Abstract

A new method of efficient sum-frequency generation for broadband input fields is proposed and analyzed. It involves the mixing of controlled phase-modulated waves for phase matching over a broad bandwidth. Regardless of the form of the modulation, phase matching can be maintained over the whole pulse duration, provided that the ratio of the chirp parameters of the incident waves is correctly chosen, thereby driving highly efficient sum-frequency generation. The case of 1.05-μm frequency tripling with KDP crystals is analyzed in detail and is shown to be applicable to the efficient generation of either broadband nanosecond pulses or ultrashort and intense pulses at 351 nm.

© 1996 Optical Society of America

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  1. W. Seka, S. D. Jacobs, J. E. Rizzo, R. Boni, and R. S. Craxton, “Demonstration of high efficiency third harmonic conversion of high power ND glass laser radiation,” Opt. Commun. 34, 469–473 (1980).
    [CrossRef]
  2. P. J. Wegner, M. A. Henesian, D. R. Speck, C. Bibeau, R. B. Ehrlich, C. W. Laumann, J. K. Lawson, and T. L. Weiland, “Harmonic conversion of large-aperture 1.05-μ m laser beams for inertial confinement fusion research,” Appl. Opt. 31, 6414–6426 (1992).
    [CrossRef] [PubMed]
  3. R. H. Lehmberg, A. J. Schmitt, and S. E. Bodner, “Theory of induced spatial incoherence,” J. Appl. Phys. 62, 2680–2683 (1987); R. H. Lehmberg and S. P. Obenschain, “Use of induced spatial incoherence for uniform illumination of laser fusion targets,” Opt. Commun. 46, 27–31 (1983).
    [CrossRef]
  4. D. Véron, G. Thiell, and C. Gouédard, “Optical smoothing of the high power PHEBUS Nd-glass laser using the multi-mode optical fiber technique,” Opt. Commun. 97, 259–271 (1993); D. Véron, H. Ayral, C. Gouédard, D. Husson, J. Lauriou, O. Martin, B. Meyer, M. Rostaing, and C. Sauteret, “Optical smoothing of Nd-glass laser beam,” Opt. Commun. 65, 42–45 (1988).
    [CrossRef]
  5. S. Skupsky, R. W. Short, T. Kessler, R. S. Craxton, S. Letzring, and J. M. Soures, “Improved laser-beam uniformity using the angular dispersion of frequency-modulated light,” J. Appl. Phys. 66, 3456–3642 (1989).
    [CrossRef]
  6. D. M. Pennington, M. A. Henesian, S. N. Dixit, H. T. Powell, C. E. Thompson, and T. L. Weiland, “Effect of bandwidth on beam smoothing and frequency conversion at the third harmonic of the Nova laser,” in Laser Coherence Control: Technology and Applications, T. J. Kessler and H. T. Powell, eds., Proc. SPIE1870, 175–185 (1993).
  7. V. D. Volosov, S. G. Karpenko, N. E. Kornienko, and V. L. Strishevkii, “Method for compensating the phase-matching dispersion in nonlinear optics,” Sov. J. Quantum Electron. 4, 1090–1098 (1975).
    [CrossRef]
  8. V. D. Volosov and E. V. Goryachkina, “Compensation of phase-matching dispersion in generation of non monochromatic radiation harmonics. I. Doubling of neodymium– glass radiation frequency under free oscillation,” Sov. J. Quantum Electron. 6, 854–857 (1976).
    [CrossRef]
  9. M. D. Skeldon, T. J. Kessler, R. S. Craxton, S. Skupsky, W. Seka, and J. M. Soures, “Efficient third harmonic generation with a broadband laser,” in Conference on Lasers and Electro-Optics, Vol. 11 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D. C., 1989), pp. 168–170.
  10. M. D. Skeldon, R. S. Craxton, T. J. Kessler, W. Seka, R. W. Short, S. Skupsky, and J. M. Soures, “Efficient third harmonic generation with a broadband laser,” IEEE J. Quantum Electron. 28, 1389–1399 (1992).
    [CrossRef]
  11. G. Szabo and Z. Bor, “Broadband frequency doubler for femtosecond pulses,” Appl. Phys. B 50, 51–54 (1990); “Frequency conversion of ultra-short pulses,” Appl. Phys. B 58, 237–241 (1994).
    [CrossRef]
  12. Y. Wang, B. Luther-Davies, Y. H. Chuang, R. S. Craxton, and D. D. Meyerhofer, “Highly efficient conversion of picosecond Nd laser pulses with the use of group velocity mismatched frequency doubling in KDP,” Opt. Lett. 16, 1862–1864 (1991).
    [CrossRef] [PubMed]
  13. C. Radzewicz, J. S. Krasinski, and Y. B. Band, “Increased efficiency for sum-frequency generation for broadband input fields,” Opt. Lett. 18, 331–333 (1993).
