# Nonlinear Waves and Turbulence in Photonics 2022 - Abstract

**Taki, Majid**

*Characterization of spatiotemporal chaos in unidimensional chain of plasmonic nanoparticles*

Nonlinear plasmonics is an emerging research field where nonlinear processes are enhanced through optical excitations in metal nanostructures by an external field. Here, we study nonlinear collective behaviors in periodic arrays of silver spherical nanoparticles embedded into a silica matrix, that are excited normally by an external field with the frequency close to the frequency of the localized surface plasmon resonance. These nanoparticles have a Kerr-like nonlinear response and theire response is described by coupled equations for slowly varying amplitudes of the particle dipole moments, obtained in reference [1]. Noskov et al. analyzed the Modulation Instability and Bistability and discussed several novel nonlinear effects, which include solitons, oscillons and domain walls [1,2]. We have extended this work by analyzing the linear stability of the stationary states with respect to weak spatiotemporal perturbations .We have also characterized a number of nonlinear effects in this plasmonics system, in particular spatiotemporal chaos. In that work [3], we use an analytical method to separate stable and instable areas in the steady state curve and also in the bifurcation diagram. As we are interested in spatiotemporal chaos, we characterize it as a function of the frequency and the intensity of the external field, using computation of Lyapunov exponents and York-Kaplan dimension [4], and finally present the slop of the latter as a function of our control setting validating the consistency of our system [5].

**References**

[1] R. E. Noskov, P. A. Belov, and Y. S. Kivshar, Phys. Rev. Lett. 108, (2012).

[2] R. Noskov, P. Belov, and Y. Kivshar, Sci. Rep. 2, (2012).

[3] Z. Ziani, G. Lévêque, S. Coulibaly, M. Taki and A. Akjoujy, PRB 100, 165423 (2019)

[4] M. G. Clerc, M. A. Ferré, S. Coulibaly, R. G. Rojas, and M. Tlidi, Opt. Lett. 42, 2906 (2017).

[5] Z. Ziani, G. Lévêque, S. Coulibaly, M. Taki and A. Akjoujy, Ann. Phys. (Berlin) (2020), 2000240