Ionization rate of O₂ vs. local instantaneous laser intensity from an 800 nm ultrashort laser inferred from electron and ion product count data

The optical cycle averaged ionization rate <W>_t of O₂ vs. local instantaneous laser intensity I for linear and circular polarized 800 nm light is determined up to 800 TW/cm² by spatiotemporal data inversion of aperture limited measurements proportional to the total O₂⁺ plus O₂²⁺ population vs. peak intensity I₀ that results from a focused ultrashort pulsed Ti:sapphire laser. The data used is that published by C. Guo, et. al, Phys. Rev. A 58, R4271, 1998. The proportionality constant is determined from the signal below I₀ = 27 TW/cm², where the multiphoton approximation <W>_t = σ₈I⁸ is applicable. The σ₈ value is based on total electron yield measurements of A. Sharma, et. al, Scientific Reports, 8:2874, 2018. However, it is recalculated based on a different temperature estimate and use of electron momentum transfer collision frequency ν_c in air to determine the electron oscillation amplitude resulting from diffusive transport instead of the elastic collision frequency. The result is σ₈ = 2.3±0.3×10^-130 W^-8 m¹⁶s^-1. Sharma, et. al's methodology used to calculate σ₈ assumes the signal results from a diffraction limited focused beam with both a Gaussian cross section and pulse envelope waveform. It is generalized for our analysis for an arbitrary <W>_t vs. I dependence (instead of I⁸) and an apertured collection length. The closed form analytic solution presented makes the method portable to other wavelengths and molecular species, given similar data.