International Journal of Physics | Vol. 4, No. 10, October 2013 | pp. 73–80
DOI: 10.46882/2013/IJP/000042
Research Article
Title: Soliton Stability and Modulational Instability in Non-Local Nonlinear Optical Media with Exponential Response Functions
Names of Authors: G. S. Campbell¹, F. Z. Al-Rawi²
Authors’ Affiliations: ¹Research School of Physics and Engineering, Australian National University, Canberra, ACT 2601, Australia; ²Department of Physics, Faculty of Science, University of Baghdad, Baghdad 10071, Iraq
Abstract: Non-local nonlinear optical media provide unique opportunities for steering and controlling light beams due to their non-local spatial interactions. This study analyzes the structural stability of spatial optical solitons and characterizes modulational instability parameters within a non-local medium governed by an exponential response function. We developed an analytical model using the non-local nonlinear Schrödinger equation. This model was solved via a variational approach combined with split-step Fourier numerical simulations. The analytical framework derives the exact power thresholds required to initiate stable spatial soliton propagation across varying degrees of non-locality. The results show that a highly non-local response completely suppresses collapse modes, stabilizing two-dimensional localized structures that are unstable in local Kerr media. The modulation instability growth rate was calculated as a function of perturbation frequency. This analysis revealed a maximum gain value of g = 2.45 cm^-1 under an input beam intensity of 1.5 kW/cm². Increasing the non-locality parameter from 0.5 mm to 3.0 mm reduces the maximum instability gain by 62.0% and shifts the peak gain toward longer perturbation wavelengths. These findings provide strategies for controlling filamentation in laser beams and optimizing data transport in soft-matter waveguide networks.
Keywords: Nonlinear optics; spatial solitons; nonlinear Schrödinger equation; modulational instability; non-local media; split-step Fourier method
Manuscript Timeline: Received: June 04, 2013; Revised: July 28, 2013; Accepted: August 18, 2013; Published: October 14, 2013
Citation: Campbell, G. S., & Al-Rawi, F. Z. (2013). Soliton Stability and Modulational Instability in Non-Local Nonlinear Optical Media with Exponential Response Functions. International Journal of Physics, 4(10), 73–80.
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