Infinite hierarchy of solitons: Interaction of Kerr nonlinearity with even orders of dispersion

Runge, Antoine F. J.; Qiang, Y. Long; Alexander, Tristram J.; Rafat, M. Z.; Hudson, Darren D.; Blanco‐Redondo, Andrea; Sterke, C. Martijn de

doi:10.1103/physrevresearch.3.013166

Cited by 50 publications

(47 citation statements)

References 42 publications

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“…The stability analysis of the different solitons as solutions of the GNLSE, that is, of the PDE, remains a considerable challenge. Finally, recent experiments [33] have shown the feasibilities of creating waveguides with higher even order dispersions, such as sextic (β 6 ), octic (β 8 ), and decic (β 10 ) dispersions. Our analysis constitutes the first step towards understanding the existence of solitons for different configuration of such higher-order dispersion terms.…”

Section: Discussionmentioning

confidence: 99%

Infinitely Many Multipulse Solitons of Different Symmetry Types in the Nonlinear Schrödinger Equation with Quartic Dispersion

Bandara,

Giraldo,

Broderick

et al. 2021

Preprint

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We show that the generalised nonlinear Schrödinger equation (GNLSE) with quartic dispersion supports infinitely many multipulse solitons for a wide parameter range of the dispersion terms. These solitons exist through the balance between the quartic and quadratic dispersions with the Kerr nonlinearity, and they come in infinite families with different signatures. A travelling wave ansatz, where the optical pulse does not undergo a change in shape while propagating, allows us to transform the GNLSE into a fourth-order nonlinear Hamiltonian ordinary differential equation with two reversibilities. Studying families of connecting orbits with different symmetry properties of this reduced system, connecting equilibria to themselves or to periodic solutions, provides the key to understanding the overall structure of solitons of the GNLSE. Integrating a perturbation of them as solutions of the GNLSE suggests that some of these solitons may be observable experimentally in photonic crystal wave-guides over several dispersion lengths.

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Section: Discussionmentioning

confidence: 99%

Infinitely Many Multipulse Solitons of Different Symmetry Types in the Nonlinear Schrödinger Equation with Quartic Dispersion

Bandara,

Giraldo,

Broderick

et al. 2021

Preprint

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“…Thus, across the bandwidth of the signal-pulse, the dispersion profile is ideally symmetric about the central wavelength-e.g., for ultrashort <100 fs pulses, the dispersion profile should be symmetric across a bandwidth range less than 50 nm. There are a plethora of waveguides that satisfy this symmetry requirement from dispersion engineered photonic crystal fibers to the system described in [35]. Furthermore, we find from full numerical simulations that the symmetry condition is not strictly necessary (see Section 3 for related discussion) and introduces little error for moderate odd-order dispersion coefficients (taken about the central wavelength of the signal) if Equation ( 4) is modified to Equation ( 5), given as follows:…”

Section: Control-pulse Formulationmentioning

confidence: 99%

Maintaining Constant Pulse-Duration in Highly Dispersive Media Using Nonlinear Potentials

Zia

2021

Photonics

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A method is shown for preventing temporal broadening of ultrafast optical pulses in highly dispersive and fluctuating media for arbitrary signal-pulse profiles. Pulse pairs, consisting of a strong-field control-pulse and a weak-field signal-pulse, co-propagate, whereby the specific profile of the strong-field pulse precisely compensates for the dispersive phase in the weak pulse. A numerical example is presented in an optical system consisting of both resonant and gain dispersive effects. Here, we show signal-pulses that do not temporally broaden across a vast propagation distance, even in the presence of dispersion that fluctuates several orders of magnitude and in sign (for example, within a material resonance) across the pulse’s bandwidth. Another numerical example is presented in normal dispersion telecom fiber, where the length at which an ultrafast pulse does not have significant temporal broadening is extended by at least a factor of 10. Our approach can be used in the design of dispersion-less fiber links and navigating pulses in turbulent dispersive media. Furthermore, we illustrate the potential of using cross-phase modulation to compensate for dispersive effects on a signal-pulse and fill the gap in the current understanding of this nonlinear phenomenon.

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“…Following the experimental observation of bright solitons supported by fourth-order dispersion [1], the theory of bright solitons with pure-quartic dispersion [2], mixed second-and fourth-order dispersion [3] and pure dispersion of higher even orders [4] has become well established. The experimental work was enabled by the development of a fiber laser with conveniently programmable dispersion [4,5]. All of these bright solitons exist when the highest-order of dispersion is negative.…”

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confidence: 99%

“…The effect of dominant higher-order normal dispersion was considered in the φ 4 Klein-Gordon model, in both the pure quartic form [19,20] and in the presence of both quadratic and quartic terms [21]. These results for real fields point to intricate soliton interactions.…”

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confidence: 99%

“…Given the complexities of controlling dispersion (e.g., using a WaveShaper) in the bright soliton case [4,5], the careful pulse control of early dark soliton generation experiments [11] appears to be practically challenging. We therefore restrict considerations to an, arguably, prototypical initial condition of a CW state with intensity notches, either of Gaussian form or domain wall-like form using a hyperbolic tangent.…”

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confidence: 99%

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Dark solitons under higher order dispersion

Alexander,

Tsolias,

Demirkaya

et al. 2021

Preprint

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We show theoretically that dark solitons can exist in the presence of pure quartic dispersion, and also in the presence of both quadratic and quartic dispersive effects, displaying a much greater variety of possible solutions and dynamics than for pure quadratic dispersion. The interplay of the two dispersion orders may lead to oscillatory non-vanishing tails, which enables the possibility of bound, potentially stable, multisoliton states. Dark soliton-like states which connect to low amplitude oscillations are also shown to be possible. Dynamical evolution results corroborate the stability picture obtained, and possible avenues for dark soliton generation are explored.

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Infinite hierarchy of solitons: Interaction of Kerr nonlinearity with even orders of dispersion

Cited by 50 publications

References 42 publications

Infinitely Many Multipulse Solitons of Different Symmetry Types in the Nonlinear Schrödinger Equation with Quartic Dispersion

Infinitely Many Multipulse Solitons of Different Symmetry Types in the Nonlinear Schrödinger Equation with Quartic Dispersion

Maintaining Constant Pulse-Duration in Highly Dispersive Media Using Nonlinear Potentials

Dark solitons under higher order dispersion

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