    [CrossRef] [PubMed]
  14. Part of this research has been presented: A. C. L. Boscheron and C. J. Sauteret, “Mixing of chirped pulses for broadband harmonic generation,” in Proceedings of the IAEA Technical Committee Meeting on Drivers for Inertial Confinement Fusion, J. Coutant, ed. (International Atomic Energy Agency, Paris, November14–18, 1994), pp. 109–120; A. C. L. Boscheron, C. Sauteret, and A. Migus, “Efficient broadband frequency mixing using phase-modulation matching,” in First Annual International Conference on Solid-State Lasers for Application to Inertial Confinement Fusion, M. André and H. T. Powell, eds., Proc. SPIE2633, 494–500 (1995).
    [CrossRef]
  15. C. P. Page, “Instantaneous power spectra,” J. Appl. Phys. 23, 103–106 (1952).
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  16. J. H. Eberly and K. Wodkiewicz, “The time dependent physical spectrum of light,” J. Opt. Soc. Am. 67, 1252–1261 (1977).
    [CrossRef]
  17. A. A. Altes, “Detection, estimation and classification with spectrograms,” J. Acoust. Soc. Am. 67, 1232–1246 (1980).
    [CrossRef]
  18. W. Koenig, H. K. Dunn, and L. Y. Lacy, “The sound spectrograph,” J. Acoust. Soc. Am. 18, 19–49 (1946).
    [CrossRef]
  19. J. Paye, “The chronocycle representation of ultra-short light pulses,” IEEE J. Quantum. Electron. 28, 2262–2273 (1992).
    [CrossRef]
  20. J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
    [CrossRef]
  21. R. C. Eckardt and J. Reintjes, “Phase matching limitations of high efficiency second harmonic generation,” IEEE J. Quantum Electron. 20, 1178–1187 (1984).
    [CrossRef]
  22. R. W. Short and S. Skupsky, “Frequency conversion of broad band bandwidth laser light,” IEEE J. Quantum Electron. 26, 580–588 (1990).
    [CrossRef]
  23. B. H. Kolner, “Space–time duality and the theory of temporal imaging,” IEEE J. Quantum Electron. 30, 1951–1963 (1994).
    [CrossRef]
  24. H. Nakatsuka, D. Grischkowsky, and A. C. Balant, “Nonlinear picosecond-pulse propagation through optical fiber with positive group-velocity dispersion,” Phys. Rev. Lett. 47, 910–913 (1981).
    [CrossRef]
  25. R. N. Thurston, J. P. Heritage, A. K. M. Weiner, and J. W. J. Tomlinson, “Analysis of picosecond pulse shape synthesis by spectral masking in a grating pulse compressor,” IEEE J. Quantum Electron. 22, 682–696 (1986).
    [CrossRef]
  26. F. Zernike, “Refractive indices of ammonium dihydrogen phosphate and potassium dihydrogen phosphate between 2000 Å and 1.5 μ m,” J. Opt. Soc. Am. 54, 1215–1220 (1964).
    [CrossRef]
  27. D. Eimerl, “Electro-optic, linear and nonlinear optical properties of KDP and its isomorph,” Ferroelectrics 72, 95–139 (1987).
    [CrossRef]
  28. M. S. Webb, D. Eimerl, and S. P. Velsko, “Wavelength insensitive phasematched second-harmonic generation in partially deuterated KDP,” J. Opt. Soc. Am. B 9, 1118–1127 (1992).
    [CrossRef]
  29. A. Morimoto and T. Kobayashi, “Temporal coherence control by electrooptic phase modulation,” in First Annual International Conference on Solid-State Lasers for Application to Inertial Confinement Fusion, M. André and H. T. Powell, eds., Proc. SPIE2633, 622–626 (1995).
    [CrossRef]
  30. J. Sauteret, T. Duvillier, and A. Adolf, “Harmonic generation with noncollinear laser beams. Application to pulse stacking,” Opt. Commun. 44, 135–138 (1982).
    [CrossRef]
  31. R. S. Craxton, “High efficiency tripling schemes for high power Nd glass lasers,” IEEE J. Quantum Electron. 17, 1771–1782 (1981).
    [CrossRef]
  32. J. Paye, J.-L. Bruneau, and P. Coffin, “Protection of final optics in megajoule-class lasers by steering of UV beams using diffraction gratings,” in First Annual International Conference on Solid-State Lasers for Application to Inertial Confinement Fusion, M. André and H. T. Powell, eds., Proc. SPIE2633, 116–120 (1995).
    [CrossRef]
  33. N. Blanchot, C. Rouyer, C. Sauteret, and A. Migus, “Amplification of sub-100-TW femtosecond pulses by shifted amplifying media: theory and experiments,” Opt. Lett. 20, 395–397 (1995).
    [CrossRef]

