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Higher-order Solitons

Author: the photonics expert Dr. Rüdiger Paschotta (RP)

Definition: optical pulses in a nonlinear and dispersive medium which exhibit periodic oscillations of their temporal and spectral shape

More general term: solitons

Categories: article belongs to category fiber optics and waveguides fiber optics and waveguides, article belongs to category light pulses light pulses

DOI: 10.61835/9mq Cite the article: BibTex plain text HTML Link to this page LinkedIn

A fundamental soliton is an optical pulse which can propagate in a dispersive medium (e.g. an optical fiber) with a constant shape of the temporal intensity profile, i.e., without any temporal broadening as is usually caused by dispersion. This can happen when the pulse has a certain shape and an energy which is determined by the parameters of the medium (in particular, by the dispersion and nonlinearity) and the pulse duration.

A higher-order soliton is a soliton pulse the energy of which is higher than that of a fundamental soliton by a factor which is the square of an integer number (i.e. 4, 9, 16, etc.). The temporal shape of such a pulse is not constant, but rather varies periodically during propagation (see Figures 1 and 2). The period of their evolution is the so-called soliton period.

temporal evolution of third-order soliton — Figure 1: Temporal evolution of a third-order soliton.

spectral evolution of third-order soliton — Figure 2: Spectral evolution of a third-order soliton.

Figure 3: Temporal evolution of a third-order soliton. The color scale shows the optical power. The soliton period is 50.4 m, i.e. the displayed range corresponds to about two soliton periods.

In this video, we explain how simulations can make R & D more effective.

Higher-order solitons can be used for nonlinear pulse compression: a sech²-shaped pulse with a suitable energy, injected into an optical fiber with anomalous dispersion, can evolve as a higher-order soliton, and after a certain propagation distance the pulse duration can be substantially decreased. High soliton orders allow for strong compression, but also lead to a critical choice of the pump wavelength.

Whereas fundamental solitons are usually fairly stable, higher-order solitons can break up into fundamental solitons under the influence of various effects, such as higher-order dispersion, Raman scattering, or two-photon absorption. Such soliton breakup sometimes plays an essential role in the process of supercontinuum generation in photonic crystal fibers.

Case Studies

Case Study: Numerical Experiments With Soliton Pulses in Fibers

We investigate various details of soliton pulse propagation in passive fibers, using numerical simulations.

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Case studies:

Case Study: Numerical Experiments With Soliton Pulses in Fibers

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Bibliography

[1]	V. E. Zakharov and A. B. Shabat, “Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media”, Sov. Phys. JETP 34, 62 (1972)
[2]	L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers”, Phys. Rev. Lett. 45 (13), 1095 (1980); https://doi.org/10.1103/PhysRevLett.45.1095
[3]	W. Hodel and H. P. Weber, “Decay of femtosecond higher-order solitons in an optical fiber induced by Raman self-pumping”, Opt. Lett. 12 (11), 924 (1987); https://doi.org/10.1364/OL.12.000924
[4]	S. R. Friberg and K. W. DeLong, “Breakup of bound higher-order solitons”, Opt. Lett. 17 (14), 979 (1992); https://doi.org/10.1364/OL.17.000979

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