On optical Airy beams in integrable and non-integrable systems

The interaction of an accelerating Airy beam and a solitary wave is investigated for integrable and non-integrable equations governing nonlinear optical propagation in various media. For the integrable nonlinear Schrodinger equation, by way of a Backlund transformation, we show that no momentum exchange takes place, as the only effect of the interaction is to modulate the amplitude of the solitary wave. The latter result also holds for propagation in anisotropic media with birefringent walkoff and nonlocality, as specifically addressed with reference to uniaxial nematic liquid crystals in the absence of beam curvature. When the wavefront curvature characteristic of accelerating Airy beams is accounted for, both asymptotic and numerical solutions show that a small amount of momentum is initially exchanged, with the solitary wave rapidly settling to a state of constant momentum. (C) 2014 Elsevier B.V. All rights reserved.