Conference on Localized Excitations in Nonlinear Complex Systems - LENCOS 2012 Sevilla, 10 th july 2012 Ultrasolitons: multistability and subcritical power threshold from HOKE HOKE DAVID NOVOA EPL 98, 44003 (2012)
Ultrasolitons: multistability and subcritical power threshold from HOKE OUTLINE • Introduction. • Mathematical model. Multistability condition. • Localized solutions. Ultrasolitons. • The quest for a hidden soliton family. • Soliton switching. • Conclusions. 2
Ultrasolitons: multistability and subcritical power threshold from HOKE 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)] � The existence of HOKE have led to an intense debate among the experts owing to its crucial implications on intense laser filamentation . 3
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 In our particular situation, the refractive index correction involves a polynomial expansion up to the fourth order in the intensity 4
Ultrasolitons: multistability and subcritical power threshold from HOKE Mathematical Model � For q=1,2 � Cubic-Quintic media � quadratic-like effective potential LIQUID LIGHT CONDENSATES Michinel, Paz-Alonso and Pérez-García, PRL 96, 023903 (2006 ) Novoa, Michinel and Tommasini, PRL 103, 023903 (2009) 5
Ultrasolitons: multistability and subcritical power threshold from HOKE Mathematical Model � The canonical case f 2q =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. Novoa, Michinel and Tommasini, PRL 105, 203904 (2010) 6
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) � This double-hump structure suggests the emergence of multistability. Novoa, Tommasini and Michinel, EPL 98, 44003 (2012) 7
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 being the pressure field � In the case of a flat-top eigenstate They satisfy the Young-Laplace equation governing the equilibrium of the high-power solitons Novoa, Michinel and Tommasini, PRL 103, 023903 (2009) 8
Ultrasolitons: multistability and subcritical power threshold from HOKE Analytic condition for multistability � 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 This equation has three-real roots (limiting plane waves) provided that the following condition is fulfilled Novoa, Tommasini and Michinel, EPL 98, 44003 (2012) 9
Ultrasolitons: multistability and subcritical power threshold from HOKE Multistability domain � Previous studies were performed outside the multistability region � just one real root exists � CQ-like behavior!!. Our choice 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…) 10
Ultrasolitons: multistability and subcritical power threshold from HOKE Localized solutions. Ultrasolitons � We search for localized (nodeless) stationary states ¿? � Ultrasolitons: solitary waves that exist over a certain intensity threshold 11
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 A g ∞ 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. 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. 12
Ultrasolitons: multistability and subcritical power threshold from HOKE The quest for a hidden soliton family � Moreover, the limiting plane wave of the ghost branch is linearly unstable. � Direct excitation of flat-top states show that the possible third branch would not comprise stable light condensates! 13
Ultrasolitons: multistability and subcritical power threshold from HOKE Soliton switching C.E ~ 30 % C.E ~ 90 % 14
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. � We have given physical arguments supporting the non-existence of the “hidden” branch based on the hydrodynamic analogy. � 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. 15
Ultrasolitons: multistability and subcritical power threshold from HOKE LENCOS Conference 2012 Thank you for your attention!!
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