Conjugate Wave Research Articles

QUANTUM MECHANICS AS A THEORY BASED ON THE GENERAL THEORY OF RELATIVITY

In this paper, we obtain the quantum dynamics in the framework of the general theory of relativity, where a quantum partide is described by a distribution of matter, with amplitude functions of the matter density, in the two conjugate spaces of the spațial coordinates and of the momentum, called wave functions. For a free partide, these wave functions are conjugate wave packets in the coordinate and momentum spaces, with time dependent phases proporțional to the relativistic lagrangian, as the wave velocities in the coordinate space are equal to the distribution velocity described by the wave packet in this space. From the wave velocities of the partide wave functions, we obtain lorentz’s force and the maxwell equations. For a quantum partide in electromagnetic field, we obtain dynamic equations in the coordinate and momentum spaces, and the partide and antiparticle wave functions. We obtain the scattering or tunneling rate in an electromagnetic field, for the two possible cases, with the spin conservation, or inversion

Breathers and double-pole solutions of coupled mixed derivative nonlinear Schrödinger equations from optical fibers

In this paper, the coupled mixed derivative nonlinear Schrödinger equations are investigated, which govern the propagation of the femtosecond optical pulse in optical fibers. First of all, based on the soliton solutions in bilinear form, the breathers are constructed by choosing a pair of complex conjugate wave numbers. Then, the interactions between a breather and either an anti-dark soliton or a dark soliton are studied according to the existence conditions of dark and anti-dark solitons. The double-pole solution can also be obtained by a coalescence of two wave numbers. In addition, the influence of physical parameters on the phases and propagation direction of the breathers and double-pole solitons is studied by the qualitative analysis and graphical illustration.

Highly accelerated parallel MRI using wave encoding and virtual conjugate coils.

To propose a novel model incorporating virtual conjugate coil (VCC) reconstruction and wave encoding (Wave) for improved parallel MRI. A novel model (VCC-Wave) incorporating VCC and Wave is proposed. The correlation matrix of the encoding operator is introduced to analyze the encoding capability. In addition, simulation experiments are conducted to gain insights into VCC-Wave. In vivo experiments are performed to compare VCC-Wave with alternative methods. The correlation matrix and the simulation experiments show that the proposed VCC-Wave can utilize more priors of Wave under the VCC framework. In vivo experiments show that the proposed VCC-Wave can achieve good image quality at a 6-fold acceleration in high-resolution and high-bandwidth cases, indicating an improvement over the original Wave technique. The proposed VCC-Wave can not only combine the advantages of both the VCC and Wave but also exploit more priors of Wave under the VCC framework. The improvement in VCC-Wave alleviates the limitation of Wave in high-resolution and high-bandwidth cases.

Numerical simulation of the interaction of wave phase conjugation with bubble clouds

The interaction of the Wave Phase Conjugation (WPC) process with bubble cloud dynamics is investigated via numerical modeling in application to bubble size measurements. The WPC simulator by Modarreszadeh and Timofeev (Computers and Fluids 197, 104353) is used as a starting point. In the simulator, a modified version of the high-order Nodal Discontinuous Galerkin method is used for modeling of acoustic wave propagation in the active WPC conjugator and the surrounding linear or non-linear fluid in 2D/axisymmetric domains. The effects of bubble dynamics are incorporated with the help of induced volume fractions. The modified Keller–Miksis model is employed to simulate vibrations of bubbles subjected to acoustic waves. After thorough verification and validation of the numerical scheme and the physical model, the interaction of various bubble clouds, including poly-disperse ones, with the WPC process is examined with the help of some existing and newly suggested descriptive indicators, e.g., the amplification factor and the absolute and relative signal intensities. The results show that signals scattered from bubble-plane clouds, in which the bubbles are non-physically synced, are strong enough to affect the modulation process if the stimulation frequency is close to the natural frequency of bubbles. For more realistic bubble clouds, the modulation process is almost intact. However, conjugate waves do carry some signatures of bubble-cloud dynamics, e.g., signals with frequencies higher than the natural frequency of bubbles are significantly diminished. The study demonstrates that WPC-based techniques have a promising potential to be used for measuring bubble dimensions.

Multi-complexiton solutions of the (2+1)-dimensional asymmetrical Nizhnik-Novikov-Veselov equation

In this paper, the (2+1)-dimensional asymmetrical Nizhnik-Novikov-Veselov equation is investigated to acquire the complexiton solutions by the Hirota direct method. It is essential to transform the equation into Hirota bi-linear form and to build N-compilexiton solutions by pairs of conjugate wave variables.

