The self-organization is the compensation of antagonist effects. The laser energy propagating modifies the nonlinear matter, e.g. nanoparticles in water suspension [1]. Such a nonlinear modification induces a feedback mechanism on the laser energy, causing its instability. The stabilization occurs whenever the omnipresent self-defocusing diffraction is compensated by nonlinear self-focusing effects, self-organizing spatial optical solitons [2-4]. Therefore, nanoparticles are, by their controlled change of density, collectively tweezed along the axes of soliton inducing its self-focusing. In its turn, this self-focusing compensates the diffraction and other defocusing effects. Consequently, a stable perfectly collimated soliton-tweezer with a conserved profile, is self-trapped in nanosuspension [1-4]. The synergetic balance of antagonist self-focusing and self-defocusing actions leads to the self-trapped dynamical equilibrium of soliton-tweezer in nanosuspension [1]. Usually, soliton electric field, E is described by nonlinear Schrodinger equation (NLS). However, in experiments we are measuring soliton input and output electric intensity, I=EE. Consequently, we established a novel synergetic soliton-tweezer complex intensity (I=EE) equation (SSTCIE). The left hand side of SSTCIE corresponds to conservative NLS and contains the diffraction term, positive cubic self-focusing term and negative quintic self-defocusing term. The dissipative imaginary right hand side contains the positive cubic gain and negative linear and quintic losses. Coefficients in front of all terms are fixed from experiments. SSTCIE establishes a direct self-organized bridge between the theory and experiment, via numerical simulations.
References
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[2] V. Skarka, N. B. Aleksic, H. Leblond, B. A. Malomed, and D. Mihalache, Phys. Rev. Lett. 105, 213901 (2010).
[3] V. Skarka, M. M. Lekic, G. A. Kovacevic, B. Zarkov, and Z. N. Romcevic, Opt. Quant. Electron. 50, 37 (2018).
[4] E. L. Falcao-Filho, C. B. de Araujo, G. Boudebs, H. Leblond, and V. Skarka, Phys. Rev. Lett. 110, 013901 (2013).