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Alfven waves are a ubiquitous feature of the solar wind. One approach to studying the evolution of such waves has been to study exact solutions to approximate evolution equations. Here we compare soliton solutions of the Derivative Nonlinear Schrodinger evolution equation (DNLS) to solutions of the compressible MHD equations.
This work focuses on the study of the stability of trapped soliton-like solutions of a (1 + 1)-dimensional nonlinear Schrödinger equation (NLSE) in a nonlocal, nonlinear, self-interaction potential of the form [|Ψ(x,t)| 2 +|Ψ(-x,t)| 2 ] κ where κ is an arbitrary nonlinearity parameter. Although the system with κ = 1 (i.e. fully integrable case) was first reported by Yang (2018 Phys. Rev. E 98 042202), here in the present work, we extend this model to the one in which κ is arbitrary. This allows us to compare the stability properties of the now trapped solutions to previously found solutions of the more usual NLSE with κ ≠ 1 which are moving soliton solutions. We show that there is a simple, one-component, nonlocal Lagrangian and corresponding action governing the dynamics of the system. Using a collective coordinate method derived from the action as well as assuming the validity of Derrick's theorem, we find that these trapped solutions are stable for 0 < κ < 2 and unstable when κ > 2. At the critical value of κ, i.e. κ = 2, the solution can either collapse or blowup linearly in time when q 0 = 0, where q 0 is the center of the initial density ρ(x, t = 0) = ψ*ψ of the solution. For q 0 ≠ 0 the displaced solution collapses. When κ > 2 initial small displacements from the origin also lead to collapse of the wave function. This phenomenon is not seen in the usual NLSE.
We simulate experimental conditions for nonlinear spectral broadening and compression of multi-joule, sub-picosecond, and femtosecond laser systems focusing on 1 μm center wavelength. The spatial, spectral, and temporal properties of two distinct cases are investigated in detail. The first system is a short multi-pass cell with 0.1–0.5 J pulse energy operated at higher helium pressures, used to illustrate the transition between Kerr-effect induced spectral broadening and spectral broadening in plasma. The second case is a long ten-joule multi-pass cell operated at few Pascal pressure range. These examples cover the operational extent of plasma spectral broadening in a multi-pass cell. Here effects pertaining to plasma spectral broadening, including imperfect spatial beam profiles and initial non-zero nonlinear phase, are investigated, as well as scalability.
The evolution of strongly nonlinear, strongly modulated wave packets is investigated in a dispersive plasma using a hybrid numerical code. These wave packets have amplitudes exceeding the strength of the external magnetic field, along which they propagate. Alfven (left helicity) wave packets show strong steepening for p < 1, while fast (fight heIicity) wave packets hardly steepen for any beta. Substantial regions of opposite helicity form on the leading side of steepened Alfven wave packets. This behavior differs qualitatively from that exhibited by the solutions to the derivative nonlinear Schrodinger (DNLS) equation.
Nonlinear optics is the result of laser beam interaction with materials and started with the advent of lasers in the early 1960s. The field is growing daily and plays a major role in emerging photonic technology. Nonlinear optics play a major role in many of the optical applications such as optical signal processing, optical computers, ultrafast switches, ultra-short pulsed lasers, sensors, laser amplifiers, and many others. This special review volume on Nonlinear Optics and Applications is intended for those who want to be aware of the most recent technology. This book presents a survey of the recent advances of nonlinear optical applications. Emphasis will be on novel devices and materials, switching technology, optical computing, and important experimental results. Recent developments in topics which are of historical interest to researchers, and in the same time of potential use in the fields of all-optical communication and computing technologies, are also included. Additionally, a few new related topics which might provoke discussion are presented. The book includes chapters on nonlinear optics and applications; the nonlinear Schrodinger and associated equations that model spatio-temporal propagation; the supercontinuum light source; wideband ultrashort pulse fiber laser sources; lattice fabrication as well as their linear and nonlinear light guiding properties; the second-order EO effect (Pockels), the third-order (Kerr) and thermo-optical effects in optical waveguides and their applications in optical communication; and, the effect of magnetic field and its role in nonlinear optics, among other chapters.
Theoretical and numerical works in atmospheric turbulence have used the Navier-Stokes fluid equations exclusively for describing large-scale motions. Controversy over the existence of an average temperature gradient for the very large eddies in the atmosphere suggested that a new theoretical basis for describing large-scale turbulence was necessary. A new soliton formalism as a fluid analogue that generalizes the Schrodinger equation and the Zakharov equations has been developed. This formalism, processing all the nonlinearities including those from modulation provided by the density fluctuations and from convection due to the emission of finite sound waves by velocity fluctuations, treats large-scale turbulence as coalescing and colliding solitons. The new soliton system describes large-scale instabilities more explicitly than the Navier-Stokes system because it has a nonlinearity of the gradient type, while the Navier-Stokes has a nonlinearity of the non-gradient type. The forced Schrodinger equation for strong fluctuations describes the micro-hydrodynamical state of soliton turbulence and is valid for large-scale turbulence in fluids and plasmas where internal waves can interact with velocity fluctuations.
