Application of the Generalized Bessel Function to Two-Color Phase-of-the-Phase Spectroscopy

In two-color strong field ionization of atoms, dynamical characteristics such as ionization rate and electron trajectory depend heavily on the relative phase of the strong fundamental field and its second harmonic. The phase-of-the-phase spectroscopy method reveals the oscillation of the photoelectron momentum distribution with the relative phase of the two-color field, and the relative phase contrast and its phase are usually obtained by the fitting process. Instead, we apply the generalized Bessel function to the strong field approximation and derive analytical expressions for the first- and second-order relative phase contrast and phase-of-the-phase spectra. Our analytical results are in good agreement with fitting-based ones, but calculating them is much less computationally intensive. We illustrate the advantage of using generalized Bessel functions in two-color phase-of-the-phase spectroscopy of argon.