Theoretical Study On The Trajectory Of Momentum Spectrum Of Hydrogen Atoms In Two-color Circularly Polarized Fields

Comparing with linear polarized field or monochromatic field,bicircular fields are more effective to obtain the process of ionizing.In this work,the photoelectron momentum distribution of hydrogen atom is calculated in the case of both co-rotating and counter-rotating bicircular fields.On the base of the original theoretical method,two restrictions are introduced to make it suitable for solving the problem of two-color circular fields.The corresponding momentum spectrum can be obtained by changing the parameters of the combined electric field in the bicircular laser fields.The interference fringes in the momentum spectrum evolved with the change of laser intensity ratio.And the different characteristics of interference fringes correspond to different physical processes.Photoelectron momentum spectra show petal structure,and the number of petals is related to the parameter "q" in the electric field However,in co-rotating field "q-1"lobes region appeared but "q+1" for counter-rotating fieldAt one point in the momentum spectrum,the temporal and spatial distributions of all tunneling photoelectrons with the same final momentum can be found.The relationship among them is given in this work.It is to say that,any momentum point can be fond the corresponding tunneling photoelectrons' time and space distribution,and their trajectories that in the laser fields.The principle of interference fringes in momentum spectra with few cycles is discussed in this work.In the photoelectron momentum spectrum,there are obvious interference fringes along the axisymmetric direction of vector potential.There are more than one type interference fringes in the momentum spectrumThe momentum points are selected at the circular interference fringes and the cross interference fringes respectively.By tracking the temporal and spatial distribution of tunneling photoelectrons and combining with the characteristics of the corresponding trajectories,four types of trajectory that lead to interference fringes have been revealed.And the conditions for producing interference fringes are given.It is pointed out that only two specific cases can produce interference fringes on the obtained momentum spectrum.The first case is that two kinds of trajectories with similar spatial window and similar ionization probability produce circular interference fringes.The second case is that two kinds of trajectory with similar tunneling time window and ionization probability produce cross interference fringes.In the second case,the initial transverse momentum of the tunneling photoelectron determines the classification of the trajectory and the final interference fringe structure on the momentum spectrum.By analyzing the phase change of interference fringes,the relationship between phase change of interference fringes and the number of frequency field is found in the case of co-rotating and counter-rotating.