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

Multiphoton ionization (MPI) is a fundamental first step in high-energy laser-matter interaction and is important for understanding the mechanism of plasma formation. With the discovery of MPI more than 50 years ago, there were numerous attempts to determine the basic physical constants of this process in direct experiments, namely photoionization rates and cross-sections of the MPI; however, no reliable data was available until now, and the spread in the literature values often reaches 2-3 orders of magnitude. This is due to the inability to conduct absolute measurements of plasma electron numbers generated by MPI, which leads to uncertainties and, sometimes, contradictions between MPI cross-section values utilized by different researchers across the field. Here, we report the first direct measurement of absolute plasma electron numbers generated at MPI of air, and subsequently we precisely determine the ionization rate and cross-section of eight-photon ionization of oxygen molecule by 800 nm photons σ₈ = (3.3 ± 0.3)×10^-130 W^-8m¹⁶s^-1. The method, based on the absolute measurement of the electron number created by MPI using elastic scattering of microwaves off the plasma volume in Rayleigh regime, establishes a general approach to directly measure and tabulate basic constants of the MPI process for various gases and photon energies.