Theoretical modeling and analysis on the absorption cross section of the two-photon excitation in Rb

The cross-section is crucial for quantitative characterization and analysis of the absorption process. A model on the absorption cross-section of the simultaneous two-photon excitation in Rb-vapor four-wave mixing process is established by using the coupled-wave equation. Taken into account of the hyperfine structures for Rb and Rb, the third-order susceptibility and hyperfine line strength are calculated respectively. Then, the influences of hyperfine transition on cross section are investigated and simulation results agree well with the experiment results. The calculated results suggest that high pumping power intensity is essential in Rb two-photon excitation, while narrow linewidth is the limiting factor of high absorption efficiency by comparing normalized absorption profile between pumping beam and two-photon excitation process. Additionally, two approaches to improving absorption efficiency, linewidth narrowness of the pumping beam and absorption linewidth broadening, are proposed.