## Intense supercontinuum generation exceeding 300eV using a two-color field in combination with a 400-nm few-cycle control pulse |

Optics Express, Vol. 21, Issue 18, pp. 21337-21348 (2013)

http://dx.doi.org/10.1364/OE.21.021337

Acrobat PDF (999 KB)

### Abstract

We propose a method to control the harmonic process by using a two-color field in combination with a 400-nm few-cycle control pulse for the generation of an ultra-broadband supercontinuum with high efficiency. The ionization and acceleration steps in the harmonic process can be simultaneously controlled by using a three-color field synthesized by a 2000-nm driving pulse and two weak 800-nm and 400-nm control pulses. Then an intense supercontinuum covered by the spectral range from 140eV to 445eV is produced. The 3D macroscopic propagation is also employed to select the short quantum path of the supercontinuum, then intense isolated sub-100-as pulses with tunable central wavelengths are directly obtained within water window region. In addition, the generation of isolated attosecond pulses in the far field is also investigated. An isolated 52-as pulse can be generated by using a filter centered on axis to select the harmonics in the far field.

© 2013 OSA

## 1. Introduction

1. R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Atomic transient recorder,” Nature (London) **427**, 817–821 (2004). [CrossRef]

3. M. I. Stockman, M. F. Kling, U. Kleineberg, and F. Krausz, “Attosecond nanoplasmonic-field microscope,” Nat. Photonics **1**, 539–544 (2007). [CrossRef]

4. M. Hentschel, R. Kienberger, Ch. Spielmann, G. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature (London) **414**, 509–513 (2001). [CrossRef]

10. K. Zhao, Q. Zhang, M. Chini, Y. Wu, X. Wang, and Z. Chang, “Tailoring a 67 attosecond pulse through advantageous phase-mismatch,” Opt. Lett. **37**, 3891–3893 (2012). [CrossRef] [PubMed]

*et. al.*[6

6. E. Goulielmakis, M. Schultze, M. Hofstetter, V. Yakovlev, J. Gagnon, M. Uiberacker, A. Aquila, E. Gullikson, D. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science **320**, 1614–1617 (2008). [CrossRef] [PubMed]

*et. al.*[10

10. K. Zhao, Q. Zhang, M. Chini, Y. Wu, X. Wang, and Z. Chang, “Tailoring a 67 attosecond pulse through advantageous phase-mismatch,” Opt. Lett. **37**, 3891–3893 (2012). [CrossRef] [PubMed]

11. P. Corkum, “Plasma perspective on strong-field multiphoton ionization,” Phys. Rev. Lett. **71**, 1994–1997 (1993). [CrossRef] [PubMed]

12. I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “High-harmonic generation of attosecond pulses in the ’single-cycle’ regime,” Phys. Rev. Lett. **78**, 1251–1254 (1997). [CrossRef]

13. J. J. Carrera, X. M. Tong, and Shih.-I. Chu, “Creation and control of a single coherent attosecond xuv pulse by few-cycle intense laser pulses,” Phys. Rev. A **74**, 023404 (2006). [CrossRef]

14. P. Corkum, N. Burnett, and M. Ivanov, “Subfemtosecond pulses,” Opt. Lett. **19**, 1870–1872 (1994). [CrossRef] [PubMed]

19. H. Du and B. Hu, “Broadband supercontinuum generation method combining mid-infrared chirped-pulse modulation and generalized polarization gating,” Opt. Express **18**, 25958–25966 (2010). [CrossRef] [PubMed]

20. K. T. Kim, C. M. Kim, M.-G. Baik, G. Umesh, and C. H. Nam, “Single sub-50-attosecond pulse generation from chirp-compensated harmonic radiation using material dispersion,” Phys. Rev. A **69**, 051805 (2004). [CrossRef]

22. T. Sekikawa, A. Kosuge, T. Kanai, and S. Watanabe, “Nonlinear optics in the extreme ultraviolet,” Nature (London) **432**, 605–608 (2004). [CrossRef]

