Sequence Of Solitons Research Articles

Dark spatial solitons splitting in logarithmically saturable nonlinear media

We numerically simulate the evolution of the dark-notch-bearing optical beam in the logarithmically saturable nonlinear media based on beam propagation method (BPM). The simulation results indicate that the multiple dark spatial solitons are deep, possible in this type of nonlinear media. The number of multiple dark spatial solitons depends on the width of the dark notch, the initial conditions and the peak intensity of the initial input beam. Under the odd and even initial conditions, the odd and even number sequence of multiple dark spatial solitons can be obtained, respectively. For an input beam with fixed optical intensity, the number of dark solitons increases with the width of the initial input dark notch. The behavior of the multiple dark solitons in this type of media is similar to that in a photorefractive nonlinear crystal.

Stable long-distance propagation and on-off switching of colliding soliton sequences with dissipative interaction

We study propagation and on-off switching of two colliding soliton sequences in the presence of second-order dispersion, Kerr nonlinearity, linear loss, cubic gain, and quintic loss. Employing a Lotka-Volterra (LV) model for dynamics of soliton amplitudes along with simulations with two perturbed coupled nonlinear Schr\"odinger (NLS) equations, we show that stable long-distance propagation can be achieved for a wide range of the gain-loss coefficients, including values that are outside of the perturbative regime. Furthermore, we demonstrate robust on-off and off-on switching of one of the sequences by an abrupt change in the ratio of cubic gain and quintic loss coefficients, and extend the results to pulse sequences with periodically alternating phases. Our study significantly strengthens the recently found relation between collision dynamics of sequences of NLS solitons and population dynamics in LV models, and indicates that the relation might be further extended to solitary waves of the cubic-quintic Ginzburg-Landau equation.

Steady-state multiple dark photovoltaic spatial solitons

We theoretically study the formation of the steady state multiple dark photovoltaic spatial solitons in the photovoltaic photorefractive crystal under open-circuit conditions. The results indicate that the initial dark notch width at the entrance face of the crystal is a key parameter for generating an even (or odd) number sequence of multiple dark photovoltaic solitons. The dark notch is generated from a phase or amplitude discontinuity in the center of the input beam. If the initial width of the dark notch is small, only a fundamental soliton or a Y-junction soliton is generated. As the initial width of the dark notch is increased, the dark notch tends to split into an odd (or even) number of multiple dark photovoltaic solitons, realizing a progressive transition from a lower-order soliton to the higher-order multiple solitons. When the multiple dark photovoltaic solitons are generated, the separations between adjacent dark solitons become smaller. Solitons pairs become progressively wider and less visible as their transverse distance from the central dark soliton increases and they move away from each other as they propagate in the photorefractive nonlinear crystal.

Formation of multiple dark photovoltaic spatial solitons

We theoretically study the formation of multiple dark photovoltaic soliton splitting in the quasi-steady-state and steady-state regimes under open-circuit conditions. We find that the initial width of the dark notch at the entrance face of the crystal is a key parameter for generating an even (or odd) number sequence of dark coherent photovoltaic solitons. If the initial width of the dark notch is small, only a fundamental soliton or Y-junction soliton pair is generated. As the initial width of the dark notch is increased, the dark notch tends to split into an odd (or even) number of multiple dark photovoltaic solitons, which realizes a progressive transition from a low-order soliton to a sequence of higher-order solitons. The soliton pairs far away from the centre have bigger width and less visibility. In addition, when the distance from the centre of the dark notch increases, the separations between adjacent dark stripes become slightly smaller.

Ultrafast two-bit all-optical analog-to-digital conversion based on femtosecond soliton sequence sampling

Realization of two-bit all-optical analog-to-digital conversion for an analog signal sampled by a femtosecond soliton sequence is investigated. Two approaches are suggested. The first one is based on filtering the broadened soliton spectrum after evolution over half of the soliton period in a standard single-mode fiber. In the second approach, the pulse is temporally sampled at the specified times after propagating through one soliton period. The sampled soliton sequence must be amplified to achieve an initial peak power of between 0 and 75 kW for the first method and between 0 and 66 kW for the second method. The soliton pulse-width is 50 fs. Based on the resulted peak power, the "0" or "1" bit is generated with reference to the threshold values. Subsequently, the digital gray code is produced at the outputs. The effect of inaccuracy in filter frequency and fiber length are also studied in this paper. The first method is sensitive to variations in the filter frequency, whereas the second method is affected by the fiber length inaccuracy.

