A method is proposed for arbitrarily engineering the high-order harmonic generation phase achieved by shaping a laser pulse and employing xuv light or x rays for ionization. This renders the production of bandwidth-limited attosecond pulses possible while avoiding the use of filters for chirp compensation. By adding the first 8 Fourier components to a sinusoidal field of 10¹⁶ W/cm², the bandwidth-limited emission of 8 as is shown to be possible from a Li²⁺ gas. The scheme is extendable to the zs-scale.

© 2011 Optical Society of America

1. E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008). [CrossRef] [PubMed]
2. F. Ferrari, F. Calegari, M. Lucchini, C. Vozzi, S. Stagira, G. Sansone, and M. Nisoli, “High-energy isolated attosecond pulses generated by above-saturation few-cycle fields,” Nat. Photonics 4, 875–879 (2010). [CrossRef]
3. D. H. Ko, K. T. Kim, J. Park, J.-H. Lee, and C. H. Nam, “Attosecond chirp compensation over broadband high-order harmonics to generate near transform-limited 63 as pulses,” N. J. Phys. 12, 063008 (2010). [CrossRef]
4. M.-C. Chen, P. Arpin, T. Popmintchev, M. Gerrity, B. Zhang, M. Seaberg, 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]
5. P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71, 1994–1997 (1993). [CrossRef] [PubMed]
6. Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovačev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft x-rays,” Science 302, 1540–1543 (2003) (and supplementary material.). [CrossRef] [PubMed]
7. S. Kazamias, and Ph. Balcou, “Intrinsic chirp of attosecond pulses: Single-atom model versus experiment,” Phys. Rev. A 69, 063416 (2004). [CrossRef]
8. A. Morlens, P. Balcou, P. Zeitoun, C. Valentin, V. Laude, and S. Kazamias, “Compression of attosecond harmonic pulses by extreme-ultraviolet chirped mirrors,” Opt. Lett. 30, 1554–1556 (2005). [CrossRef] [PubMed]
9. K. T. Kim, C. M. Kim, M. 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(R) (2004). [CrossRef]
10. R. López-Martens, K. Varjú, P. Johnsson, J. Mauritsson, Y. Mairesse, P. Salières, M. B. Gaarde, K. J. Schafer, A. Persson, S. Svanberg, C. Wahlström, and A. L’Huillier, “Amplitude and phase control of attosecond light pulses,” Phys. Rev. Lett. 94, 033001 (2005). [CrossRef] [PubMed]
11. K. T. Kim, K. S. Kang, M. N. Park, T. Imran, G. Umesh, and C. H. Nam, “Self-compression of attosecond high-order harmonic pulses,” Phys. Rev. Lett. 99, 223904 (2007). [CrossRef]
12. L. Poletto, F. Frassetto, and P. Villoresi, “Design of an extreme-ultraviolet attosecond compressor,” J. Opt. Soc. Am. B 25, B133–B136 (2008). [CrossRef]
13. G. Doumy, J. Wheeler, C. Roedig, R. Chirla, P. Agostini, and L. F. DiMauro, “Attosecond synchronization of high-order harmonics from midinfrared drivers,” Phys. Rev. Lett. 102, 093002 (2009). [CrossRef] [PubMed]
14. Y. Zheng, Z. Zeng, P. Zou, L. Zhang, X. Li, P. Liu, R. Li, and Z. Xu, “Dynamic chirp control and pulse compression for attosecond high-order harmonic emission,” Phys. Rev. Lett. 103, 043904 (2009). [CrossRef] [PubMed]
15. P. Zou, Z. Zeng, Y. Zheng, Y. Lu, P. Liu, R. Li, and Z. Xu, “Coherent control of broadband isolated attosecond pulses in a chirped two-color laser field,” Phys. Rev. A 81, 033428 (2010). [CrossRef]
16. K. Ishikawa, “Photoemission and ionization of He+ under simultaneous irradiation of fundamental laser and high-order harmonic pulses,” Phys. Rev. Lett. 91, 043002 (2003). [CrossRef] [PubMed]
17. K. J. Schafer, M. B. Gaarde, A. Heinrich, J. Biegert, and U. Keller, “Strong field quantum path control using attosecond pulse trains,” Phys. Rev. Lett. 92, 023003 (2004). [CrossRef] [PubMed]
