Theoretical Phase Shifts Research Articles

Diversity of states in a chiral magnet nanocylinder

The diversity of three-dimensional magnetic states in a FeGe nanocylinder is studied using micromagnetic simulations and off-axis electron holography in the transmission electron microscope. In particular, we report the observation of a dipole string—a spin texture composed of two coupled Bloch points—which becomes stable under geometrical confinement. Quantitative agreement is obtained between experimental and theoretical phase shift images by taking into account the presence of a damaged layer on the surface of the nanocylinder. The theoretical model is based on the assumption that the damaged surface layer, which results from focused ion beam milling during sample preparation, has similar magnetic properties to those of an amorphous FeGe alloy. The results highlight the importance of considering the magnetic properties of the surface layers of such nanoscale samples, which influence their magnetic states.

Investigation on phase-modulation characteristics and transmission of the liquid crystal device under continuous-wave laser irradiation

Liquid crystal devices (LCDs) are widely used in several applications involving high-power lasers, such as laser processing, laser shaping, laser communication, laser radar and so on. Investigation on the performance of the LCDs working in high-power laser has always been of concern. In this study, a modified nearly common-path interferometry technique is proposed to investigate the phase modulation characteristics of the LCD irradiated by 1064 nm continuous-wave (CW) laser with Gaussian beam profile and an effective area of 0.1 cm2. In addition, the temperature rise of the LCD induced by laser irradiation was synchronously measured with an infrared thermal imager. A quantitative and dynamic investigation of the relation between the thermal effect caused by the laser and the phase-modulation variation is reported. Experimental results showed that the trend of temperature increase of the LCD was similar to that of phase shift variation. The theoretical phase shift calculated using the temperature-dependent LC refractive index coincided with the experimental results. This indicated that the refractive index change induced by temperature was the main reason for the phase-modulation variation of the LCD under laser irradiation. When the laser power was further increased, interference fringe distortion appeared, and morphological changes in the LC were observed. This implied that the laser-induced temperature rise had reached the clearing point of the LC and that the LCD was inactive. The temperature simulation along the laser incidence direction implied that, under the irradiation CW laser, indium tin oxide (ITO) layer absorbs laser energy, resulting in a temperature rise and a small temperature gradient between the ITO, polyimide (PI) and LC layers. The rising temperature is too low to induced damage of ITO layer and PI layer, but influences the refractive index of the LC. Compared with other layers of the LCD, the LC material will fail first when the irradiated laser power is further risen. The transmission variation of an LCD induced by laser irradiation was found. Possibly owing to the refractive index change of the LC as well as the multilayer film structure of the LCD, there seemed to be a cyclical transmission variation.

Elastic Scattering of Slow Electrons by Noble Gases—The Effective Range Theory and the Rigid Sphere Model

We report on an extensive semi-empirical analysis of scattering cross-sections for electron elastic collision with noble gases via the Markov Chain Monte Carlo-Modified Effective Range Theory (MCMC−MERT). In this approach, the contribution of the long-range polarization potential (∼r−4) to the scattering phase shifts is precisely expressed, while the effect of the complex short-range interaction is modeled by simple quadratic expression (the so-called effective range expansion with several adjustable parameters). Additionally, we test a simple potential model of a rigid sphere combined with r−4 interaction. Both models, the MERT and the rigid sphere are based on the analytical properties of Mathieu functions, i.e., the solutions of radial Schrödinger equation with pure polarization potential. However, in contrast to MERT, the rigid sphere model depends entirely upon one adjustable parameter—the radius of a hard-core. The model’s validity is assessed by a comparative study against numerous experimental cross-sections and theoretical phase shifts. We show that this simple approach can successfully describe the electron elastic collisions with helium and neon for energies below 1 eV. The purpose of the present analysis is to give insight into the relations between the parameters of both models (that translate into the cross-sections in the very low energy range) and some “macroscopic” features of atoms such as the polarizability and atomic “radii”.

