EHO) in tokamaks was observed in the edge transport barrier discharge in the Compact Helical System (CHS) [K. Matsuoka et al., Plasma Physics and Controlled Nuclear Fusion Research, 1988 (International Atomic Energy Agency, Vienna, 1989), Vol. 2, pp. 441] using beam emission spectroscopy (BES). The fluctuation had both fundamental (f=4.5 kHz) and second-harmonic (2f=9 kHz) frequencies. EHO in CHS had a peak amplitude at approximately ρ=0.95. The mode has a continuous phase shift in the radial direction. If this is interpreted as the radial propagation, the mode propagates in the outer radial direction at an apparent phase velocity of several hundreds of meters per second, which is a characteristic similar to the radial phase shift of EHO in tokamaks.

Calculation of matrix elements for mixed extreme-ultraviolet–infrared two-photonabove-threshold ionization of argon

We present calculations of two-photon matrix elements for two-photon two-colourionization. We focus on ionization processes that use one infrared and oneextreme-ultraviolet photon. The paper describes a novel algorithm used for thecalculation of radial matrix elements, and also of radial phase shifts of continuumstates.

Low-frequency oscillation in magnetized plasmas with radial electron density and temperature gradients in opposite directions

Low-frequency electron temperature and density oscillations in a cylindrical magnetoplasma are analysed numerically. Special attention is attached to the case of electron temperature and density gradients of opposite sign, which appear in RF-ring discharges. To guarantee best possible description of experimental findings, the analysis includes ambipolar electric fields, ion inertia and radial phase shifts of the perturbed plasma quantities, as a consequence of which spiral structures appear. The formalism is restricted neither to magnetized nor to cold ions.

Fine structure of the intracochlear potential field. II. Tone-evoked waveforms and cochlear microphonics.

1. Extracellular evoked potentials to low-frequency pure-tone stimuli were recorded in the second cochlear turn of the anesthetized guinea pig. Spatial variations of the field potentials were characterized by advancing and withdrawing micropipettes along radial tracks in scala tympani (ST) and scala vestibuli (SV). Compound action potentials (CAPs) and cochlear microphonics (CM) are the major components of the evoked responses to 50- to 1,600- Hz stimuli. The relative contribution of CM and CAP to the evoked potentials varies with cochlear scala and location within the scala as well as with stimulus frequency and intensity. 2. In the 50- to 800-Hz frequency range, the largest CM in the second turn was recorded from scala media (SM). Below 500 Hz the CM in SV is larger than in ST, whereas above 500 Hz a larger CM is present in ST. The CM in SV is nearly in phase with the CM in SM, although it is smaller by a factor of two to four. The CM diminishes by another factor of two over a 100-microns depth range as an electrode is withdrawn out of SV through the spiral ligament. While the electrode is in SV or in the fluid outside the spiral ligament, the CM magnitude does not change by greater than 10%. The shape of the radial CM magnitude profile along tracks in SV shows little or no dependence on intensity in the 65- to 105-dB SPL range or on frequency in the 50- to 800-Hz range. 3. Unlike the CM profiles in SV, the shape of the CM magnitude and phase profiles in ST are a complex function of frequency and intensity. Below 500 Hz, the CM goes through a 140-180 degree radial phase shift over a 100-microns distance near the spiral ligament bordering ST. Concomitant with the large radial phase shift is a local minimum of the CM magnitude. The location of this "virtual ground point" can shift radially by as much as 100 microns over a 30-dB intensity range. The CM magnitude deep in ST is always larger than the CM outside the spiral ligament bordering ST. However, the ratio of the CM magnitudes at these two locations can vary from 0.1 to 0.8, the ratio tending to increase with intensity in the 200- to 800-Hz range.(ABSTRACT TRUNCATED AT 400 WORDS)

Elastic Yield Zone Around an Interfacial Crack Tip

A closed-form approximate solution for a small-scale yielding (SSY) plastic zone around a planar interfacial crack tip, occurring between two dissimilar ideally-bonded elastic half spaces, is obtained by equating the elastically-calculated Mises equivalent stress with the material yield strength, σys. The dimensionless parameter ζ(θ), which is defined as ζ(θ) = ∠K + εlnrp (θ), where ∠K is the phase angle of the complex stress intensity factor K, ε is the bimaterial constant, and rp (θ), is the polar representation of the plastic zone radius, naturally arises. The SSY interfacial load angle (ILPA), defined as ζ0 = ∠K + εln(KK/σ2ysπcosh2(πε)), leads to periodic zone growth. The ILPA characterizes the overall applied load phase by combining the oscillatory radial phase shift, attributable to the increase in zone size due to increased loading, with ∠K. At a particular angle θ0 from the uncracked interface, the plastic zone radius thus calculated is independent of ∠K, proportional to KK, and has no oscillatory radial phase dependence. The derived plastic zone expression reproduces the shape characteristics, and it modestly reproduces the zone size when compared with solutions for an elastic/perfectly-plastic solid adjoint to an elastic solid. As the strain-hardening exponent in the plastically deforming medium decreases, agreement between the approximation and various accurate numerical solutions improves. In the limiting case when ε = 0, the well-known homogeneous elastic solutions for pure Mode I and Mode II are recovered, as well as all possible mixed-mode combinations. Approximate validity conditions for the existence of Williams-type asymptotic fields (traction-free crack faces) are presented.

Experimental investigation of a whistler parametric instability

A parametric decay of a whistler wave into an upper sideband whistler and a corresponding low frequency wave, both with harmonic structure, is investigated. The decay has been observed over a wide range of pump frequencies, 0.45<or= omega / omega ce<or=0.95 and has a threshold of approximately 1 W. The waves satisfy the energy conservation condition omega o= omega u+ omega l, where the subscripts o, u and l denote the pump, the upper sideband, and the negative energy low frequency waves, respectively. Wavelengths and directions of propagation of the pump and upper sideband are measured and found to be nearly equal and in the same direction. As implied by the wave momentum conservation equation, ko=ku+kl, the low frequency wave has no measurable axial phase shift, nor does it have a measurable radial phase shift over the central part of the column.