18. E. J. Takahashi, T. Kanai, K. L. Ishikawa, Y. Nabekawa, and K. Midorikawa, “Dramatic enhancement of high-order harmonic generation,” Phys. Rev. Lett. 99, 053904 (2007). [CrossRef] [PubMed]
19. C. F. M. de Faria, and P. Salières, “High-order harmonic generation with a strong laser field and an attosecond-pulse train: the Dirac-delta comb and monochromatic limits,” Laser Phys. 17, 390–400 (2007). [CrossRef]
20. M. B. Gaarde, K. J. Schafer, A. Heinrich, J. Biegert, and U. Keller, “Large enhancement of macroscopic yield in attosecond pulse train-assisted harmonic generation,” Phys. Rev. A 72, 013411 (2005). [CrossRef]
21. M. Klaiber, K. Z. Hatsagortsyan, C. Müller, and C. H. Keitel, “Coherent hard x rays from attosecond pulse train-assisted harmonic generation,” Opt. Lett. 33, 411–413 (2010). [CrossRef]
22. K. Z. Hatsagortsyan, M. Klaiber, K. Z. Hatsagortsyan, C. Müller, M. C. Kohler, and C. H. Keitel, “Laser-driven relativistic recollisions,” J. Opt. Soc. Am. B 25, B92–B103 (2008). [CrossRef]
23. T. Pfeifer, D. Walter, C. Winterfeldt, C. Spielmann, and G. Gerber, “Controlling the spectral shape of coherent soft x-rays,” Appl. Phys. B 80, 277–280 (2005). [CrossRef]
24. L. E. Chipperfield, J. S. Robinson, J. W. G. Tisch, and J. P. Marangos, “Ideal waveform to generate the maximum possible electron recollision energy for any given oscillation period,” Phys. Rev. Lett. 102, 063003 (2009). [CrossRef] [PubMed]
25. M. Klaiber, K. Z. Hatsagortsyan, and C. H. Keitel, “Relativistic ionization rescattering with tailored laser pulses,” Phys. Rev. A 74051803(R) (2006). [CrossRef]
26. M. Klaiber, K. Z. Hatsagortsyan, and C. H. Keitel, “Fully relativistic laser-induced ionization and recollision processes,” Phys. Rev. A 75, 063413 (2007). [CrossRef]
27. M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49, 2117–2132 (1994). [CrossRef] [PubMed]
28. M. W. Walser, C. H. Keitel, A. Scrinzi, and T. Brabec, “High harmonic generation beyond the electric dipole approximation,” Phys. Rev. Lett. 85, 5082–5085 (2000). [CrossRef] [PubMed]
29. M. C. Kohler, M. Klaiber, K. Z. Hatsagortsyan, and C. H. Keitel, “Phase-matched coherent hard x-rays from relativistic high-order harmonic generation,” arxiv:1008.0511.
30. J. Peatross, S. Voronov, and I. Prokopovich, “Selective zoning of high harmonic emission using counter-propagating light,” Opt. Express 1, 114–125 (1997). [CrossRef] [PubMed]
31. O. Cohen, X. Zhang, A. L. Lytle, T. Popmintchev, M. M. Murnane, and H. C. Kapteyn, “Grating-assisted phase matching in extreme nonlinear optics,” Phys. Rev. Lett. 99, 053902 (2007). [CrossRef] [PubMed]
32. C. Serrat and J. Biegert, “All-regions tunable high harmonic enhancement by a periodic static electric field,” Phys. Rev. Lett. 104, 073901 (2010). [CrossRef] [PubMed]
33. I. P. Christov, H. Kapteyn, and M. Murnane, “Quasi-phase matching of high-harmonics and attosecond pulses in modulated waveguides,” Opt. Express 7, 362–367 (2000). [CrossRef] [PubMed]
34. A. Paul, R. A. Bartels, R. Tobey, H. Green, S. Weiman, I. P. Christov, M. M. Murnane, H. C. Kapteyn, and S. Backus, “Quasi-phase-matched generation of coherent extreme-ultraviolet light,” Nature 421, 51–54 (2003). [CrossRef] [PubMed]
35. E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H. C. Kapteyn, “Coherent soft x-ray generation in the water window with quasi-phase matching,” Science 302, 95–98 (2003). [CrossRef] [PubMed]
36. M. C. Kohler, C. Ott, P. Raith, R. Heck, I. Schlegel, C. H. Keitel, and T. Pfeifer, “High harmonic generation via continuum wave-packet interference,” Phys. Rev. Lett. 105, 203902 (2010). [CrossRef]

