Topological charge influence on self-action of femtosecond optical vortices in the range of anomalous group velocity dispersion

The self-action of femtosecond optical vortices in LiF crystal at wavelength 1800 nm in the range of anomalous group velocity dispersion is considered. The influence of the topological charge on the spatio-temporal dynamics of the pulse and peak intensity values in the formation of ring light bullets is analyzed. The propagation of femtocesond pulses in a nonlinear medium can be accompanied by a phenomenon of filamentation, when a long thin filament of a laser field with a high localization of light energy is formed [1]. Femtosecond filamentation is influenced by the group velocity dispersion (GVD) of the pulse. In the conditions of anomalous GVD the formation of so-called “light bullets”, which are relatively stable in space and time, is possible [2]. Filamentation in presence of light bullets has been widely studied for Gaussian beams [3]. Self-action of ring beams with a phase dislocation optical vortices, where a helical wavefront prevents the localization of the field on the optical axis, was analyzed significantly less [4]. Potential applications of such beams are associated with obtaining micromodification of the refractive index of the ring shape [5]. The self-action of femtosecond vortices in condensed media was studied both under conditions of normal [6] and anomalous [7, 8] GVD. Spatiotemporal dynamics, multifocus spatial structure, quantitative characteristics of light bullets, arising during propagation, and spectral transformation of pulse energy were studied. The purpose of this work is to analyze the influence of the vortex topological charge on the spatiotemporal pulse dynamics in LiF crystal at wavelength lying in the region of the anomalous GVD. Numerical simulation of the self-action of femtosecond optical vortices was carried out by solving a nonlinear system of equations for complex amplitude of the light field A (r, t, z), written in slowly varying wave approximation [9], and plasma concentration Ne (r, t). On the input surface of the LiF crystal the optical vortex takes the form: Am(r, t, 0) = A(r, t, 0) exp{imφ} = A0 ( r r0 ) m exp {− r 2r0 2} exp {− t 2t0 2} exp{imφ}, where r0 and t0 are the characteristic spatial and temporal scales of the vortex. We considered vortex beams with topological charges m = 1 and m = 2 at two central wavelengths λ0 = * Corresponding author: vasilev.evgeniy@physics.msu.ru © The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0 (http://creativecommons.org/licenses/by/4.0/). EPJ Web of Conferences 220, 02019 (2019) https://doi.org/10.1051/epjconf/201922002019 IWQO-2019

The propagation of femtocesond pulses in a nonlinear medium can be accompanied by a phenomenon of filamentation, when a long thin filament of a laser field with a high localization of light energy is formed [1]. Femtosecond filamentation is influenced by the group velocity dispersion (GVD) of the pulse. In the conditions of anomalous GVD the formation of so-called "light bullets", which are relatively stable in space and time, is possible [2]. Filamentation in presence of light bullets has been widely studied for Gaussian beams [3]. Self-action of ring beams with a phase dislocation -optical vortices, where a helical wavefront prevents the localization of the field on the optical axis, was analyzed significantly less [4]. Potential applications of such beams are associated with obtaining micromodification of the refractive index of the ring shape [5]. The self-action of femtosecond vortices in condensed media was studied both under conditions of normal [6] and anomalous [7,8] GVD. Spatiotemporal dynamics, multifocus spatial structure, quantitative characteristics of light bullets, arising during propagation, and spectral transformation of pulse energy were studied. The purpose of this work is to analyze the influence of the vortex topological charge on the spatiotemporal pulse dynamics in LiF crystal at wavelength lying in the region of the anomalous GVD.
Numerical simulation of the self-action of femtosecond optical vortices was carried out by solving a nonlinear system of equations for complex amplitude of the light field ( , , ), written in slowly varying wave approximation [9], and plasma concentration ( , ). On the input surface of the LiF crystal the optical vortex takes the form: where 0 and 0 are the characteristic spatial and temporal scales of the vortex. We considered vortex beams with topological charges = 1 and = 2 at two central wavelengths 0 = 1800 nm and 0 = 3000 nm, corresponding to moderate ( 2 ≃ −39 fs 2 /mm) and strong ( 2 ≃ −239 fs 2 /mm) anomalous GVD. The pulse peak power 0 exceeded the critical power ( ) for a given topological charge m by five times.
At the beginning of the pulse propagation in nonlinear medium, a five-fold excess of the peak power over the critical power leads to spatial self-focusing of the vortex in the ring, which is accompanied by simultaneous self-compression in time leading to the formation of an annular bullet. For a fixed topological charge, the distances to the first focus at different wavelengths approximately coincide (Fig. 1).

Fig. 1. Optical vortices with topological charges
= 1 (solid lines) and = 2 (dotted lines) peak intensity dependence on the propagation distance under self-action in the LiF crystal at central wavelengths 0 = 1800 nm (thin lines) and 0 = 3000 nm (thick lines).
The first nonlinear focus of vortices with = 1 is located at a distance of about 0.75 cm, while for vortices with = 2 the nonlinear focus is located in the vicinity of = 0.6 cm. Topological charge promotes self-focusing of radiation in the ring providing a faster increase in intensity. The radius of the last (third) annular bullet increases with the topological charge. For an optical vortex with m = 2, it is three times larger than for m = 1. Fig. 1 shows that the global maximum of intensity in vortices with = 1 is reached in the last nonlinear focus, while for vortices with = 2 -in the first focus. Thus, an increase in the topological charge complicates the appearance of near-axial light bullets and prevents peak intensity increase in the nonlinear focus as the pulse propagates. This work was supported by grant No. 18-02-00624 from the Russian Foundation for Basic Research and was carried out using the equipment of the shared research facilities of HPC computing resources at Lomonosov Moscow State University.