Abstract

Noncollinear quasi-phase matching, in combination with spectral angular dispersion, can be used to broaden the bandwidth of second-harmonic generation (SHG) beyond the bandwidth for collinear, nondispersed interactions. A general theoretical treatment is presented, in addition to a solution that predicts the generated field for the case of a Gaussian input field; a comparison is made between this technique and others available for broadband SHG. An experiment in periodically poled lithium niobate demonstrates SHG of a 138 fs pulse at 1550 nm in a 1 cm length crystal (with a collinear acceptance bandwidth 13 times narrower than the first-harmonic bandwidth) with minimal spectral narrowing.

© 2005 Optical Society of America

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  1. 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, 2631-2654 (1992).
    [CrossRef]
  2. G. Imeshev, M. A. Arbore, M. M. Fejer, A. Galvanauskas, M. Fermann, and D. Harter, "Ultrashort-pulse second-harmonic generation with longitudinally nonuniform quasi-phase-matching gratings: pulse compression and shaping," J. Opt. Soc. Am. B 17, 304-318 (2000).
    [CrossRef]
  3. D. H. Jundt, "Temperature-dependent Sellmeier equation for the index of refraction, ne, in congruent lithium niobate," Opt. Lett. 22, 1553-1555 (1997).
    [CrossRef]
  4. M. S. Webb, D. Eimerl, and S. P. Velsko, "Wavelength insensitive phase-matched second-harmonic generation in partially deuterated KDP," J. Opt. Soc. Am. B 9, 1118-1127 (1992).
    [CrossRef]
  5. K. Hayata and M. Koshiba, "Group-velocity-matched second-harmonic generation: an efficient scheme for femtosecond ultraviolet pulse generation in periodically domain-inverted beta-BaB2O4," Appl. Phys. Lett. 622188-2190 (1993).
    [CrossRef]
  6. N. E. Yu, J. H. Ro, M. Cha, S. Kurimura, and T. Taira, "Broadband quasi-phase-matched second-harmonic generation in MgO-doped periodically poled LiNbO3 at the communications band," Opt. Lett. 27, 1046-1048 (2002).
    [CrossRef]
  7. N. E. Yu, S. Kurimura, and K. Kitamura, "Broadband second harmonic generation with simultaneous group-velocity matching and quasi-phase matching," Jpn. J. Appl. Phys. Part 1 42, L821-L823 (2003).
    [CrossRef]
  8. N. E. Yu, S. Kurimura, K. Kitamura, J. H. Ro, M. Cha, S. Ashihara, T. Shimura, K. Kuroda, and T. Taira, "Efficient frequency doubling of a femtosecond pulse with simultaneous group-velocity matching and quasi phase matching in periodically poled, MgO-doped lithium niobate," Appl. Phys. Lett. 82, 3388-3390 (2003).
    [CrossRef]
  9. H. Zhu, T. Wang, W. Zheng, P. Yuan, L. Qian, and D. Fan, "Efficient second harmonic generation of femtosecond laser at 1 µm," Opt. Express 12, 2150-2155 (2004).
    [CrossRef] [PubMed]
  10. M. L. Bortz, M. Fujimura, and M. M. Fejer, "Increased acceptance bandwidth for quasi-phase-matched second harmonic generation in LiNbO3 waveguides," Electron. Lett. 30, 34-35 (1994).
    [CrossRef]
  11. M. A. Arbore, O. Marco, and M. M. Fejer, "Pulse compression during second-harmonic generation in aperiodic quasi-phase-matching gratings," Opt. Lett. 22, 865-867 (1997).
    [CrossRef] [PubMed]
  12. V. D. Volosov, S. G. Karpenko, N. E. Kornienko, and V. L. Strizhevskii, "Method for compensating the phase-matching dispersion in nonlinear optics," Sov. J. Quantum Electron. 4, 1090-1098 (1975).
    [CrossRef]
  13. V. D. Volosov and E. V. Goryachkina, "Compensation of phase-matching dispersion in generation of nonmonochromatic radiation harmonics. I. Doubling of neodymium-glass radiation frequency under free-oscillation conditions," Sov. J. Quantum Electron. 6, 854-857 (1976).
    [CrossRef]
  14. S. Saikan, "Automatically tunable second-harmonic generation of dye lasers," Opt. Commun. 18, 439-443 (1976).
    [CrossRef]
  15. O. E. Martinez, "Achromatic phase matching for second harmonic generation of femtosecond pulses," IEEE J. Quantum Electron. 25, 2464-2468 (1989).
    [CrossRef]
  16. G. Szabo and Z. Bor, "Broadband frequency doubler for femtosecond pulses," Appl. Phys. B 50, 51-54 (1990).
    [CrossRef]
  17. A. V. Smith, "Group-velocity-matched three-wave mixing in birefringent crystals," Opt. Lett. 26, 719-721 (2001).
    [CrossRef]
  18. T. R. Zhang, H. R. Choo, and M. C. Downer, "Phase and group velocity matching for second harmonic generation of femtosecond pulses," Appl. Opt. 29, 3927-3933 (1990).
    [CrossRef] [PubMed]
  19. S. Saikan, D. Ouw, and F. P. Schafer, "Automatic phase-matched frequency-doubling system for the 240-350-nm region," Appl. Opt. 18, 193-196 (1979).
    [CrossRef] [PubMed]
  20. B. A. Richman, S. E. Bisson, R. Trebino, E. Sidick, and A. Jacobsen, "All-prism achromatic phase matching for second-harmonic generation," Appl. Opt. 38, 3316-3323 (1999).
    [CrossRef]
  21. P. Baum, S. Lochbrunner, and E. Riedle, "Tunable sub-10-fs ultraviolet pulses generated by achromatic frequency doubling," Opt. Lett. 29, 1686-1688 (2004).
    [CrossRef] [PubMed]
  22. M. Aoyama, T. Zhang, M. Tsukakoshi, and K. Yamakawa, "Noncollinear second-harmonic generation with compensation of phase mismatch by controlling frequency chirp and tilted pulse fronts of femtosecond laser pulses," Jpn. J. Appl. Phys. Part 1 39, 3394-3399 (2000).
    [CrossRef]
  23. S. Ashihara, T. Shimura, and K. Kuroda, "Group-velocity matched second-harmonic generation in tilted quasi-phase-matched gratings," J. Opt. Soc. Am. B 20, 853-856 (2003).
    [CrossRef]
  24. S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, Optics of Femtosecond Laser Pulses (American Institute of Physics, 1992).
  25. G. D. Boyd and D. A. Kleinman, "Parametric interactions of focused Gaussian light beams," J. Appl. Phys. 39, 3597-3639 (1968).
    [CrossRef]
  26. T. F. Johnson, "Beam propagation (M2) measurement made as easy as it gets: the four-cuts method," Appl. Opt. 37, 4840-4850 (1998).
    [CrossRef]

