Soliton Energy Research Articles

Cardy-like formula for the Schwarzschild black hole entropy

The main part of this work is to present a formula allowing a microscopic derivation of the Schwarzschild black hole entropy in arbitrary dimension. More generally, this Cardy-like formula applies for static black holes whose gravitational entropy scales as a power of the temperature, and is also effective for negative heat capacity solutions. The formula involves the scaling power, the black hole mass and the energy of a gravitational soliton identified as the ground state of the theory. The robustness of this formula is verified in the most famous example of solution with negative heat capacity, namely the Schwarzschild black hole. The mass of the Schwarzschild regular soliton is computed using the counterterm method for asymptotically flat spacetimes. Corrections of the black hole entropy of the order of logarithm of the area are shown to arise for dimensions strictly greater than four. Finally, we will see that a slight modification of the Cardy-like formula involving the angular generator, perfectly reproduces the four-dimensional Kerr entropy.

Parton-like soliton structures in nonlinear coherent states

Nonlinear analogues of coherent states arise in the framework of the nonlinear Schrödinger equation models with confining harmonic oscillator potentials. We clarify the profound physical linkage between the quantum-mechanical Schrödinger coherent states and their nonlinear solitonic analogues. Guided by remarkable, but obviously only formal analogy between the soliton negative self-action energy and the nuclear binding energy, we reveal how the nonlinear ground and coherent states could be built up from the parton-like solitonic constituents when the absolute value of the soliton binding energy increases. The enhancement of the soliton binding energy contribution in the total conserved energy of the nonlinear ground and coherent states radically changes their internal structures and allows one to apply the formal analogies from the parton model of nucleons.

Manipulating Soliton Polarization in Soliton Self-Frequency Shift and Its Application to 3-Photon Microscopy in Vivo

Soliton self-frequency shift (SSFS) enables energetic femtosecond pulse generation and deep-brain 3-photon microscopy (3PM) in animal models in vivo. The signal level in 3PM is currently limited by the available soliton energy. Here we propose a new maneuverable physical parameter that enables more energetic soliton generation through SSFS in a photonic-crystal (PC) rod. Through both theory and experiment, we demonstrate that circularly-polarized solitons are 1.5 times more energetic than previously reported linearly-polarized solitons. We further demonstrate comparative 3PM of the white matter layer in the mouse brain in vivo with both circularly-polarized and linearly-polarized solitons. The 3.7 times higher 3PM signal excited with circularly-polarized solitons indicates that this novel nonlinear optical technique is promising for 3PM.

Propagation characteristics of parallel dark solitons in silicon-on-insulator waveguide**Project supported by the National Natural Science Foundation of China (Grant No. 61741509).

The propagation characteristic of two identical and parallel dark solitons in a silicon-on-insulator (SOI) waveguide is simulated numerically using the split-step Fourier method. The parallel dark solitons imposed by the initial chirp are investigated mainly by changing their power, their relative time delay. The simulation shows that the time delay deforms the parallel dark soliton pulse, forming a bright-like soliton in the transmission process and making the transmission quality down. By increasing the power of one dark soliton, the energy of the other dark soliton can be increased, and larger increase in a soliton’s power leads to larger increase in the energy of the other. When the initial chirp is introduced into one of the dark solitons, higher energy consumption is observed. In particular, positive chirps resulting in pulse broadening width while negative chirps narrowing, with an obvious compression effect on the other dark soliton. Finally, large negative chirps are found to have a profound impact on parallel and nonparallel dark solitons.

Investigations of energy and an exchange of energies between electrostatic solitons: higher-order corrections and efficiency improvement of semiconductor plasmas

ABSTRACT Investigations of the nonlinear excitation and collisions of electrostatic solitons in a dense semiconductor plasma composed of electrons and holes are improved by using the higher-order corrections. Applying the extended Poincaré-Lighthill-Kuo (EPLK) method to obtain the Korteweg–de Vries (KdV) equations, which govern the nonlinear excitation of electrostatic solitons. Furthermore, the phase shift equations due to the collisions between electrostatic solitons are obtained. A theoretical analysis is improved by employing the KdV equations with the effects of the fifth – order dispersion terms. The numerical illustrations demonstrate that the higher-order soliton energy depends significantly on the quantum semiconductor plasma number density. On the other hand, the density of the semiconductor plasma has a weak effect on the lowest-order soliton energy. Therefore, one has to be careful about the choosing semiconductor plasma parameters to avoid any deficiency of the modern semiconductor devices.

