Tri-window common-path interferometer for quantifying phase objects.

Three-frame generalized phase-shifting interferometry by a Euclidean matrix norm algorithm

We introduce a new method to calculate phase shifts on noisy intermediate scale quantum (NISQ) hardware platforms using a wave packet edge time delay. The method uses the early and intermediate stages of the collision because the standard method based on the asymptotic out-state behavior is unreachable using today’s NISQ platforms. The calculation was implemented on a 4-site transverse Ising model in one spatial dimension with and without a potential interaction. A time evolution operator describing the progression of the system was constructed and transmission and reflection coefficients were calculated based on the identified quantum Fourier transformed momentum states. The detailed analysis of the phase shift calculations on both IBM superconducting transmon and University of Maryland ion trap quantum computers shows the platform independence of the methodology. This successful implementation of this wave packet preparation and projection on momentum eigenstates can now be performed with actual quantum computing hardware platforms. This method provides a procedure for calculating phase shifts and opens the possibility of using noisy intermediate scale quantum devices to perform real-time quantum mechanics and quantum field theory scattering calculations.

A new method is proposed and demonstrated for fabricating phase-shifted fiber Bragg gratings (FBGs) using a variable-velocity scanning UV laser beam in combination with a shielded phase mask. The transmission properties of phase-shifted FBGs were analyzed based on coupled-mode theory and a transfer matrix method. The grating is divided into three parts to allow for easier analysis of FBG properties. These segments included a uniform FBG1 and FBG2 which were separated by a shielded section. A novel phase-shifted FBG was fabricated using this method, in which the refractive indices of FBG1 and FBG2 were different. Transmission properties of these phase-shifted FBGs were simulated numerically using MATLAB, and the experimental results and simulated results are in good agreement. In addition to the length and effective refractive index of the shielded section, the phase shift value of a phase-shifted FBG was also found to be dependent on the lengths and effective refractive indices of FBG1 and FBG2. Moreover, we predicted that changing the scanning velocity for fabricating FBG2 would adjust phase shift value, which exhibits a positive linear relationship with the scanning velocity. These results can provide guidelines for fabricating any phase shift value FBGs. This technique is simple, convenient, and may be developed further for use in fabricating novel tunable fiber filters or DFB fiber lasers.

A recapitulation of the up-to-date methods for accurate calculation of the differential phase shift provided by the azimuthally magnetized circular ferrite waveguide, under normal TE <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0n</sub> modes excitation, is presented. The debate is focused on two groups of numerical techniques, each of which incorporates three schemes, connected with definite physical working regimes of the structure. The key point in all of them is the repeated application of an iterative procedure, yielding the positive purely imaginary zeros of the complex Kummer function Φ(a, c; x) of specially selected parameters and variable, accepted as wave function for propagation, for a fluctuating imaginary part of its complex parameter a The first set of routines allows to obtain the phase shifting diagram (the aggregate of the area of phase shifter operation and of the differential phase shift characteristics) of the configuration for the normal TE <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">01</sub> mode in the r <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> -Δβ-plane, while the second one - the same in the |α|-Δβ-plane. (r <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> and Δβ are the normalized in an appropriate way guide radius and phase shift of the wave and α is the off-diagonal ferrite permeability tensor element.) The main result of the study is that for fixed r <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> , Δβ is almost proportional to α in the whole area in which it might be afforded.

System-induced depolarisation of single-polarised satellite beacon signals can be cancelled with vector cancellation. It is demonstrated that the residual error after application of this bias removal technique depends only on the polarisation tilt angle and the XPD of the satellite antenna. It appears that for the calculation of the atmospheric-induced differential attenuation A and phase shift β, correction of the system-induced differential phase shift for the copolar and crosspolar signals is necessary. An experiment is described to measure this system-induced differential phase shift. It is demonstrated that it is possible to clearly distinguish between rain and ice depolarisation by looking at the scatterplots of the calculated A and β against measured copolar attenuation.

We report the spectral features of a phase-shifted parity and time ($\mathcal{PT}$)-symmetric fiber Bragg grating (PPTFBG) and demonstrate its functionality as a demultiplexer in the unbroken $\mathcal{PT}$-symmetric regime. The length of the proposed system is of the order of millimeters and the lasing spectra in the broken $\mathcal{PT}$-symmetric regime can be easily tuned in terms of intensity, bandwidth and wavelength by varying the magnitude of the phase shift in the middle of the structure. Surprisingly, the multi-modal lasing spectra are suppressed by virtue of judiciously selected phase and the gain-loss value. Also, it is possible to obtain sidelobe-less spectra in the broken $\mathcal{PT}$-symmetric regime, without a need for an apodization profile, which is a traditional way to tame the unwanted sidelobes. The system is found to show narrow band single-mode lasing behavior for a wide range of phase shift values for given values of gain and loss. Moreover, we report the intensity tunable reflection and transmission characteristics in the unbroken regime via variation in gain and loss. At the exceptional point, the system shows unidirectional wave transport phenomenon independent of the presence of phase shift in the middle of the grating. For the right light incidence direction, the system exhibits zero reflection wavelengths within the stopband at the exceptional point. We also investigate the role of multiple phase shifts placed at fixed locations along the length of the FBG and the variations in the spectra when the phase shift and gain-loss values are tuned. In the broken $\mathcal{PT}$-symmetric regime, the presence of multiple phase shifts aids in controlling the number of reflectivity peaks besides controlling their magnitude.