Appl. Phys. B

• T. Pfeifer, D. Walter, C. Winterfeldt, C. Spielmann, and G. Gerber, “Controlling the spectral shape of coherent soft x-rays,” Appl. Phys. B 80, 277–280 (2005). [CrossRef]

J. Opt. Soc. Am. B

• K. Z. Hatsagortsyan, M. Klaiber, K. Z. Hatsagortsyan, C. Müller, M. C. Kohler, and C. H. Keitel, “Laser-driven relativistic recollisions,” J. Opt. Soc. Am. B 25, B92–B103 (2008). [CrossRef]
• L. Poletto, F. Frassetto, and P. Villoresi, “Design of an extreme-ultraviolet attosecond compressor,” J. Opt. Soc. Am. B 25, B133–B136 (2008). [CrossRef]

Laser Phys.

• C. F. M. de Faria, and P. Salières, “High-order harmonic generation with a strong laser field and an attosecond-pulse train: the Dirac-delta comb and monochromatic limits,” Laser Phys. 17, 390–400 (2007). [CrossRef]

N. J. Phys.

• D. H. Ko, K. T. Kim, J. Park, J.-H. Lee, and C. H. Nam, “Attosecond chirp compensation over broadband high-order harmonics to generate near transform-limited 63 as pulses,” N. J. Phys. 12, 063008 (2010). [CrossRef]

Nat. Photonics

• F. Ferrari, F. Calegari, M. Lucchini, C. Vozzi, S. Stagira, G. Sansone, and M. Nisoli, “High-energy isolated attosecond pulses generated by above-saturation few-cycle fields,” Nat. Photonics 4, 875–879 (2010). [CrossRef]

Nature

• A. Paul, R. A. Bartels, R. Tobey, H. Green, S. Weiman, I. P. Christov, M. M. Murnane, H. C. Kapteyn, and S. Backus, “Quasi-phase-matched generation of coherent extreme-ultraviolet light,” Nature 421, 51–54 (2003). [CrossRef] [PubMed]

Opt. Express

• I. P. Christov, H. Kapteyn, and M. Murnane, “Quasi-phase matching of high-harmonics and attosecond pulses in modulated waveguides,” Opt. Express 7, 362–367 (2000). [CrossRef] [PubMed]
• J. Peatross, S. Voronov, and I. Prokopovich, “Selective zoning of high harmonic emission using counter-propagating light,” Opt. Express 1, 114–125 (1997). [CrossRef] [PubMed]

Opt. Lett.

• M. Klaiber, K. Z. Hatsagortsyan, C. Müller, and C. H. Keitel, “Coherent hard x rays from attosecond pulse train-assisted harmonic generation,” Opt. Lett. 33, 411–413 (2010). [CrossRef]
• A. Morlens, P. Balcou, P. Zeitoun, C. Valentin, V. Laude, and S. Kazamias, “Compression of attosecond harmonic pulses by extreme-ultraviolet chirped mirrors,” Opt. Lett. 30, 1554–1556 (2005). [CrossRef] [PubMed]

Phys. Rev. A

• K. T. Kim, C. M. Kim, M. 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(R) (2004). [CrossRef]
• P. Zou, Z. Zeng, Y. Zheng, Y. Lu, P. Liu, R. Li, and Z. Xu, “Coherent control of broadband isolated attosecond pulses in a chirped two-color laser field,” Phys. Rev. A 81, 033428 (2010). [CrossRef]
• S. Kazamias, and Ph. Balcou, “Intrinsic chirp of attosecond pulses: Single-atom model versus experiment,” Phys. Rev. A 69, 063416 (2004). [CrossRef]
• M. B. Gaarde, K. J. Schafer, A. Heinrich, J. Biegert, and U. Keller, “Large enhancement of macroscopic yield in attosecond pulse train-assisted harmonic generation,” Phys. Rev. A 72, 013411 (2005). [CrossRef]
• M. Klaiber, K. Z. Hatsagortsyan, and C. H. Keitel, “Relativistic ionization rescattering with tailored laser pulses,” Phys. Rev. A 74051803(R) (2006). [CrossRef]
• M. Klaiber, K. Z. Hatsagortsyan, and C. H. Keitel, “Fully relativistic laser-induced ionization and recollision processes,” Phys. Rev. A 75, 063413 (2007). [CrossRef]
• M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49, 2117–2132 (1994). [CrossRef] [PubMed]

Phys. Rev. Lett.