On Intrinsic Rotation of Bodies

Spontaneous rotation of matter is investigated. The results provide further evidence in support of earlier indications of a wave-only reality in which the quantum energy packet exists in the form of a conjugate wave—particle doublet. It reveals that matter, be it wave or particle, is a harmonic oscillator defined with full spectrum of the usual mechanical properties of simple harmonic motion SHM. Notably, the quantum energy packet’s stress field correlates with radius to generate intrinsic torque, it motivates spontaneous rotation at all levels of the cosmic mass scale from the electron to the universe; its atomic and natural units are and respectively for matter’s wave (bosonic) and particulate (fermionic) forms. The proton’s observational internal pressure Pa reported recently by Burkert et al. deviates markedly from the theoretical value ~1022 Pa, the difference attributes to challenges with existing energy measurement procedures. Velocities of electron waveform in random thermal motion evaluated with the new approach agree remarkably well with values obtained with kinetic-molecular theory KT; much more importantly, the analysis reveals existence, at standard conditions, of electron waveform’s hyper-luminal root-mean-square velocity, , if verified, this finding might inform on-going neutrino research. The evidence suggests that effects formalized in the theories of thermodynamics and kinetics trace to mobile torque fields.

A novel scheme of cascaded four-wave mixing for phase-sensitive amplification in nonlinear optical fibre

We propose and numerically verify a scheme of phase-sensitive amplifier (PSA) using four-wave mixing (FWM) in cascaded highly nonlinear fibres (HNLFs), without requiring initial phase-locking between signal and pump. The first HNLF is used to generate two phase-conjugate waves, which act as two pumps for FWM process in second HNLF. We feed the two pumps from opposite ends of second HNLF and a signal co-propagating with one of the pumps. We keep the signal frequency in the middle of two pump frequencies to obtain phase-conjugate wave at the same frequency as the signal by FWM process in second HNLF. Signal and phase-conjugate wave appear at opposite ends of the second HNLF and combined to obtain PSA. The frequency-shift-free operation of phase conjugation helps in preserving the frequency of input signal during phase-sensitive amplification. We derive the expression for PSA signal output and PSA gain and show analytically that PSA gain depends upon signal phase only, as the two pumps are phase conjugate to each other. Thus, eliminating the need of phase locking between signal and pump waves. We show that PSA provides high gain for in-phase component and almost cancellation for quadrature-phase component of signal. We show the broadband nature of PSA due to minimum effect of group velocity and group velocity dispersion owing to counter-propagating nature of signal and conjugate waves. We study the performance of PSA under the effects of pump-signal detuning, amplifier length and input signal phase. Simulation results show that PSA output is forced to attain 0 or phase regardless of large variation of phase in the input signal. Nonlinear phase noise reduction of 100 Gbps DPSK signal transmitted over 1000-km standard single-mode fibre confirms phase regeneration by PSA.

Complexiton and resonant multiple wave solutions to the (2+1)-dimensional Konopelchenko–Dubrovsky equation

In this paper, the (2+1)-dimensional Konopelchenko–Dubrovsky (KD) equation is investigated. Using the Hirota direct method and linear superposition principle, the complexiton and resonant multiple wave solutions are successfully constructed. For the Hirota direct method, it is essential that finding the bilinear form to the KD equation and applying its 2N-soliton formulation in real field to build the N-complexiton solutions under the action of pairs of conjugate wave variables. The linear superposition in real field of exponential traveling waves can generate the resonant multiple wave solutions, and then generalize linear superposition principle to complex field, we obtain some new resonant multiple wave type solutions. The phenomena of complexiton, resonant multiple wave and new resonant multiple wave type solutions are presented by figures.

Polymeric particle phase conjugator using degenerate four-wave mixing confocal microscopy

ABSTRACTWe have exploited a new microscope system for absorptive organic materials observation. The microscope includes a confocal optical system with a degenerate four-wave mixing (DFWM) system. The DFWM system increases backward scattering signal intensity. The DFWM causes wave mixing in a nonlinear optical (NLO) microsphere and generates phase conjugate wave by energy coupling based on polarization conversion. As a result, the experimental system, which causes energy coupling, can greatly improve in-plane contrast resolution of the existing microscope by applying it to observation of organic materials.

