Abstract
We investigate the breathing of optical spatial solitons in highly nonlocal media. We use a generalization of the Ehrenfest theorem (1990 Am. J. Phys. 58 742) leading to a fourth-order ordinary differential equation, the latter ruling the beam width evolution in propagation. In actual highly nonlocal materials, the original accessible soliton model by Snyder and Mitchell (1997 Science 276 1538) cannot accurately describe the dynamics of self-confined beams: the transverse size oscillations have a period which not only depends on power, but also on the initial width. Modeling the nonlinear response by a Poisson equation driven by the beam intensity we verify the theoretical results against numerical simulations.
Highlights
Since the invention of the laser, optics has played an important role in nonlinear physics
We investigate the breathing of optical spatial solitons in highly nonlocal media
While in the simplest limit the change in refractive index depends on the local intensity value, in nonlocal media the nonlinear perturbation depends on the intensity in neighboring points
Summary
Since the invention of the laser, optics has played an important role in nonlinear physics. Even in the absence of losses, self-trapped beams in nonlocal media undergoes variations in transverse size owing to a dynamic balance between selffocusing and diffractive spreading [27, 28]. Such behavior resembles the collective excitation phenomena in condensed matter, e.g. the collective modes in Bose-Einstein condensates where the center of mass or the condensate size in a harmonic trap undergo oscillations [29]. If the index well associated with the nonlinear response depends only on input power, nonlinear beam propagation can be described by a linear quantum harmonic oscillator and the breathing is purely periodic [30]. It was shown numerically that soliton breathing remains periodic in a (1+1)D simplified model, connecting this result with the
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