23. E. Takahashi, P. Lan, O. Mücke, Y. Nabekawa, and K. Midorikawa, “Infrared two-color multicycle laser field synthesis for generating an intense attosecond pulse,” Phys. Rev. Lett. **104**, 233901 (2010). [CrossRef] [PubMed]

36. C. L. Xia, G. T. Zhang, J. Wu, and X. S. Liu, “Single attosecond pulse generation in an orthogonally polarized two-color laser field combined with a static electric field,” Phys. Rev. A **81**, 043420 (2010). [CrossRef]

37. H. Du, L. Luo, X. Wang, and B. Hu, “Attosecond ionization control for broadband supercontinuum generation using a weak 400-nm few-cycle controlling pulse,” Opt. Express **20**, 27226–27241 (2012). [CrossRef] [PubMed]

## 2. Theoretical methods

38. M. Lewenstein, Ph. Balcou, M. Ivanov, A. L’Huillier, and P. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A **49**, 2117–2132 (1994). [CrossRef] [PubMed]

*E*(

*t*) is the electric field of the laser pulse,

*A*(

*t*) is its associated vector potential,and

*ε*is a positive regularization constant.

*p*and

_{st}*S*are the stationary momentum and quasiclassical action, which are given by where

_{st}*I*is the ionization energy of the atom, and

_{p}*d*(

*p*) is the dipole matrix element for transitions from the ground state to the continuum state. For hydrogenlike atoms, it can be approximated as The

*g*(

*t′*) in Eq. (1) represents the ground state amplitude: where

*ω*(

*t″*) is the ionization rate which is calculated by ADK tunneling model [39]: where where

*Z*is the net resulting charge of the atom, and

*I*is the ionization potential of the hydrogen atom, and

_{ph}*e*and

*m*are electron charge and mass, respectively.

_{e}*a⃗*(

*t*): where

*a⃗*(

*t*) =

*d̈*(

_{nl}*t*),

*T*and

*ω*are the duration and frequency of the driving pulse, respectively.

*q*corresponds to the harmonic order.

40. E. Priori, G. Cerullo, M. Nisoli, S. Stagira, S. De Silvestri, P. Villoresi, L. Poletto, P. Ceccherini, C. Altucci, R. Bruzzese, and C. de Lisio, “Nonadiabatic three-dimentional model of high-order harmonic generation in the few-optical cycle regime,” Phys. Rev. A **61**, 063801 (2000). [CrossRef]

*E*and

*E*are the laser and high harmonic field;

_{h}*ω*is the plasma frequency and is given by

_{p}*P*= [

_{nl}*n*

_{0}−

*n*(

_{e}*ρ,z,t*)]

*d*(

_{nl}*ρ,z,t*) is the nonlinear polarization generated by the medium.

*n*

_{0}is the gas density and

40. E. Priori, G. Cerullo, M. Nisoli, S. Stagira, S. De Silvestri, P. Villoresi, L. Poletto, P. Ceccherini, C. Altucci, R. Bruzzese, and C. de Lisio, “Nonadiabatic three-dimentional model of high-order harmonic generation in the few-optical cycle regime,” Phys. Rev. A **61**, 063801 (2000). [CrossRef]

*n*can be approximately described by the refractive index in vacuum (

*n*= 1). These equations can be solved with Crank-Nicholson method. The calculation details can be found in [40

40. E. Priori, G. Cerullo, M. Nisoli, S. Stagira, S. De Silvestri, P. Villoresi, L. Poletto, P. Ceccherini, C. Altucci, R. Bruzzese, and C. de Lisio, “Nonadiabatic three-dimentional model of high-order harmonic generation in the few-optical cycle regime,” Phys. Rev. A **61**, 063801 (2000). [CrossRef]