Monsoon regulation of Lombok Strait internal waves

[1] We use satellite imagery and numerical modeling to investigate the characteristics of Lombok Strait nonlinear internal waves in relation to the dominant monsoon seasonality. Two basic wave types are identified, the first of which represents the well-known arc-like internal wave (AIW) that radiates uniformly away from its generation region near the sill in regular sequences of ranked solitons. This component is best defined to the north of the strait and is the main focus of our paper. A second type (termed here the “irregular internal wave”) manifests to the south in association with extensive throughflow plumes and appears in distorted, braided assemblages with orientations that are incompatible with uniform outward motion from the sill. Synthetic aperture radar (SAR) data show that the northward-propagating AIWs are often observed during the boreal winter monsoon, when the southward throughflow weakens. A potential cause of this seasonal behavior is revealed by advanced numerical modeling, which indicates that strong southward throughflows during the southeast monsoon greatly constrain the northward tidal influx, particularly near the surface, thereby inhibiting embryonic wave growth at the leading edge of the intrusion and producing comparatively weak internal wave release. This new mechanism operates alongside other possible seasonal influences on SAR internal wave detection relating, for example, to wind or stratification. Our findings suggest that long-term modifications to the Lombok Strait throughflow, due to evolution of the monsoon and/or the El Nino–Southern Oscillation, could retune the energy, composition, and directionality of internal wavefields radiated from the passage.

Multiple incoherent gray photorefractive spatial solitons

We show that an even-number sequence of multiple incoherent gray photorefractive spatial screening solitons is possible. When the external voltage is small, only an incoherent Y-junction photorefractive spatial screening soliton is generated, corresponding to the lowest order in the even-number incoherent soliton sequence. When the external voltage is increased, the incoherent gray soliton beam splits into an even-number sequence of multiple incoherent gray photorefractive spatial screening solitons. For a given physical system such an even-number sequence of multiple incoherent gray photorefractive spatial screening solitons is obtained by either increasing the external voltage and decreasing the full width half maximum (FWHM) of the beam's intensity or increasing the external voltage and decreasing the beam's grayness.

Observation of the modulation instability and spin wave solitons in ferromagnetic films under the conditions of coexistence of four-wave and three-wave parametric processes

Nonlinear phenomena that arise during the propagation of spin waves in thin ferromagnetic films under conditions of the simultaneous existence of three-wave and four-wave parametric processes have been investigated. Investigations have been performed for single-frequency and double-frequency regimes of excitation of intense spin waves. The spontaneous modulation instability of the monochromatic running spin wave has been revealed for the first time at frequencies at which three-wave decay processes are allowed. The pronounced generation of a periodic sequence of bright spin wave solitons has been observed under excitation of two monochromatic spin waves at the same frequencies.

Convergence of Compact Ricci Solitons

We show that sequences of unit-volume compact gradient Ricci solitons converge to complete orbifold gradient solitons, assuming constraints on the Ln/2-norm of curvature, the soliton constant λ, and the auxiliary constant C1. The strongest results are in dimension 4, where L2 curvature bounds are equivalent to bounds on the Euler number, given the other constraints. We obtain necessary and sufficient conditions for limits to be compact.

Long-Range Interaction between Two Periodic Solitons through Growing-and-Decaying Mode in the Davey–Stewartson I Equation