A new phenomenon in nonlinear dispersive systems, including a Bose-Einstein Condensate (BEC), has been described. It is based upon a resonance between an externally induced soliton and 'eigen-solitons' of the homogeneous cubic Schrodinger equation. There have been shown that a moving source of positive /negative potential induces bright /dark solitons in an attractive / repulsive Bose condensate.
We present a theoretical study of temporal, spectral, and spatial reshaping of intense, ultrafast x-ray pulses propagating through a resonant medium. Our calculations are based on the solution of a three-dimensional time-dependent Schrodinger-Maxwell equation, with the incident x-ray photon energy on resonance with the core-level is-3p transition in neon. We study the evolution of the combined incident and medium-generated field, including the effects of stimulated emission, absorption, ionization, and Auger decay, as a function of the input pulse energy and duration. We find that stimulated Raman scattering between core-excited states 1s -1 3p and 2p -1 3p occurs at high x-ray intensity, and that the emission around this frequency is strongly enhanced when also including the similar 1s -1 -2p -1 response of the ion. We also explore the dependence of x-ray self-induced transparency (SIT) and self-focusing on the pulse intensity and duration, and we find that the stimulated Raman scattering plays an important role in both effects. Finally, we discuss how these nonlinear effects may potentially be exploited as control parameters for pulse properties of x-ray free-electron laser sources.
Second-order nonlinear optical processes including second-harmonic generation, optical rectification, and difference-frequency generation associated with intersubband transitions in wurtzite GaN/AlGaN quantum well (QW) are investigated theoretically. Taking into account the strain-induced piezoelectric (PZ) effects, we solve the electronic structure of the QW from coupled effective-mass Schrodinger equation and Poisson equation including the exchange-correlation effect under the local-density approximation. We show that the large PZ field in the QW breaks the symmetry of the confinement potential profile and leads to large second-order susceptibilities. We also show that the interband optical pump-induced electron-hole plasma results in an enhancement in the maximum value of the nonlinear coefficients and a redshift of the peak position in the nonlinear optical spectrum. By use of the difference-frequency generation, THz radiation can be generated from a GaN/Al(0.75)Ga(0.25)N with a pump laser of 1.55 micron.
Imaging laser-induced rotational dynamics is an important and active field due to its applications in capturing reactions in the molecular frame and in molecular imaging. Experimental measurement of the molecular orientation distribution, as a function of the Euler angles, has only been demonstrated for special cases when the detectable signal is generated along the molecular symmetry axis. Here we developed the general theory that maps the probability density distribution of the molecular orientation to the atom-pair angular distributions for nonlinear molecules. With the theory, the molecular orientation distribution can be retrieved from the measured atom-pair angular distribution, which we demonstrate experimentally using ultrafast electron diffractive imaging of impulsively aligned trifluoro-iodomethane molecules. Here, the retrieved molecular orientation distribution is in good agreement with direct numerical simulations of the time-dependent Schrodinger equation using the experimental conditions. Unlike the existing retrieval methods, the retrieval method does not require solving Schrodinger equation, works for any alignment method, and is in principle applicable to asymmetric top molecules.