2004

2003

S. Ashihara, T. Shimura, and K. Kuroda, "Group-velocity matched second-harmonic generation in tilted quasi-phase-matched gratings," J. Opt. Soc. Am. B 20, 853-856 (2003).
[CrossRef]

N. E. Yu, S. Kurimura, and K. Kitamura, "Broadband second harmonic generation with simultaneous group-velocity matching and quasi-phase matching," Jpn. J. Appl. Phys. Part 1 42, L821-L823 (2003).
[CrossRef]

N. E. Yu, S. Kurimura, K. Kitamura, J. H. Ro, M. Cha, S. Ashihara, T. Shimura, K. Kuroda, and T. Taira, "Efficient frequency doubling of a femtosecond pulse with simultaneous group-velocity matching and quasi phase matching in periodically poled, MgO-doped lithium niobate," Appl. Phys. Lett. 82, 3388-3390 (2003).
[CrossRef]

2002

2001

2000

M. Aoyama, T. Zhang, M. Tsukakoshi, and K. Yamakawa, "Noncollinear second-harmonic generation with compensation of phase mismatch by controlling frequency chirp and tilted pulse fronts of femtosecond laser pulses," Jpn. J. Appl. Phys. Part 1 39, 3394-3399 (2000).
[CrossRef]

G. Imeshev, M. A. Arbore, M. M. Fejer, A. Galvanauskas, M. Fermann, and D. Harter, "Ultrashort-pulse second-harmonic generation with longitudinally nonuniform quasi-phase-matching gratings: pulse compression and shaping," J. Opt. Soc. Am. B 17, 304-318 (2000).
[CrossRef]

1999

1998

1997

1994

M. L. Bortz, M. Fujimura, and M. M. Fejer, "Increased acceptance bandwidth for quasi-phase-matched second harmonic generation in LiNbO3 waveguides," Electron. Lett. 30, 34-35 (1994).
[CrossRef]

1993

K. Hayata and M. Koshiba, "Group-velocity-matched second-harmonic generation: an efficient scheme for femtosecond ultraviolet pulse generation in periodically domain-inverted beta-BaB2O4," Appl. Phys. Lett. 622188-2190 (1993).
[CrossRef]

1992

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, 2631-2654 (1992).
[CrossRef]

M. S. Webb, D. Eimerl, and S. P. Velsko, "Wavelength insensitive phase-matched second-harmonic generation in partially deuterated KDP," J. Opt. Soc. Am. B 9, 1118-1127 (1992).
[CrossRef]

1990

1989

O. E. Martinez, "Achromatic phase matching for second harmonic generation of femtosecond pulses," IEEE J. Quantum Electron. 25, 2464-2468 (1989).
[CrossRef]

1979

1976

V. D. Volosov and E. V. Goryachkina, "Compensation of phase-matching dispersion in generation of nonmonochromatic radiation harmonics. I. Doubling of neodymium-glass radiation frequency under free-oscillation conditions," Sov. J. Quantum Electron. 6, 854-857 (1976).
[CrossRef]

S. Saikan, "Automatically tunable second-harmonic generation of dye lasers," Opt. Commun. 18, 439-443 (1976).
[CrossRef]

1975

V. D. Volosov, S. G. Karpenko, N. E. Kornienko, and V. L. Strizhevskii, "Method for compensating the phase-matching dispersion in nonlinear optics," Sov. J. Quantum Electron. 4, 1090-1098 (1975).
[CrossRef]

1968

G. D. Boyd and D. A. Kleinman, "Parametric interactions of focused Gaussian light beams," J. Appl. Phys. 39, 3597-3639 (1968).
[CrossRef]

Akhmanov, S. A.

S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, Optics of Femtosecond Laser Pulses (American Institute of Physics, 1992).

Aoyama, M.

M. Aoyama, T. Zhang, M. Tsukakoshi, and K. Yamakawa, "Noncollinear second-harmonic generation with compensation of phase mismatch by controlling frequency chirp and tilted pulse fronts of femtosecond laser pulses," Jpn. J. Appl. Phys. Part 1 39, 3394-3399 (2000).
[CrossRef]

Arbore, M. A.

Ashihara, S.

N. E. Yu, S. Kurimura, K. Kitamura, J. H. Ro, M. Cha, S. Ashihara, T. Shimura, K. Kuroda, and T. Taira, "Efficient frequency doubling of a femtosecond pulse with simultaneous group-velocity matching and quasi phase matching in periodically poled, MgO-doped lithium niobate," Appl. Phys. Lett. 82, 3388-3390 (2003).
[CrossRef]

S. Ashihara, T. Shimura, and K. Kuroda, "Group-velocity matched second-harmonic generation in tilted quasi-phase-matched gratings," J. Opt. Soc. Am. B 20, 853-856 (2003).
[CrossRef]

Baum, P.

