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Sawtooth grating-assisted phase-matchingPavel Sidorenko, Maxim Kozlov, Alon Bahabad, Tenio Popmintchev, Margaret Murnane, Henry Kapteyn, and Oren Cohen »View Author Affiliations
Pavel Sidorenko,1,*
Maxim Kozlov,1
Alon Bahabad,2
Tenio Popmintchev,2
Margaret Murnane,2
Henry Kapteyn,2
and Oren Cohen1
1Solid State Institute and Physics Department, Technion–Israel Institute of Technology, Haifa 32000, Israel 2JILA and Department of Physics, University of Colorado at Boulder, Boulder, Colorado 80309, USA *Corresponding author: sidor@tx.technion.ac.il |
Optics Express, Vol. 18, Issue 22, pp. 22686-22692 (2010)
http://dx.doi.org/10.1364/OE.18.022686
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Abstract
We show that a sawtooth phase-modulation is the optimal profile for grating assisted phase matching (GAPM). Perfect (sharp) sawtooth modulation fully corrects the phase-mismatch, exhibiting conversion equal to conventional phase matching, while smoothened, approximate sawtooth structures are more efficient than sinusoidal or square GAPM modulations that were previously studied. As an example, we demonstrate numerically optically-induced sawtooth GAPM for high harmonic generation. Sawtooth GAPM is the most efficient method for increasing the conversion efficiency of high harmonic generation through quasi-phase-matching, with an ultimate efficiency that closely matches the ideal phase-matching case.
© 2010 OSA
OCIS Codes
(190.0190) Nonlinear optics : Nonlinear optics
ToC Category:
Nonlinear Optics
History
Original Manuscript: August 24, 2010
Revised Manuscript: October 6, 2010
Manuscript Accepted: October 7, 2010
Published: October 11, 2010
Citation
Pavel Sidorenko, Maxim Kozlov, Alon Bahabad, Tenio Popmintchev, Margaret Murnane, Henry Kapteyn, and Oren Cohen, "Sawtooth grating-assisted phase-matching," Opt. Express 18, 22686-22692 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-22-22686
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References
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- A. Bahabad, O. Cohen, M. M. Murnane, and H. C. Kapteyn, “Quasi-phase-matching and dispersion characterization of harmonic generation in the perturbative regime using counterpropagating beams,” Opt. Express 16(20), 15923–15931 (2008). [CrossRef] [PubMed]
- X. Zhang, A. L. Lytle, T. Popmintchev, X. Zhou, H. C. Kapteyn, M. M. Murnane, and O. Cohen, “Quasi-phase-matching and quantum-path control of high-harmonic generation using counterpropagating light,” Nat. Phys. 3(4), 270–275 (2007). [CrossRef]
- 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(5), 053902 (2007). [CrossRef] [PubMed]
- O. Cohen, A. L. Lytle, X. Zhang, M. M. Murnane, and H. C. Kapteyn, “Optimizing quasi-phase matching of high harmonic generation using counterpropagating pulse trains,” Opt. Lett. 32(20), 2975–2977 (2007). [CrossRef] [PubMed]
- J. Khurgin, S. Colak, R. Stolzenberger, and R. N. Bhargava, “Mechanism of efficient blue second harmonic generation in periodically segmented waveguides,” Appl. Phys. Lett. 57(24), 2540–2542 (1990). [CrossRef]
- M. V. Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field,” Sov. Phys. JETP 64, 1191 (1986).
