Spectrally-broadened femtosecond vortex beams in air with longitudinal pressure distribution

The spectral broadening of femtosecond vortex beams in air with different longitudinal pressure distributions is studied numerically. By introducing a symmetrical pressure distribution, a sufficiently broadened spectrum while preserving vortex characteristics of the beam for different input energies can be generated. The proposed pressure distribution involves an increase during the self-focusing stage, followed by a flat-top and symmetric decrease. This approach takes advantage of the mechanism that the strong Kerr nonlinearity in the high-pressure filamentation region results in a broader spectrum towards the blue side through the self-phase modulation and ionization, while the weak Kerr nonlinearity in the low-intensity regions before and after filamentation with low pressure leads to the decrease of the intensity fluctuation and the preservation of vortex characteristics due to weak modulation instability. Consequently, the resulting vortex beam exhibits a broad enough spectrum, and the transform-limit duration reaches a single cycle. This study provides a valuable approach for generating single-cycle vortex beams.