Enhancement Of High-order Harmonic And Attosecond Pulse Generation From H₂⁺ By Two-color Circularly Polarized Laser Fields

Attosecond pulse is a powerful tool to probe electron dynamics,helping people further understand microscopic field,which attracts much attention.Nowadays,people can obtain attosecond pulse by high-order harmonic generation?HHG?,Thomson scattering and Raman scattering.It is a promising way to generate attosecond pulse using HHG because of the broad spectral range.The HHG has the following features: the efficiency at lower order decrease rapidly,then it keeps for a broad plateau,eventually moves to a sharp cutoff.The semi-classical three-step model can well explain the mechanism of HHG.First,the Coulomb potential can be distorted by the intense laser field,which makes the electron has the chance to tunnel through the barrier;then,the ionized electron moves along with the laser field ignoring the Coulomb potential;finally,when the laser reverse its direction,the electron has the chance recombining with parent ion,emitting high energy photon,which is the HHG.Many schemes have been proposed to obtain the attosecond pulse in theoretical and experimental research,such as two-color laser field scheme,polarization gate scheme and few cycle laser field scheme and so on.In this paper,the initial wave function is constructed by the imaginary time-propagation method.And by solving the two-dimension?2D?Schr?dinger equation by the splitting-operator technique,we investigate the HHG of H₂⁺ and corresponding attosecond pulse in circularly polarized laser field,two-color circularly polarized laser field and the combined laser field with static field.The detailed works are described as follows:Firstly,we investigate the generation of HHG and attosecond pulse of H₂⁺ in circularly polarized combined field with a static field.The theoretical results show HHG in circularly polarized field has low efficiency and cutoff energy.After adding a static field on x direction,the intensity and cutoff energy of HHG becomes higher.We investigate the HHG in combined field by taking as an example,when a?28?0.25 the static field is added on x direction,the intensity of HHG increase by about 3⁵ orders of magnitude,the cutoff can be broadened around 230 e V,with a flat plateau between 170 e V²30e V.The time-frequency analysis is in good correspondence with the results from the semi-classical three-step model with non-zero initial transverse velocity.Besides,the trajectories show that electron can move further and gain much more energy than circularly polarized only case,which is the reason for broadened plateau.Finally,an attosecond pulse of 101 as can be obtained.Secondly,the HHG of H₂⁺ by two-color circularly polarized field?combined with left circularly polarized field of 750 nm and right circularly polarized field of 375 nm?is investigated.The intensity of HHG is strengthened and the cutoff energy is higher compared to the circularly polarized field case.We also investigate the HHG after adding a static field on x direction,we take as an example static0E?28?aE a?28?0.3to investigate the mechanism of the phenomena cause it has less modulations and higher cutoff energy.It can be seen from HHG spectra and the time-frequency analysis that,the plateau is broadened by 65 e V with cutoff energy around 165 e V.It shows less modulations between 90 e V¹65 e V.An attosecond pulse with a duration of 159 as can be obtained by superposing the harmonics in the range of 140 e V¹65 e V.Finally,we investigate the HHG when the right circularly polarized field is changed.The frequency of the left circularly polarized field is fixed at,and the 1wfrequency of right circularly polarized field is changed with,and.12.5w12w11.5wThe time-frequency analysis and HHG spectra show that,the plateau is well broadened with less modulation at case.And an attosecond pulse in the 11.5wduration of 106 as is obtained by superposing the harmonics from 85¹20 e V.