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Laser induced plasmas have found numerous applications includingplasma-assisted combustion, combustion diagnostics, laser induced breakdownspectroscopy, light detection and ranging techniques (LIDAR), microwaveguiding, reconfigurable plasma antennae etc. Multiphoton ionization (MPI) is afundamental first step in high-energy laser-matter interaction and is importantfor understanding of the mechanism of plasma formation. With the discovery ofMPI more than 50 years ago, there were numerous attempts to determine basicphysical constants of this process in the direct experiments, namelyphotoionization rates and cross-sections of the MPI, however, no reliable datais available until today and spread in the literature values often reaches 2-3orders of magnitude. This is due to inability to conduct absolute measurementsof plasma electron numbers generated by MPI which leads to uncertainties and,sometimes, contradictions between the MPI cross-section values utilized bydifferent researchers across the field. Here we report first direct measurementof absolute plasma electron numbers generated at MPI of air and subsequently weprecisely determine ionization rate and cross-section of eight-photonionization of oxygen molecule by 800 nm photons${\sigma}_8=(3.32{\pm}0.3)*10^{-130} W^{-8}m^{16}s^{-1}$. Method is based onthe absolute measurement of electron number created by MPI using elasticscattering of microwaves off the plasma volume in Rayleigh regime andestablishes a general approach to directly measure and tabulate basic constantsof the MPI process for various gases and photon energies.

Counting the electrons in a multiphoton ionization by elastic scattering of microwaves