Phase Shift-Cavity Ring Down Spectroscopy in Linear and Active Fiber Cavities for Sensing Applications at 1550 nm

Liquid phase sensing applications at 1550 nm are highly desirable due to widely available off-the-shelf components. Generally, liquids at 1550 nm induce a high absorption loss that limits the overall sensor’s sensitivity and detection limit. One solution is to use an active fiber loop in conjunction with cavity ring down spectroscopy to overcome these absorption losses. However, the amplifier inside the fiber loop suffers from inherent gain fluctuations that limit the sensing system’s overall performance. Here, we provide a novel sensor using the wavelength-scanned phase shift-cavity ring down spectroscopy (PS-CRDS) in conjunction with a linear active fiber cavity that potentially offers a more sensitive solution than traditional fiber loop sensors. We use a tapered fiber as a sensing head inside the active cavity built from fiber Bragg gratings. We derive a theoretical phase shift expression for our system and simulate it using the finite element method to determine optimum tapered fiber diameter for glucose sensing in DI water. Compared to a non-amplified system, we find that our amplified system can increase the sensitivity by fourteen times via the amplifier gain tuning. We also conduct experimental measurements using 0-15.5 mM glucose solutions and find them in excellent agreement with our theoretical predictions. Experimentally we obtain the sensor’s sensitivity of 0.768°/mM (1164°/RIU) and detection limit of 0.75 mM ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$4.5\times 10^{-4}$ </tex-math></inline-formula> RIU) without any temperature stabilization in the system. We anticipate that the present work will find a wide range of sensing applications in fiber cavities, ring resonators, and other microcavity structures.

Triangular Phase Shift Detector for Drone Precise Vertical Landing RF Systems

This article presents a circuit for the precise vertical landing of drones based on a three phase-shifts detection of a single frequency transmitted from the landing point. The circuit can be considered as a new navigation sensor that assists in guidance corrections for landing at a specific point. The circuit has three inputs to which the signal transmitted from an oscillator located at the landing point arrives with different delays. The input signals are combined in pairs in each of the three analog phase detectors, after having passed through 3 dB at 90° hybrid couplers that guarantee a theoretical nonambiguous phase shift range of ±90°. Each output has a voltage that is proportional to the phase shift between each of the input signals, which in turn depends on the position relative to the landing point. A simple landing algorithm based on phase shift values is proposed, which could be integrated into the same flight control platform, thus avoiding the need to add additional processing components. To demonstrate the feasibility of the proposed design, a triangular phase shift detector prototype has been implemented using commercial devices. Calibration and measurements at 2.46 GHz show a dynamic range of 30 dB and a nonambiguous detection range of ±80° in the worst cases. Those specs let us track the drone during the landing maneuver in an inverted cone formed by a surface with a ±4.19 m radius at 10 m high and the landing point.

Linear damped interfacial wave theory for an orbitally shaken upright circular cylinder

We present a new theoretical model describing gravity–capillary waves in orbitally shaken cylindrical containers. Our model can account for both one-layer free-surface and two-layer interfacial wave systems. A set of modal equations for irrotational waves is formulated that we complement with viscous damping rates to incorporate energy dissipation. This approach allows us to calculate explicit formulas for the phase shifts between wave and shaker which are practically important for the mixing efficiency in orbitally shaken bioreactors. Resonance dynamics is described using eight dimensionless numbers, revealing a variety of different effects influencing the forced wave amplitudes. As an unexpected result, the model predicts the formation of novel spiral wave patterns resulting from a damping-induced symmetry breaking mechanism. For validation, we compare theoretical amplitudes, fluid velocities and phase shifts with three different and independent experiments and, when using the slightly deviating experimental values of the resonance frequencies, find a good agreement within the theoretical limits.

Tidal Amplitude Delta Factors and Phase Shifts for an Oceanic Earth

M.S. Molodenskiy’s problem, which describes the state of an elastic self-gravitating compressible sphere, is generalized to the case of a biaxial hydrostatically equilibrium rotating elliptical inelastic shell. The system of sixth-order equations is supplemented with corrections due to the relative and Coriolis accelerations. The ordinary and load Love numbers of degree 2 are calculated with allowance for their latitude dependence and dissipation for different models of the Earth’s structure (the AK135, IASP91, and PREM models). The problem is solved by Love’s method. The theoretical amplitude delta factors and phase shifts of second-order tidal waves for an oceanic Earth are compared with their most recent empirical counterparts obtained by the GGP network superconducting gravimeters. In particular, it is shown that a good matching (up to the fourth decimal place) of the theoretical and observed amplitude factors of semidiurnal tides does not require the application of the nonhydrostatic theory.