Contribution of higher order corrections to the dust acoustic soliton energy in non-Maxwellian dusty plasma

The contribution of higher order corrections to the DA soliton energy in the presence of nonthermal ions is investigated. Our plasma model is inspired from the experimental study of Bandyopadhyay et al. [P. Bandypadhyay, G. Prasad, A. Sen, P.K. Kaw, Phys. Rev. Lett. 101, 065006 (2008)]. Using the approach based on the expansion of Sagdeev potential up to the fourth-order, a second order inhomogeneous differential equation termed dressed soliton is obtained. The latter is divided into two contributions, the usual K-dV solution and the higher order correction structure. Our results reveal that the main quantities of these localized structures are significantly modified by the nonthermality effects. In particular, an increase of ion’s nonthermal character leads to an increase of the amplitude and width of all the structures. The role the higher order corrections and nonthermal ions may play on the energy carried by the DA soliton is then examined. For a given value of nonthermal parameter α, it is shown that due to the higher order correction contribution, the departure between the K-dV soliton energy and the dressed one becomes more important as soliton velocity λ increases. For the sake of comparison, the presented model is reduced to a Maxwellian plasma and the results are compared to their experimental counterparts.

Improvements of Soliton Pulse Energy and Peak Power in Thulium-Doped Fiber Laser

We report on improvements of mode-locked soliton pulse energy and peak power in a thulium-doped fiber laser. At the pump power of 370 mW, conventional soliton can be first generated using nonlinear polarization rotation technology. By increasing the pump power to 550 mW and appropriately adjusting cavity polarization state, the conventional soliton pulse can be converted into the Gaussian pulse. Due to dispersion management, excess accumulation of nonlinear phase shifts in the cavity can be avoided. In this case, the pulse energy and peak power can be increased from 77 pJ to 1.38 nJ and from 106.9 W to 2.67 kW, respectively. These improvements indicate that the Gaussian pulse operation can effectively enhance the pulse energy and peak power of the thulium-doped fiber laser.

Soliton bursts and deterministic dissipative Kerr soliton generation in auxiliary-assisted microcavities

Dissipative Kerr solitons in resonant frequency combs offer a promising route for ultrafast mode-locking, precision spectroscopy and time-frequency standards. The dynamics for the dissipative soliton generation, however, are intrinsically intertwined with thermal nonlinearities, limiting the soliton generation parameter map and statistical success probabilities of the solitary state. Here, via use of an auxiliary laser heating approach to suppress thermal dragging dynamics in dissipative soliton comb formation, we demonstrate stable Kerr soliton singlet formation and soliton bursts. First, we access a new soliton existence range with an inverse-sloped Kerr soliton evolution—diminishing soliton energy with increasing pump detuning. Second, we achieve deterministic transitions from Turing-like comb patterns directly into the dissipative Kerr soliton singlet pulse bypassing the chaotic states. This is achieved by avoiding subcomb overlaps at lower pump power, with near-identical singlet soliton comb generation over twenty instances. Third, with the red-detuned pump entrance route enabled, we uncover unique spontaneous soliton bursts in the direct formation of low-noise optical frequency combs from continuum background noise. The burst dynamics are due to the rapid entry and mutual attraction of the pump laser into the cavity mode, aided by the auxiliary laser and matching well with our numerical simulations. Enabled by the auxiliary-assisted frequency comb dynamics, we demonstrate an application of automatic soliton comb recovery and long-term stabilization against strong external perturbations. Our findings hold potential to expand the parameter space for ultrafast nonlinear dynamics and precision optical frequency comb stabilization.

