Ultraviolet Source Assisted Enhancement of Attosecond Pulse

Li-qiang FengHang Liu

a.College of Science,Liaoning University of Technology,Jinzhou 121000,China

b.State Key Laboratory of Molecular Reaction Dynamics,Dalian Institute of Chemical Physics,Chinese Academy of Sciences,Dalian 116023,China

c.School of Chemical and Environmental Engineering,Liaoning University of Technology,Jinzhou 121000,China

Ultraviolet Source Assisted Enhancement of Attosecond Pulse

Li-qiang Fenga,b∗,Hang Liuc∗

a.College of Science,Liaoning University of Technology,Jinzhou 121000,China

b.State Key Laboratory of Molecular Reaction Dynamics,Dalian Institute of Chemical Physics,Chinese Academy of Sciences,Dalian 116023,China

c.School of Chemical and Environmental Engineering,Liaoning University of Technology,Jinzhou 121000,China

A promising method to improve the attosecond pulse intensity has been theoretically presented by properly adding an ultraviolet pulse into the orthogonal two-color feld.The results show that by properly adding a 125 nm ultraviolet pulse to the orthogonal two-color feld, not only the harmonic yield is enhanced by 2 orders of magnitude compared with the original orthogonal two-color feld case,but also the single short quantum path,which is selected to contribute to the harmonic spectrum,results in an ultrabroad 152 eV bandwidth.Moreover, by optimizing the laser parameters,we fnd that the harmonic enhancement is not very sensitive to the pulse duration and the polarized angle of the assisted ultraviolet pulse,which is much better for experimental realization.As a result,an isolated pulse with duration of 38 as can be obtained,which is 2 orders of magnitude improvement in comparison with the original two-color orthogonal feld case.

High-order harmonic generation,Isolated pulse,Two-color orthogonal feld, Ultraviolet source

I.INTRODUCTION

Attosecond extreme-ultraviolet pulse(XUV)generation has been a hot issue due to its potential applications,such as probing and controlling the electron motions inside atoms,molecules,solids[1]and tracing the bound electron motion[2−4]etc.Currently,one of the most successful ways to achieve this attosecond pulse is connected with the high-order harmonic generation(HHG)from the rare gases[5−7],which can be well understood by means of the“three-step”model[8], where harmonics are emitted through the steps of tunneling ionization,acceleration,and recombination.Further,an attosecond pulse could be produced by making an inverse Fourier transformation of several harmonics [9−18].However,the applications of the generated attosecond pulses[9−18]are limited due to the low output energy.Hence,how to enhance the attosecond pulse intensity poses an interesting but challenging issue in attosecond science.

Recently,an alternative technique,named as ultrashort ultraviolet(UV)pulse assisted enhancement of the attosecond sources has attracted much attention [19].For instance,Liet al.[20]obtained an intense 26 as pulse by combination of an 800 nm chirped feld and its 27th harmonic pulse.Fenget al.[21]obtained an intense 41 as pulse by using the two-color feld combined with the ultrashort 29.6 nm pulse.

However,the method mentioned above has some limitations,i.e.(i)the high intensity ultrashort UV pulse (τUV=0.5 fs in the former investigations)is difcult to be obtained in many laboratories,(ii)the model used in all the above theories is for He+ion,which is still an experimental challenge for the generation of an ionic gas with sufcient density,(iii)the fundamental felds used in the former investigations are all linear polarization.As we know that the HHG process is highly dependent on the ellipticity of the laser feld[22−24], therefore,the time-varying polarization gating is a very important technique to the harmonic selection.

In this work,we present another efcient method to attosecond pulse enhancement by properly adding a UV pulse into the two-color feld.Here,the model we used is the neutral He atom,which is much easier to obtain in experiment,and the fundamental feld is chosen to be the orthogonal polarization two-color feld.It shows that with the introduction of a proper 125 nm UV pulse into the two-color orthogonal feld,the harmonic intensity is enhanced by 2 orders of magnitude. Moreover,the harmonic plateau is contributed by the single short quantum path.Further analyses show that this harmonic enhancement is independent of the pulse duration and the polarized angle of the controlling UV pulse.Finally,by properly Fourier transformation of these enhanced harmonics,a 38 as pulse with 2 orders of magnitude improvement can be obtained.

II.THEORY

In this work,the HHG spectra can be investigated by solving the time-dependent Schr¨odinger equation (TDSE).In the dipole approximation and the length gauge,the TDSE is given by the following equation, atomic units(a.u.)are used throughout this work unless stated otherwise.

whereV(x,y)is the soft Coulomb potential of He atom. We use the sine basis functions to depict a DVR for the translational coordinatesxandy[25,26]as follows,

hereEiandωi(i=1−3)are the amplitudes and the frequencies of the two-color orthogonal feld and the UV pulse,respectively.τdelayis the delay time between the orthogonal feld and the UV pulse.θis the polarized angle of the UV pulse(the angle between the two polarization axes).The envelope function is,

whereτi(i=1−3)are the pulse durations of the three pulses.

