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

TL;DR

This paper reveals that the nonlinear propagation of axicon-generated Bessel beams can be understood through the stability of a specific attractor, the nonlinear unbalanced Bessel beam, which determines steady or unsteady filamentation regimes.

Contribution

It introduces a unified framework based on attractor stability to explain the propagation regimes of Bessel beams in nonlinear media, including a simple analytical formula for the attractor.

Findings

Steady and unsteady propagation regimes are explained by attractor stability.

The nonlinear unbalanced Bessel beam (NL-UBB) acts as the key attractor.

Unsteady regimes involve complex dynamics like chaos after small unstable modes grow.

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 H\"ankel 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.