Abstract
We present shape-preserving self-accelerating beams of Maxwell's equations with optical nonlinearities. Such beams are exact solutions to Maxwell's equations with Kerr or saturable nonlinearity. The nonlinearity contributes to self-trapping and causes backscattering. Those effects, together with diffraction effects, work to maintain shape-preserving acceleration of the beam on a circular trajectory. The backscattered beam is found to be a key issue in the dynamics of such highly non-paraxial nonlinear beams. To study that, we develop two new techniques: projection operator separating the forward and backward waves, and reverse simulation. Finally, we discuss the possibility that such beams would reflect themselves through the nonlinear effect, to complete a 'U' shaped trajectory.
Highlights
The research on accelerating beams has been growing rapidly since it was introduced into the domain of optics, by Demetri Christodoulides, in 2007 [1,2]
The effect is caused by interference: the waves emitted from all points on the Airy profile maintain a propagation-invariant structure, which shifts laterally along a parabola
We present the first nonlinear self-trapped accelerating beams of the full time harmonic Maxwell equations [23]. These beams accelerate along a circular trajectory in a shape-preserving manner. We show that such nonlinear non-paraxial accelerating beams involve coupling between forward- and backward-propagating beams, giving rise to unique effects: part of the beam is reflected due to the nonlinear change of the permittivity
Summary
The research on accelerating beams has been growing rapidly since it was introduced into the domain of optics, by Demetri Christodoulides, in 2007 [1,2]. “Self-accelerating optical beams in highly nonlocal nonlinear media,” Opt. Express 19(24), 23706–23715 (2011). In spite of this general opinion, we have shown [5] that a specific design of the beam profile can make it accelerate in a shape-preserving manner while propagating in the nonlinear Kerr [5,6] nonlocal [7], and quadratic [5,8] media.
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