- D. Faccio, C. Serrat, J. M. Cela, A. Farrés, P. Di Trapani, and J. Biegert, “Modulated phase matching and high-order harmonic enhancement mediated by the carrier-envelope phase,” Phys. Rev. A 81, 011803 (2010). [CrossRef]
- M. Zepf, B. Dromey, M. Landreman, P. Foster, and S. M. Hooker, “Bright quasi-phase-matched soft-X-ray harmonic radiation from argon ions,” Phys. Rev. Lett. 99(14), 143901 (2007). [CrossRef] [PubMed]
- D. Faccio, C. Serrat, J. M. Cela, A. Farrés, P. Di Trapani, and J. Biegert, “Modulated phase matching and high-order harmonic enhancement mediated by the carrier-envelope phase,” Phys. Rev. A 81, 011803 (2010). [CrossRef]
- D. Faccio, C. Serrat, J. M. Cela, A. Farrés, P. Di Trapani, and J. Biegert, “Modulated phase matching and high-order harmonic enhancement mediated by the carrier-envelope phase,” Phys. Rev. A 81, 011803 (2010). [CrossRef]
- M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28(11), 2631–2654 (1992). [CrossRef]
- M. Zepf, B. Dromey, M. Landreman, P. Foster, and S. M. Hooker, “Bright quasi-phase-matched soft-X-ray harmonic radiation from argon ions,” Phys. Rev. Lett. 99(14), 143901 (2007). [CrossRef] [PubMed]
- J. P. van der Ziel, M. Ilegems, P. W. Foy, and R. M. Mikulyak, “Phase-Matched Second-Harmonic Generation in a Periodic GaAs Waveguide,” Appl. Phys. Lett. 29(12), 775–777 (1976). [CrossRef]
- M. Geissler, G. Tempea, and T. Brabec, “Phase-matched high-order harmonic generation in the nonadiabatic limit,” Phys. Rev. A 62(3), 033817 (2000). [CrossRef]
- T. Popmintchev, M.-C. Chen, A. Bahabad, M. Gerrity, P. Sidorenko, O. Cohen, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “Phase matching of high harmonic generation in the soft and hard X-ray regions of the spectrum,” Proc. Natl. Acad. Sci. U.S.A. 106(26), 10516–10521 (2009). [CrossRef] [PubMed]
- 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(6918), 51–54 (2003). [CrossRef] [PubMed]
- M. Zepf, B. Dromey, M. Landreman, P. Foster, and S. M. Hooker, “Bright quasi-phase-matched soft-X-ray harmonic radiation from argon ions,” Phys. Rev. Lett. 99(14), 143901 (2007). [CrossRef] [PubMed]
- J. P. van der Ziel, M. Ilegems, P. W. Foy, and R. M. Mikulyak, “Phase-Matched Second-Harmonic Generation in a Periodic GaAs Waveguide,” Appl. Phys. Lett. 29(12), 775–777 (1976). [CrossRef]
- M. Y. Ivanov, T. Brabec, and N. Burnett, “Coulomb corrections and polarization effects in high-intensity high-harmonic emission,” Phys. Rev. A 54(1), 742–745 (1996). [CrossRef] [PubMed]
- M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28(11), 2631–2654 (1992). [CrossRef]
- A. Bahabad, M. M. Murnane, and H. C. Kapteyn, “Quasi Phase Matching of Momentum and Energy in Nonlinear Optical Processes,” Nat. Photonics 4(8), 571 (2010). [CrossRef]
- T. Popmintchev, M.-C. Chen, A. Bahabad, M. Gerrity, P. Sidorenko, O. Cohen, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “Phase matching of high harmonic generation in the soft and hard X-ray regions of the spectrum,” Proc. Natl. Acad. Sci. U.S.A. 106(26), 10516–10521 (2009). [CrossRef] [PubMed]
- A. Bahabad, O. Cohen, M. M. Murnane, and H. C. Kapteyn, “Quasi-phase-matching and dispersion characterization of harmonic generation in the perturbative regime using counterpropagating beams,” Opt. Express 16(20), 15923–15931 (2008). [CrossRef] [PubMed]
- X. Zhang, A. L. Lytle, T. Popmintchev, X. Zhou, H. C. Kapteyn, M. M. Murnane, and O. Cohen, “Quasi-phase-matching and quantum-path control of high-harmonic generation using counterpropagating light,” Nat. Phys. 3(4), 270–275 (2007). [CrossRef]
- 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(5), 053902 (2007). [CrossRef] [PubMed]
- O. Cohen, A. L. Lytle, X. Zhang, M. M. Murnane, and H. C. Kapteyn, “Optimizing quasi-phase matching of high harmonic generation using counterpropagating pulse trains,” Opt. Lett. 32(20), 2975–2977 (2007). [CrossRef] [PubMed]
- 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(6918), 51–54 (2003). [CrossRef] [PubMed]
- Z. Chang, A. Rundquist, H. Wang, I. Christov, H. C. Kapteyn, and M. M. Murnane, “Temporal phase control of soft-x-ray harmonic emission,” Phys. Rev. A 58(1), R30–R33 (1998). [CrossRef]
- J. Khurgin, S. Colak, R. Stolzenberger, and R. N. Bhargava, “Mechanism of efficient blue second harmonic generation in periodically segmented waveguides,” Appl. Phys. Lett. 57(24), 2540–2542 (1990). [CrossRef]
- M. V. Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field,” Sov. Phys. JETP 64, 1191 (1986).