Our research and technology are focused on nonlinear issues in the aerothermochemistry of gases and materials and the associated physics and dynamics of interfaces. Our program is now organized to aggressively support the NASA Aeronautics Enterprise so as to: (a) develop a new generation of environmentally compatible, economic subsonic aircraft; (b) develop the technology base for an economically viable and environmentally compatible high-speed civil transport; (c) develop the technology options for new capabilities in high-performance aircraft; (d) develop hypersonic technologies for air-breathing flight; and (e) develop advanced concepts, understanding of physical phenomena, and theoretical, experimental, and computational tools for advanced aerospace systems. The implications from our research for aeronautical and aerospace technology have been both broad and deep. For example, using advanced computational techniques, we have determined exact solutions for the Schrodinger equation in electron-molecule scattering allowing us to evaluate atmospheric models important to reentry physics. We have also found a new class of exact solutions for the Navier Stokes equations. In experimental fluid dynamics, we have found explicit evidence of turbulence modification of droplet sizes in shock tube flow with condensation. We have developed a new diagnostic tool for the direct estimation of flow velocities at MHz sampling rates in quasi-one dimensional turbulent flow. This procedure suggests an unexpected confirmation of the possibility of 'natural' closure in Reynolds stresses with deep implications for the development of turbulent models. A transient increase is observed in both the spectral energy decay rate and the degree of chaotic complexity at the interface of a shock wave and a turbulent ionized gas. Even though the gas is apparently brought to rest by the shock wave, no evidence is found either of the expected relaminarization. A unique diamond-shaped nozzle has been designed for a detailed investigation of the effect of significant streamwise vorticity on the acoustic and IR characteristics of supersonic jets. Our results provide convincing evidence of the significant effect of vorticity on the far-field noise for the diamond jet as compared to the conventional round jets. We have found that the countercurrent shear layer mixes much more efficiently than conventional coflowing shear layers. We also developed the fluid thrust vectoring procedures which use counter flow to vector a jet. Our materials research has shown that the steep stress gradients at the fiber-matrix interface could be the primary cause of interface cracks after the processing of metallic and intermetallic matrix composites. New techniques have been evolved for: the microcharacterization of materials including microplastic strain and, point by point, the misorientation and plasticity for matrix composites; thermally induced stress measurements and load relaxation; the growth and characterization of metallic matrix composite interfaces; and for the growth of ferrite materials by pulsed laser deposition. The FAMU commitment to the HBCU Research Center also continues to be broad and deep.
Motivated by a similar approach for Born-Oppenheimer molecular dynamics, this paper proposes an extended "shadow" Lagrangian density for quantum states of superfluids. The extended Lagrangian contains an additional field variable that is forced to follow the wave function of the quantum state through a rapidly oscillating extended harmonic oscillator. By considering the adiabatic limit for large frequencies of the harmonic oscillator, we can derive the two equations of motions, a Schrödinger-type equation for the quantum state and a wave equation for the extended field variable. The equations are coupled in a nonlinear way, but each equation individually is linear with respect to the variable that it defines. The computational advantage of this new system is that it can be easily discretized using linear time stepping methods, where we propose to use a Crank-Nicolson-type approach for the Schrödinger equation and an extended leapfrog scheme for the wave equation. Furthermore, the difference between the quantum state and the extended field variable defines a consistency error that should go to zero if the frequency tends to infinity. By coupling the time-step size in our discretization to the frequency of the harmonic oscillator we can extract an easily computable consistency error indicator that can be used to estimate the numerical error without additional costs. The findings are illustrated in numerical experiments.
One of the most surprising consequences of quantum mechanics is entanglement of two or more distance particles. The two-particle entangled state was mathematically formulated by Schrodinger. Based on this unusual quantum behavior, EPR defined their 'physical reality' and then asked the question: 'Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?' One may not appreciate EPR's criterion of physical reality and insist that 'no elementary quantum phenomenon is a phenomenon until it is a recorded phenomenon'. Optical spontaneous parametric down conversion (SPDC) is the most effective mechanism to generate an EPR type entangled two-photon state. In SPDC, an optical beam, called the pump, is incident on a birefringent crystal. The pump is intense enough so that nonlinear effects lead to the conversion of pump photons into pairs of photons, historically called signal and idler. Technically, the SPDC is said to be type-1 or type-2, depending on whether the signal and idler beams have parallel or orthogonal polarization. The SPDC conversion efficiency is typically on the order of 10(exp -9) to 10(exp -11), depending on the SPDC nonlinear material. The signal and idler intensities are extremely low, only single photon detection devices can register them. The quantum entanglement nature of SPDC has been demonstrated in EPR-Bohm experiments and Bell's inequality measurements. The following two experiments were recently performed in our laboratory, which are more closely related to the original 1935 EPR gedankenezperiment. The first experiment is a two-photon optical imaging type experiment, which has been named 'ghost image' by the physics community. The signal and idler beams of SPDC are sent in different directions, so that the detection of the signal and idler photons can be performed by two distant photon counting detectors. An aperture object (mask) is placed in front of the signal photon detector and illuminated by the signal beam through a convex lens. Surprisingly, an image of this aperture is observed in the idler beam, by scanning the idler photon detector in the transverse plane of the idler beam, if we are sure that the idler photon detector 'catches' the 'twin brother' of the signal, which can be easily performed by a coincidence measurement. This effect is even more striking when we found that the object-lens-image relationship satisfies the Gaussian thin lens equation. The second experiment demonstrates two-photon 'ghost' interference-diffraction. The experimental set up is similar to the image experiment, except that rather than a lens and an aperture it is a Young's double-slit (or a single-slit) inserted into the path of the signal beam. We could not find any interference (or diffraction) pattern behind the slit. Surprisingly, an interference (or diffraction) pattern is observed when scanning the detector in the idler beam, if we are sure that the idler photon detector 'catches' the 'twin brother' of the signal.