Bisson, S. E.

Bor, Z.

G. Szabo and Z. Bor, "Broadband frequency doubler for femtosecond pulses," Appl. Phys. B 50, 51-54 (1990).
[CrossRef]

Bortz, M. L.

M. L. Bortz, M. Fujimura, and M. M. Fejer, "Increased acceptance bandwidth for quasi-phase-matched second harmonic generation in LiNbO3 waveguides," Electron. Lett. 30, 34-35 (1994).
[CrossRef]

Boyd, G. D.

G. D. Boyd and D. A. Kleinman, "Parametric interactions of focused Gaussian light beams," J. Appl. Phys. 39, 3597-3639 (1968).
[CrossRef]

Byer, R. L.

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, 2631-2654 (1992).
[CrossRef]

Cha, M.

N. E. Yu, S. Kurimura, K. Kitamura, J. H. Ro, M. Cha, S. Ashihara, T. Shimura, K. Kuroda, and T. Taira, "Efficient frequency doubling of a femtosecond pulse with simultaneous group-velocity matching and quasi phase matching in periodically poled, MgO-doped lithium niobate," Appl. Phys. Lett. 82, 3388-3390 (2003).
[CrossRef]

N. E. Yu, J. H. Ro, M. Cha, S. Kurimura, and T. Taira, "Broadband quasi-phase-matched second-harmonic generation in MgO-doped periodically poled LiNbO3 at the communications band," Opt. Lett. 27, 1046-1048 (2002).
[CrossRef]

Chirkin, A. S.

S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, Optics of Femtosecond Laser Pulses (American Institute of Physics, 1992).

Choo, H. R.

Downer, M. C.

Eimerl, D.

Fan, D.

Fejer, M. M.

G. Imeshev, M. A. Arbore, M. M. Fejer, A. Galvanauskas, M. Fermann, and D. Harter, "Ultrashort-pulse second-harmonic generation with longitudinally nonuniform quasi-phase-matching gratings: pulse compression and shaping," J. Opt. Soc. Am. B 17, 304-318 (2000).
[CrossRef]

M. A. Arbore, O. Marco, and M. M. Fejer, "Pulse compression during second-harmonic generation in aperiodic quasi-phase-matching gratings," Opt. Lett. 22, 865-867 (1997).
[CrossRef] [PubMed]

M. L. Bortz, M. Fujimura, and M. M. Fejer, "Increased acceptance bandwidth for quasi-phase-matched second harmonic generation in LiNbO3 waveguides," Electron. Lett. 30, 34-35 (1994).
[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, 2631-2654 (1992).
[CrossRef]

Fermann, M.

Fujimura, M.

M. L. Bortz, M. Fujimura, and M. M. Fejer, "Increased acceptance bandwidth for quasi-phase-matched second harmonic generation in LiNbO3 waveguides," Electron. Lett. 30, 34-35 (1994).
[CrossRef]

Galvanauskas, A.

Goryachkina, E. V.

V. D. Volosov and E. V. Goryachkina, "Compensation of phase-matching dispersion in generation of nonmonochromatic radiation harmonics. I. Doubling of neodymium-glass radiation frequency under free-oscillation conditions," Sov. J. Quantum Electron. 6, 854-857 (1976).
[CrossRef]

Harter, D.

Hayata, K.

K. Hayata and M. Koshiba, "Group-velocity-matched second-harmonic generation: an efficient scheme for femtosecond ultraviolet pulse generation in periodically domain-inverted beta-BaB2O4," Appl. Phys. Lett. 622188-2190 (1993).
[CrossRef]

Imeshev, G.

Jacobsen, A.

Johnson, T. F.

Jundt, D. H.

D. H. Jundt, "Temperature-dependent Sellmeier equation for the index of refraction, ne, in congruent lithium niobate," Opt. Lett. 22, 1553-1555 (1997).
[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, 2631-2654 (1992).
[CrossRef]

Karpenko, S. G.

V. D. Volosov, S. G. Karpenko, N. E. Kornienko, and V. L. Strizhevskii, "Method for compensating the phase-matching dispersion in nonlinear optics," Sov. J. Quantum Electron. 4, 1090-1098 (1975).
[CrossRef]

Kitamura, K.

N. E. Yu, S. Kurimura, K. Kitamura, J. H. Ro, M. Cha, S. Ashihara, T. Shimura, K. Kuroda, and T. Taira, "Efficient frequency doubling of a femtosecond pulse with simultaneous group-velocity matching and quasi phase matching in periodically poled, MgO-doped lithium niobate," Appl. Phys. Lett. 82, 3388-3390 (2003).
[CrossRef]

N. E. Yu, S. Kurimura, and K. Kitamura, "Broadband second harmonic generation with simultaneous group-velocity matching and quasi-phase matching," Jpn. J. Appl. Phys. Part 1 42, L821-L823 (2003).
[CrossRef]

Kleinman, D. A.

G. D. Boyd and D. A. Kleinman, "Parametric interactions of focused Gaussian light beams," J. Appl. Phys. 39, 3597-3639 (1968).
[CrossRef]

Kornienko, N. E.

V. D. Volosov, S. G. Karpenko, N. E. Kornienko, and V. L. Strizhevskii, "Method for compensating the phase-matching dispersion in nonlinear optics," Sov. J. Quantum Electron. 4, 1090-1098 (1975).
[CrossRef]

Koshiba, M.