- J. Seres, V. Yakovlev, J. Seres, C. Streli, P. Wobrauschek, C. Spielmann, and F. Krausz, “Coherent superposition of laser-driven soft-x-ray harmonics from successive sources,” Nat. Phys. 3(12), 878–883 (2007). [CrossRef]
- M. Lewenstein, P. Salières, and A. L’Huillier, “Phase of the atomic polarization in high-order harmonic generation,” Phys. Rev. A 52(6), 4747–4754 (1995). [CrossRef] [PubMed]
- M. Zepf, B. Dromey, M. Landreman, P. Foster, and S. M. Hooker, “Bright quasi-phase-matched soft-X-ray harmonic radiation from argon ions,” Phys. Rev. Lett. 99(14), 143901 (2007). [CrossRef] [PubMed]
- M. Lewenstein, P. Salières, and A. L’Huillier, “Phase of the atomic polarization in high-order harmonic generation,” Phys. Rev. A 52(6), 4747–4754 (1995). [CrossRef] [PubMed]
- O. Cohen, A. L. Lytle, X. Zhang, M. M. Murnane, and H. C. Kapteyn, “Optimizing quasi-phase matching of high harmonic generation using counterpropagating pulse trains,” Opt. Lett. 32(20), 2975–2977 (2007). [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(5), 053902 (2007). [CrossRef] [PubMed]
- X. Zhang, A. L. Lytle, T. Popmintchev, X. Zhou, H. C. Kapteyn, M. M. Murnane, and O. Cohen, “Quasi-phase-matching and quantum-path control of high-harmonic generation using counterpropagating light,” Nat. Phys. 3(4), 270–275 (2007). [CrossRef]
- M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28(11), 2631–2654 (1992). [CrossRef]
- A. V. Balakin, V. A. Bushuev, B. I. Mantsyzov, I. A. Ozheredov, E. V. Petrov, A. P. Shkurinov, P. Masselin, and G. Mouret, “Enhancement of sum frequency generation near the photonic band gap edge under the quasiphase matching conditions,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 63(4 Pt 2), 046609 (2001). [CrossRef] [PubMed]
- A. V. Balakin, V. A. Bushuev, B. I. Mantsyzov, I. A. Ozheredov, E. V. Petrov, A. P. Shkurinov, P. Masselin, and G. Mouret, “Enhancement of sum frequency generation near the photonic band gap edge under the quasiphase matching conditions,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 63(4 Pt 2), 046609 (2001). [CrossRef] [PubMed]
- J. P. van der Ziel, M. Ilegems, P. W. Foy, and R. M. Mikulyak, “Phase-Matched Second-Harmonic Generation in a Periodic GaAs Waveguide,” Appl. Phys. Lett. 29(12), 775–777 (1976). [CrossRef]
- A. V. Balakin, V. A. Bushuev, B. I. Mantsyzov, I. A. Ozheredov, E. V. Petrov, A. P. Shkurinov, P. Masselin, and G. Mouret, “Enhancement of sum frequency generation near the photonic band gap edge under the quasiphase matching conditions,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 63(4 Pt 2), 046609 (2001). [CrossRef] [PubMed]
- A. Bahabad, M. M. Murnane, and H. C. Kapteyn, “Quasi Phase Matching of Momentum and Energy in Nonlinear Optical Processes,” Nat. Photonics 4(8), 571 (2010). [CrossRef]
