Study On Polarized Properties Of High-order Harmonics And Attosecond Pulse Trains Of Helium Atom Driven By Tri-circular Laser Field

High-order harmonic is a highly nonlinear process that occurs when the atoms or molecules interact with strong laser field.High order harmonic can be used to track the quantum dynamics of electrons of atoms or molecules,and generate attosecond pulse,or as a tabletop source of bright.Circularly polarized extreme ultraviolet and soft X-ray can be used to analyze the structure and electric-magnetic properties of material,such as photon-electron circular dichroism in chiral molecules.Recently,ones have found that high-harmonic generated by two color bi-circularly polarized laser field are circularly polarized.By superimposing a group of high harmonics generated by bi-circularly polarized laser filed,one can obtain circularly or elliptically polarized attosecond pulse trains.In this paper,the following result is carried out by using strong field approximation method.Firstly,when the s-state helium atom driven by counter-rotating bi-circular laser field.for two color bi-circular laser field with frequencies ? and 3?,the emitted harmonics have order 3N±1,and the 2N harmonics are forbidden.For bi-circular laser field with frequency ? and 3?,the emitted harmonics must have order 4N±1,while the 2N harmonics are forbidden.The reason of the emitted harmonics have the orders 4N+1 can be explained through conservation of energy and conservation of angular momentum.Orders 4N+1 corresponding to the net absorption of N+1 ? photons and N 3? photons,respectively,orders 4N-1 corresponding to net absorption N-1 ? photons and N ? photons.Reemission of the absorbed photons as a harmonic occurs by the electron recombination to the initial state,with corotating with the ?(3?)field.When atoms exposed to a bi-circularly polarized laser field,each harmonic electric field of single order is circularly polarized,the left-circularly polarized and right-circularly polarized harmonics are alternately distributed on the harmonic spectrum.Secondly,we have studied the polarized properties of high order harmonic generation of He atom driven by tri-circularly polarized laser field with frequencies ?,2?,4?,or ?,3?,5?,and ?,2?,3?.The result shows that the harmonic spectrum driven by tri-circular laser field with frequencies ?,2?,4? is similar to the spectrum of bi-circular laser field with frequencies ?,2?.The emitted harmonics have orders 3N±1,and orders 3N are forbidden,the degree of circular polarization of order 3N+1 and order 3N-1 are different.By using a group of harmonics,we can obtain a ellipticity circularly polarized attosecond pulse trains.The result of tri-circular laser field with frequencies ?,3?,5? is similar to the result of bi-circular laser field with frequencies ?,3?.While,the harmonic spectrum of He atom driven by tri-circular laser field with frequencies ?,2?,3? is different with ?,3?.The orders 2N are emitted,and the intensity of orders 2N are weakly than orders 4N±1,and orders 2N co-rotating with field ? or 3? depends upon order 2N-1 which co-rotating with field ? or 3? when tri-circular laser field is driven field.Due to the appearance of the 2N harmonics,one can obtain attosecond pulse trains with large ellipticity by superimposing groups of harmonics with different intensity.