Phase-shifted PT -symmetric periodic structures

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

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.

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

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)

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.

The link between soil water content (SWC) and evapotranspiration (ET) is of great importance in ecohydrology, agroecosystem management, and land-atmosphere interaction of earth-system analysis. There is still a need to understand the key processes linking SWC and ET in different vegetated ecosystems, especially at larger scales. Therefore, in this work, we used wavelet coherence analysis to explore the long-term relationship between SWC and ET among the predominant land use types (cropland, evergreen needleleaf forest, mixed forest, open shrubland, wooden tundra, grassland, and mixed tundra) in Europe during the last four decades (1980-2020). To this end, first a principal component analysis was performed among the SWC and ET data from GLDAS, GLEAM, and ERA5-land, and the first component was then used for further analyses when the target variable was in demand. Using the first component, then, we averaged SWC and ET data over the pixels covered by each land use type. Then, for each land-use types, we averaged the data daily for each decade to account for a representative decadal year of daily data. Then, wavelet coherence analysis was conducted between those averaged data of SWC and ET for each land-use type. The results showed a negative correlation between ET and SWC for all land use types, with ET lagging behind SWC, with an average phase shift value of 134 days for grassland (the minimum) and 168 days for mixed tundra (the maximum). Converting the phase shift values to a time lag [lag = n/2 - phase shift for the case phase shift < -n/4 where n represents the period (1/frequency) of the signals] shows (Fig. 1) that ET controls SWC with a lag of 15 days in mixed tundra (the minimum) and 48 days in grassland (the maximum). Moreover, we applied Mann-Kendall trend analysis test and found that the lag between SWC and ET decreases in mixed and wooden tundras with a slope value of -2.4 days/year, while it increases in cropland and grassland with a slope value of 1.6 days/year. Although there is a significant downward trend in evergreen needleleaf forests (with a slope value of -0.3 days/year) and an increasing trend in mixed forests and open shrublands (with a slope value of 0.4 days/year), the lower slope values in these land use types indicate that the change is slower compared to grasslands, croplands, and tundras. Figure 1- Temporal evolution of the lag between soil water content and evapotranspiration in the annual cycle in different land use types in Europe 

We analyse the diffraction behaviour of a parity-time (PT) symmetric transmission grating. This kind of grating consists of a periodic structure with balanced real and imaginary parts of the refractive index. The bimodal interferometric operation (Mach-Zehnder like) is modified by the introduction of balanced gain and loss, leading to efficient switching around an exceptional point.

Parity-time symmetric Bragg gratings produce unidirectional reflection around the exceptional point. We propose and explore directional coupling of gain and loss modulated waveguide Bragg gratings operating at around 880 nm with long-range surface plasmon polaritons. Step-in-width modulation of a Ag stripe supporting long-range plasmons combined with a periodic modulation of the cladding were used to balance the real and imaginary index perturbation of the gratings. IR140 dye molecules in solvent forms a portion of the uppercladding, providing gain under optical pumping. We investigate directional coupling between a pair of parity-time symmetric waveguide Bragg gratings operating near their exceptional point, arranged in various configurations - duplicate, duplicate-shifted and duplicate-flipped. We also investigate coupling to a bus waveguide and to a conventional waveguide Bragg grating. Unidirectional multi-wavelength reflection and coupled supermode conversion are predicted.

A new method is presented using a tri-window common-path interferometer (TriWCPI) for quantitative phase measurement. The prior method obtains the phase shift introduced by the Ronchi grating and the intensity value of the incident light with interferograms acquired offline without any objects. As a consequence, an improved recovery algorithm is established using the phase shift, the intensity value of the incident light, and the interferograms for a phase object acquired by camera in a single shot. The phase of an object then can be reconstructed from the improved algorithm. Because the calculation of phase shift and intensity value can be performed offline only once after the TriWCPI is built, the real-time ability and stability of the TriWCPI remains in this method. But the method avoids the normalization process and thus improves phase-retrieval precision. Experiments are demonstrated to prove the precision, real-time ability, and stability of the proposed method.