- T. Popmintchev, M.-C. Chen, A. Bahabad, M. Gerrity, P. Sidorenko, O. Cohen, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “Phase matching of high harmonic generation in the soft and hard X-ray regions of the spectrum,” Proc. Natl. Acad. Sci. U.S.A. 106(26), 10516–10521 (2009). [CrossRef] [PubMed]
- A. Bahabad, O. Cohen, M. M. Murnane, and H. C. Kapteyn, “Quasi-phase-matching and dispersion characterization of harmonic generation in the perturbative regime using counterpropagating beams,” Opt. Express 16(20), 15923–15931 (2008). [CrossRef] [PubMed]
- X. Zhang, A. L. Lytle, T. Popmintchev, X. Zhou, H. C. Kapteyn, M. M. Murnane, and O. Cohen, “Quasi-phase-matching and quantum-path control of high-harmonic generation using counterpropagating light,” Nat. Phys. 3(4), 270–275 (2007). [CrossRef]
- 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(5), 053902 (2007). [CrossRef] [PubMed]
- O. Cohen, A. L. Lytle, X. Zhang, M. M. Murnane, and H. C. Kapteyn, “Optimizing quasi-phase matching of high harmonic generation using counterpropagating pulse trains,” Opt. Lett. 32(20), 2975–2977 (2007). [CrossRef] [PubMed]
- 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(6918), 51–54 (2003). [CrossRef] [PubMed]
- Z. Chang, A. Rundquist, H. Wang, I. Christov, H. C. Kapteyn, and M. M. Murnane, “Temporal phase control of soft-x-ray harmonic emission,” Phys. Rev. A 58(1), R30–R33 (1998). [CrossRef]
- A. V. Balakin, V. A. Bushuev, B. I. Mantsyzov, I. A. Ozheredov, E. V. Petrov, A. P. Shkurinov, P. Masselin, and G. Mouret, “Enhancement of sum frequency generation near the photonic band gap edge under the quasiphase matching conditions,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 63(4 Pt 2), 046609 (2001). [CrossRef] [PubMed]
- 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(6918), 51–54 (2003). [CrossRef] [PubMed]
- A. V. Balakin, V. A. Bushuev, B. I. Mantsyzov, I. A. Ozheredov, E. V. Petrov, A. P. Shkurinov, P. Masselin, and G. Mouret, “Enhancement of sum frequency generation near the photonic band gap edge under the quasiphase matching conditions,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 63(4 Pt 2), 046609 (2001). [CrossRef] [PubMed]
- T. Popmintchev, M.-C. Chen, A. Bahabad, M. Gerrity, P. Sidorenko, O. Cohen, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “Phase matching of high harmonic generation in the soft and hard X-ray regions of the spectrum,” Proc. Natl. Acad. Sci. U.S.A. 106(26), 10516–10521 (2009). [CrossRef] [PubMed]
- X. Zhang, A. L. Lytle, T. Popmintchev, X. Zhou, H. C. Kapteyn, M. M. Murnane, and O. Cohen, “Quasi-phase-matching and quantum-path control of high-harmonic generation using counterpropagating light,” Nat. Phys. 3(4), 270–275 (2007). [CrossRef]
- 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(5), 053902 (2007). [CrossRef] [PubMed]
- Z. Chang, A. Rundquist, H. Wang, I. Christov, H. C. Kapteyn, and M. M. Murnane, “Temporal phase control of soft-x-ray harmonic emission,” Phys. Rev. A 58(1), R30–R33 (1998). [CrossRef]