Complexiton solutions to soliton equations by the Hirota method

We apply the Hirota direct method to construct complexiton solutions (complexitons). The key is to use Hirota bilinear forms. We prove that taking pairs of conjugate wave variables in the 2N-soliton solutions generates N-complexion solutions. The general theory is used to construct multi-complexion solutions to the Korteweg–de Vries equation.

Three-dimensional measurement of chloroplast with degenerate four-wave mixing nonlinear confocal microscope

ABSTRACTWe report new confocal microscopy using degenerate four-wave mixing (DFWM) geometry for three-dimensional measurement of biological samples. DFWM nonlinear confocal microscope that applies phase conjugate (PC) wave to the conventional confocal microscope obtains optical resonant properties of the focal region. As a result, the microscope provides three-dimensional image of biological samples with high spatial resolution.

Enhancement of Photosensitivity of Photorefractive Ferroelectric Liquid Crystal Blends to Green and Red Wavelength Regions Using Oligothiophene Photoconductive Dopants

The photorefractive effect can be used to generate rewritable holograms in a material, and it is utilized in various devices, including three-dimensional displays, optical tomography units, novelty filters, phase conjugate wave generators, and optical amplifiers. Ferroelectric liquid crystal (FLC) blends composed of a smectic liquid crystalline mixture, a chiral photoconductive dopant, and an electron trap reagent exhibit significant photorefractivity together with rapid responses. In previous studies, terthiophene derivatives were used as chiral photoconductive dopants and the resulting photorefractive effects were examined at 488 nm. In order to utilize the photorefractive ferroelectric liquid crystals in practical devices such as photoacoustic interferometers and ultrasound imaging units, the wavelength sensitivity of the material should be extended to longer regions. In the present work, chiral dopants possessing quarter-thiophene chromophores, sexithiophenes, and other photoconductive compounds with ...

Inverse focusing inside turbid media by creating an opposite virtual objective.

Limited by the penetration depth, imaging of thick bio-tissues can be achieved only by epi-detection geometry. Applications based on forward-emitted signals or bidirectional illumination are restricted by lack of an opposite objective. A method for creating an opposite virtual objective inside thick media through phase conjugation was first proposed. Under forward illumination, the backward scattering light from the media was collected to generate a phase conjugate wave, which was sent back to the media and formed an inverse focusing light. Samples combined with a diffuser or a mouse skin were used as specimens. Inverse focusing was successfully demonstrated by applying holography-based optical phase conjugation with a BaTiO3. This result indicates the capability to create an opposite virtual objective inside live tissues. The proposed method is compatible with current coherent imaging and super-resolution imaging technologies. It creates a possible way for forward-emitted signals collection and bidirectional illumination in thick specimens.

Experimental demonstration of optical phase conjugation using counter-propagating dual pumped four-wave mixing in semiconductor optical amplifier

We report optical phase conjugation in C-band by counter-propagating dual pumped non-degenerate four-wave mixing in a semiconductor optical amplifier (SOA). The co-propagating signal and pump waves create a grating inside SOA which diffracts counter-propagating pump and generates the conjugate wave. Since the signal and conjugate waves appear at opposite ends, the conjugate is easily filtered out from the rest of spectrum with minimal spectral shift of the conjugate with respect to the incoming signal. With pump powers of −3.2dBm each and signal input power of −7dBm, conjugate power was of −27.2dBm, giving a conversion efficiency of 1% at 18GHz pump-signal detuning. By modulating the signal by a periodic pattern ‘1000’ at 10Gbps using a non-zero chirp intensity modulator and resolving the temporal profile of the electric field envelope of the conjugate wave, we demonstrate spectral inversion.

Coherent backscattering of phase conjugate ultrasound waves in dispersive systems

Processes of the propagation of phase conjugate ultrasound waves in stationary and moving random media containing micro-inclusions in the form of gas bubbles and solid spheres are studied experimentally and theoretically. The wave phase conjugation of sound at a frequency of 10 MHz is conducted via supercritical parametric conversion. The qualitative difference between the statistical properties of scattered and phase conjugate acoustic fields is established. Unlike the detected stochastic signals from scattered waves, the signals of the phase conjugate waves are regular and more useful in determining the concentrations and parameters of the scatterers. A theoretical model describing the observed features of the coherent backscattering of phase conjugate waves is developed.

Cascade generation of a phase conjugate wave in a magnetoordered acoustic medium

The cascade generation of second acoustic harmonics accompanied by simultaneous parametric wave phase conjugation in an α-Fe2O3 antiferromagnetic crystal in a transverse electromagnetic field is studied experimentally and theoretically. The necessary conditions for generation upon varying the direction of magnetization relative to the crystallographic axes and the direction of transverse sound wave propagation are determined. The observed effect is caused by magnetoelastic interaction and is described using the theory of giant effective elastic anharmonicity.