• M. W. Walser, C. H. Keitel, A. Scrinzi, and T. Brabec, “High harmonic generation beyond the electric dipole approximation,” Phys. Rev. Lett. 85, 5082–5085 (2000). [CrossRef] [PubMed]
• O. Cohen, X. Zhang, A. L. Lytle, T. Popmintchev, M. M. Murnane, and H. C. Kapteyn, “Grating-assisted phase matching in extreme nonlinear optics,” Phys. Rev. Lett. 99, 053902 (2007). [CrossRef] [PubMed]
• C. Serrat and J. Biegert, “All-regions tunable high harmonic enhancement by a periodic static electric field,” Phys. Rev. Lett. 104, 073901 (2010). [CrossRef] [PubMed]
• L. E. Chipperfield, J. S. Robinson, J. W. G. Tisch, and J. P. Marangos, “Ideal waveform to generate the maximum possible electron recollision energy for any given oscillation period,” Phys. Rev. Lett. 102, 063003 (2009). [CrossRef] [PubMed]
• K. Ishikawa, “Photoemission and ionization of He+ under simultaneous irradiation of fundamental laser and high-order harmonic pulses,” Phys. Rev. Lett. 91, 043002 (2003). [CrossRef] [PubMed]
• K. J. Schafer, M. B. Gaarde, A. Heinrich, J. Biegert, and U. Keller, “Strong field quantum path control using attosecond pulse trains,” Phys. Rev. Lett. 92, 023003 (2004). [CrossRef] [PubMed]
• E. J. Takahashi, T. Kanai, K. L. Ishikawa, Y. Nabekawa, and K. Midorikawa, “Dramatic enhancement of high-order harmonic generation,” Phys. Rev. Lett. 99, 053904 (2007). [CrossRef] [PubMed]
• G. Doumy, J. Wheeler, C. Roedig, R. Chirla, P. Agostini, and L. F. DiMauro, “Attosecond synchronization of high-order harmonics from midinfrared drivers,” Phys. Rev. Lett. 102, 093002 (2009). [CrossRef] [PubMed]
• Y. Zheng, Z. Zeng, P. Zou, L. Zhang, X. Li, P. Liu, R. Li, and Z. Xu, “Dynamic chirp control and pulse compression for attosecond high-order harmonic emission,” Phys. Rev. Lett. 103, 043904 (2009). [CrossRef] [PubMed]
• R. López-Martens, K. Varjú, P. Johnsson, J. Mauritsson, Y. Mairesse, P. Salières, M. B. Gaarde, K. J. Schafer, A. Persson, S. Svanberg, C. Wahlström, and A. L’Huillier, “Amplitude and phase control of attosecond light pulses,” Phys. Rev. Lett. 94, 033001 (2005). [CrossRef] [PubMed]
• K. T. Kim, K. S. Kang, M. N. Park, T. Imran, G. Umesh, and C. H. Nam, “Self-compression of attosecond high-order harmonic pulses,” Phys. Rev. Lett. 99, 223904 (2007). [CrossRef]
• M.-C. Chen, P. Arpin, T. Popmintchev, M. Gerrity, B. Zhang, M. Seaberg, 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]
• P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71, 1994–1997 (1993). [CrossRef] [PubMed]
• M. C. Kohler, C. Ott, P. Raith, R. Heck, I. Schlegel, C. H. Keitel, and T. Pfeifer, “High harmonic generation via continuum wave-packet interference,” Phys. Rev. Lett. 105, 203902 (2010). [CrossRef]

Science

• Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovačev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft x-rays,” Science 302, 1540–1543 (2003) (and supplementary material.). [CrossRef] [PubMed]
• E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008). [CrossRef] [PubMed]
• E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H. C. Kapteyn, “Coherent soft x-ray generation in the water window with quasi-phase matching,” Science 302, 95–98 (2003). [CrossRef] [PubMed]

Other

• M. C. Kohler, M. Klaiber, K. Z. Hatsagortsyan, and C. H. Keitel, “Phase-matched coherent hard x-rays from relativistic high-order harmonic generation,” arxiv:1008.0511.

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