41. A. L’Huillier, P. Balcou, S. Candel, K. Schafer, and K. Kulander, “Calculations of high-order harmonic-generation processes in xenon at 1064nm,” Phys. Rev. A **46**, 2778–2790 (1992). [CrossRef]

43. C. Jin, A.-T. Le, and C. Lin, “Medium propagation effects in high-order harmonic generation of Ar and N_{2},” Phys. Rev. A **83**, 023411 (2011). [CrossRef]

*J*

_{0}is the zero-order Bessel function,

*z′*is the exit position of a gas medium,

*z*is the far-field position from the laser focus,

_{f}*r*is the transverse coordinate in the far field,

_{f}*r*is the transverse coordinate at the exit face of a gas medium, and the wave vector

*k*is given by

*k*=

*ω/c*.

## 3. Results and discussions

*E*

_{1},

*E*

_{2}and

*E*

_{3}are the amplitudes of the driving and control electric fields, respectively.

*ω*

_{1},

*ω*

_{2}and

*ω*

_{3}are the frequencies of the driving and control pulses.

*τ*

_{1}=

*τ*

_{2}= 2

*T*

_{1}and

*τ*

_{3}= 2

*T*

_{3}are the pulse durations of the driving and control pulses(full width at half maximum), where

*T*

_{1}and

*T*

_{3}are the optical periods of the driving and 400-nm control pulses.

*τ*

_{delay}_{2}and

*τ*

_{delay}_{3}are the time delays of the 800-nm and 400-nm control pulses.

*ϕ*

_{1},

*ϕ*

_{2}and

*ϕ*

_{3}are the carrier-envelope phases of the driving and control pulses, and are set as 0, 0 and

*π*, respectively. In calculation, we choose

*E*

_{1}= 0.095

*a.u.*,

*E*

_{2}= 0.021

*a.u.*and

*E*

_{3}= 0.06

*a.u.*, and the time delays of the 800-nm and 400-nm control pulses are set as

*τ*

_{delay}_{2}= −0.45

*T*

_{2}and

*τ*

_{delay}_{3}= 0.45

*T*

_{1}, respectively. Experimentally, this scheme can be carried out by using a Ti: sapphire laser system. The 2000-nm driving pulse can be achieved via the optical parametric amplification (OPA) technology [44

44. M. -C. Chen, P. Arpin, T. Popmintchev, M. Gerrity, B. Zhang, M. Seabery, D. Popmintchev, M. M. Murnane, and H. C. Kapteyn, “Bright, coherent, ultrafast soft X-Ray harmonics spanning the water window from a tabletop light source,” Phys. Rev. Lett. **105**, 173901 (2010). [CrossRef]

45. C. Trallero-Harrero, C. Jin, B. E. Schmidt, A. D. Shiner, J.-C. Kieffer, P. B. Corkum, D. M. Villeneuve, C. D. Lin, F. Légaré, and A. T. Le, “Generation of broad XUV continuous high harmonic spectra and isolated attosecond pulses with intense mid-infrared lasers,” J. Phys. B **45**, 011001 (2012). [CrossRef]

46. H. Mashiko, S. Gilbertson, C. Li, S. D. Khan, M. M. Shakya, E. Moon, and Z. Chang, “Double optical gating of high-order harmonic generation with carrier-envelope phase stabilized lasers,” Phys. Rev. Lett. **100**, 103906 (2008). [CrossRef] [PubMed]

11. P. Corkum, “Plasma perspective on strong-field multiphoton ionization,” Phys. Rev. Lett. **71**, 1994–1997 (1993). [CrossRef] [PubMed]

*ω*

_{1}, 535

*ω*

_{1}and 326

*ω*

_{1}, respectively. Consequently, the harmonics above 535

*ω*

_{1}are mainly emitted by the quantum path P1, and form a supercontinuum with the bandwidth of 67eV. In order to further extend the harmonic cutoff and generate a broadband supercontinuum, we can control the acceleration process by adding a 800-nm control pulse. The results are shown in Fig. 2. One can clearly see that the maximum energy of the quantum path P1 is increased to 702