K. Hayata and M. Koshiba, "Group-velocity-matched second-harmonic generation: an efficient scheme for femtosecond ultraviolet pulse generation in periodically domain-inverted beta-BaB2O4," Appl. Phys. Lett. 622188-2190 (1993).
[CrossRef]

Kurimura, S.

N. E. Yu, S. Kurimura, and K. Kitamura, "Broadband second harmonic generation with simultaneous group-velocity matching and quasi-phase matching," Jpn. J. Appl. Phys. Part 1 42, L821-L823 (2003).
[CrossRef]

N. E. Yu, S. Kurimura, K. Kitamura, J. H. Ro, M. Cha, S. Ashihara, T. Shimura, K. Kuroda, and T. Taira, "Efficient frequency doubling of a femtosecond pulse with simultaneous group-velocity matching and quasi phase matching in periodically poled, MgO-doped lithium niobate," Appl. Phys. Lett. 82, 3388-3390 (2003).
[CrossRef]

N. E. Yu, J. H. Ro, M. Cha, S. Kurimura, and T. Taira, "Broadband quasi-phase-matched second-harmonic generation in MgO-doped periodically poled LiNbO3 at the communications band," Opt. Lett. 27, 1046-1048 (2002).
[CrossRef]

Kuroda, K.

S. Ashihara, T. Shimura, and K. Kuroda, "Group-velocity matched second-harmonic generation in tilted quasi-phase-matched gratings," J. Opt. Soc. Am. B 20, 853-856 (2003).
[CrossRef]

N. E. Yu, S. Kurimura, K. Kitamura, J. H. Ro, M. Cha, S. Ashihara, T. Shimura, K. Kuroda, and T. Taira, "Efficient frequency doubling of a femtosecond pulse with simultaneous group-velocity matching and quasi phase matching in periodically poled, MgO-doped lithium niobate," Appl. Phys. Lett. 82, 3388-3390 (2003).
[CrossRef]

Lochbrunner, S.

Magel, G. A.

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, 2631-2654 (1992).
[CrossRef]

Marco, O.

Martinez, O. E.

O. E. Martinez, "Achromatic phase matching for second harmonic generation of femtosecond pulses," IEEE J. Quantum Electron. 25, 2464-2468 (1989).
[CrossRef]

Ouw, D.

Qian, L.

Richman, B. A.

Riedle, E.

Ro, J. H.

N. E. Yu, S. Kurimura, K. Kitamura, J. H. Ro, M. Cha, S. Ashihara, T. Shimura, K. Kuroda, and T. Taira, "Efficient frequency doubling of a femtosecond pulse with simultaneous group-velocity matching and quasi phase matching in periodically poled, MgO-doped lithium niobate," Appl. Phys. Lett. 82, 3388-3390 (2003).
[CrossRef]

N. E. Yu, J. H. Ro, M. Cha, S. Kurimura, and T. Taira, "Broadband quasi-phase-matched second-harmonic generation in MgO-doped periodically poled LiNbO3 at the communications band," Opt. Lett. 27, 1046-1048 (2002).
[CrossRef]

Saikan, S.

Schafer, F. P.

Shimura, T.

S. Ashihara, T. Shimura, and K. Kuroda, "Group-velocity matched second-harmonic generation in tilted quasi-phase-matched gratings," J. Opt. Soc. Am. B 20, 853-856 (2003).
[CrossRef]

N. E. Yu, S. Kurimura, K. Kitamura, J. H. Ro, M. Cha, S. Ashihara, T. Shimura, K. Kuroda, and T. Taira, "Efficient frequency doubling of a femtosecond pulse with simultaneous group-velocity matching and quasi phase matching in periodically poled, MgO-doped lithium niobate," Appl. Phys. Lett. 82, 3388-3390 (2003).
[CrossRef]

Sidick, E.

Smith, A. V.

Strizhevskii, V. L.

V. D. Volosov, S. G. Karpenko, N. E. Kornienko, and V. L. Strizhevskii, "Method for compensating the phase-matching dispersion in nonlinear optics," Sov. J. Quantum Electron. 4, 1090-1098 (1975).
[CrossRef]

Szabo, G.

G. Szabo and Z. Bor, "Broadband frequency doubler for femtosecond pulses," Appl. Phys. B 50, 51-54 (1990).
[CrossRef]

Taira, T.

N. E. Yu, S. Kurimura, K. Kitamura, J. H. Ro, M. Cha, S. Ashihara, T. Shimura, K. Kuroda, and T. Taira, "Efficient frequency doubling of a femtosecond pulse with simultaneous group-velocity matching and quasi phase matching in periodically poled, MgO-doped lithium niobate," Appl. Phys. Lett. 82, 3388-3390 (2003).
[CrossRef]

N. E. Yu, J. H. Ro, M. Cha, S. Kurimura, and T. Taira, "Broadband quasi-phase-matched second-harmonic generation in MgO-doped periodically poled LiNbO3 at the communications band," Opt. Lett. 27, 1046-1048 (2002).
[CrossRef]

Trebino, R.

Tsukakoshi, M.

M. Aoyama, T. Zhang, M. Tsukakoshi, and K. Yamakawa, "Noncollinear second-harmonic generation with compensation of phase mismatch by controlling frequency chirp and tilted pulse fronts of femtosecond laser pulses," Jpn. J. Appl. Phys. Part 1 39, 3394-3399 (2000).
[CrossRef]

Velsko, S. P.

Volosov, V. D.

V. D. Volosov and E. V. Goryachkina, "Compensation of phase-matching dispersion in generation of nonmonochromatic radiation harmonics. I. Doubling of neodymium-glass radiation frequency under free-oscillation conditions," Sov. J. Quantum Electron. 6, 854-857 (1976).
[CrossRef]

V. D. Volosov, S. G. Karpenko, N. E. Kornienko, and V. L. Strizhevskii, "Method for compensating the phase-matching dispersion in nonlinear optics," Sov. J. Quantum Electron. 4, 1090-1098 (1975).
[CrossRef]

Vysloukh, V. A.