1995 (1)

1994 (1)

B. H. Kolner, “Space–time duality and the theory of temporal imaging,” IEEE J. Quantum Electron. 30, 1951–1963 (1994).
[CrossRef]

1993 (2)

D. Véron, G. Thiell, and C. Gouédard, “Optical smoothing of the high power PHEBUS Nd-glass laser using the multi-mode optical fiber technique,” Opt. Commun. 97, 259–271 (1993); D. Véron, H. Ayral, C. Gouédard, D. Husson, J. Lauriou, O. Martin, B. Meyer, M. Rostaing, and C. Sauteret, “Optical smoothing of Nd-glass laser beam,” Opt. Commun. 65, 42–45 (1988).
[CrossRef]

C. Radzewicz, J. S. Krasinski, and Y. B. Band, “Increased efficiency for sum-frequency generation for broadband input fields,” Opt. Lett. 18, 331–333 (1993).
[CrossRef] [PubMed]

1992 (4)

P. J. Wegner, M. A. Henesian, D. R. Speck, C. Bibeau, R. B. Ehrlich, C. W. Laumann, J. K. Lawson, and T. L. Weiland, “Harmonic conversion of large-aperture 1.05-μ m laser beams for inertial confinement fusion research,” Appl. Opt. 31, 6414–6426 (1992).
[CrossRef] [PubMed]

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

M. D. Skeldon, R. S. Craxton, T. J. Kessler, W. Seka, R. W. Short, S. Skupsky, and J. M. Soures, “Efficient third harmonic generation with a broadband laser,” IEEE J. Quantum Electron. 28, 1389–1399 (1992).
[CrossRef]

J. Paye, “The chronocycle representation of ultra-short light pulses,” IEEE J. Quantum. Electron. 28, 2262–2273 (1992).
[CrossRef]

1991 (1)

1990 (2)

R. W. Short and S. Skupsky, “Frequency conversion of broad band bandwidth laser light,” IEEE J. Quantum Electron. 26, 580–588 (1990).
[CrossRef]

G. Szabo and Z. Bor, “Broadband frequency doubler for femtosecond pulses,” Appl. Phys. B 50, 51–54 (1990); “Frequency conversion of ultra-short pulses,” Appl. Phys. B 58, 237–241 (1994).
[CrossRef]

1989 (1)

S. Skupsky, R. W. Short, T. Kessler, R. S. Craxton, S. Letzring, and J. M. Soures, “Improved laser-beam uniformity using the angular dispersion of frequency-modulated light,” J. Appl. Phys. 66, 3456–3642 (1989).
[CrossRef]

1987 (2)

R. H. Lehmberg, A. J. Schmitt, and S. E. Bodner, “Theory of induced spatial incoherence,” J. Appl. Phys. 62, 2680–2683 (1987); R. H. Lehmberg and S. P. Obenschain, “Use of induced spatial incoherence for uniform illumination of laser fusion targets,” Opt. Commun. 46, 27–31 (1983).
[CrossRef]

D. Eimerl, “Electro-optic, linear and nonlinear optical properties of KDP and its isomorph,” Ferroelectrics 72, 95–139 (1987).
[CrossRef]

1986 (1)

R. N. Thurston, J. P. Heritage, A. K. M. Weiner, and J. W. J. Tomlinson, “Analysis of picosecond pulse shape synthesis by spectral masking in a grating pulse compressor,” IEEE J. Quantum Electron. 22, 682–696 (1986).
[CrossRef]

1984 (1)

R. C. Eckardt and J. Reintjes, “Phase matching limitations of high efficiency second harmonic generation,” IEEE J. Quantum Electron. 20, 1178–1187 (1984).
[CrossRef]

1982 (1)

J. Sauteret, T. Duvillier, and A. Adolf, “Harmonic generation with noncollinear laser beams. Application to pulse stacking,” Opt. Commun. 44, 135–138 (1982).
[CrossRef]

1981 (2)

R. S. Craxton, “High efficiency tripling schemes for high power Nd glass lasers,” IEEE J. Quantum Electron. 17, 1771–1782 (1981).
[CrossRef]

H. Nakatsuka, D. Grischkowsky, and A. C. Balant, “Nonlinear picosecond-pulse propagation through optical fiber with positive group-velocity dispersion,” Phys. Rev. Lett. 47, 910–913 (1981).
[CrossRef]

1980 (2)