According to the Ehrenfest theorem[34],the timedependent dipole acceleration can be written in the form,

FIG.1 HHG spectra of the linear two-color feld and the orthogonal two-color feld.The laser felds are 5 fs/800 nm,I1=1.0×1015W/cm2and 10 fs/1600 nm,I2=1.0×1014W/cm2.

The HHG spectra can be obtained by Fourier transforming the time-dependent dipole accelerationa(t),

Finally,the attosecond pulse can be obtained by harmonic superposing as follows,

III.RESULTS AND DISCUSSION

Figure 1 shows the HHG spectra driven by the linear and the orthogonal two-color feld,respectively.The two-color feld is 5 fs/800 nm,I1=1.0×1015W/cm2and 10 fs/1600 nm,I2=1.0×1014W/cm2.Clearly,with the introduction of the polarized angle of the two-color feld (here is the orthogonal polarized feld),the modulation on the harmonic spectrum is remarkably decreased in comparison with the linear two-color feld case,which is benefcial to the isolated pulse selection.

FIG.2(a)HHG spectra of the orthogonal two-color feld and the orthogonal two-color feld combined with the 1 fs/125 nm,I3=5.0 kW/cm2UV pulse withθ=0.0π,ω1τdelay=0.8π.(b)HHG spectra of the orthogonal twocolor feld and the orthogonal two-color feld combined with the 1 fs/125 nm,I3=5.0 kW/cm2UV pulse withθ=0.5π,ω1τdelay=0.8π.(c)Polarized angle(θ)efect on the harmonic spectra.

Figure 2(a)and(b)show the HHG spectra of the orthogonal two-color feld combined with the 1 fs/125 nm,I3=5.0×103W/cm2UV pulse withθ=0.0π,ω1τdelay=0.8π(which means adding the 125 nm pulse inxdirection)andθ=0.5π,ω1τdelay=0.8π(which means adding the 125 nm pulse inydirection),respectively.Clearly,with the introduction of the 125 nm pulse atω1τdelay=0.8π(this is the optimal time delay both inxandydirections),the harmonic yields have been enhanced by 2 orders of magnitude compared with the original two feld case,which is benefcial to the isolated pulse enhancement.Figure 2(c)shows the polarized angle(θ)efect on the harmonic enhancement. The other parameters are the same as those in Fig.2(a) and(b).It shows that the harmonic enhancement phenomenon is not very sensitive to the polarized angle(θ). It means that one can add this UV pulse with an arbitrary polarized angle,and the harmonic enhancement can always happen,which is much better for experimental realization.

According to the“three-step model”[8]and the previous investigations[20,21],we know that the harmonic yields are strongly dependent on the ionization probabilities(IPs).Therefore,to understand the physical origin of the harmonic enhancement,in Fig.3,we calculate the IPs of the above cases.We see that with the introduction of the UV pulse,the IPs are enhanced compared with the original two-color feld case,thus leading to a largely augmented harmonic efciency[21].Moreover, the enhanced IPs produce no distinct changes with the variety of the polarized angle,which is responsible for the harmonic insensities to the polarized angle.

To better understand the harmonic emission process, in Fig.4,we present the time-frequency of harmonic spectra,obtained by using the wavelet transformation of the dipole accelerationa(t)[35].For the linear twocolor feld case,as shown in Fig.4(a),there are fve energy bursts on the harmonic emission process.Moreover,each burst receives similar contributions from the right path(called the long quantum path having earlier ionization and later recollision)and the left path(called the short quantum path with later ionization but earlier recollision)[36],which is responsible for the large modulation on the harmonic.For the orthogonal two-color feld case,as shown in Fig.4(b),we see that for the maximum energy burst,the contribution of the short quantum path is much larger than that of the long quantumpath,which is responsible for the small interference on the harmonic spectrum.While for the cases of the orthogonal two-color feld combined with the UV pulse inxandydirections withω1τdelay=0.8π,as shown in Fig.4 (c)and(d),the harmonic intensity has been remarkably enhanced in comparison with the orthogonal two-color feld case(see the color-bar).Moreover,the single short quantum path has also been selected to contribute to the maximum harmonic emission burst,which is benefcial to the isolated attosecond pulse generation.

FIG.3 Ionization probabilities of(a)the orthogonal twocolor feld and the combined feld(two-color feld+125 nm pulse)with diferent polarized angle ofω1τdelay=0.8π,θ=0.5π,0.3π,0.1π,and 0.0π.