Construction of lambda-nucleon s-wave potential through quantum inverse scattering at fixed angular momentum

Quantum systems with a strangeness degree of freedom are very important as they provide an extra dimension, and hence a deeper insight into nuclear matter. Usually phenomenological potentials obtained through meson exchange theories are used in investigating these hypernuclear systems. In this paper potentials for lambda-nucleon interactions in the spin singlet and spin triplet states, constructed through fixed-angular momentum inversion based on Marchenko theory, are presented. Owing to experimental difficulties in obtaining a sufficient number of lambda-nucleon scattering events, theoretical phase shifts are used as input for the inversion. The constructed potential is energy-independent, making it more suitable for quantum-mechanical few-body calculations.

High-Sensitivity High-Resolution Optical Phase Shift Detection Technique Using a Si Photodiode Operating in Photovoltaic Mode

In this paper, we report the optimization of the operating conditions and the maximization of the performances of the phase shift detection technique allowing to approach the best sensitivity and resolution in terms of light power variations. The system is based on the synchronous demodulation technique and uses a Si photodiode operating in photovoltaic mode biased through a small amplitude sinusoidal modulating signal. Employing a commercial lock-in amplifier for phase measurements and varying the signal modulating frequency, we prove that it is possible to obtain the maximum theoretical phase shift variation range equal to 90° with a resulting sensitivity and resolution equal to 3100°/ $\mu \text{W}$ and 3 pW, respectively. We demonstrate that these results are more than two orders of magnitude greater than those ones achievable by employing a Si photodiode in photoconductive mode. As a case-example for chemical applications, we apply the proposed technique to detect the variations of the molar concentration of a methylene blue solution by measuring the variations of the transmittance of a laser beam passing through the substance. The experimental findings are compared with those ones achieved by using a commercial spectrophotometer and the conventional amplitude detection technique employing the lock-in amplifier. Despite the achieved results are limited by the fixed phase resolution of the employed lock-in amplifier, here, the proposed approach allows to measure molar concentration variations with a resolution of 79 pM resulting 1354 times higher than that one obtained using the spectrophotometer and 33 times better than the value achieved with the amplitude detection technique.

Surface layer independent model fitting by phase matching: theory and application to HD 49933 and HD 177153 (aka Perky)

Aims. To describe the theory of surface layer independent model fitting by phase matching and to apply this to the stars HD49933 observed by CoRoT, and HD177153 (aka Perky), observed by Kepler Methods. We use theoretical analysis, phase shifts, and model fitting. Results. We define the inner and outer phase shifts of a frequency set of a model star and show that the outer phase shifts are (almost) independent of degree $\ell$, and that a function of the inner phase shifts (the phase function) collapses to an $\ell$ independent function of frequency in the outer layers. We then show how to use this result in a model fitting technique to find a best fit model to an observed frequency set by calculating the inner phase shifts of a model using the observed frequencies and determining the extent to which the phase function collapses to a single function of frequency in the outer layers. We give two examples applying this technique to the frequency sets of HD49933 observed by CoRoT and HD177153 (aka Perky) observed by Kepler, and compare our results with those of previous studies and show that they are compatible with those obtained using different techniques. We show that there can be many different models that fit the data within the errors and that better precision on the frequencies is needed to discriminate between the models. We compare this technique to that using the ratios of small to large separations, showing that in principle it is more accurate and avoids the problem of correlated errors in separation ratio fitting.

Calculation of Average Collision Cross Sections of Low Energy for Elastic e-Ar Scattering Using MERT4

Cross sections in the very low energy range are also represented by the modified effective-range theory (MERT) for low-energy electron scattering from the rare gas (argon). Simulations using published (theoretical) phase shifts indicate that extended versions of the standard effective-range theory with four adjustable parameters are required to give an adequate description of the phase shifts for argon. A four-parameter MERT fit gives a good representation of a recent electron–argon (e-Ar) total cross section experiment at energies less than 10.0 eV. Cross section Q(l) (E) for collision in dilute gases is given for any order l. Here Q(l) (E) are presented for l = 1. . .6. We present calculations for the elastic cross sections for electron scattering from argon. The improvement in the agreement between our theoretical calculations and the experimental measurements in the case of argon in scattering calculations are showed. Differential scattering experiments have been performed for the systems e-Ar in the energy range E = 0–10 eV and the angular range θ = 0–20° using a crossed-beam arrangement. Differential and integrated cross sections for the elastic scattering of low- and intermediate-energy (0–50 eV) electrons by argon atoms are calculated. For each impact energy, the phase shifts of the lower partial waves are obtained exactly by numerical integration of the radial equation. Transport coefficients of argon plasma are requested exactly, which is why we calculated the average collision cross sections for s = 1. . .11, l = 1. . .6.

