Propagation of Gaussian beam in strongly nonlocal nonlinear media with inhomogeneous diffraction

Abstract

Solitons in a strongly nonlocal nonlinear medium have attracted considerable attention in recent years due to their unique and distinctive characteristics from those observed in the local nonlinear medium. In this work, we investigate the propagation of a Gaussian beam in strongly nonlocal nonlinear media with spatially varying diffraction. Using analytical and numerical approaches, we examine the propagation dynamics and stability characteristics of the nonlocal soliton. For representative cases of diffraction profiles, our results show that diffraction tailoring strongly influences key beam properties, including amplitude, beam width, phase-front curvature, and phase-space evolution. All diffraction modulation supports the formation of diffraction-managed breather solitons, with excellent agreement between theory and simulations. Furthermore, the modulation instability (MI) studies systematically explored the stability characteristics under various diffraction landscapes. The obtained results demonstrate that by engineering diffraction in such nonlocal media, one can effectively control beam dynamics, thereby opening new possibilities for applications in nonlinear light control, beam shaping, and all-optical system design.

Figures (14)

• Figure 1: Schematic of the six distinct diffraction profiles, including the constant diffraction case. Panel (a) displays the constant, linearly decreasing, and exponentially decreasing diffraction profiles, while Panel (b) shows the step-like ($\tanh$), barrier-type ($\hbox{sech}$), and periodic ($\sin$) diffraction profiles.
• Figure 2: Beam characteristics for constant diffraction $\mu(z)=\mu_0=0.3$: (a) Amplitude, (b) Beam width, (c) Phase-front curvature, (d) Phase space trajectory, shown for three different power conditions: $P_0 < P_c$ (blue line), $P_0 = P_c$ (red dotted line) and $P_0 > P_c$ (yellow dashed-dotted line).
• Figure 3: Beam characteristics for linear diffraction $\mu(z)=\mu_0 [\frac{1-\beta}{\beta L}z + 1]$: (a) Amplitude, (b) Beam width, (c) Phase-front curvature, (d) Phase space trajectory, shown for three different power conditions: $P_0 < P_c$ (blue), $P_0 = P_c$ (red) and $P_0 > P_c$ (yellow).
• Figure 4: Numerical simulation of the evolution of a Gaussian beam in the SNNM at $P_0 >P_c$ with a (a) Constant diffraction, (b) For linearly decreasing diffraction
• Figure 5: Step-like modulation of diffraction profile $\mu(z) = \mu_0 +\mu_1 \tanh(\mu_2 z + \mu_3)$ on the beam dynamics is shown for the power $P_0 = P_c$. (a) Amplitude, (b) Beam width, (c) Phasefront curvature, (d) Phase space trajectory. The constants are $\mu_0=1.25$, $\mu_1=0.65$, $\mu_2=1.25$ and $\mu_3=0.05$.