*ω*

_{1}, and that of the quantum path P2 is decreased to 470

*ω*

_{1}. Consequently, the harmonics above 470

*ω*

_{1}are mainly emitted by the quantum path P1, and form a supercontinuum with the bandwidth of 144eV. We also clearly see from Fig. 2(a) that the corresponding ionization rate of the quantum path P1 is enhanced, which leads to the efficient generation of the supercontinuum. Taking into account the above results, we can conclude that the 800-nm control pulse can simultaneously enhance the yields and extend the cutoff of the generated supercontinuum. To further enhance the yields of the supercontinuum, we introduce a 400-nm few-cycle control pulse to enhance the corresponding ionization rate of the quantum path P1. Figure 3 presents the classical sketch of the HHG process in the three-color field. As shown in Fig. 3(a), there is only one ionization peak within the pulse duration. Therefore, there is only one quantum path P1 contributing to the harmonic generation, as shown in Fig. 3(b). Moreover, the corresponding ionization rate of the quantum path P1 is approximately 2 orders of the magnitude higher than that in Fig. 2(a).

*E*

_{3}> 0.03

*a.u.*and

*τ*

_{delay}_{3}varying from 0.4

*T*

_{1}and 0.5

*T*

_{1}.

38. M. Lewenstein, Ph. Balcou, M. Ivanov, A. L’Huillier, and P. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A **49**, 2117–2132 (1994). [CrossRef] [PubMed]

*ω*

_{1}, and only the harmonics near the cutoff are continuous in the 2000-nm driving pulse alone. A supercontinuum with bandwidth of 67eV is produced near the cutoff. The harmonic cutoff can be dramatically extended to 717

*ω*

_{1}and a broadband supercontinuum with the bandwidth of 144eV can be obtained by adding the 800-nm control pulse. Moreover, the yields of the supercontinuum are stronger than those of the harmonics in the driving pulse alone. When the 400-nm control pulse is added, the harmonics above 226

*ω*

_{1}is supercontinuous and an ultra-broadband supercontinuum with the bandwidth of 305eV is generated. The modulations on the supercontinuum are due to the interference of the short and the long quantum paths. Moreover, the harmonic intensity is 2 or 3 orders of the magnitude higher than that in the two-color field. Therefore, an intense ultra-broadband supercontinuum exceeding 300eV can be produced with the three-color field scheme. In order to further understand the emission times of the harmonics, figure 4(b) shows the time-frequency distribution in the three-color field. It is clear that there is only one quantum path P1 contributing to the generation of the supercontinuum. And the intensity of the short quantum path is comparable with that of the long quantum path, which leads to the modulations on the supercontinuum. These results are in good agreement with the above classical results in Fig. 3.

47. P. Balcou, P. Salieres, A. L’Huillier, and M. Lewenstein, “Generalized phase-matching conditions for high harmonics: the role of the field-gradient forces,” Phys. Rev. A **55**, 3204–3210 (1997). [CrossRef]

**61**, 063801 (2000). [CrossRef]

*μm*and a 1.5-mm long gas jet with a density of 1.0 × 10

^{18}/

*cm*

^{3}. The gas jet is placed 1mm after the laser focus. Other parameters are the same as in Fig. 3. Figure 5 presents the continuous part of the macroscopic harmonics in the three-color field. For comparison, the single-atom result is also presented (thin red curve). One can clearly see that the interference fringes through the plateau to the cutoff are all removed after propagation, which implies that only one quantum path is further selected. Then a macroscopic supercontinuum with the bandwidth of 305eV can be obtained, which covers the spectral range from ultraviolet to water window x ray.

