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Higher-order Solitons

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

More general term: solitons

German: Solitonen höherer Ordnung

Categories: fiber optics and waveguides, light pulses


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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.
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.
third-order soliton
Figure 4: Spectral evolution of a third-order soliton. The color scale shows the power spectral density.

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.


[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), DOI: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), DOI: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), DOI:10.1364/OL.17.000979

See also: solitons, soliton period

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