Phase conjugation of ultrasound waves in comparison with backscattering in disordered medium

Ultrasound wave phase conjugation in randomly scattering media is studied experimentally and treated theoretically in comparison with ordinary backscattering phenomenon. The experiments are carried out on a scattering sample made of a cylindrical agar gel matrix containing a set of glass micro-spheres of 300μm diameter. The sample was immersed in water and turned slowly for simulation of a statistical ensemble of scatterers. Phase conjugation of the scattered acoustic waves at frequency 10 MHz was implemented by the parametric technique. The signals of backscattered (BSW) and phase conjugate (PCW) waves were detected by the same ultrasonic transceiver. In contrast with the stochastic behaviour of the BSW signal, the PCW amplitude is found almost regular and insensitive to the statistical features of the scattering ensemble. The mean values of amplitudes and the signal to noise ratios for PCW are one order of value higher than for BSW. A variation of the number of scatterers in the aperture of the incident acoustic beam revealed the proportionality of the mean values of PCW amplitude and BSW signal intensity. The results are in quantitative agreement with the developed theory. The advantages of the phase conjugation technique in comparison with the backscattering method for testing of randomly scattering media are discussed.

Research of Voltage Amplitude Fluctuation and Compensation for Wound Rotor Brushless Doubly-Fed Machine

This paper presents an unexpected fluctuation of voltage for a 30-kW wound rotor brushless doubly-fed machine (BDFM) in a standalone power generation system. To address this issue, an improved method of harmonic injection is introduced. A voltage and current double closed-loop control strategy, based on control winding (CW) current decoupling, is applied through the entire experiment. Consequently, the experimental outcomes are fairly aligned with the dynamic simulations in most conditions. However, the voltage fluctuation in the power winding (PW) can be observed for a certain speed range. Harmonic analysis is then carried out on experimental data of PW voltage and CW current. A pair of interharmonic waves, which are symmetric with respect to the fundamental wave, is demonstrated to exist in PW voltage and CW current. Due to the analysis, these harmonic conjugate waves are caused by the high-order magnetomotive force tooth harmonics and current harmonics within a specific speed range. Accordingly, the control strategy of harmonic injection is employed to effectively eliminate these harmonic conjugate waves. The experimental results further highlight that the voltage amplitude can be maintained with less harmonic contents by our tailored control scheme. In addition, the formation and presence of harmonic conjugate waves may lead to the voltage amplitude fluctuation of BDFM in the standalone power generation system.

Time reversal technique for gas leakage detection.

The acoustic remote sensing of subsea gas leakage traditionally uses sonars as active acoustic sensors and hydrophones picking up the sound generated by a leak as passive sensors. When gas leaks occur underwater, bubbles are produced and emit sound at frequencies intimately related to their sizes. The experimental implementation of an acoustic time-reversal mirror (TRM) is now well established in underwater acoustics. In the basic TRM experiment, a probe source emits a pulse that is received on an array of sensors, time reversed, and re-emitted. After time reversal, the resulting field focuses back at the probe position. In this study, a method for enhancing operation of the passive receiving system has been proposed by using it in the regime of TRM. Two factors, the local character of the acoustic emission signal caused by the leakage and a resonant nature of the bubble radiation at their birth, make particularly effective scattering with the conjugate wave (CW). Analytical calculations are performed for the scattering of CW wave on a single bubble when CW is formed by bubble birthing wail received on an array, time reversed, and re-emitted. The quality of leakage detection depends on the spatio-temporal distribution of ambient noise.

Acoustic phase conjugation in a three-phase medium

Acoustic phase conjugation is studied in a sandy marine sediment that contains air bubbles in its fluid fraction. The considered phase conjugation is a four-wave nonlinear parametric sound interaction caused by nonlinear bubble oscillations which are known to be dominant in acoustic nonlinear interactions in three-phase marine sediments. Two various mechanisms of phase conjugation are studied. One of them is based on the stimulated Raman-type sound scattering on resonance bubble oscillations. The other is associated with sound interactions with bubble oscillations whose frequencies are far from resonance bubble frequencies. Nonlinear equations to solve the phase conjugation problem are derived, expressions for acoustic wave amplitudes with a conjugate wave front are obtained and compared for various frequencies of the excited bubble oscillations.