In this paper, a new class of wideband phase shifters on multimode resonator is proposed and developed. Compared with its conventional counterparts, these new phase shifters have a few advantageous features such as simple structure, intrinsic wideband characteristic, large phase-shift value, and easy adjustment in phase shift. The phase properties of multimode resonator are at first studied to derive the quantitative relationship between the phase slope and their respective resonant frequencies. On the one hand, a prescribed wideband phase shift can be achieved by adjusting the impedance ratio $R_{z}$ of the multimode resonator and the electrical length of the reference line. On the other hand, the wide operating band can be intrinsically obtained over a frequency range covered by multiple resonant frequencies in the multimode resonator. In this context, the transmission-line models of the proposed phase shifters are deduced and synthesized to design these phase shifters with a prescribed phase shift value and return loss within the operating band. Moreover, the synthesized model can be directly mapped into all the physical dimensions, thus allowing for a quick design process. Finally, two 180° wideband phase shifters are designed, fabricated, and tested to verify the proposed design method and predicted frequency responses.

SUMMARY We performed pumping tests with a periodic succession of injection and production intervals in a field of three shallow boreholes penetrating a jointed sandstone formation. Tests were conducted at periods ranging from 10 to 5400 s and pumping rates between 5 and 20 l min−1. Two types of analysis for the periodic pumping tests are presented. Injectivity analysis rests on the determination of the amplitude ratio and phase shift between the periodic flow rate and pressure records from the pumping well. Interference analysis is based on an evaluation of attenuation and phase shift between the periodic pressure signals at the pumping and monitoring wells. A periodic excitation permits to employ standard signal processing tools, such as fast Fourier transformation, facilitating the evaluation of weak signals. The observed amplitude ratio and phase shift values are compared to analytical predictions of 1-D and radial flow models. Results of interference tests are particularly diagnostic for the applicability of a subsurface model. Our test results do not fully agree with any of the considered analytical models suggesting a heterogeneous subsurface. We suppose that the two analysis methods yield averaged hydraulic properties of different volumes of a heterogeneous subsurface. Periodic injectivity tests screen the subsurface to increasing penetration depth if pumping period is systematically increased, while the subsurface volume between pumping and monitoring well dominates the outcome of an interference test at all periods. Periodic pumping provides several operational advantages compared to conventional testing, such as drawdown, pulse or shut-in tests. Periodic testing can be superposed on a long-term operation reducing operational conflicts and permitting continuous monitoring of changes in subsurface properties. Processing of periodic signals provides results even in a field with strong transient changes in fluid pressure related, for example, to operations in nearby wells. Periodic pumping can be performed in a closed loop minimizing the total fluid volume involved.

A system of two mutually coupled quantum dot lasers, each with corresponding longitudinal modes, has been studied in this article. Using multimode rate equation model, we demonstrate how this model in conjunction with coupled-mode theory lead to a set of effective Hamiltonians with characteristics inarguably akin to those Hamiltonians associated to the conventional PT-symmetric systems. A fixed frequency detuning has been introduced by a minute difference in cavity lengths in the current system and the strength of optical coupling plays a decisive role in the emergence of the exceptional points at which the so- called non-conventional PT-symmetry breaks. It has also been shown that the predictions about amplification or attenuation of supermodes associated to the longitudinal modes based on effective Hamiltonians, happen to be supported by the multimode rate equation model, yet in the presence of weak coupling. Eventually, the overall output spectrum is potent to be manipulated and in particular exhibit a single longitudinal mode behavior in the vicinity of the exceptional point through the interplay between the frequency detuning and the coupling coefficient. Owing to the inhomogeneous broadening of the optical spectrum, a considerable rise in the number of photons for the single amplified supermode is witnessed within time having the attenuated modes out of the picture via proper mode selection in the present non-conventional PT-symmetric system.