W. Seka, S. D. Jacobs, J. E. Rizzo, R. Boni, and R. S. Craxton, “Demonstration of high efficiency third harmonic conversion of high power ND glass laser radiation,” Opt. Commun. 34, 469–473 (1980).
[CrossRef]

A. A. Altes, “Detection, estimation and classification with spectrograms,” J. Acoust. Soc. Am. 67, 1232–1246 (1980).
[CrossRef]

1977 (1)

1976 (1)

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

1975 (1)

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

1964 (1)

1962 (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

1952 (1)

C. P. Page, “Instantaneous power spectra,” J. Appl. Phys. 23, 103–106 (1952).
[CrossRef]

1946 (1)

W. Koenig, H. K. Dunn, and L. Y. Lacy, “The sound spectrograph,” J. Acoust. Soc. Am. 18, 19–49 (1946).
[CrossRef]

Adolf, A.

J. Sauteret, T. Duvillier, and A. Adolf, “Harmonic generation with noncollinear laser beams. Application to pulse stacking,” Opt. Commun. 44, 135–138 (1982).
[CrossRef]

Altes, A. A.

A. A. Altes, “Detection, estimation and classification with spectrograms,” J. Acoust. Soc. Am. 67, 1232–1246 (1980).
[CrossRef]

Armstrong, J. A.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Balant, A. C.

H. Nakatsuka, D. Grischkowsky, and A. C. Balant, “Nonlinear picosecond-pulse propagation through optical fiber with positive group-velocity dispersion,” Phys. Rev. Lett. 47, 910–913 (1981).
[CrossRef]

Band, Y. B.

Bibeau, C.

Blanchot, N.

Bloembergen, N.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Bodner, S. E.

R. H. Lehmberg, A. J. Schmitt, and S. E. Bodner, “Theory of induced spatial incoherence,” J. Appl. Phys. 62, 2680–2683 (1987); R. H. Lehmberg and S. P. Obenschain, “Use of induced spatial incoherence for uniform illumination of laser fusion targets,” Opt. Commun. 46, 27–31 (1983).
[CrossRef]

Boni, R.

W. Seka, S. D. Jacobs, J. E. Rizzo, R. Boni, and R. S. Craxton, “Demonstration of high efficiency third harmonic conversion of high power ND glass laser radiation,” Opt. Commun. 34, 469–473 (1980).
[CrossRef]

Bor, Z.

G. Szabo and Z. Bor, “Broadband frequency doubler for femtosecond pulses,” Appl. Phys. B 50, 51–54 (1990); “Frequency conversion of ultra-short pulses,” Appl. Phys. B 58, 237–241 (1994).
[CrossRef]

Boscheron, A. C. L.

Part of this research has been presented: A. C. L. Boscheron and C. J. Sauteret, “Mixing of chirped pulses for broadband harmonic generation,” in Proceedings of the IAEA Technical Committee Meeting on Drivers for Inertial Confinement Fusion, J. Coutant, ed. (International Atomic Energy Agency, Paris, November14–18, 1994), pp. 109–120; A. C. L. Boscheron, C. Sauteret, and A. Migus, “Efficient broadband frequency mixing using phase-modulation matching,” in First Annual International Conference on Solid-State Lasers for Application to Inertial Confinement Fusion, M. André and H. T. Powell, eds., Proc. SPIE2633, 494–500 (1995).
[CrossRef]

Bruneau, J.-L.

J. Paye, J.-L. Bruneau, and P. Coffin, “Protection of final optics in megajoule-class lasers by steering of UV beams using diffraction gratings,” in First Annual International Conference on Solid-State Lasers for Application to Inertial Confinement Fusion, M. André and H. T. Powell, eds., Proc. SPIE2633, 116–120 (1995).
[CrossRef]

Chuang, Y. H.

Coffin, P.

J. Paye, J.-L. Bruneau, and P. Coffin, “Protection of final optics in megajoule-class lasers by steering of UV beams using diffraction gratings,” in First Annual International Conference on Solid-State Lasers for Application to Inertial Confinement Fusion, M. André and H. T. Powell, eds., Proc. SPIE2633, 116–120 (1995).
[CrossRef]

Craxton, R. S.

