Limits...
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.

Show MeSH
(a) Experimental setup. PM: phase modulator. IM: intensity modulator. EDFA: Erbium doped fibre amplifier. SMF: single mode fibre: OSA: optical spectrum analayser. OSO: optical sampling oscilloscope. (b) Ideal KM soliton at minimum intensity for aKM = 0.66 (black) compared with the experimentally synthesized modulated field (red).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC3376454&req=5

f3: (a) Experimental setup. PM: phase modulator. IM: intensity modulator. EDFA: Erbium doped fibre amplifier. SMF: single mode fibre: OSA: optical spectrum analayser. OSO: optical sampling oscilloscope. (b) Ideal KM soliton at minimum intensity for aKM = 0.66 (black) compared with the experimentally synthesized modulated field (red).

Mentions: From an experimental viewpoint, the results above have allowed us to design experiments where the predictions of the analytic KM soliton theory can be tested for the first time. Our experimental set up is shown in Fig. 3 (see Methods). We use high speed telecommunications-grade components to strongly modulate a continuous wave 1550 nm laser diode. The modulation strength and period are chosen such that the characteristics of each cycle match a particular KM soliton as shown in Fig. 2(a). We aim to synthesize an input field at the fibre input z = 0 corresponding to a KM soliton of governing parameter aKM. The initial conditions are written in dimensional form as such that the field varies between minimum “background” amplitude of and a maximum value of . Note that P0 here is the background field power in W. We study propagation in SMF-28 optical fibre with group velocity dispersion β2 [s2 m−1] and nonlinearity γ[W−1 m−1]. The dimensional field A(z,T) [W1/2] is: and defining a timescale T0 = (/β2/ LNL)1/2, the dimensional distance time T [s] is T = τT0. We also define a characteristic length LNL = (γP0)−1 such that the dimensional distance z [m] is (where zp corresponds to one period of the KM cycle so that our initial conditions above are injected at z = 0.)


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) Experimental setup. PM: phase modulator. IM: intensity modulator. EDFA: Erbium doped fibre amplifier. SMF: single mode fibre: OSA: optical spectrum analayser. OSO: optical sampling oscilloscope. (b) Ideal KM soliton at minimum intensity for aKM = 0.66 (black) compared with the experimentally synthesized modulated field (red).
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f3: (a) Experimental setup. PM: phase modulator. IM: intensity modulator. EDFA: Erbium doped fibre amplifier. SMF: single mode fibre: OSA: optical spectrum analayser. OSO: optical sampling oscilloscope. (b) Ideal KM soliton at minimum intensity for aKM = 0.66 (black) compared with the experimentally synthesized modulated field (red).
Mentions: From an experimental viewpoint, the results above have allowed us to design experiments where the predictions of the analytic KM soliton theory can be tested for the first time. Our experimental set up is shown in Fig. 3 (see Methods). We use high speed telecommunications-grade components to strongly modulate a continuous wave 1550 nm laser diode. The modulation strength and period are chosen such that the characteristics of each cycle match a particular KM soliton as shown in Fig. 2(a). We aim to synthesize an input field at the fibre input z = 0 corresponding to a KM soliton of governing parameter aKM. The initial conditions are written in dimensional form as such that the field varies between minimum “background” amplitude of and a maximum value of . Note that P0 here is the background field power in W. We study propagation in SMF-28 optical fibre with group velocity dispersion β2 [s2 m−1] and nonlinearity γ[W−1 m−1]. The dimensional field A(z,T) [W1/2] is: and defining a timescale T0 = (/β2/ LNL)1/2, the dimensional distance time T [s] is T = τT0. We also define a characteristic length LNL = (γP0)−1 such that the dimensional distance z [m] is (where zp corresponds to one period of the KM cycle so that our initial conditions above are injected at z = 0.)

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