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Observation of Kuznetsov-Ma soliton dynamics in optical fibre.

Kibler B, Fatome J, Finot C, Millot G, Genty G, Wetzel B, Akhmediev N, Dias F, Dudley JM - Sci Rep (2012)

Bottom Line: However, although the first solution of this type was the Kuznetzov-Ma (KM) soliton derived in 1977, there have in fact been no quantitative experiments confirming its validity.We report here novel experiments in optical fibre that confirm the KM soliton theory, completing an important series of experiments that have now observed a complete family of soliton on background solutions to the NLSE.Our results also show that KM dynamics appear more universally than for the specific conditions originally considered, and can be interpreted as an analytic description of Fermi-Pasta-Ulam recurrence in NLSE propagation.

View Article: PubMed Central - PubMed

Affiliation: Laboratoire Interdisciplinaire Carnot de Bourgogne, UMR 6303 CNRS - Universite´ de Bourgogne, Dijon, France.

ABSTRACT
The nonlinear Schrödinger equation (NLSE) is a central model of nonlinear science, applying to hydrodynamics, plasma physics, molecular biology and optics. The NLSE admits only few elementary analytic solutions, but one in particular describing a localized soliton on a finite background is of intense current interest in the context of understanding the physics of extreme waves. However, although the first solution of this type was the Kuznetzov-Ma (KM) soliton derived in 1977, there have in fact been no quantitative experiments confirming its validity. We report here novel experiments in optical fibre that confirm the KM soliton theory, completing an important series of experiments that have now observed a complete family of soliton on background solutions to the NLSE. Our results also show that KM dynamics appear more universally than for the specific conditions originally considered, and can be interpreted as an analytic description of Fermi-Pasta-Ulam recurrence in NLSE propagation.

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(a) False color plot of experimental and theoretical intensity evolution with propagation distance. (b) plots the evolution of the power at the centre of the modulation cycle as a function of normalised distance (zp = 5.3 km) comparing experiment (red), the theoretical evolution of the KM soliton (black) and simulation (blue). (c) compares time-domain and frequency-domain properties of the KM soliton for maximum temporal compression at z = zp/2.
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f4: (a) False color plot of experimental and theoretical intensity evolution with propagation distance. (b) plots the evolution of the power at the centre of the modulation cycle as a function of normalised distance (zp = 5.3 km) comparing experiment (red), the theoretical evolution of the KM soliton (black) and simulation (blue). (c) compares time-domain and frequency-domain properties of the KM soliton for maximum temporal compression at z = zp/2.

Mentions: Our experimental results are shown in Fig. 4. Figure 4(a) is a false color plot of the measured temporal intensity profiles at each propagation distance, compared with the profiles of an ideal KM soliton. There is clearly very good qualitative agreement, and this is confirmed quantitatively in Fig. 4(b) by comparing the instantaneous power at the centre of the modulation cycle (T = 0) from experiment (red circles) with the corresponding power evolution for an ideal KM soliton (solid line). Note that there are no free parameters used when plotting the expected theoretical KM soliton evolution. The small discrepancy between experiment and theory arises from fibre loss, but performing numerical simulations of the propagation of the experimental input field including loss (blue dashed line) reproduces experiment near-exactly.


Observation of Kuznetsov-Ma soliton dynamics in optical fibre.

Kibler B, Fatome J, Finot C, Millot G, Genty G, Wetzel B, Akhmediev N, Dias F, Dudley JM - Sci Rep (2012)

(a) False color plot of experimental and theoretical intensity evolution with propagation distance. (b) plots the evolution of the power at the centre of the modulation cycle as a function of normalised distance (zp = 5.3 km) comparing experiment (red), the theoretical evolution of the KM soliton (black) and simulation (blue). (c) compares time-domain and frequency-domain properties of the KM soliton for maximum temporal compression at z = zp/2.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3376454&req=5

f4: (a) False color plot of experimental and theoretical intensity evolution with propagation distance. (b) plots the evolution of the power at the centre of the modulation cycle as a function of normalised distance (zp = 5.3 km) comparing experiment (red), the theoretical evolution of the KM soliton (black) and simulation (blue). (c) compares time-domain and frequency-domain properties of the KM soliton for maximum temporal compression at z = zp/2.
Mentions: Our experimental results are shown in Fig. 4. Figure 4(a) is a false color plot of the measured temporal intensity profiles at each propagation distance, compared with the profiles of an ideal KM soliton. There is clearly very good qualitative agreement, and this is confirmed quantitatively in Fig. 4(b) by comparing the instantaneous power at the centre of the modulation cycle (T = 0) from experiment (red circles) with the corresponding power evolution for an ideal KM soliton (solid line). Note that there are no free parameters used when plotting the expected theoretical KM soliton evolution. The small discrepancy between experiment and theory arises from fibre loss, but performing numerical simulations of the propagation of the experimental input field including loss (blue dashed line) reproduces experiment near-exactly.

Bottom Line: However, although the first solution of this type was the Kuznetzov-Ma (KM) soliton derived in 1977, there have in fact been no quantitative experiments confirming its validity.We report here novel experiments in optical fibre that confirm the KM soliton theory, completing an important series of experiments that have now observed a complete family of soliton on background solutions to the NLSE.Our results also show that KM dynamics appear more universally than for the specific conditions originally considered, and can be interpreted as an analytic description of Fermi-Pasta-Ulam recurrence in NLSE propagation.

View Article: PubMed Central - PubMed

Affiliation: Laboratoire Interdisciplinaire Carnot de Bourgogne, UMR 6303 CNRS - Universite´ de Bourgogne, Dijon, France.

ABSTRACT
The nonlinear Schrödinger equation (NLSE) is a central model of nonlinear science, applying to hydrodynamics, plasma physics, molecular biology and optics. The NLSE admits only few elementary analytic solutions, but one in particular describing a localized soliton on a finite background is of intense current interest in the context of understanding the physics of extreme waves. However, although the first solution of this type was the Kuznetzov-Ma (KM) soliton derived in 1977, there have in fact been no quantitative experiments confirming its validity. We report here novel experiments in optical fibre that confirm the KM soliton theory, completing an important series of experiments that have now observed a complete family of soliton on background solutions to the NLSE. Our results also show that KM dynamics appear more universally than for the specific conditions originally considered, and can be interpreted as an analytic description of Fermi-Pasta-Ulam recurrence in NLSE propagation.

Show MeSH