S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, Optics of Femtosecond Laser Pulses (American Institute of Physics, 1992).

Wang, T.

Webb, M. S.

Yamakawa, K.

M. Aoyama, T. Zhang, M. Tsukakoshi, and K. Yamakawa, "Noncollinear second-harmonic generation with compensation of phase mismatch by controlling frequency chirp and tilted pulse fronts of femtosecond laser pulses," Jpn. J. Appl. Phys. Part 1 39, 3394-3399 (2000).
[CrossRef]

Yu, N. E.

N. E. Yu, S. Kurimura, and K. Kitamura, "Broadband second harmonic generation with simultaneous group-velocity matching and quasi-phase matching," Jpn. J. Appl. Phys. Part 1 42, L821-L823 (2003).
[CrossRef]

N. E. Yu, S. Kurimura, K. Kitamura, J. H. Ro, M. Cha, S. Ashihara, T. Shimura, K. Kuroda, and T. Taira, "Efficient frequency doubling of a femtosecond pulse with simultaneous group-velocity matching and quasi phase matching in periodically poled, MgO-doped lithium niobate," Appl. Phys. Lett. 82, 3388-3390 (2003).
[CrossRef]

N. E. Yu, J. H. Ro, M. Cha, S. Kurimura, and T. Taira, "Broadband quasi-phase-matched second-harmonic generation in MgO-doped periodically poled LiNbO3 at the communications band," Opt. Lett. 27, 1046-1048 (2002).
[CrossRef]

Yuan, P.

Zhang, T.

M. Aoyama, T. Zhang, M. Tsukakoshi, and K. Yamakawa, "Noncollinear second-harmonic generation with compensation of phase mismatch by controlling frequency chirp and tilted pulse fronts of femtosecond laser pulses," Jpn. J. Appl. Phys. Part 1 39, 3394-3399 (2000).
[CrossRef]

Zhang, T. R.

Zheng, W.

Zhu, H.

Appl. Opt.

Appl. Phys. B

G. Szabo and Z. Bor, "Broadband frequency doubler for femtosecond pulses," Appl. Phys. B 50, 51-54 (1990).
[CrossRef]

Appl. Phys. Lett.

N. E. Yu, S. Kurimura, K. Kitamura, J. H. Ro, M. Cha, S. Ashihara, T. Shimura, K. Kuroda, and T. Taira, "Efficient frequency doubling of a femtosecond pulse with simultaneous group-velocity matching and quasi phase matching in periodically poled, MgO-doped lithium niobate," Appl. Phys. Lett. 82, 3388-3390 (2003).
[CrossRef]

K. Hayata and M. Koshiba, "Group-velocity-matched second-harmonic generation: an efficient scheme for femtosecond ultraviolet pulse generation in periodically domain-inverted beta-BaB2O4," Appl. Phys. Lett. 622188-2190 (1993).
[CrossRef]

Electron. Lett.

M. L. Bortz, M. Fujimura, and M. M. Fejer, "Increased acceptance bandwidth for quasi-phase-matched second harmonic generation in LiNbO3 waveguides," Electron. Lett. 30, 34-35 (1994).
[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, 2631-2654 (1992).
[CrossRef]

O. E. Martinez, "Achromatic phase matching for second harmonic generation of femtosecond pulses," IEEE J. Quantum Electron. 25, 2464-2468 (1989).
[CrossRef]

J. Appl. Phys.

G. D. Boyd and D. A. Kleinman, "Parametric interactions of focused Gaussian light beams," J. Appl. Phys. 39, 3597-3639 (1968).
[CrossRef]

J. Opt. Soc. Am. B

Jpn. J. Appl. Phys. Part 1

M. Aoyama, T. Zhang, M. Tsukakoshi, and K. Yamakawa, "Noncollinear second-harmonic generation with compensation of phase mismatch by controlling frequency chirp and tilted pulse fronts of femtosecond laser pulses," Jpn. J. Appl. Phys. Part 1 39, 3394-3399 (2000).
[CrossRef]

N. E. Yu, S. Kurimura, and K. Kitamura, "Broadband second harmonic generation with simultaneous group-velocity matching and quasi-phase matching," Jpn. J. Appl. Phys. Part 1 42, L821-L823 (2003).
[CrossRef]

Opt. Commun.

S. Saikan, "Automatically tunable second-harmonic generation of dye lasers," Opt. Commun. 18, 439-443 (1976).
[CrossRef]

Opt. Express

Opt. Lett.

Sov. J. Quantum Electron.

V. D. Volosov, S. G. Karpenko, N. E. Kornienko, and V. L. Strizhevskii, "Method for compensating the phase-matching dispersion in nonlinear optics," Sov. J. Quantum Electron. 4, 1090-1098 (1975).
[CrossRef]

V. D. Volosov and E. V. Goryachkina, "Compensation of phase-matching dispersion in generation of nonmonochromatic radiation harmonics. I. Doubling of neodymium-glass radiation frequency under free-oscillation conditions," Sov. J. Quantum Electron. 6, 854-857 (1976).
[CrossRef]

Other

S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, Optics of Femtosecond Laser Pulses (American Institute of Physics, 1992).

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Figures (12)

Fig. 1
Fig. 1

Frequency-domain picture of plane-wave noncollinear QPM SHG. (a) QPM condition at frequency ω. (b) QPM condition at frequency ω (solid lines), where the dotted lines indicate the QPM condition at ω. If θ and ϕ are chosen appropriately, Δ k ( ω ) = Δ k ( ω ) and angular dispersion compensates material dispersion to maintain a constant phase mismatch.