- M. Lewenstein, P. Salières, and A. L’Huillier, “Phase of the atomic polarization in high-order harmonic generation,” Phys. Rev. A 52(6), 4747–4754 (1995). [CrossRef] [PubMed]
- J. Seres, V. Yakovlev, J. Seres, C. Streli, P. Wobrauschek, C. Spielmann, and F. Krausz, “Coherent superposition of laser-driven soft-x-ray harmonics from successive sources,” Nat. Phys. 3(12), 878–883 (2007). [CrossRef]
- J. Seres, V. Yakovlev, J. Seres, C. Streli, P. Wobrauschek, C. Spielmann, and F. Krausz, “Coherent superposition of laser-driven soft-x-ray harmonics from successive sources,” Nat. Phys. 3(12), 878–883 (2007). [CrossRef]
- C. Serrat and J. Biegert, “All-regions tunable high harmonic enhancement by a periodic static electric field,” Phys. Rev. Lett. 104(7), 073901 (2010). [CrossRef] [PubMed]
- D. Faccio, C. Serrat, J. M. Cela, A. Farrés, P. Di Trapani, and J. Biegert, “Modulated phase matching and high-order harmonic enhancement mediated by the carrier-envelope phase,” Phys. Rev. A 81, 011803 (2010). [CrossRef]
- A. V. Balakin, V. A. Bushuev, B. I. Mantsyzov, I. A. Ozheredov, E. V. Petrov, A. P. Shkurinov, P. Masselin, and G. Mouret, “Enhancement of sum frequency generation near the photonic band gap edge under the quasiphase matching conditions,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 63(4 Pt 2), 046609 (2001). [CrossRef] [PubMed]
- T. Popmintchev, M.-C. Chen, A. Bahabad, M. Gerrity, P. Sidorenko, O. Cohen, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “Phase matching of high harmonic generation in the soft and hard X-ray regions of the spectrum,” Proc. Natl. Acad. Sci. U.S.A. 106(26), 10516–10521 (2009). [CrossRef] [PubMed]
- S. Somekh and A. Yariv, “Phase-matchable nonlinear optical interactions in periodic thin films,” Appl. Phys. Lett. 21(4), 140–141 (1972). [CrossRef]
- J. Seres, V. Yakovlev, J. Seres, C. Streli, P. Wobrauschek, C. Spielmann, and F. Krausz, “Coherent superposition of laser-driven soft-x-ray harmonics from successive sources,” Nat. Phys. 3(12), 878–883 (2007). [CrossRef]
- J. Khurgin, S. Colak, R. Stolzenberger, and R. N. Bhargava, “Mechanism of efficient blue second harmonic generation in periodically segmented waveguides,” Appl. Phys. Lett. 57(24), 2540–2542 (1990). [CrossRef]
- J. Seres, V. Yakovlev, J. Seres, C. Streli, P. Wobrauschek, C. Spielmann, and F. Krausz, “Coherent superposition of laser-driven soft-x-ray harmonics from successive sources,” Nat. Phys. 3(12), 878–883 (2007). [CrossRef]
- M. Geissler, G. Tempea, and T. Brabec, “Phase-matched high-order harmonic generation in the nonadiabatic limit,” Phys. Rev. A 62(3), 033817 (2000). [CrossRef]
- 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(6918), 51–54 (2003). [CrossRef] [PubMed]
- J. P. van der Ziel, M. Ilegems, P. W. Foy, and R. M. Mikulyak, “Phase-Matched Second-Harmonic Generation in a Periodic GaAs Waveguide,” Appl. Phys. Lett. 29(12), 775–777 (1976). [CrossRef]
