Stationary nonlinear Airy beams

We demonstrate the existence of an additional class of stationary accelerating Airy wave forms that exist in the presence of third-order (Kerr) nonlinearity and nonlinear losses. Numerical simulations and experiments, in agreement with the analytical model, highlight how these stationary solutions sustain the nonlinear evolution of Airy beams. The generic nature of the Airy solution allows extension of these results to other settings, and a variety of applications are suggested.

Figure 1

Nonlinear Airy wave forms for (a) a pure Kerr focusing (green dotted line) and defocusing (red dashed line) nonlinearity with no NLLs; (b) NLLs alone with $K=5$ (red dashed line) and $\mathrm{Kerr}+\mathrm{NLLs}$ (blue dotted line). (c) Domain of existence (shaded region) of the NAB solution in the case of water at ${\lambda }_0=800$ nm as a function of peak intensity and width of the linear solution. The circles indicate the peak intensities at which numerical simulations were performed (Fig. 2).

Figure 2

Numerical results: propagation in water with focal length $f=20$ cm. Solid blue line, linear Airy profile; dashed red line, nonlinear Airy profile; black dotted line, nonlinear case with artificially increased NLLs. All profiles are shown in the focal plane of lens $f$ ($z=20$ cm).

Figure 3

Experimental results: (a) Experimental layout. (b)–(e) Output Airy beam fluence profiles in logarithmic scale.(b) Water at three input energies 25 nJ (solid line), 350 $\mu$J (dashed line), and 530 (dotted line) $\mu$J and for an input Airy pulse with a main lobe FWHM of 159 $\mu$m. (c) Water at same energies as in (b) and a main lobe FWHM of 182 $\mu$m. (d) PMMA at three input energies 25 nJ (solid line), 78 $\mu$J (dashed line), and 196 (dotted line) $\mu$J and for an input Airy main lobe FWHM of 78 $\mu$m. (e) PMMA at same energies as in (d) and a main lobe FWHM of 136 $\mu$m.