Fig. 2
Fig. 2

Time-domain picture of tilted pulse-front group-velocity-matched SHG. The solid outline indicates the FH envelope; the gray shaded area indicates the SH envelope. With appropriately chosen pulse-front tilt angle ψ, the field overlap is maintained with propagation and the group velocities are effectively matched. The angle ψ is related to the spectral angular dispersion through Eq. (6).

Fig. 3
Fig. 3

Schematic diagram of the PPLN experiment with spectral angular dispersion. (a) FH light incident on a diffraction grating acquires spectral angular dispersion. A lens images this spot into the PPLN crystal where SH light is generated. This SH is then reimaged onto an output diffraction grating where the spectral angular dispersion is undone. (b) A closeup view of the SHG interaction illustrating the noncollinear interaction in a tilted QPM grating.

Fig. 4
Fig. 4

Results of SHG with spectral angular dispersion in PPLN. Autocorrelation (left) and spectrum (right) of tilted pulse-front SHG (top) and collinear SHG in an identical length crystal in the presence of group-velocity walk-off (bottom). With spectral angular dispersion, the measured autocorrelation has a FWHM of 240 fs and a spectral FWHM of 8.3 nm, nearly 14 times broader than the spectrum of collinear SHG in a crystal of identical length.

Fig. 5
Fig. 5

Field envelope of a tilted pulse with (a) tilt angle ψ and (b) an untilted pulse. The width Δ x that determines the importance of diffraction may be much less than the beam width w 0 for a tilted pulse. Such a tilted field will experience diffractive effects with a characteristic length L R = k 0 Δ x 2 rather than the diffraction length L R = k 0 w 0 2 determined by the beam width w 0 .

Fig. 6
Fig. 6

SH amplitude reduction I 0 ( D ) . The solid curve is I 0 ( D ) , and the dashed–dotted lines indicate asymptotic behavior for D 1 where I 0 ( D ) 1 and D 1 where I 0 ( D ) 2 D .

Fig. 7
Fig. 7

Evaluation of the response function I 2 ( q ) for several values of D, normalized to the value at q = 0 . When D 1 , I 2 ( q ) sinc ( q 2 ) . When D 1 , I 2 ( q ) is asymmetric with a slowly decaying tail.

Fig. 8
Fig. 8

SHG acceptance bandwidth versus effective GVD mismatch parameter δ D defined in Eq. (50) for several values of the FH effective dispersion parameter D. Here we neglect spatial walk-off and assume that q δ D Ω 2 2 . Minimal loss of bandwidth results when δ D < 1 regardless of the magnitude of D.

Fig. 9
Fig. 9

Effects of spatial walk-off on beam profile for several values of the spatial walk-off parameter A = L L a . On the left is plotted the near-field SH amplitude versus x, and on the right the field amplitude versus spatial frequency (proportional to the far-field SH amplitude distribution after angular dispersion has been compensated) is shown. The shape of the response function I 2 ( q ) is influenced by the dispersion parameter D, while increasing A changes the scaling of the width of the response function in the spatial-frequency domain since q = A ξ . When A 1 , the response function is much wider than the polarization distribution, and both the near-field and far-field distributions are Gaussian for all values of D. When A > 1 , the response function is narrower than the polarization distribution, and the SH amplitude is influenced by the shape of I 2 ( q ) . When D 1 (top graphs), I 2 ( q ) sinc ( q ) and the near-field distribution approaches a flat-top function. For larger D (middle and bottom graphs), I 2 ( q ) departs from the sinc ( q ) behavior as shown in Fig. 7, and the near-field and far-field distributions reflect the distortion of the response function when A > 1 .

Fig. 10
Fig. 10

(a) Surface plot of the efficiency reduction factor h ( A , D ) as a function of A = L L a and D = L L D , 1 . When both spatial walk-off and effective dispersion are ignored ( A 1 and D 1 ), h ( A , D ) 1 . Increased effective dispersion ( D > 1 ) leads to pulse spreading, and the length over which the intensity is at its maximum is reduced, resulting in a decreased conversion efficiency. Increased spatial walk-off ( A > 1 ) results in a generated SH field that propagates away from the peak FH intensity also resulting in a reduced effective interaction length and decreasing conversion efficiency. (b) Plot of h ( A , D ) at fixed selected values of D. For A 1 , h ( A , D ) I 0 2 as given in Eq. (53) determined only by the effective dispersion parameter D.

Fig. 11
Fig. 11

Normalized SH amplitude is proportional to the function D I 0 ( D ) 2 and demonstrates a peak at D = 1.73 . The dashed–dotted lines indicate asymptotic behavior for D 1 where I 0 ( D ) 1 and D 1 where I 0 ( D ) 2 D .

Fig. 12
Fig. 12

Trade-off of normalized conversion efficiency (top) and beam size and quality (bottom) with optimum dispersion parameter D = 1.73 in the presence of spatial walk-off. At a fixed value of D, the spatial walk-off parameter A = L L a is increased by decreasing the beam size w 0 . The increased intensity results in higher conversion efficiency, but the resulting increase in spatial walk-off causes an increase in SH beam size and poor SH spatial mode quality. A compromise may be reached for A 3 , where the conversion efficiency reaches 71% of its maximum value, but the beam is approximately equal to the FH beam size with a beam quality parameter M 2 = 1.10 ( M 2 = 1 implies a Gaussian TEM 00 mode).

