The High-order Harmonic Generation Driven By Bichromatic Elliptically Polarized And Inhomogeneous Laser Fields

High-order harmonic generation(HHG)is a process from the nonlinear interaction of intense laser pulse with atoms or molecules,new frequencies in the extreme ultraviolet(XUV)and soft-x-ray range are generated.High-order harmonic radiation has excellent features such as equal frequency interval the and wide spectral range.HHG has been intensively studied in experimental and theoretical investigations,it promises both applications for generating attosecond pulses and probing basic ultra fast electronic processes and the molecular structure.Therefore,the research of the high harmonic characteristics has always been an important subject in strong field physics.The physical mechanism of HHG can be understood intuitively in terms of a three-step model.The electron is first ionized when atoms(or molecules)encounter a strong laser electric field,then it is accelerated and obtains kinetic energy under the effect of the laser field.Finally,the electric field reverses its direction,simultaneously the electrons recombines with the parent ion and emits a harmonic photon.At present,the research on the HHG mainly focus on how to extend the cutoff of harmonic spectrum and how to enhance the conversion efficiency of HHG.In this letter,we mainly investigate the process that the regulation of ionization and acceleration of electrons by controlling the changes of some parameters of laser pulses,to obtain HHG with certain characteristics and to generateattosecond pulses.With the development of the HHG in the vicinity of metallic nanostructure from atomic responses,the harmonic generation in the vicinity of metallic nanostructure from molecules has also been investigated.The HHG from H2+ in bowtie-shaped nanostructure is investigated by solving the one-dimensional time-dependent Schr?dinger equation within the non-Born-Oppenheimer approximation by the splitting-operator fast-Fourier transform technique.We find that the spatial position of the inhomogeneous field inside the nanostructure has a great influence on the harmonic spectrum.When the spatial position of the inhomogeneous field is translated from 30 a.u.to-30 a.u.,the cutoff of the HHG can be extended and the smoother supercontinuum harmonic spectrum is formed.The underlying physical mechanism can be well demonstrated by the time-frequency distribution,the three-step model,the ionization probability and electric field of the driving laser.The effects of the carrier-envelope phase on HHG is also demonstrated.We find that with the change of the carrier-envelope phase,their overall trends are the same,that is,the cutoff of the HHG is extended when the spatial position of the inhomogeneous field is translated from 30 a.u.to-30 a.u..When the spatial position of the inhomogeneous field is-30 a.u.and the carrier-envelope phase is 0.2?,by superposing from 40 th to70th of harmonic spectrum,we generate an isolated attosecond pulse with width of119 as.We theoretically investigate the HHG by solving a two-dimensional time-dependent Schr?dinger equation for a two-dimensional model of an Ar+ cluster in a elliptically polarized laser fields.We choice the number of ions surrounding the central atom is(28)8gN and(28)24gN.We find that the harmonic plateau has been extended and enhanced with the number of ions surrounding the central atom,but the harmonic plateau has been shorted with the increase of the ellipticity.We explained the characteristics of harmonic spectrum by using the time-frequency analysis.Thenwe theoretically investigate the HHG and isolated attosecond pulse generation in a elliptically polarized inhomogeneous laser fields.The results show that moderate the inhomogeneity,not only the harmonic plateau has been extended and enhanced but also the single short quantum path has been selected to contribute to the harmonic.As a result,a series of 79 as pulses around the extreme ultraviolet and the x-ray regions have been obtained.An efficient method is investigated for the generation of circularly polarized high-order harmonics by a bichromatic laser field whose two components with wavelength 800 nm and 400 nm are circularly polarized in the same plane,but rotate in opposite directions.We find that change the relative intensity ratio,not only the harmonic plateau has been enhanced but also the polarization properties of the harmonic field has been changed.The relative intensity ratio(28)4.1E? is the highest harmonic efficiency,which is consistent with the results in the literature[193].We explained the characteristics of harmonic spectrum by using the time-frequency analysis,the semi-classical three step model and lissajou figures.Forthermore,we superposition the harmonic fields of different frequencies with different relative intensity ratio and find that the rotation of the harmonic field is the same as that of the incident laser pulse.However,the polarization properties of the harmonic field are changed under the different relative intensity ratio.Therefore,the enhance of the harmonic plateau and the rotation polarization characteristics are regulated by the change of relative intensity ratio.We investigate the harmonic spectra of Ar atom with the bichromatic counter-rotating elliptically polarized laser fields which consists of two coplanar components having the frequencies r = 1 and s(28)2,s(28)3,s(28)4 by numerically solving the time-dependent Schr?dinger equation(TDSE).We found that the high harmonic spectrum is consistent with the selection rule in reference[206]reported by Milo?evic 2015(J.Phys.B 48,171001).The numerical results demonstrate that theHHG is consistent with the selection rule(6.5)for the usual bicircular laser field,and the HHG is consistent with the selection rule(6.6)for the bichromatic elliptically polarized laser field.Furthermore,the HHG process is demonstrated by using the lissajou figures.