M. D. Skeldon, R. S. Craxton, T. J. Kessler, W. Seka, R. W. Short, S. Skupsky, and J. M. Soures, “Efficient third harmonic generation with a broadband laser,” IEEE J. Quantum Electron. 28, 1389–1399 (1992).
[CrossRef]

Y. Wang, B. Luther-Davies, Y. H. Chuang, R. S. Craxton, and D. D. Meyerhofer, “Highly efficient conversion of picosecond Nd laser pulses with the use of group velocity mismatched frequency doubling in KDP,” Opt. Lett. 16, 1862–1864 (1991).
[CrossRef] [PubMed]

S. Skupsky, R. W. Short, T. Kessler, R. S. Craxton, S. Letzring, and J. M. Soures, “Improved laser-beam uniformity using the angular dispersion of frequency-modulated light,” J. Appl. Phys. 66, 3456–3642 (1989).
[CrossRef]

R. S. Craxton, “High efficiency tripling schemes for high power Nd glass lasers,” IEEE J. Quantum Electron. 17, 1771–1782 (1981).
[CrossRef]

W. Seka, S. D. Jacobs, J. E. Rizzo, R. Boni, and R. S. Craxton, “Demonstration of high efficiency third harmonic conversion of high power ND glass laser radiation,” Opt. Commun. 34, 469–473 (1980).
[CrossRef]

M. D. Skeldon, T. J. Kessler, R. S. Craxton, S. Skupsky, W. Seka, and J. M. Soures, “Efficient third harmonic generation with a broadband laser,” in Conference on Lasers and Electro-Optics, Vol. 11 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D. C., 1989), pp. 168–170.

Dixit, S. N.

D. M. Pennington, M. A. Henesian, S. N. Dixit, H. T. Powell, C. E. Thompson, and T. L. Weiland, “Effect of bandwidth on beam smoothing and frequency conversion at the third harmonic of the Nova laser,” in Laser Coherence Control: Technology and Applications, T. J. Kessler and H. T. Powell, eds., Proc. SPIE1870, 175–185 (1993).

Ducuing, J.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Dunn, H. K.

W. Koenig, H. K. Dunn, and L. Y. Lacy, “The sound spectrograph,” J. Acoust. Soc. Am. 18, 19–49 (1946).
[CrossRef]

Duvillier, T.

J. Sauteret, T. Duvillier, and A. Adolf, “Harmonic generation with noncollinear laser beams. Application to pulse stacking,” Opt. Commun. 44, 135–138 (1982).
[CrossRef]

Eberly, J. H.

Eckardt, R. C.

R. C. Eckardt and J. Reintjes, “Phase matching limitations of high efficiency second harmonic generation,” IEEE J. Quantum Electron. 20, 1178–1187 (1984).
[CrossRef]

Ehrlich, R. B.

Eimerl, D.

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

D. Eimerl, “Electro-optic, linear and nonlinear optical properties of KDP and its isomorph,” Ferroelectrics 72, 95–139 (1987).
[CrossRef]

Goryachkina, E. V.

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

Gouédard, C.

D. Véron, G. Thiell, and C. Gouédard, “Optical smoothing of the high power PHEBUS Nd-glass laser using the multi-mode optical fiber technique,” Opt. Commun. 97, 259–271 (1993); D. Véron, H. Ayral, C. Gouédard, D. Husson, J. Lauriou, O. Martin, B. Meyer, M. Rostaing, and C. Sauteret, “Optical smoothing of Nd-glass laser beam,” Opt. Commun. 65, 42–45 (1988).
[CrossRef]

Grischkowsky, D.

H. Nakatsuka, D. Grischkowsky, and A. C. Balant, “Nonlinear picosecond-pulse propagation through optical fiber with positive group-velocity dispersion,” Phys. Rev. Lett. 47, 910–913 (1981).
[CrossRef]

Henesian, M. A.

P. J. Wegner, M. A. Henesian, D. R. Speck, C. Bibeau, R. B. Ehrlich, C. W. Laumann, J. K. Lawson, and T. L. Weiland, “Harmonic conversion of large-aperture 1.05-μ m laser beams for inertial confinement fusion research,” Appl. Opt. 31, 6414–6426 (1992).
[CrossRef] [PubMed]

D. M. Pennington, M. A. Henesian, S. N. Dixit, H. T. Powell, C. E. Thompson, and T. L. Weiland, “Effect of bandwidth on beam smoothing and frequency conversion at the third harmonic of the Nova laser,” in Laser Coherence Control: Technology and Applications, T. J. Kessler and H. T. Powell, eds., Proc. SPIE1870, 175–185 (1993).

Heritage, J. P.

R. N. Thurston, J. P. Heritage, A. K. M. Weiner, and J. W. J. Tomlinson, “Analysis of picosecond pulse shape synthesis by spectral masking in a grating pulse compressor,” IEEE J. Quantum Electron. 22, 682–696 (1986).
[CrossRef]

Jacobs, S. D.

W. Seka, S. D. Jacobs, J. E. Rizzo, R. Boni, and R. S. Craxton, “Demonstration of high efficiency third harmonic conversion of high power ND glass laser radiation,” Opt. Commun. 34, 469–473 (1980).
[CrossRef]

Karpenko, S. G.

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

Kessler, T.

