Analytic formula of the efficiency of optical-optical double-color double-resonance multi-photon ionization (OODR-MPI) is derived from the dynamic rate equation about the interaction of photon and material. Based on this formula, the influence of characteristic of the pump and probe laser on the ionization efficiency of (1+2+1) OODR-MPI process is simulated theoretically. It is shown that the pump laser will affect the ionization efficiency by the number control of the molecules excited to the first resonance state. The ionization efficiency is decided by the probe laser directly. Both of the excited molecules and ionization efficiency increase with the intensity and pulse duration of the laser until saturation. It is also found that the longer the delay time of the probe laser to the pump one is, the lower the ionization efficiency would be. The delay time ought to be smaller than the lifetime of the excited molecule in the practical use of the OODR-MPI technique.

The analytic formula of the ionization efficiency in the process of double resonance enhanced multi-photon ionization (DREMPI) is derived from the dynamic rate equation about the interaction of photon and material. Based on this formula, the ionization efficiency and the laser power index versus laser intensity in the DREMPI process of NO molecule, via A2\sum and S2\sum intermediate resonant states, is numerically simulated. It is shown that the ionization efficiency of NO molecule increases with the laser intensity until getting saturation, while the laser power index decreases with the enhancement of the laser intensity and changes to zero at last. The variation of the laser power index with the laser intensity indicates that the ionization efficiency reaches saturation in the one, two, and three excitation steps respectively. It is also found that the narrower the laser pulse duration is, the higher becomes the laser intensity for saturation.