Super-sech Soliton Dynamics in Optical Metamaterials with Generally Parabolic Law of Nonlinearity Using Lagrangian Variational Method

Aims/ Objectives: This paper studies the impact of the generally parabolic law of nonlinearity on the evolution of the energy of super-sech soliton dynamics.Study Design: generally parabolic law of nonlinearity terms study.
 Place and Duration of Study: Department of Physics, Faculty of Sciences and Technology(FAST),
 University of Abomey Calavi, B´ enin. between Febuary 2018 and January 2019.
 Methodology: Variational approach, namely, the Lagrangian Variational Method (LVM) is presented. The different results are obtained using standard fourth order Runge-Kutta method for integration of the system of ordinary differential equation systems.Results: Dynamics of the different parameters (amplitude, center position, pulse width, chirp, frequency and phase) has been presented with respect to propagating distance.Conclusion: This study reveals that the generally parabolic law of nonlinearity terms don’t affect the energy of the system but influence the pulse phase.

Externally driven nonlinear Dirac equation revisited: theory and simulations

The externally driven nonlinear Dirac (NLD) equation with scalar-scalar self-interaction studied in (2016 J. Phys. A: Math. Theor. 49 065402) is revisited. By using a variational method and an ansatz with five collective coordinates, the dynamics of the NLD solitons is well described. It is shown that this new ansatz possesses certain advantages, namely the canonical momentum agrees with the field momentum, the energy associated to the collective coordinate equations agrees with the energy of the NLD soliton, whereas the ansatz with either three or four collective coordinates does not. Thus the study of the whole phase space of the system is enhanced. It is also shown that this approach is equivalent to the method of moments: the time variation of the charge, the momentum, the energy, and the first moment of the charge. The advantages of the new ansatz are illustrated by means of numerical simulations.

Energy-sharing collisions and the dynamics of degenerate solitons in the nonlocal Manakov system

In this paper, by considering the degenerate two bright soliton solution of the nonlocal Manakov system, we bring out three different types of energy-sharing collisions for two different parametric conditions. Among the three, two of them are new which do not exist in the local Manakov equation. By performing an asymptotic analysis to the degenerate two-soliton solution, we explain the changes which occur in the quasi-intensity/quasi-power, phase shift and relative separation distance during the collision process. Remarkably, the intensity redistribution reveals that in the new types of shape-changing collisions, the energy difference of soliton in the two modes is not preserved during collision. In contrast to this, in the other shape-changing collision, the total energy of soliton in the two modes is conserved during collision. In addition to this, by tuning the imaginary parts of the wave numbers, we observe localized resonant patterns in both the scenarios. We also demonstrate the existence of bound states in the nonlocal Manakov equation during the collision process for certain parametric values.

25 nJ, 634 ps and 1 MHz all-fiber passively mode-locked fiber laser based on a GaAs saturable absorber

We demonstrate an all-fiber passively mode-locked Tm-Ho co-doped fiber laser based on a GaAs saturable absorber (SA) fiber laser at 1875.2 nm. With a 10% output coupler, the fiber laser outputs 1.13 MHz, 634 ps and 25 nJ pulses at 1875.2 nm with a 3 dB-bandwidth of 18.4 nm. The Q-switched mode-locking (QML), the mode-locking at fundamental repetition rate (FRR) and the mode-locking at second harmonic of repetition rate (SHRR) are also observed with the increase of the pump power. The main reason of the SHRR is soliton pulse energy quantization effect.

Wave‐Packet Dynamics in Nonlinear Disordered Chains under the Effect of Acoustic Waves

In this work, the wave‐packet dynamics is considered under the effect of diagonal disorder distribution, electron–lattice interaction, and acoustic‐wave pumping. Electronic transport is taken into account quantum mechanically, whereas lattice vibrations are described through a classical nonlinear Morse Hamiltonian. The electronic hopping term takes the form of an exponential function of the effective distance between nearest‐neighbor lattice elements. The electron wave‐packet is initially localized at the first site of the chain alongside a Gaussian pulse generator. The results suggest that the disorder distribution breaks down the solitonic energy profile that exists within this kind of nonlinear Morse lattice. On the other hand, it is shown that the acoustic pumping sustains the wave packet dynamics within this disordered nonlinear model.

Effect of Superthermal Polarization Force on Dust Acoustic Nonlinear Structures

Abstract An investigation of the dust acoustic shock waves as well as solitary waves in an unmagnetized dusty plasma consisting of fluid of negatively charged dust grains, superthermal ions, and Maxwellian electrons under the influence of superthermally modified polarization force is presented. The polarization force is significantly influenced by superthermal ions. Reductive perturbation technique has been used to derive the Korteweg-de Vries-Burgers equation. It is illustrated that the superthermal polarization force significantly alters the characteristics of the negative polarity shock and solitary waves. It is also examined that the soliton energy gets depleted by the influence of superthermal polarization force.

