Effective soliton order approach for scaling of pulse self-compression in hollow-core fibers

Optical solitons can undergo extreme temporal and spectral reshaping at high pulse intensities. These dynamics can be utilized to extract few-cycle pulses in the negative dispersion region in the case of higher-order spatial modes in hollow fibers. One can achieve self-compression up to few-cycle duration in hollow capillary fibers without any external optical post-compression schemes using this technique. These intense few-cycle pulses are an essential tool for revealing the ultrafast dynamics in the femtosecond to attosecond timescale, where the tunability and scalability of few-cycle pulses are a necessity. Utilizing the soliton dynamics, we can scale the pulses up to multi-millijoule energies as well as terawatts of peak power. Scaling relations are relations that can be used to produce propagation dynamics that are invariant and essentially identical for multiple sets of input conditions. But, for the same input soliton order, the scaling relations derived under different dispersion conditions, such as different gas pressure, result in somewhat different scaling laws. This leads to an ambiguity in the compression factor and compression length for any particular soliton order N. It is thus necessary to find an accurate soliton order which can scale the self-compression dynamics over different dispersion conditions. We numerically simulate soliton self-compression in an argon gas-filled HCF across a wide range of dispersion conditions and present a set of efficient scaling laws for soliton dynamics. We introduce an effective soliton order Nef f for explaining the behavior of the dynamics in systems with high third-order dispersion (TOD) such as the HCF. The proficiency of the new scaling laws over the earlier scaling laws in literature is elucidated in this work. Thus, an inclusive set of scaling laws for generating high-energy few-cycle pulses are defined which are critical for generating single and trains of attosecond pulses, as well as electron and ion acceleration strategies in intense laser pulses.