The spatial wandering of a femtosecond laser filament caused by the filament heating effect in air has been studied. An empirical formula has also been derived from the classical Karman turbulence model, which determines quantitatively the displacement of the beam center as a function of the propagation distance and the effective turbulence structure constant. After fitting the experimental data with this formula, the effective turbulence structure constant has been estimated for a single filament generated in laboratory environment. With this result, one may be able to estimate quantitatively the displacement of a filament over long distance propagation and interpret the practical performance of the experiments assisted by femtosecond laser filamentation, such as remote air lasing, pulse compression, high order harmonic generation (HHG), etc.

In the present work, femtosecond laser filament generation by focusing the laser pulse with an axicon in air is studied at different input laser powers both experimentally and numerically. It is found that the length of the filament increases almost linearly with the input laser power. Moreover, the laser intensity inside the filament starts to saturate at a power much higher than the critical power of self-focusing for a Gaussian beam. We have also observed the laser pulse self-compression during nonlinear propagation. The shortest pulse duration could be obtained at the center of the effective focal region produced by the axicon.

Nanostructured materials offer many advantages over bulk materials in nonlinear optical phenomena. For example, the subwavelength scale allows the neglect of phase-matching issues. The ability to control tight confinement and large resonant enhancement of electromagnetic fields also results in higher nonlinear frequency conversion efficiencies than bulk materials. Compared with plasmonic nanostructures, high-index dielectric nanostructures render larger mode volumes and show great promise for enhanced nonlinear optical processes. In this work, we present resonantly enhanced second-harmonic generation from L-shaped AlGaAs nanoantennas. By tuning the nanostructure thickness, arm length, and width, the overlap of resonances at fundamental and second-harmonic wavelengths can be achieved using any pump wavelength in a broad near-infrared spectral region. We predict SHG efficiency exceeding 4 × 10 − 3 with a pump intensity of 1 G W / c m 2 at two representative pump wavelengths of 1675 and 1800 nm. Our findings are valuable for applications involving all-dielectric nanoantennas, such as efficient sensing and single biomolecule tracking microscopy.

Multiple filaments generation by using an axicon to focus optics in the turbulent air has been studied based on numerical simulation. We came to the conclusion that the axicon could produce multiple filaments with an initial cylindrical symmetrical Gaussian laser beam in the turbulent air. Further, we have studied the threshold power of the initial beam and the threshold turbulence intensity for the formation of multi-filamentation in quantification. This result is valuable in using an axicon to control the filament.