Dynamics of pulse propagation in gas-filled hollow-core photonic crystal fibers

As a new approach based on a multiple scale perturbation theory, we have founded clearly that ionization in a hollow-core photonic crystal fiber filled by an ionizable gas leads to a soliton self-frequency blueshift, opposite to redshift due to Raman self-frequency. To analyze the hollow-core photonic crystal fiber under a general perturbation, we convert the problem into a system of ordinary differential equations which govern on the soliton parameters. It is worth comparing the results with those of Saleh et al [Phys.Rev.Lett. 107, 203902 (2011)] applying a variational perturbation method with a posteriori. We obtain just the same result with no posteriori.