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Conference on Localized Excitations in Nonlinear Complex Systems - LENCOS 2012

Ultrasolitons: multistability and subcritical power threshold from HOKE

Sevilla, 10th july 2012

HOKE

DAVID NOVOA EPL 98, 44003 (2012)

Ultrasolitons: multistability and subcritical power threshold from HOKE

OUTLINE

• Introduction.
• Mathematical model. Multistability condition.
• Localized solutions. Ultrasolitons.

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• The quest for a hidden soliton family.
• Soliton switching.
• Conclusions.

Introduction

Motivation :

Recent experiments performed in air and its constituents have revealed for first time a sign inversion of the refractive index correction at high intensities [V. Loriot et al., Opt. Express 17, 13429 (2009)]

Ultrasolitons: multistability and subcritical power threshold from HOKE

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• The existence of HOKE have led to an intense debate among the

experts owing to its crucial implications on intense laser filamentation.

Ultrasolitons: multistability and subcritical power threshold from HOKE

Mathematical Model

• We will be interested in the analysis of the physical implications of

this HOKE response on the existence and dynamics of solitary waves

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In our particular situation, the refractive index correction involves a polynomial expansion up to the fourth order in the intensity

Ultrasolitons: multistability and subcritical power threshold from HOKE

Mathematical Model

• For q=1,2 Cubic-Quintic media quadratic-like effective potential

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Michinel, Paz-Alonso and Pérez-García, PRL 96, 023903 (2006) Novoa, Michinel and Tommasini, PRL 103, 023903 (2009)

LIQUID LIGHT CONDENSATES

Ultrasolitons: multistability and subcritical power threshold from HOKE

Mathematical Model

• The canonical case f2q=1 was investigated by L. Dong et al.

[Physica D 194, 219 (2004)], and results similar to those of the CQ media were found.

Moreover, even in the case of using the nonlinear coefficients obtained

in the experiment, the results were also compatible with those of the CQ system.

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Novoa, Michinel and Tommasini, PRL 105, 203904 (2010)

Ultrasolitons: multistability and subcritical power threshold from HOKE

Analytic condition for multistability

• Other combinations of the nonliner coefficients can give rise to

distorsions in the effective potential (refractive index)

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• This double-hump structure suggests the emergence of multistability.

Novoa, Tommasini and Michinel, EPL 98, 44003 (2012)

Ultrasolitons: multistability and subcritical power threshold from HOKE

Analytic condition for multistability

Effective hydrodynamic theory: the NLSE can be derived by the

minimization of the following Landau Grand Potential (LGP): being the pressure field

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being the pressure field

• In the case of a flat-top eigenstate

They satisfy the Young-Laplace equation governing the equilibrium

• f the high-power solitons

Novoa, Michinel and Tommasini, PRL 103, 023903 (2009)

Ultrasolitons: multistability and subcritical power threshold from HOKE

• We will look for the limiting values of the localized solutions of the

system, which correspond to plane waves with specific amplitudes and propagation constants. For , the central pressure vanishes, leading to the identity

Analytic condition for multistability

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This equation has three-real roots (limiting plane waves) provided that the following condition is fulfilled

Novoa, Tommasini and Michinel, EPL 98, 44003 (2012)

Ultrasolitons: multistability and subcritical power threshold from HOKE

• Previous studies were performed outside the multistability region

just one real root exists CQ-like behavior!!.

Multistability domain

Our choice

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Our choice (without loss of generality)

• With those conditions we know where to look for new solutions!!

(otherwise, you could expend your entire life shooting randomly…)

Ultrasolitons: multistability and subcritical power threshold from HOKE

Localized solutions. Ultrasolitons

• We search for localized (nodeless) stationary states

¿?

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• Ultrasolitons: solitary waves that exist over a certain intensity threshold

Ultrasolitons: multistability and subcritical power threshold from HOKE

The quest for a hidden soliton family

As discussed before, we were able to find just two soliton branches.

The “hidden” third family that should be linked to the existence of the Ag

∞ root does not exist WHY?

The surface tension associated with the flat-top states of the system is

a real constant, in order to ensure the validity of the YL equation.

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a real constant, in order to ensure the validity of the YL equation.

“Third-branch-solitons” do not satisfy the YL equation, which means

that their existence is physically forbidden.

Ultrasolitons: multistability and subcritical power threshold from HOKE

The quest for a hidden soliton family

Moreover, the limiting plane wave

• f the ghost branch is linearly unstable.

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Direct

excitation

• f

flat-top states show that the possible third branch would not comprise stable light condensates!

Ultrasolitons: multistability and subcritical power threshold from HOKE

Soliton switching

C.E ~ 30 %

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C.E ~ 90 %

Ultrasolitons: multistability and subcritical power threshold from HOKE

Conclusions

We have put forward new phenomenology related to the existence of HOKE.

The Ultrasolitons arise in a specific nonlinear regime owing to nonlinear

• multistability. They feature high-intensity, strong localization and, in certain

cases, subcritical powers.

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We have extended the analysis to highly-charged vortices and the same phenomenology was found (in preparation). In addition, we expect to apply these results to the 3D case and also to study the influence of the HOKE in the modeling of ultrashort pulse filamentation. We have given physical arguments supporting the non-existence of the “hidden” branch based on the hydrodynamic analogy.

Thank you for your attention!!

Ultrasolitons: multistability and subcritical power threshold from HOKE LENCOS Conference 2012