Dark gap solitons in exciton-polariton condensates in a periodic potential.

We show that dark spatial gap solitons can occur inside the band gap of an exciton-polariton condensate (EPC) in a one-dimensional periodic potential. The energy dispersions of an EPC loaded into a periodic potential show a band-gap structure. Using the effective-mass model of the complex Gross-Pitaevskii equation with pump and dissipation in an EPC in a periodic potential, dark gap solitons are demonstrated near the minimum energy points of the band center and band edge of the first and second bands, respectively. The excitation energies of dark gap solitons are below these minimum points and fall into the band gap. The spatial width of a dark gap soliton becomes smaller as the pump power is increased.

Spectral methods for coupled channels with a mass gap

We develop a method to compute the vacuum polarization energy for coupled scalar fields with different masses scattering off a background potential in one space dimension. As an example we consider the vacuum polarization energy of a kink-like soliton built from two real scalar fields with different mass parameters.

Dissipative nonlinear waves in a gravitating quantum fluid

Nonlinear wave propagation is studied analytically in a dissipative, self-gravitating Bose Einstein condensate, in the framework of Gross-Pitaevskii model. The linear dispersion relation shows that the effect of dissipation is to suppress dynamical instabilities that destabilize the system. The small amplitude analysis using reductive perturbation technique is found to yield a modified form of KdV equation. The soliton energy, amplitude and velocity are found to decay with time, whereas the soliton width increases, such that the soliton exists for a finite time only

Energy of nonlinear electron acoustic solitons in electron positron ion plasma

A rigorous theoretical investigation is made to find energy of EASWs in unmagnetized collisionless plasma having stationary ions, cold electrons, hot electrons and hot positrons. By employing reductive perturbation method KdV equation is derived and solution of KdV equation is proposed by homotopy perturbation method (HPM) in two cases, i.e. in kappa distribution and in Cairns distribution. The consequences of different parameters variation on soliton profile have been studied. It is noticed amplitude and width of soliton are sensitive to k (spectral index of kappa distributed populations) i.e. increasing k makes an increase in soliton amplitude and width. It is also found dip and hump type solitons exist due to presence of electrons and positrons and σ=Te/TP affects the dip and hump type solitons profile. Also we found energy of soliton in kappa distribution and in Cairns distribution. This work may be helpful for astronomers and space investigators, working on planetary magneto spheres, earth's ionosphere auroral zone, and interstellar space plasmas etc.

Soliton dynamics for a nonintegrable model of light-colloid interactive fluids

A nonintegrable model with the super-Kerr nonlinearity is investigated, which describes the light-matter interactions in a fluidic suspension of colloidal nanoparticles. Existence of the solitons with semi-analytic forms is shown for this model via the variational method. Numerical simulation is performed to demonstrate the good accordance with the variational analysis. Soliton interactions and soliton bound states are discussed in both the homogeneous and inhomogeneous media. In particular, inelastic interactions of two solitons are presented, and we find that there is an energy distribution $$P_\pm $$ , which has a dependence with the velocity of the high-energy solitons. Simulations also reveal that the maximum value of $$P_-$$ relates with the soliton energy and the model parameter $$\beta $$ . Moreover, two different patterns of the three-soliton interactions are depicted as manifestation of the nonintegrability.

Dzyaloshinskii–Moriya solitons in anisotropic ferromagnetic nanowires driven by magnetic field and spin-polarized current

We theoretically investigate the Dzyaloshinskii–Moriya solitons driven by the magnetic field and spin-polarized current in anisotropic ferromagnetic nanowires. The external field and Dzyaloshinskii–Moriya interaction determine the formation region of soliton solution and the corresponding phase diagram is given for different types of solitons. The Dzyaloshinskii–Moriya interaction affects the internal structure distortion of solitons which determines the soliton energy. Also, we obtain the critical value of Dzyaloshinskii–Moriya interaction for soliton formation. The roles of Dzyaloshinskii–Moriya interaction effect on the soliton energy are completely opposite for the solitons of type I and type II in ferromagnetic nanowires.