Underlying conservation and stability laws in nonlinear propagation of axicon-generated Bessel beams

Abstract

In light filamentation induced by axicon-generated, powerful Bessel beams, the spatial propagation dynamics in the nonlinear medium determines the geometry of the filament channel and hence its potential applications. We show that the observed steady and unsteady Bessel beam propagation regimes can be understood in a unified way from the existence of an attractor and its stability properties. The attractor is identified as the nonlinear unbalanced Bessel beam (NL-UBB) whose inward Hänkel beam amplitude equals the amplitude of the linear Bessel beam that the axicon would generate in linear propagation. A simple analytical formula that determines de NL-UBB attractor is given. Steady or unsteady propagation depends on whether the attracting NL-UBB has a small, exponentially growing, unstable mode. In case of unsteady propagation, periodic, quasi-periodic or chaotic dynamics after the axicon reproduces similar dynamics after the development of the small unstable mode into the large perturbation regime.

9 pages, 7 figures

References in corpus (1)

• Non-diffracting and non-attenuating vortex light beams in media with nonlinear absorption of orbital angular momentum

Cited by in corpus (4)

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• Optical vortex trapping and annihilation by means of nonlinear Bessel beams in nonlinearly absorbing media
• Stationary and stable light beam propagation in Kerr media with nonlinear absorption with controllable dissipation patterns
• Control of spatial four wave mixing efficiency in Bessel beams using longitudinal intensity shaping