*μm*) to select harmonics near the axis in the far field, an isolated 80-as pulse can be obtained, as shown in Fig. 8(b). To further shorten the duration of the attosecond pulse, one can superpose much more harmonics. In Fig. 9(a), the spatiotemporal distribution of the attosecond pulse generated by filtering the 270th–420th harmonics in the far field is shown. By using a spatial filter (indicated by a solid white curve, with a radius of 100

*μm*) to select harmonics near the axis in the far field, an isolated 52-as pulse can be obtained, as shown in Fig. 9(b).

## 4. Conclusion

*μm*centered on axis to select the 270th–420th harmonics in the far field, an isolated 52-as pulse can be obtained.

## Acknowledgments

## References and links

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12. | I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “High-harmonic generation of attosecond pulses in the ’single-cycle’ regime,” Phys. Rev. Lett. |

13. | J. J. Carrera, X. M. Tong, and Shih.-I. Chu, “Creation and control of a single coherent attosecond xuv pulse by few-cycle intense laser pulses,” Phys. Rev. A |

14. | P. Corkum, N. Burnett, and M. Ivanov, “Subfemtosecond pulses,” Opt. Lett. |

15. | Z. Chang, “Single attosecond pulse and xuv supercontinuum in the high-order harmonic plateau,” Phys. Rev. A |

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41. | A. L’Huillier, P. Balcou, S. Candel, K. Schafer, and K. Kulander, “Calculations of high-order harmonic-generation processes in xenon at 1064nm,” Phys. Rev. A |

42. | V. Tosa, K. Kim, and C. Nam, “Macroscopic generation of attosecond-pulse trains in strongly ionized media,” Phys. Rev. A |

43. | C. Jin, A.-T. Le, and C. Lin, “Medium propagation effects in high-order harmonic generation of Ar and N |

44. | M. -C. Chen, P. Arpin, T. Popmintchev, M. Gerrity, B. Zhang, M. Seabery, D. Popmintchev, M. M. Murnane, and H. C. Kapteyn, “Bright, coherent, ultrafast soft X-Ray harmonics spanning the water window from a tabletop light source,” Phys. Rev. Lett. |

45. | C. Trallero-Harrero, C. Jin, B. E. Schmidt, A. D. Shiner, J.-C. Kieffer, P. B. Corkum, D. M. Villeneuve, C. D. Lin, F. Légaré, and A. T. Le, “Generation of broad XUV continuous high harmonic spectra and isolated attosecond pulses with intense mid-infrared lasers,” J. Phys. B |

46. | H. Mashiko, S. Gilbertson, C. Li, S. D. Khan, M. M. Shakya, E. Moon, and Z. Chang, “Double optical gating of high-order harmonic generation with carrier-envelope phase stabilized lasers,” Phys. Rev. Lett. |

47. | P. Balcou, P. Salieres, A. L’Huillier, and M. Lewenstein, “Generalized phase-matching conditions for high harmonics: the role of the field-gradient forces,” Phys. Rev. A |

**OCIS Codes**

(190.4160) Nonlinear optics : Multiharmonic generation

(300.6560) Spectroscopy : Spectroscopy, x-ray

(320.7110) Ultrafast optics : Ultrafast nonlinear optics

**ToC Category:**

Ultrafast Optics

**History**

Original Manuscript: June 18, 2013

Revised Manuscript: July 31, 2013

Manuscript Accepted: August 26, 2013

Published: September 4, 2013

**Citation**

Hongchuan Du, Yizhen Wen, Xiaoshan Wang, and Bitao Hu, "Intense supercontinuum generation exceeding 300eV using a two-color field in combination with a 400-nm few-cycle control pulse," Opt. Express **21**, 21337-21348 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-18-21337

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### References

- R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Atomic transient recorder,” Nature (London)427, 817–821 (2004). [CrossRef]
- F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys.81, 163–234 (2009). [CrossRef]
- M. I. Stockman, M. F. Kling, U. Kleineberg, and F. Krausz, “Attosecond nanoplasmonic-field microscope,” Nat. Photonics1, 539–544 (2007). [CrossRef]
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