Polarization control of multi-photon absorption under intermediate femtosecond laser field

It has been shown that the femtosecond laser polarization modulation is a very simple and well-established method to control the multi-photon absorption process by the light-matter interaction. Previous studies mainly focused on the multiphoton absorption control in the weak field. In this paper, we further explore the polarization control behavior of multiphoton absorption process in the intermediate femtosecond laser field. In the weak femtosecond laser field, the secondorder perturbation theory can well describe the non-resonant two-photon absorption process. However, the higher order nonlinear effect (e.g., four-photon absorption) can occur in the intermediate femtosecond laser field, and thus it is necessary to establish new theoretical model to describe the multi-photon absorption process, which includes the two-photon and four-photon transitions. Here, we construct a fourth-order perturbation theory to study the polarization control behavior of this multi-photon absorption under the intermediate femtosecond laser field excitation, and our theoretical results show that the two-photon and four-photon excitation pathways can induce a coherent interference, while the coherent interference is constructive or destructive that depends on the femtosecond laser center frequency. Moreover, the two-photon and fourphoton transitions have the different polarization control efficiency, and the four-photon absorption can obtain the higher polarization control efficiency. Thus, the polarization control efficiency of the whole excitation process can be increased or decreased by properly designing the femtosecond laser field intensity and laser center frequency. These studies can provide a clear physical picture for understanding and controlling the multi-photon absorption process in the intermediate femtosecond laser field, and also can provide a theoretical guidance for the future experimental realization.