Activation of the Self-Focusing Process in Hollow-Core Fibers: Influence of the Spatio-Temporal Dynamics

Summary form only given. The first nonlinear effect that appears when an ultrashort laser pulse propagates through an amorphous medium, such as a gas or a glass, is related to an intensity-dependent refractive index: the optical Kerr effect. One of the consequences of the Kerr effect is the self-focusing of the beam, which takes place for input peak powers above a threshold value, the critical power (P
_cr
) [1,2]. Another consequence of the optical Kerr effect is the spectral broadening related to the self-phase modulation. This spectral broadening is used to generate ultrashort pulses in post-compression schemes, most of them based on the nonlinear propagation of a pulse inside a hollow-core fiber (HCF) [3]. We have recently realized that the optimum configuration to achieve the cleanest short pulse from a post compression scheme based on the nonlinear propagation inside a HCF requires the prevention of the appearance of highly nonlinear effects such as a noticeable ionization, which are usually connected to tighter spatial confinement (the activation of self-focusing) [4]. In this contribution we present a detailed study of the self focusing dynamics of a beam propagating inside a HCF in order to gain insight into the energy scaling limits. We have verified that the collapse dynamics of the fundamental mode inside the HCF, the EHii mode [5], is enhanced compared to its propagation in free space, especially for peak powers close to P er , reducing the maximum input pulse energy that can be used. The activation of the self-focusing process is related to the appearance of new HCF spatial modes, which induces a very rich spatio-temporal dynamics. We observe a strong pulse self-compression, that takes places together with the self-focusing process, which allows the spatial collapse of the beam even for input peak powers below P e r. This unexpected activation of the self-focusing dynamics is directly related to the nonlinear energy transfer between the different HCF spatial modes, which depends on several parameters, especially on the pulse temporal duration. We have numerically proved that the evolution of the contributions of the different HCF spatial modes is clearly linked to the self -focusing process inside the HCF. In summary, we have identified the relevance of the multimodal nature of the nonlinear propagation of a laser pulse inside a HCF in order to fi nd the energy scaling limits of this post-compression technique. We have also been able to understand how this complex multimodal propagation might activate the self-focusing process even for input peak powers below Per[6].