Theoretical and Experimental Estimations of Volumetric Inductive Phase Shift in Breast Cancer Tissue

Impedance measurements based on magnetic induction for breast cancer detection has been proposed in some studies. This study evaluates theoretical and experimentally the use of a non-invasive technique based on magnetic induction for detection of patho-physiological conditions in breast cancer tissue associated to its volumetric electrical conductivity changes through inductive phase shift measurements. An induction coils-breast 3D pixel model was designed and tested. The model involves two circular coils coaxially centered and a human breast volume centrally placed with respect to the coils. A time-harmonic numerical simulation study addressed the effects of frequency-dependent electrical properties of tumoral tissue on the volumetric inductive phase shift of the breast model measured with the circular coils as inductor and sensor elements. Experimentally; five female volunteer patients with infiltrating ductal carcinoma previously diagnosed by the radiology and oncology departments of the Specialty Clinic for Women of the Mexican Army were measured by an experimental inductive spectrometer and the use of an ergonomic inductor-sensor coil designed to estimate the volumetric inductive phase shift in human breast tissue. Theoretical and experimental inductive phase shift estimations were developed at four frequencies: 0.01, 0.1, 1 and 10 MHz. The theoretical estimations were qualitatively in agreement with the experimental findings. Important increments in volumetric inductive phase shift measurements were evident at 0.01MHz in theoretical and experimental observations. The results suggest that the tested technique has the potential to detect pathological conditions in breast tissue associated to cancer by non-invasive monitoring. Further complementary studies are warranted to confirm the observations.

ANALYSIS OF THE PERFORMANCE OF INJECTION LOCKED OSCILLATORS IN A DATA TRANSMITTING POLARISATION AGILE ANTENNA APPLICATION

In this work, a polarisation agile antenna based on an array of two injection locked oscillators is presented. The proposed topology provides a theoretical relative phase shift range of 360degrees between the output signals, which can be easily controlled through two DC voltages. The behaviour of the system is studied, both through simulations and measurements of the manufactured prototype, focusing on the joint performance of the oscillators. The data transmission capabilities of the system are analysed, proposing a solution for phase modulated signals.

Kaon-nucleon interaction in the extended chiral SU(3) quark model

The chiral SU(3) quark model is extended to include the coupling between the quark and vector chiral fields. The one-gluon exchange (OGE) that dominantly governs the short-range quark\char21{}quark interaction in the original chiral SU(3) quark model is now nearly replaced by the vector-meson exchange. By use of this model, the isospin $I=0$ and $I=1$ kaon-nucleon $S,P,D,F$ wave phase shifts are dynamically studied by solving the resonating group method (RGM) equation. Similar to those given by the original chiral SU(3) quark model, the calculated results for many partial waves are consistent with the experiment, while there is no improvement in this new approach for the ${P}_{13}$ and ${D}_{15}$ channels, of which the theoretical phase shifts are too repulsive and too attractive, respectively, when the laboratory momentum of the kaon meson is greater than 300 MeV.

Short wave phase shifts by large free surface solitary waves: Experiments and models

In this paper, we compare experiments on short gravity wave phase shifting by surface solitary waves to a Wentzel–Kramers–Brillouin–Jeffreys (WKBJ) refraction theory. Both weak interactions (head-on interaction) and strong interactions (overtaking interaction) are examined. We derive a dispersion relation and wave action conservation relation which are similar to the ones obtained for short waves refraction on slowly varying media. The model requires an exact solitary wave solution. To this end, a steady wave solution is numerically computed using the algorithm devised by Byatt-Smith [Proc. R. Soc. London, Ser. A 315, 405 (1970)]. However, two other solitary wave solutions are incorporated in the model, namely the classical Korteweg and De Vries (KdV) [Phil. Mag. 39, 422 (1895)] solution (weakly nonlinear/small amplitude solitary wave) and the Rayleigh [Phil. Mag. 1, 257 (1876)] solution (strongly nonlinear/large amplitude solitary wave). Measurements of the short wave phase shift show better agreement with the theoretical predictions based on the Byatt-Smith numerical solution and the Rayleigh solution rather than the Korteweg and De Vries one for large amplitude solitary waves. Theoretical phase shifts predictions based on Rayleigh and Byatt-Smith numerical solutions agree with the experiments for A/h0⩽0.5. A new heuristic formula for the phase shift allowing for large amplitude solitary waves is proposed as a limiting case when the short wave wave number increases.