S. Skupsky, R. W. Short, T. Kessler, R. S. Craxton, S. Letzring, and J. M. Soures, “Improved laser-beam uniformity using the angular dispersion of frequency-modulated light,” J. Appl. Phys. 66, 3456–3642 (1989).
[CrossRef]

Kessler, T. J.

M. D. Skeldon, R. S. Craxton, T. J. Kessler, W. Seka, R. W. Short, S. Skupsky, and J. M. Soures, “Efficient third harmonic generation with a broadband laser,” IEEE J. Quantum Electron. 28, 1389–1399 (1992).
[CrossRef]

M. D. Skeldon, T. J. Kessler, R. S. Craxton, S. Skupsky, W. Seka, and J. M. Soures, “Efficient third harmonic generation with a broadband laser,” in Conference on Lasers and Electro-Optics, Vol. 11 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D. C., 1989), pp. 168–170.

Kobayashi, T.

A. Morimoto and T. Kobayashi, “Temporal coherence control by electrooptic phase modulation,” in First Annual International Conference on Solid-State Lasers for Application to Inertial Confinement Fusion, M. André and H. T. Powell, eds., Proc. SPIE2633, 622–626 (1995).
[CrossRef]

Koenig, W.

W. Koenig, H. K. Dunn, and L. Y. Lacy, “The sound spectrograph,” J. Acoust. Soc. Am. 18, 19–49 (1946).
[CrossRef]

Kolner, B. H.

B. H. Kolner, “Space–time duality and the theory of temporal imaging,” IEEE J. Quantum Electron. 30, 1951–1963 (1994).
[CrossRef]

Kornienko, N. E.

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

Krasinski, J. S.

Lacy, L. Y.

W. Koenig, H. K. Dunn, and L. Y. Lacy, “The sound spectrograph,” J. Acoust. Soc. Am. 18, 19–49 (1946).
[CrossRef]

Laumann, C. W.

Lawson, J. K.

Lehmberg, R. H.

R. H. Lehmberg, A. J. Schmitt, and S. E. Bodner, “Theory of induced spatial incoherence,” J. Appl. Phys. 62, 2680–2683 (1987); R. H. Lehmberg and S. P. Obenschain, “Use of induced spatial incoherence for uniform illumination of laser fusion targets,” Opt. Commun. 46, 27–31 (1983).
[CrossRef]

Letzring, S.

S. Skupsky, R. W. Short, T. Kessler, R. S. Craxton, S. Letzring, and J. M. Soures, “Improved laser-beam uniformity using the angular dispersion of frequency-modulated light,” J. Appl. Phys. 66, 3456–3642 (1989).
[CrossRef]

Luther-Davies, B.

Meyerhofer, D. D.

Migus, A.

Morimoto, A.

A. Morimoto and T. Kobayashi, “Temporal coherence control by electrooptic phase modulation,” in First Annual International Conference on Solid-State Lasers for Application to Inertial Confinement Fusion, M. André and H. T. Powell, eds., Proc. SPIE2633, 622–626 (1995).
[CrossRef]

Nakatsuka, H.

H. Nakatsuka, D. Grischkowsky, and A. C. Balant, “Nonlinear picosecond-pulse propagation through optical fiber with positive group-velocity dispersion,” Phys. Rev. Lett. 47, 910–913 (1981).
[CrossRef]

Page, C. P.

C. P. Page, “Instantaneous power spectra,” J. Appl. Phys. 23, 103–106 (1952).
[CrossRef]

Paye, J.

J. Paye, “The chronocycle representation of ultra-short light pulses,” IEEE J. Quantum. Electron. 28, 2262–2273 (1992).
[CrossRef]

J. Paye, J.-L. Bruneau, and P. Coffin, “Protection of final optics in megajoule-class lasers by steering of UV beams using diffraction gratings,” in First Annual International Conference on Solid-State Lasers for Application to Inertial Confinement Fusion, M. André and H. T. Powell, eds., Proc. SPIE2633, 116–120 (1995).
[CrossRef]

Pennington, D. M.

D. M. Pennington, M. A. Henesian, S. N. Dixit, H. T. Powell, C. E. Thompson, and T. L. Weiland, “Effect of bandwidth on beam smoothing and frequency conversion at the third harmonic of the Nova laser,” in Laser Coherence Control: Technology and Applications, T. J. Kessler and H. T. Powell, eds., Proc. SPIE1870, 175–185 (1993).

Pershan, P. S.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Powell, H. T.

D. M. Pennington, M. A. Henesian, S. N. Dixit, H. T. Powell, C. E. Thompson, and T. L. Weiland, “Effect of bandwidth on beam smoothing and frequency conversion at the third harmonic of the Nova laser,” in Laser Coherence Control: Technology and Applications, T. J. Kessler and H. T. Powell, eds., Proc. SPIE1870, 175–185 (1993).