- Z. Chang, A. Rundquist, H. Wang, I. Christov, H. C. Kapteyn, and M. M. Murnane, “Temporal phase control of soft-x-ray harmonic emission,” Phys. Rev. A 58(1), R30–R33 (1998). [CrossRef]
- 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(6918), 51–54 (2003). [CrossRef] [PubMed]
- J. Seres, V. Yakovlev, J. Seres, C. Streli, P. Wobrauschek, C. Spielmann, and F. Krausz, “Coherent superposition of laser-driven soft-x-ray harmonics from successive sources,” Nat. Phys. 3(12), 878–883 (2007). [CrossRef]
- J. Seres, V. Yakovlev, J. Seres, C. Streli, P. Wobrauschek, C. Spielmann, and F. Krausz, “Coherent superposition of laser-driven soft-x-ray harmonics from successive sources,” Nat. Phys. 3(12), 878–883 (2007). [CrossRef]
- S. Somekh and A. Yariv, “Phase-matchable nonlinear optical interactions in periodic thin films,” Appl. Phys. Lett. 21(4), 140–141 (1972). [CrossRef]
- M. Zepf, B. Dromey, M. Landreman, P. Foster, and S. M. Hooker, “Bright quasi-phase-matched soft-X-ray harmonic radiation from argon ions,” Phys. Rev. Lett. 99(14), 143901 (2007). [CrossRef] [PubMed]
- O. Cohen, A. L. Lytle, X. Zhang, M. M. Murnane, and H. C. Kapteyn, “Optimizing quasi-phase matching of high harmonic generation using counterpropagating pulse trains,” Opt. Lett. 32(20), 2975–2977 (2007). [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(5), 053902 (2007). [CrossRef] [PubMed]
- X. Zhang, A. L. Lytle, T. Popmintchev, X. Zhou, H. C. Kapteyn, M. M. Murnane, and O. Cohen, “Quasi-phase-matching and quantum-path control of high-harmonic generation using counterpropagating light,” Nat. Phys. 3(4), 270–275 (2007). [CrossRef]
- X. Zhang, A. L. Lytle, T. Popmintchev, X. Zhou, H. C. Kapteyn, M. M. Murnane, and O. Cohen, “Quasi-phase-matching and quantum-path control of high-harmonic generation using counterpropagating light,” Nat. Phys. 3(4), 270–275 (2007). [CrossRef]
Acad. Sci., Paris, C. R.
- P. Appel, “Sur l'inversion approchée de certaines intégrales réelles et sur l'extension de Kepler et des fonctions de Bessel,” Acad. Sci., Paris, C. R. 160, 419 (1915).
Appl. Phys. Lett.
- S. Somekh and A. Yariv, “Phase-matchable nonlinear optical interactions in periodic thin films,” Appl. Phys. Lett. 21(4), 140–141 (1972). [CrossRef]
- J. P. van der Ziel, M. Ilegems, P. W. Foy, and R. M. Mikulyak, “Phase-Matched Second-Harmonic Generation in a Periodic GaAs Waveguide,” Appl. Phys. Lett. 29(12), 775–777 (1976). [CrossRef]
- J. Khurgin, S. Colak, R. Stolzenberger, and R. N. Bhargava, “Mechanism of efficient blue second harmonic generation in periodically segmented waveguides,” Appl. Phys. Lett. 57(24), 2540–2542 (1990). [CrossRef]
IEEE J. Quantum Electron.
- M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28(11), 2631–2654 (1992). [CrossRef]
Nat. Photonics
- A. Bahabad, M. M. Murnane, and H. C. Kapteyn, “Quasi Phase Matching of Momentum and Energy in Nonlinear Optical Processes,” Nat. Photonics 4(8), 571 (2010). [CrossRef]
Nat. Phys.