Phase-shift analysis of p-p and n-p elastic scattering at 735 MeV

New phase shift formulas and stability of waveplate in oblique incident beam

The increased usage of the phase shifting transformers in various fields within power systems has introduced new challenges in performing on-site maintenance testing. These special transformers were used as converter transformers, rectifier transformers, harmonic mitigating transformers, zigzag transformers and quadrature boosters with unconventional vector groups, having an additional phase shift such as +/-7.50, +/-150 combined with normal `Delta and Star' configurations. The challenges now faced by the increased use of these transformers are testing them for accuracy on the voltage ratio and phase shift at site during commissioning and maintenance. Different test methods were performed / studied and were compared. A prototype of a three-phase converter transformer with variable ratio taps and vector groups was constructed and tested. The prototype transformer is constructed to have variable parameters for test trials on different vector groups and ratios. The three phase converter transformer prototype will have options to regulate the output voltage on varying input voltage using the tap changer and also can vary the phase shift by varying the vector group combinations. On-site testing of ratio and phase shift will be done on different types of traction rectifier transformers. The approach for factory testing and onsite testing of the special transformers will be different. The effect on the phase shift values when the ratio taps are changed will be the focus and the results compared. The study on the importance of phase shift on these special transformers is presented. The test results of different test methods using modern portable test equipment and conventional classical methods were compared and presented. The results of the ratio testing and the phase shift measurement variation during vector group variation and tap change were presented. (6 pages)

A self-consistent method is used for the first time to calculate the characteristics of ring lasers with intracavity acousto-optical interference components. The results obtained by this method are shown to differ considerably from those obtained traditional methods. The traditional methods for the calculation of losses, phase shifts, and phase and amplitude anisotropies of such acousto-optical components cannot be used to determine the output parameters of typical solid-state ring lasers because the frequency dispersion of such components is exceptionally high.

Within the framework of the method of coupling-constant evolution an approach is developed for description of elastic pion-nucleus scattering. An iteration procedure for calculation of partial phase shifts of pion-nucleus scattering is constructed. In the low-energy limit the scattering amplitude satisfies the condition of two-body unitarity. In the lowest approximation of the theory the pion-nucleus phase shifts can be expressed in terms of the elementary phase shifts of ..pi..N scattering and nuclear form factors. A satisfactory description of pion elastic scattering by light nuclei (/sup 4/He, /sup 12/C) is obtained in the pion-energy region below 70--80 MeV.

Use of a simple semiclassical estimate of Bessel function phase for arbitrary argument avoids the modulo π errors which the conventional approach tends to introduce into the calculation of absolute quantal phase shifts for high partial waves. This has significant implications for the direct quantum mechanical calculation of second virial coefficients at high temperatures.

An approach is presented for the calculation of the electron optical phase shift experienced by high-energy electrons in a transmission electron microscope, when they interact with the magnetic field associated with superconducting fluxons in a thin specimen tilted with respect to the beam. It is shown that by decomposing the vector potential in its Fourier components and by calculating the phase shift of each component separately, it is possible to obtain the Fourier transform of the electron optical phase shift, which can be inverted either analytically or numerically. It will be shown how this method can be used to recover the result, previously obtained by the real-space approach, relative to the case of a straight flux tube perpendicular to the specimen surfaces. Then the method is applied to the case of a London fluxon in a thin film, where the bending and the broadening of the magnetic-field lines due to the finite specimen thickness are now correctly taken into account and not treated approximately by means of a parabolic fit. Finally, it will be shown how simple models for the pancake structure of the fluxon can be analyzed within this framework and the main features of electron transmission images predicted.

Using the variational technique for the calculation of the zeroth-order phase shift and the perturbational technique for obtaining the higher order phase shifts, an analytic expression is derived for the total scattering cross section of ionized impurity scattering in degenerate semiconductors. The formula obtained may be looked upon as resulting from a refinement of the first Born approximation and its significance lies in the fact that it is valid in a doping region where neither the uncorrected Born approximation nor the simplest form of the partial-wave method (based on using only a variationally determined zeroth-order phase shift) can be applied for the calculation of the resistivity of ionized impurity scattering.

Nonlinear acoustic oscillations of large amplitude created in a gas-filled tube under the action of two pistons located at the ends of the pipe are numerically investigated. The pistons oscillate according to the harmonic law at one of the natural frequencies and with different values of phase shift. The movement of the gas is described by mathematical equations of conservation for the main determining relations for the flow, which are estimated by applying the finite volume method based on OpenFOAM package. The non-stationary forced oscillatory motion of a gas inside an axisymmetric tube from a state of rest to a periodic steady motion is investigated. The features of nonlinear acoustic fluctuations of gas in cylindrical duct under the action of two pistons are found. The effect of the phase shift value has a strong effect on the oscillation amplitude of gas, when pistons oscillating at equal natural frequencies, in turn, when the pistons oscillate at different natural frequencies, the effect is very small. In particular, resonant oscillations are detected when the pistons vibrate at the same frequency values equal to odd values of their own higher harmonics in the absence of a phase shift value. In the case when the frequency values are equal to even values of the natural harmonics, resonant oscillations occur when the pistons move in anti-phase. The numerical method appears to work well and would be hoped for practical computations of different resonators.