where r is constant. One important feature of the solutions to the DS I equation is the reversion of the unstable wave train to its initial state. The analytical solution for the nonlinear evolution of a modulational unstable mode is given by the growing-and-decaying (GD) mode solution. This shows that an unstable mode grows exponentially in its early stage. After reaching a maximummodulation, the unstable mode vanishes with time to reproduce the initial unmodulated state. The DS equation has a periodic soliton solution, which represents the spatial structure of the inclined sequence of algebraic solitons in addition to the dark line soliton and algebraic soliton solutions. In previous studies, we investigated the interactions between two periodic solitons, and between the periodic soliton and other types of solitons. Note that there are two types of singular interaction: the resonant interaction, in which two solitons interact so as to generate a single soliton, and the extremely long-range interaction, in which two solitons interchange each other infinitely apart through the messenger soliton, which is similar to a periodic soliton. Recently, the interaction between a soliton and a GD mode has been investigated, and the existence of resonant interactions has been demonstrated. We reported that the existence of the periodic soliton changed the evolution of the modulational instability markedly, as if the soliton dominated the evolution of instability. These results suggest the possible existence of an interaction between two solitons through the GD mode. The purpose of the present note is to show that a long-range interaction exists between two parallel periodic solitons through the GD mode. Using the N-soliton solution of Satsuma and Ablowitz, the solution that describes the interaction between two periodic solitons, which have the same real part ð ; Þ and different imaginary parts ð 1; 1Þ and ð 2; 2Þ of complex wave numbers, is written as

Sequential formation of incoherent multiple gray solitons in biased photorefractive–photovoltaic crystals

We show that incoherent gray soliton splitting is possible in biased photorefractive–photovoltaic crystals. If the full width half maximum (FWHM) of the incoherent beam’s intensity or the incoherent beam’s grayness is small, only a Y-junction soliton is generated, corresponding to the lowest order in even-number soliton sequence. If the intensity FWHM of the incoherent beam or the incoherent beam’s grayness is increased, the gray soliton beam splits into an even-number sequence of multiple gray solitons. The properties of incoherent gray soliton splitting in biased photorefractive–photovoltaic crystals are discussed and we find that it is incoherent gray screening soliton splitting when the bulk photovoltaic effect is neglectable and incoherent gray photovoltaic soliton splitting when the external bias field is absent.

Energy exchange in fast optical soliton collisions as a random cascade model

We study the dynamics of a probe soliton propagating in an optical fiber and exchanging energy in fast collisions with a random sequence of pump solitons. The energy exchange is induced by Raman scattering or by cubic nonlinear loss/gain. We show that the equation describing the dynamics of the probe soliton's amplitude has the same form as the equation for the local space average of energy dissipation in random cascade models in turbulence. We characterize the statistics of the probe soliton's amplitude by the τ q exponents from multifractal theory and by the Cramér function S ( x ) . We find that the nth moment of the two-time correlation function and the bit-error-rate contribution from amplitude decay exhibit power-law behavior as functions of propagation distance, where the exponents can be expressed in terms of τ q or S ( x ) .

The use of NOLM for investigations of initial development of supercontinuum in fibers with anomalous dispersion

We performed a numerical study of the transmission through a nonlinear optical loop mirror (NOLM) of a sequence of solitons generated at the initial stage of the supercontinuum (SC) generation. We found that the NOLM exhibits a selective transmission that critically dependents on the amplitude of the input solitons and on the NOLM loop length. The results demonstrate that by properly selecting these parameters the NOLM behaves as an optically controlled switch that allows the transmission of solitons with similar amplitude and width. The results obtained by employing this method are reasonably good and can be used to analyze the soliton formation at the initial stage of SC generation.

Quantization of binding energy of structural solitons in passive mode-locked fiber lasers

On basis of numerical simulation of fiber laser passive mode locking, we have determined the quantum binding-energy levels for a pair of interacting structural solitons. These solitons have powerful wings and correspondingly large binding energies. It has been found that the field amplitude functions for steady states corresponding to neighboring energy levels have opposite parity. We have pointed out the analogy between the energy quantization for laser bound solitons and for a particle moving in potential well. The possibility of a coexistence of in-, opposite-, and $\ensuremath{\pi}/2$-phase soliton pairs has been found. In the case of multiple soliton trains, we have demonstrated the realization of highly stable soliton sequences with any required distribution along the soliton train of various types of bonds between neighboring pulses.

Solitary waves and nonlinear dynamic coherent structures in magnetic metamaterials

Within the framework of the extended nonlinear Schrodinger equation (ENSE), two types of nonlinear states of magnetization in a ferromagnet-dielectric-metal metamagnetic structure have been obtained and investigated. These states have an internal structure; e.g., a periodic sequence of compound solitons is formed by kink-antikink pairs (shock waves), and coherent periodic breather structures are formed by “bright” quasi-solitons. Conditions have been found under which the envelope of these states is described by a modified Korteweg-de Vries (mKdV) equation. It is shown that the compound solitons are described by an mKdV equation with repulsion, and the breather structures, by an mKdV equation with attraction. It is shown also that the characteristic properties of the solutions are determined by the sign of the group-velocity dispersion rather than by the sign of the group velocity itself. The results obtained can be used for searching new nonlinear dynamic coherent structures, e.g., compound solitons and breathers in high-dispersion magnetic metamaterials.