Many-body and model-potential calculations of low-energy photoionization parameters for francium

The photoionization cross section $\sigma$, spin-polarization parameters $P$ and $Q$, and the angular-distribution asymmetry parameter $\beta$ are calculated for the $7s$ state of francium for photon energies below 10 eV. Two distinct calculations are presented, one based on many-body perturbation theory and another based on the model potential method. Although predictions of the two calculations are similar, the detailed energy dependence of the photoionization parameters from the two calculations differ. From the theoretical p-wave phase shifts, we infer quantum defects for $p_{1/2}$ and $p_{3/2}$ Rydberg series, permitting us to calculate positions of experimentally unknown $p$ states in francium.

Short-Range Order in Se-Rich Ge–Se Glasses—An Extended X-Ray Absorption Fine Structure Study

The short-range order in vitreous Ge1−xSex(2/3≤x≤1) at 80 K was studied by EXAFS spectroscopy at the Ge and Se K-edges. The results were analyzed using theoretical phase shift and amplitude functions and by comparison to crystalline GeSe2 and Se as model compounds. The GeSe4 tetrahedron is the main structural entity for all the Ge–Se alloys. The results indicate a slight increase in Ge coordination and a decrease in Se coordination with increasing Se content. Possible sources of error are discussed, and possible origins of the structural changes are suggested.

An accurate method for measurement of transverse elastic-wave velocities

We demonstrate a novel analysis that improves the accuracy of angle-dependent elastic-wave velocities in plates for water-immersion measurements. Water-immersion measurements utilize the conversion from longitudinal to transverse mode to determine the velocities of transverse waves. However, beyond the critical angle for longitudinal waves, the phase of the transmitted transverse waves is affected by the presence of evanescent longitudinal waves at the interface. With pulse superposition analysis this effect systematically decreases the apparent velocities at some angles. Previous researchers have corrected the apparent velocities by calculating the theoretical phase shift from known parameters, but this correction requires narrow-band pulses or tone bursts as well as estimations of these parameters. An advantage of our analysis is that it eliminates the need for a priori estimations of parameters. In addition, this analysis allows the use of broad-band pulses that are more applicable to thin plates. To demonstrate these advantages, measurements were conducted on an isotropic steel plate as it was rotated in an immersion tank and insonified with a broad-band ultrasonic transducer. We compared velocities determined by the pulse-echo superposition analysis with velocities determined by our analysis. As expected, there was no significant difference between the longitudinal velocities, but systematic variations in the transverse velocities were lower with this new method.

An energy-dependent phase shift analysis of low-energy proton-deuteron elastic scattering

An energy dependent phase shift analysis of p+d elastic scattering below the deuteron breakup threshold has been conducted. The phases are fit directly to the data with a Monte Carlo Markov Chain algorithm after being sampled from a parameter space which is constrained to satisfy the Coulomb-modified effective range expansion. The mixing parameters are required to obey analyticity constraints. The overall fit in the preliminary analysis reported here was satisfactory, giving a χ 2/datum of about 2.5. The analysis indicates the existence of a singularity in the spin-doublet S-wave effective range function. The inferred value of the quartet S-wave scattering length is in excellent quantitative agreement with theoretical predictions. Small changes to the theoretical P-wave phase shifts and somewhat larger changes to the theoretical J = 1 2 mixing parameters are required to reproduce the p+d data.

The structure of sodium adsorbed c(2 × 8)Ge(111) surface

We performed SEXAFS and core level photoemission studies of Na adsorbed on c(2 × 8)-Ge(111) surface at different coverage regimes. The c(2 × 8) LEED pattern of the clean Ge(111) surface changes to a (1 × 1) with higher background after Na adsorption. A plasmon feature appears on the low energy side of Na 2p core level which indicates metallization of the Na overlayer. We determined the NaGe bond length from the SEXAFS data using the theoretical phase shift of NaGe, calculated by FEFF program. SEXAFS model calculations show that Na atoms are adsorbed on threefold-coordinated hollow sites with a NaGe bond length of 2.9 Å and a second nearest neighbour distance of 3.4 Å to the Ge atoms in the second layer.