- X. Zhang, A. L. Lytle, T. Popmintchev, X. Zhou, H. C. Kapteyn, M. M. Murnane, and O. Cohen, “Quasi-phase-matching and quantum-path control of high-harmonic generation using counterpropagating light,” Nat. Phys. 3(4), 270–275 (2007). [CrossRef]
- J. Seres, V. Yakovlev, J. Seres, C. Streli, P. Wobrauschek, C. Spielmann, and F. Krausz, “Coherent superposition of laser-driven soft-x-ray harmonics from successive sources,” Nat. Phys. 3(12), 878–883 (2007). [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(6918), 51–54 (2003). [CrossRef] [PubMed]
Opt. Express
- H. Ren, A. Nazarkin, J. Nold, and P. S. Russell, “Quasi-phase-matched high harmonic generation in hollow core photonic crystal fibers,” Opt. Express 16(21), 17052–17059 (2008). [CrossRef] [PubMed]
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Opt. Lett.
- J. Chen, A. Suda, E. J. Takahashi, M. Nurhuda, and K. Midorikawa, “Compression of intense ultrashort laser pulses in a gas-filled planar waveguide,” Opt. Lett. 33(24), 2992–2994 (2008). [CrossRef] [PubMed]
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Phys. Rev. A
- M. Lewenstein, P. Salières, and A. L’Huillier, “Phase of the atomic polarization in high-order harmonic generation,” Phys. Rev. A 52(6), 4747–4754 (1995). [CrossRef] [PubMed]
- Z. Chang, A. Rundquist, H. Wang, I. Christov, H. C. Kapteyn, and M. M. Murnane, “Temporal phase control of soft-x-ray harmonic emission,” Phys. Rev. A 58(1), R30–R33 (1998). [CrossRef]
- M. Y. Ivanov, T. Brabec, and N. Burnett, “Coulomb corrections and polarization effects in high-intensity high-harmonic emission,” Phys. Rev. A 54(1), 742–745 (1996). [CrossRef] [PubMed]
- M. Geissler, G. Tempea, and T. Brabec, “Phase-matched high-order harmonic generation in the nonadiabatic limit,” Phys. Rev. A 62(3), 033817 (2000). [CrossRef]
- D. Faccio, C. Serrat, J. M. Cela, A. Farrés, P. Di Trapani, and J. Biegert, “Modulated phase matching and high-order harmonic enhancement mediated by the carrier-envelope phase,” Phys. Rev. A 81, 011803 (2010). [CrossRef]
Phys. Rev. E Stat. Nonlin. Soft Matter Phys.
- A. V. Balakin, V. A. Bushuev, B. I. Mantsyzov, I. A. Ozheredov, E. V. Petrov, A. P. Shkurinov, P. Masselin, and G. Mouret, “Enhancement of sum frequency generation near the photonic band gap edge under the quasiphase matching conditions,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 63(4 Pt 2), 046609 (2001). [CrossRef] [PubMed]
Phys. Rev. Lett.
- 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(5), 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(7), 073901 (2010). [CrossRef] [PubMed]
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Proc. Natl. Acad. Sci. U.S.A.
- T. Popmintchev, M.-C. Chen, A. Bahabad, M. Gerrity, P. Sidorenko, O. Cohen, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “Phase matching of high harmonic generation in the soft and hard X-ray regions of the spectrum,” Proc. Natl. Acad. Sci. U.S.A. 106(26), 10516–10521 (2009). [CrossRef] [PubMed]
Sov. Phys. JETP
- M. V. Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field,” Sov. Phys. JETP 64, 1191 (1986).
