Optical Soliton Perturbations and Rogue Wave Formations in Non-Local Metamaterials with Power-Law Non-Linearities

International Journal of Physics | Vol. 6, No. 12, December 2015 | pp. 89–96

DOI: 10.46882/2015/IJP/000068

Research Article

Title: Optical Soliton Perturbations and Rogue Wave Formations in Non-Local Metamaterials with Power-Law Non-Linearities

Names of Authors: S. H. Zhang¹, E. C. Sterling²

Authors’ Affiliations: ¹Department of Physics, Tsinghua University, Beijing, China; ²Cavendish Laboratory, Department of Physics, University of Cambridge, Cambridge, UK

Abstract: Designing optical systems that can stabilize ultra-short laser pulses or safely mitigate high-power filamentation is crucial for advanced laser physics and deep-space data transmission networks. This paper solves the generalized non-linear Schrödinger equation governing optical soliton perturbations and models rogue wave formations within non-local metamaterials exhibiting a power-law non-linearity. The mathematical model includes higher-order perturbation terms, specifically third-order dispersion, self-steepening, and inter-file Raman scattering delays. We apply the inverse scattering transform method alongside a multiple-scale perturbation algorithm to derive analytical solutions for single-soliton and breathers. The results show that a high degree of spatial non-locality effectively suppresses collapse modes, stabilizing two-dimensional structures that are unstable in local Kerr media. The modulational instability growth rate was calculated as a function of perturbation frequency, revealing a maximum gain value of g = 2.84 cm^-1 under an input intensity of 1.8 kW/cm². Increasing the non-locality parameter from 0.8 mm to 4.0 mm reduces the maximum instability gain by 65.0% and shifts the peak gain toward longer perturbation wavelengths, preventing catastrophic pulse fragmentation.

Keywords: Nonlinear optics; spatial solitons; nonlinear Schrödinger equation; modulational instability; non-local media; split-step Fourier method

Manuscript Timeline: Received: August 18, 2015; Revised: October 10, 2015; Accepted: November 02, 2015; Published: December 16, 2015

Citation: Zhang, S. H., & Sterling, E. C. (2015). Optical Soliton Perturbations and Rogue Wave Formations in Non-Local Metamaterials with Power-Law Non-Linearities. International Journal of Physics, 6(12), 89–96.

Subscribe to read the full article: https://internationalscholarsjournals.org/subscribe-to-read