Following Ilya Prigogine, bringing the energy and/or matter far from thermodynamic equilibrium, dissipative structures are self-organized [1]. The self-organization is the compensation of antagonist effects. The laser energy propagating modifies the nonlinear matter. Such a modification induces a feedback mechanism on the laser light, causing instabilities. The stabilization occurs whenever the omnipresent self-defocusing diffraction is compensated by nonlinear self-focusing effects, self-generating spatial optical solitons, e.g. in water suspensions of nanoparticles [2-4]. As a consequence, nanoparticles are collectively tweezed along the axes of soliton inducing, by their controlled change of density, its self-focusing. In its turn, this self-focusing compensates the diffraction and other defocusing effects. The appearance in nanosuspension of a stable perfectly collimated beam with a conserved profile is the manifestation of such a self-trapped soliton-tweezer. The synergetic balance of antagonist self-focusing and self-defocusing actions, leads to the self-trapped dynamical equilibrium of soliton-tweezer in nanosuspension. Usually, soliton electric field, $E$ is described by nonlinear Schrödinger equation. However, we are measuring soliton input and output electric intensity, I. Consequently, we established a novel synergetic soliton-tweezer complex intensity ($I=EE$) equation (STCIE):
$$\frac{i\partial I}{\partial z} +\varepsilon \nabla_{\bot}^2 I + \eta I +(\sigma |I|-\nu |I|^2) I= 0$$ where the self-focusing and self-defocusing are characterized by the measured coefficient $\sigma$ and $\nu$. Therefore, this equation represents a direct self-organized bridge connecting the theory with experimental results.
References
[1] Nicolis, G. & Prigogine, I. Self-organization in Nonequilibrium Systems. (John Wiley, 1977).
[2] V. Skarka, N. B. Aleksić, H. Leblond, B. A. Malomed, and D. Mihalache, Phys. Rev. Lett. 105, 213901 (2010).
[3] V. Skarka, N. B. Aleksić, W. Krolikowski, D. N. Christodoulides, S. Rakotoarimalala, B. N. Aleksić, and M. Belić, Opt. Express 25, 10090 (2017).
[4] E. L. Falcao-Filho, C. B. de Araujo, G. Boudebs, H. Leblond, and V. Skarka, Phys. Rev. Lett. 110, 013901 (2013).