Performance evaluation of path-averaged soliton pulses in loss-managed 10-Gbps soliton transmission link over a long haul

In this paper, the performance evaluation of path-averaged soliton transmission link for various performance measures viz. OSNR, optical power, extinction ratio, bit error rate (BER) and Q factor at different levels of noise figure and values of pulse width (FWHM) has been carried out. The performance of soliton transmission link is studied, taking into account soliton interaction, amplified spontaneous emission (ASE) noise and noise figure. The model presented considers interaction in a random sequence of solitons and the effect of the ASE noise added in each amplification stage. The influence of ASE noise, noise figure and pulse width with different amplifier spacing on the BER and quality factor has been investigated. It has been shown that these play dominant roles in degrading the performance measures. We have demonstrated the capability of path-averaged (guiding-centre) soliton for a long-haul distance of 17,000 km at a bit rate of 10 Gbps without ASE effect and noise figure in each amplifier span length of 500 km. The average value of quality factor is found to be 16.6 dB and the average BER is of the order of 10 −12 over the transmission distance of 17,000 km. Further, it has been investigated that a severe system penalty results on the inclusion of ASE effect and noise figure in order to achieve the same level of performance. Thus, the investigations ascertain that in order to maintain the same level of BER and Q factor, the amplifier spacing and total transmission distance reduce considerably.

Multisoliton ejection from an amplifying potential trap

We study theoretically the dynamics of a beam launched inside an amplifying trap potential. Raising the amplification transforms the dynamics from linear tunneling at low amplification to periodic ejection of a sequence of identical solitons (when the amplification rate exceeds the tunneling rate) and, at strong amplification, to nonperiodic multisoliton ejection.

Compactness theorems for gradient Ricci solitons

In this paper, we prove a compactness theorem for gradient Ricci solitons. Let ( M α , g α ) be a sequence of compact gradient Ricci solitons of dimension n ≥ 4 , whose curvatures have uniformly bounded L n 2 norms, whose Ricci curvatures are uniformly bounded from below, with uniformly lower bounded volume and with uniformly upper bounded diameter; then there must exist a subsequence ( M α , g α ) converging to a compact orbifold ( M ∞ , g ∞ ) with finitely many isolated singularities, where g ∞ is a gradient Ricci soliton metric in an orbifold sense.

Evolution of a langmuir wave in a weakly inhomogeneous plasma with a positive concentration gradient

Spatial evolution of a Langmuir wave excited by external sources in a weakly inhomogeneous electron plasma without external sources is considered for a small positive gradient of the plasma concentration in the direction of propagation of the wave. At the first state of the evolution, the dispersion of the wave is close to linear. When the phase velocity is doubled, the second stage of the evolution begins. The wave loses its individuality and becomes a hybrid of two waves. Its profile acquires the shape of an alternating sequence of fragments of these waves. The wave dispersion is determined by the dispersion of each fragment. In the course of evolution, the spacing between the equilibrium values of the wave fragments increases; as a result, the wave decays into two waves, which are also loaded by trapped electrons. Prior to decay, the humps of the wave become steeper; as a result, at the instant of the decay, the wave is transformed into a sequence of solitons with different polarities.

Parametric Noise Amplification Inherent in the Coherence of Fundamental Optical Soliton Sequence Propagating in Fiber

When a highly coherent fundamental soliton sequence propagates an optical fiber, in-band amplified spontaneous emission noise is parametrically amplified, and signal-to-noise ratio is degraded thereby. We show experimental evidence that the parametric noise amplification phenomenon is inherent in the coherence of pulse sequence. The characteristics of the phenomenon obtained in normalized space is completely scalable to arbitrary physical space. Numerical studies reveal that the parametric gain of the noise increases with the propagation length and/or the duty ratio of the sequence. It is also found that for a large duty ratio, the feature of the gain depends on the relative phase difference between neighboring pulses in the sequence and that out-of-phase sequence can suppress the total gain.