A comprehensive phase-shift analysis of ${\ensuremath{\pi}}^{+}\ensuremath{-}p$ elastic-scattering data at 310-Mev incident-pion laboratory kinetic energy has been performed. The experimental data utilized include measurements of the differential and total cross sections and of the recoil-proton polarization. The $D$-wave phase shifts were found to be definitely needed in order to attain an adequate fit to the data. A general search for phase-shift solutions was carried out, using $S$-, $P$-, and $D$-wave phase shifts. One solution\char22{}of the Fermi type\char22{}was found that fits the data significantly better than any of the other solutions obtained. The calculated errors in the phase shifts of this set vary from 0.4 to 0.6 deg. Because it was felt that these errors might be deceivingly restrictive, the effects of small nuclear $F$-wave phase shifts on the results of the analysis were investigated and were found to be large: not only are the uncertainties in the original Fermi-type solution increased, but additional sets of phase shifts arise that fit the data well. One of these new solutions is similar to the original Fermi set except that the magnitudes of the phase shifts in this new fit are in general larger than those in the initial solution, and the signs of the $D$-wave phase shifts are reversed. The nuclear phase shifts in the original Fermi solution and their rms errors are (when $F$-wave phase shifts are allowed): ${S}_{3,1}=\ensuremath{-}17.2\ifmmode\pm\else\textpm\fi{}2.6$ deg, ${P}_{3,1}=\ensuremath{-}2.9\ifmmode\pm\else\textpm\fi{}4.0$ deg, ${P}_{3,3}=135.0\ifmmode\pm\else\textpm\fi{}0.6$ deg, ${D}_{3,3}=3.1\ifmmode\pm\else\textpm\fi{}2.6$ deg, ${D}_{3,5}=\ensuremath{-}4.9\ifmmode\pm\else\textpm\fi{}2.1$ deg, ${F}_{3,5}=0.5\ifmmode\pm\else\textpm\fi{}0.6$ deg, ${F}_{3,7}=\ensuremath{-}0.6\ifmmode\pm\else\textpm\fi{}1.4$ deg. Although theory appears to favor this set, further theoretical and experimental evidence is desirable. The values given here for the first five phase shifts approximate the corresponding values obtained when the $F$-wave phase shifts were assumed negligible. However, all except ${P}_{3,3}$ fall outside the limits set by the small original errors. Inelastic-scattering processes were neglected during the phase-shift analysis. Calculations indicate that, if these processes could properly be taken into account, any changes in the quoted values of the phase shifts would probably be well within the corresponding errors given here. Extension of the phase-shift inquiries to include $G$ waves was attempted, but it was observed that the available data and theory do not allow the $G$-wave interaction to be significantly incorporated into the analysis.

Chapter 11 - Highly Nonlinear Fibers

This article proposed a novel method for current sensing of multicore cables utilizing a tunnel-magnetoresistance (TMR) sensor array. In fact, multicore cables belong to multi-conductor systems. A trans-impedance is built to describe the mathematical relationship between the current phasors of the multi-conductor system and the output voltage phasors of all the magnetic sensors, based on which the current phasors can be recovered by simply performing matrix multiplication. The determination of the trans-impedance is dependent on the identification of the geometry parameters of the conductors (i.e., positions and tilt angles). Based on the output voltage phasors of the magnetic sensors at fundamental frequency, these conductor parameters can be identified by solving over-determined equations which are formulated in a form of one nonlinear least square (NLLS) problem. The value of the gain factor of the designed TMR sensor is almost a constant and the value of the corresponding phase shift is approximately zero. A real trans-impedance matrix can be obtained converted from the complex one, based on which real time current waveforms reconstruction can be achieved. Simulation study and laboratory experiments are conducted to verify the validation of the proposed current sensing method. From the simulation study, it is found that a value of lower than 5% for the maximum relative current amplitude error and the corresponding value of less than 4° for the maximum phase error can be achieved though the tilt angles of the conductors are arbitrarily varied. A probe-like current sensor is fabricated and experimentally characterized. Laboratory experiments including current phasor measurement at fundamental frequency and real-time current waveforms reconstructing are conducted. For both balanced and unbalanced three-phase cases, the testing results for current phasor measurement at fundamental frequency show that a value of lower than 8.24% for the maximum relative current amplitude error and a value of smaller than 4.46° for the corresponding maximum phase error can be achieved. Meanwhile, the current waveforms for three-phase currents having plenty of harmonics are successfully recovered in real time through experiments.