Single-shot measurement of the nonlinear refractive index of air at 9.2 µm with a picosecond terawatt CO₂ laser

We developed a simple, accurate single-shot method to determine the nonlinear refractive index of air by measuring the evolution of the spatial shape of a laser beam propagating through the atmosphere. A distinctive feature of this new method, which relies on a modified Fresnel propagation model for data analysis, is the use of a hard aperture for producing a well-defined, high-quality beam from a comparatively non-uniform quasi-flat-top beam, which is typical for high-peak-power lasers. The nonlinear refractive index of air for a very short (2 ps) long-wave infrared (LWIR) laser pulse was measured for the first time, to the best of our knowledge, yielding n₂ = 3.0 × 10⁻²³ m²/W at 9.2 µm. This result is 40% lower than a corresponding measurement with longer (200 ps) LWIR pulses at a similar wavelength.