Figure 5(a)and(b)show the controlling pulse duration(τ3)efect on the harmonic enhancement.The other parameters are the same as those in Fig.2(a) and(b),respectively.Clearly,the HHG spectra are almost invariable with the variety of the pulse duration ofτ3,suggesting that HHG is rather independent of the pulse duration.Therefore,based on the practical application,choosing the longer pulse duration(τ3=5 fs)is much better for experimental realization.Figure 5(c) and(d)show the controlling pulse intensity(I3)efect on the harmonic spectra.It shows that with the increasing of the controlling pulse intensity,the harmonic yields are further enhanced,however,the enhanced ratio is less than 1 order of magnitude.Thus,in this work, we chooseI3=5.0×1013W/cm2as a proper controlling pulse intensity and a 152 eV supercontinuum with 2 or-ders of magnitude improvement can be obtained,which will be favorite to support attosecond pulse enhancement.

FIG.4 The time-frequency distributions for(a)the linear two-color feld,(b)the orthogonal two-color feld,(c)the orthogonal two-color feld combined with the 1 fs/125 nm,I3=5.0 kW/cm2UV pulse withθ=0.0π,ω1τdelay=0.8π, and(d)the orthogonal two-color feld combined with the 1 fs/125 nm,I3=5.0 kW/cm2UV pulse withθ=0.5π,ω1τdelay=0.8π.o.c.means the optical cycle of 800 nm pulse in all the following fgures unless stated otherwise.

FIG.5(a)and(b)Controlling pulse duration(τ3)efect on the harmonic generation.(c)and(d)Controlling pulse intensity(I3)efect on the harmonic spectra.

FIG.6(a)Ionization probabilities of the combined feld with diferent controlling pulse duration.(b)Ionization probabilities of the combined feld with diferent controlling pulse intensity.

Figure 6(a)shows the IPs of the combined feld with diferentτ3.The other parameters are the same as those shown in Fig.2(a)dash line.It shows that with the increasing ofτ3,the IPs are slight decreased.But the decreased grade is very small,thus we almost can not see that changes on the harmonic spectra shown in Fig.5 (a)and(b).Figure 6(b)shows the IPs of the combined feld with diferentI3.The other parameters are the same as those shown in Fig.2(a).Clearly,with the increasing of the controlling pulse intensity,the IPs are enhanced due to the increasing of the amplitude intensity of the combined feld,which is the main reason for the harmonic enhancement shown in Fig.5(c)and(d).

Figure 7 shows the temporal profles of the attosecond pulses.Firstly,by superposing the harmonics of the linear two-color feld from the 100th to the 190th orders,a 60 as pulse with accompanying satellite pulses can be obtained,as shown in Fig.7(a).Clearly,this pulse is not benefcial to practical application.Further, by properly superposing the harmonics of the orthogonal two-color feld from the 70th to the 150th orders, an isolated 38 as pulse can be produced,as shown in Fig.7(b).Finally,if we choose the harmonic spectra of the orthogonal two-color feld combined with the UV pulse withθ=0.0π,ω1τdelay=0.8π(here,only one condition is shown because that the others are similar to it)and by properly superposing the harmonics from the 70th to the 150th orders,a 38 as isolated pulse with 2 orders of magnitude improvement can be obtained,as shown in Fig.7(c).

FIG.7 The temporal profles of the attosecond pulses by superposing harmonics of(a)the attosecond pulse generation from the linear two-color feld,(b)the orthogonal two-color feld from the 70th to the 150th orders,and(c)the orthogonal two-color feld combined with the 125 nm UV pulse withθ=0.0π,ω1τdelay=0.8πfrom the 70th to the 150th orders.

IV.CONCLUSION

We theoretically present an efective method to enhance the attosecond pulse intensity.The results show that with the proper introduction of a 125 nm UV pulse into the orthogonal two-color feld,not only the harmonic yield is reinforced by 2 orders of magnitude,but also the single short quantum path is selected to contribute to the harmonic emission.As a result,an isolated 38 as pulse with 2 orders of magnitude improvement has been obtained.Moreover,through analyzing the laser parameters,we fnd that the harmonic and the attosecond pulse enhancement phenomena are independent of the pulse duration and the polarized angle of the introduced UV pulse,which is good for experimental realization and application.Thus,it is expected that our proposed scheme may bring useful insight into practical generation and application of the intense ultrashort attosecond pulses.

V.ACKNOWLEDGMENTS

The authors thank Professor Ke-li Han for providing us the computational code used in the present work.This work was supported by the Scientifc Research Fund of Liaoning University of Technology, China(No.X201319 and No.X201312)and the Scientifc Research Fund of Liaoning Provincial Education Department(No.L2014242).

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∗Authors to whom correspondence should be addressed.E-mail：lqfeng-lngy@126.com,liuhang20@126.com

(Dated:Received on October 8,2014;Accepted on November 6,2014)