Equations (70)

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cos ϕ = K g 2 + 4 [ k ( ω ) ] 2 [ k ( 2 ω ) ] 2 4 K g k ( ω ) ,
ϕ ω ω 1 = δ ν k ( ω 1 ) θ 0 ,
δ ν = k ( ω ) ω ω 1 k ( ω ) ω ω 2 ,
ρ ω ω 2 = δ ν k ( 2 ω 1 ) θ 0 ,
1 u i = k ω ω i
ψ = arctan ( k 1 u 1 ϕ ω ω 1 ) ,
η = 2 2 π d m 2 ϵ 0 c n 2 n 1 2 λ 1 2 U 1 L 2 w x w y τ 0 ,
2 E ̂ 1 ( z , x , ω ) z 2 + 2 E ̂ 1 ( z , x , ω ) x 2 + k 2 ( ω ) E ̂ 1 ( z , x , ω ) = 0 ,
2 E ̂ 2 ( z , x , ω ) z 2 + 2 E ̂ 2 ( z , x , ω ) x 2 + k 2 ( ω ) E ̂ 2 ( z , x , ω ) = μ 0 ω 2 2 P ̂ NL ( z , x , ω ) ,
E i ( z , x , t ) = E 0 B i ( z , x , t ) exp ( i ω i t i k z , i z i k x , i x ) ,
E ̂ i ( z , x , ω ) = E 0 B ̂ i ( z , x , Ω i ) exp ( i k z , i z i k x , i x ) ,
k 2 ( ω ) k i 2 + 2 k i 1 u i Ω i + 1 u i 2 Ω i 2 + k i β i Ω i 2 ,
β i = 2 k ω 2 ω i .
d ( z , x ) d m exp ( i K g , z z + i K g , x x ) ,
P NL ( z , x , t ) = ϵ 0 d ( z , x ) E 1 2 ( z , x , t ) .
2 B 1 z 2 2 i k 1 B 1 z + 2 B 1 x 2 2 i k 1 u 1 B 1 t 1 u 1 2 2 B 1 t 2 k 1 β 1 2 B 1 t 2 = 0 ,
2 B 2 z 2 2 i k z , 2 B 2 z + 2 B 2 x 2 2 i k x , 2 B 2 x 2 i k z , 2 u 2 B 2 t 1 u 2 2 2 B 2 t 2 k 2 β 2 2 B 2 t 2 = 4 ω 1 2 d m E 0 c 2 B 1 2 exp ( i Δ k z z i Δ k x x ) .
i B 1 z ¯ 1 2 L L R , 1 2 B 1 x ¯ 2 + L L D , 1 2 B 1 T ¯ 2 = 0 ,
i B 2 z ¯ i L L g B 2 T ¯ + i L L a B 2 x ¯ 1 2 L L R , 2 2 B 2 x ¯ 2 + L L D , 2 2 B 2 T ¯ 2 c 2 B 1 2 = 0 ,
c 2 = 2 π d m E 0 L n 2 λ 1 ,
L a = w 0 tan ( θ 0 ) ,
L g = τ 0 δ ν ;
L R , i = k i w 0 2 ;
L D , i = 2 τ 0 2 β i .
γ 1 = k 1 w 0 τ 0 ϕ ( ω ) ω ω 1 ,
tan ψ = τ 0 u 1 w 0 γ 1 ,
x ¯ x ¯ γ 1 τ ¯ ,
T ¯ τ ¯ ,
2 x ¯ 2 2 x ¯ 2 + γ 1 2 2 τ ¯ 2 2 γ 1 2 x ¯ τ ¯ ,
2 T ¯ 2 2 τ ¯ 2
i B 1 z ¯ 1 2 L L R , 1 2 B 1 x ¯ 2 + L L D , 1 2 B 1 τ ¯ 2 + γ 1 L L R , 1 2 B 1 x ¯ τ ¯ = 0 ,
i B 2 z ¯ i ( L L g + γ 1 L L a ) B 2 τ ¯ + i L L a B 2 x ¯ 1 2 L L R , 2 2 B 2 x ¯ 2 + L L D , 2 2 B 2 τ ¯ 2 + γ 1 L L R , 2 2 B 2 x ¯ τ ¯ c 2 B 1 2 = 0 .
1 L D , i = 1 L D , i 1 2 γ 1 2 L R , i .
ϕ ( ω ) ω ω 1 = δ ν k 1 θ 0 ,
F ( x , τ ) = 1 2 π F ̂ ( ξ , Ω ) exp ( i Ω τ i ξ x ) d ξ d Ω ,
F ̂ ( ξ , Ω ) = 1 2 π F ( x , τ ) exp ( i Ω τ + i ξ x ) d x d τ .
i B ̂ 1 z ¯ L L D , 1 Ω ¯ 1 2 B ̂ 1 + γ 1 L L R , 1 Ω ¯ 1 ξ ¯ 1 B ̂ 1 = 0 ,
i B ̂ 2 z ¯ + L L a ξ ¯ 2 B ̂ 2 L L D , 2 Ω ¯ 2 2 B ̂ 2 + γ 1 L L R , 2 Ω ¯ 2 ξ ¯ 2 B ̂ 2 = c 2 F ̂ 2 ( z , ξ ¯ 2 , Ω ¯ 2 ) ,
F ̂ 2 ( z ¯ , ξ ¯ 2 , Ω ¯ 2 ) = 1 2 π B ̂ 1 ( z ¯ , ξ ¯ , Ω ¯ ) B ̂ 1 ( z ¯ , ξ ¯ 2 ξ ¯ , Ω ¯ 2 Ω ¯ ) d ξ ¯ d Ω ¯ .
