Data for spectral modified scaling rules

Gas-filled capillary fiber has been widely regarded as an ideal platform for generating high energy, ultrashort laser pulses with broadband wavelength tunability, highly demanded in a few scientific areas. While a variety of soliton dynamics, such as high-order soliton self-compression (HSC), dispersive-wave emission (DWE) and ionization-induced spectral blue-shift (IBS), have been intensively studied in such a capillary fiber system, the parameter-scaling rule of this system is, however, different from that of the hollow-core photonic crystal fiber system, mainly due to the non-ignorable loss of the capillary waveguide. Here, we demonstrate a modified parameter-scaling rule which includes the capillary loss term, being useful to system design and optimization. We illustrate both theoretically and experimentally that this modified scaling rule is valid for all of the HSC, DWE and IBS processes, highlighting the similarities of these nonlinear propagation processes over a large range of capillary sizes.