Radzewicz, C.

Reintjes, J.

R. C. Eckardt and J. Reintjes, “Phase matching limitations of high efficiency second harmonic generation,” IEEE J. Quantum Electron. 20, 1178–1187 (1984).
[CrossRef]

Rizzo, J. E.

W. Seka, S. D. Jacobs, J. E. Rizzo, R. Boni, and R. S. Craxton, “Demonstration of high efficiency third harmonic conversion of high power ND glass laser radiation,” Opt. Commun. 34, 469–473 (1980).
[CrossRef]

Rouyer, C.

Sauteret, C.

Sauteret, C. J.

Part of this research has been presented: A. C. L. Boscheron and C. J. Sauteret, “Mixing of chirped pulses for broadband harmonic generation,” in Proceedings of the IAEA Technical Committee Meeting on Drivers for Inertial Confinement Fusion, J. Coutant, ed. (International Atomic Energy Agency, Paris, November14–18, 1994), pp. 109–120; A. C. L. Boscheron, C. Sauteret, and A. Migus, “Efficient broadband frequency mixing using phase-modulation matching,” in First Annual International Conference on Solid-State Lasers for Application to Inertial Confinement Fusion, M. André and H. T. Powell, eds., Proc. SPIE2633, 494–500 (1995).
[CrossRef]

Sauteret, J.

J. Sauteret, T. Duvillier, and A. Adolf, “Harmonic generation with noncollinear laser beams. Application to pulse stacking,” Opt. Commun. 44, 135–138 (1982).
[CrossRef]

Schmitt, A. J.

R. H. Lehmberg, A. J. Schmitt, and S. E. Bodner, “Theory of induced spatial incoherence,” J. Appl. Phys. 62, 2680–2683 (1987); R. H. Lehmberg and S. P. Obenschain, “Use of induced spatial incoherence for uniform illumination of laser fusion targets,” Opt. Commun. 46, 27–31 (1983).
[CrossRef]

Seka, W.

M. D. Skeldon, R. S. Craxton, T. J. Kessler, W. Seka, R. W. Short, S. Skupsky, and J. M. Soures, “Efficient third harmonic generation with a broadband laser,” IEEE J. Quantum Electron. 28, 1389–1399 (1992).
[CrossRef]

W. Seka, S. D. Jacobs, J. E. Rizzo, R. Boni, and R. S. Craxton, “Demonstration of high efficiency third harmonic conversion of high power ND glass laser radiation,” Opt. Commun. 34, 469–473 (1980).
[CrossRef]

M. D. Skeldon, T. J. Kessler, R. S. Craxton, S. Skupsky, W. Seka, and J. M. Soures, “Efficient third harmonic generation with a broadband laser,” in Conference on Lasers and Electro-Optics, Vol. 11 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D. C., 1989), pp. 168–170.

Short, R. W.

M. D. Skeldon, R. S. Craxton, T. J. Kessler, W. Seka, R. W. Short, S. Skupsky, and J. M. Soures, “Efficient third harmonic generation with a broadband laser,” IEEE J. Quantum Electron. 28, 1389–1399 (1992).
[CrossRef]

R. W. Short and S. Skupsky, “Frequency conversion of broad band bandwidth laser light,” IEEE J. Quantum Electron. 26, 580–588 (1990).
[CrossRef]

S. Skupsky, R. W. Short, T. Kessler, R. S. Craxton, S. Letzring, and J. M. Soures, “Improved laser-beam uniformity using the angular dispersion of frequency-modulated light,” J. Appl. Phys. 66, 3456–3642 (1989).
[CrossRef]

Skeldon, M. D.

M. D. Skeldon, R. S. Craxton, T. J. Kessler, W. Seka, R. W. Short, S. Skupsky, and J. M. Soures, “Efficient third harmonic generation with a broadband laser,” IEEE J. Quantum Electron. 28, 1389–1399 (1992).
[CrossRef]

M. D. Skeldon, T. J. Kessler, R. S. Craxton, S. Skupsky, W. Seka, and J. M. Soures, “Efficient third harmonic generation with a broadband laser,” in Conference on Lasers and Electro-Optics, Vol. 11 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D. C., 1989), pp. 168–170.

Skupsky, S.