2010, Faccio, Phys. Rev. A
- D. Faccio, C. Serrat, J. M. Cela, A. Farrés, P. Di Trapani, and J. Biegert, “Modulated phase matching and high-order harmonic enhancement mediated by the carrier-envelope phase,” Phys. Rev. A 81, 011803 (2010). [CrossRef]
- C. Serrat and J. Biegert, “All-regions tunable high harmonic enhancement by a periodic static electric field,” Phys. Rev. Lett. 104(7), 073901 (2010). [CrossRef] [PubMed]
- A. Bahabad, M. M. Murnane, and H. C. Kapteyn, “Quasi Phase Matching of Momentum and Energy in Nonlinear Optical Processes,” Nat. Photonics 4(8), 571 (2010). [CrossRef]
- T. Popmintchev, M.-C. Chen, A. Bahabad, M. Gerrity, P. Sidorenko, O. Cohen, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “Phase matching of high harmonic generation in the soft and hard X-ray regions of the spectrum,” Proc. Natl. Acad. Sci. U.S.A. 106(26), 10516–10521 (2009). [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(5), 053902 (2007). [CrossRef] [PubMed]
- X. Zhang, A. L. Lytle, T. Popmintchev, X. Zhou, H. C. Kapteyn, M. M. Murnane, and O. Cohen, “Quasi-phase-matching and quantum-path control of high-harmonic generation using counterpropagating light,” Nat. Phys. 3(4), 270–275 (2007). [CrossRef]
- J. Seres, V. Yakovlev, J. Seres, C. Streli, P. Wobrauschek, C. Spielmann, and F. Krausz, “Coherent superposition of laser-driven soft-x-ray harmonics from successive sources,” Nat. Phys. 3(12), 878–883 (2007). [CrossRef]
- M. Zepf, B. Dromey, M. Landreman, P. Foster, and S. M. Hooker, “Bright quasi-phase-matched soft-X-ray harmonic radiation from argon ions,” Phys. Rev. Lett. 99(14), 143901 (2007). [CrossRef] [PubMed]
- 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(6918), 51–54 (2003). [CrossRef] [PubMed]
- A. V. Balakin, V. A. Bushuev, B. I. Mantsyzov, I. A. Ozheredov, E. V. Petrov, A. P. Shkurinov, P. Masselin, and G. Mouret, “Enhancement of sum frequency generation near the photonic band gap edge under the quasiphase matching conditions,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 63(4 Pt 2), 046609 (2001). [CrossRef] [PubMed]
- M. Geissler, G. Tempea, and T. Brabec, “Phase-matched high-order harmonic generation in the nonadiabatic limit,” Phys. Rev. A 62(3), 033817 (2000). [CrossRef]
- Z. Chang, A. Rundquist, H. Wang, I. Christov, H. C. Kapteyn, and M. M. Murnane, “Temporal phase control of soft-x-ray harmonic emission,” Phys. Rev. A 58(1), R30–R33 (1998). [CrossRef]
- M. Y. Ivanov, T. Brabec, and N. Burnett, “Coulomb corrections and polarization effects in high-intensity high-harmonic emission,” Phys. Rev. A 54(1), 742–745 (1996). [CrossRef] [PubMed]
- M. Lewenstein, P. Salières, and A. L’Huillier, “Phase of the atomic polarization in high-order harmonic generation,” Phys. Rev. A 52(6), 4747–4754 (1995). [CrossRef] [PubMed]
- M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28(11), 2631–2654 (1992). [CrossRef]
- J. Khurgin, S. Colak, R. Stolzenberger, and R. N. Bhargava, “Mechanism of efficient blue second harmonic generation in periodically segmented waveguides,” Appl. Phys. Lett. 57(24), 2540–2542 (1990). [CrossRef]
- M. V. Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field,” Sov. Phys. JETP 64, 1191 (1986).
- J. P. van der Ziel, M. Ilegems, P. W. Foy, and R. M. Mikulyak, “Phase-Matched Second-Harmonic Generation in a Periodic GaAs Waveguide,” Appl. Phys. Lett. 29(12), 775–777 (1976). [CrossRef]
- S. Somekh and A. Yariv, “Phase-matchable nonlinear optical interactions in periodic thin films,” Appl. Phys. Lett. 21(4), 140–141 (1972). [CrossRef]
- P. Appel, “Sur l'inversion approchée de certaines intégrales réelles et sur l'extension de Kepler et des fonctions de Bessel,” Acad. Sci., Paris, C. R. 160, 419 (1915).
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