B ̂ 1 ( z ¯ , ξ ¯ 1 , Ω ¯ 1 ) = B ̂ 0 ( ξ ¯ 1 , Ω ¯ 1 ) exp [ i ( L L D , 1 Ω ¯ 1 2 γ 1 L L R , 1 Ω ¯ 1 ξ ¯ 1 ) z ¯ ] ,
G ̂ 2 ( z ¯ , ξ ¯ 2 , Ω ¯ 2 ) = B ̂ 2 ( z ¯ , ξ ¯ 2 , Ω ¯ 2 ) exp [ i ( L L a ξ ¯ 2 L L D , 2 Ω ¯ 2 2 + γ 1 L L R , 2 Ω ¯ 2 ξ ¯ 2 ) z ¯ ] .
G ̂ 2 ( z ¯ , ξ ¯ 2 , Ω ¯ 2 ) = 1 2 1 2 i c 2 F ̂ 2 ( z , ξ ¯ 2 , Ω ¯ 2 ) exp [ i ( L L a ξ ¯ 2 L L D , 2 Ω ¯ 2 2 + γ 1 L L R , 2 Ω ¯ 2 ξ ¯ 2 ) z ¯ ] d z ¯ .
B 0 ( x ¯ , τ ¯ ) = exp ( x ¯ 2 2 τ ¯ 2 2 ) ,
B ̂ 0 ( ξ ¯ 1 , Ω ¯ 1 ) = exp ( ξ ¯ 1 2 2 Ω ¯ 1 2 2 ) .
F ̂ 2 ( z ¯ , ξ ¯ 2 , Ω ¯ 2 ) = 1 2 [ 1 + 2 i L L D , 1 z ¯ + γ 1 2 ( L L R , 1 ) 2 z ¯ 2 ] 1 2 exp [ Ω ¯ 2 2 4 ( 1 + 2 i L L D , 1 z ¯ ) ξ ¯ 2 2 4 + i γ 1 L L R , 1 Ω ¯ 2 ξ ¯ 2 z ¯ 2 ] .
G ̂ 2 ( z ¯ = 1 2 , ξ ¯ 2 , Ω ¯ 2 ) = i c 2 2 exp ( Ω ¯ 2 2 4 ξ ¯ 2 2 4 ) I 2 ( q ) ,
I 2 ( q ) = 1 2 1 2 exp ( i q z ) [ 1 + 2 i L L D , 1 z + γ 1 2 ( L L R , 1 ) 2 z 2 ] 1 2 d z ,
q = γ 1 δ R Ω ¯ 2 ξ ¯ 2 + δ D Ω ¯ 2 2 A ξ ¯ 2 .
δ R = 1 2 L L R , 1 L L R , 2 = L w 0 2 k 1 k 2 ( k 2 2 k 1 ) .
δ D = ( L L D , 2 1 2 L L D , 1 ) = L 2 τ 0 2 ( β 2 β 1 2 ) + γ 1 2 L 2 w 0 2 k 1 k 2 ( 2 k 1 k 2 ) .
A = L L a .
I 2 ( q ) = 1 2 1 2 exp ( i q z ) ( 1 2 i D z ) 1 2 d z ,
I 0 ( D ) = I 2 ( q = 0 ) = 2 I [ 1 D ( 1 i D ) 1 2 ] ,
erf ( z ) = 2 π 0 z exp ( u 2 ) d u ,
I 2 ( q ) = sgn ( q ) exp ( q 2 D ) I { ( 2 π q D ) 1 2 erf [ q 2 ( 1 D i ) ] 1 2 } ,
I 2 ( q ) sinc ( q 2 ) ,
I 2 ( q ) = sgn ( q ) ( 2 D ) 1 2 I [ ( π q ) 1 2 erf ( i q 2 ) 1 2 ] .
η = U 2 U 1 = n 2 n 1 B ̂ 2 ( z ¯ = 1 2 , ξ ¯ , Ω ¯ ) 2 d ξ ¯ d Ω ¯ B ̂ 0 ( ξ ¯ , Ω ¯ ) 2 d ξ ¯ d Ω ¯ .
c 2 2 = 8 π d m 2 ϵ 0 c n 2 2 n 1 λ 1 2 U 1 L 2 w 0 σ y τ 0 ,
η 0 = n 2 n 1 c 2 2 2 = 4 π d m 2 ϵ 0 c n 2 n 1 2 λ 1 2 U 1 L 2 w 0 σ y τ 0 .
η GVM = 38.3 d m 2 ϵ 0 c n 2 n 1 2 λ 1 2 U 1 L g 2 w 0 σ y τ 0 = 3.05 L g 2 L 2 η 0 ,
η CG = 1.37 L L g η GVM = 4.18 L g L η 0 ,
η = η 0 h ( D , A ) ,
h ( D , A ) = 1 2 π I 2 ( q ) 2 exp ( Ω ¯ 2 2 2 ξ ¯ 2 2 2 ) d Ω ¯ 2 d ξ ¯ 2 .
c 2 2 = 16 π 3 2 d m 2 L g ϵ 0 c n 2 2 n 1 1 2 λ 1 5 2 U 1 L 1 2 σ y τ 0 L L a ( L L D , 1 ) 1 2 .
η = 8 π 3 2 d m 2 L g ϵ 0 c n 2 n 1 3 2 λ 1 5 2 U 1 L 1 2 σ y τ 0 A D h ( A , D ) .
η = 79 d m 2 ϵ 0 c n 2 n 1 3 2 λ 1 5 2 δ ν U 1 L 1 2 σ y .
η opt = 141.4 d m 2 ϵ 0 c δ ν n 2 n 1 λ 1 3 U 1 .
η GVM conf = 76.7 d m 2 ϵ 0 c δ ν n 1 n 2 λ 1 3 U 1 ,
η CG conf = 1.39 η GVM conf = 106.6 d m 2 ϵ 0 c δ ν n 1 n 2 λ 1 3 U 1 ,

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