M. D. Skeldon, R. S. Craxton, T. J. Kessler, W. Seka, R. W. Short, S. Skupsky, and J. M. Soures, “Efficient third harmonic generation with a broadband laser,” IEEE J. Quantum Electron. 28, 1389–1399 (1992).
[CrossRef]

R. W. Short and S. Skupsky, “Frequency conversion of broad band bandwidth laser light,” IEEE J. Quantum Electron. 26, 580–588 (1990).
[CrossRef]

S. Skupsky, R. W. Short, T. Kessler, R. S. Craxton, S. Letzring, and J. M. Soures, “Improved laser-beam uniformity using the angular dispersion of frequency-modulated light,” J. Appl. Phys. 66, 3456–3642 (1989).
[CrossRef]

M. D. Skeldon, T. J. Kessler, R. S. Craxton, S. Skupsky, W. Seka, and J. M. Soures, “Efficient third harmonic generation with a broadband laser,” in Conference on Lasers and Electro-Optics, Vol. 11 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D. C., 1989), pp. 168–170.

Soures, J. M.

M. D. Skeldon, R. S. Craxton, T. J. Kessler, W. Seka, R. W. Short, S. Skupsky, and J. M. Soures, “Efficient third harmonic generation with a broadband laser,” IEEE J. Quantum Electron. 28, 1389–1399 (1992).
[CrossRef]

S. Skupsky, R. W. Short, T. Kessler, R. S. Craxton, S. Letzring, and J. M. Soures, “Improved laser-beam uniformity using the angular dispersion of frequency-modulated light,” J. Appl. Phys. 66, 3456–3642 (1989).
[CrossRef]

M. D. Skeldon, T. J. Kessler, R. S. Craxton, S. Skupsky, W. Seka, and J. M. Soures, “Efficient third harmonic generation with a broadband laser,” in Conference on Lasers and Electro-Optics, Vol. 11 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D. C., 1989), pp. 168–170.

Speck, D. R.

Strishevkii, V. L.

V. D. Volosov, S. G. Karpenko, N. E. Kornienko, and V. L. Strishevkii, “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); “Frequency conversion of ultra-short pulses,” Appl. Phys. B 58, 237–241 (1994).
[CrossRef]

Thiell, G.

D. Véron, G. Thiell, and C. Gouédard, “Optical smoothing of the high power PHEBUS Nd-glass laser using the multi-mode optical fiber technique,” Opt. Commun. 97, 259–271 (1993); D. Véron, H. Ayral, C. Gouédard, D. Husson, J. Lauriou, O. Martin, B. Meyer, M. Rostaing, and C. Sauteret, “Optical smoothing of Nd-glass laser beam,” Opt. Commun. 65, 42–45 (1988).
[CrossRef]

Thompson, C. E.

D. M. Pennington, M. A. Henesian, S. N. Dixit, H. T. Powell, C. E. Thompson, and T. L. Weiland, “Effect of bandwidth on beam smoothing and frequency conversion at the third harmonic of the Nova laser,” in Laser Coherence Control: Technology and Applications, T. J. Kessler and H. T. Powell, eds., Proc. SPIE1870, 175–185 (1993).

Thurston, R. N.

R. N. Thurston, J. P. Heritage, A. K. M. Weiner, and J. W. J. Tomlinson, “Analysis of picosecond pulse shape synthesis by spectral masking in a grating pulse compressor,” IEEE J. Quantum Electron. 22, 682–696 (1986).
[CrossRef]

Tomlinson, J. W. J.

R. N. Thurston, J. P. Heritage, A. K. M. Weiner, and J. W. J. Tomlinson, “Analysis of picosecond pulse shape synthesis by spectral masking in a grating pulse compressor,” IEEE J. Quantum Electron. 22, 682–696 (1986).
[CrossRef]

Velsko, S. P.

Véron, D.

D. Véron, G. Thiell, and C. Gouédard, “Optical smoothing of the high power PHEBUS Nd-glass laser using the multi-mode optical fiber technique,” Opt. Commun. 97, 259–271 (1993); D. Véron, H. Ayral, C. Gouédard, D. Husson, J. Lauriou, O. Martin, B. Meyer, M. Rostaing, and C. Sauteret, “Optical smoothing of Nd-glass laser beam,” Opt. Commun. 65, 42–45 (1988).
[CrossRef]

Volosov, V. D.

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

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

Wang, Y.

Webb, M. S.

Wegner, P. J.

Weiland, T. L.

P. J. Wegner, M. A. Henesian, D. R. Speck, C. Bibeau, R. B. Ehrlich, C. W. Laumann, J. K. Lawson, and T. L. Weiland, “Harmonic conversion of large-aperture 1.05-μ m laser beams for inertial confinement fusion research,” Appl. Opt. 31, 6414–6426 (1992).
[CrossRef] [PubMed]

D. M. Pennington, M. A. Henesian, S. N. Dixit, H. T. Powell, C. E. Thompson, and T. L. Weiland, “Effect of bandwidth on beam smoothing and frequency conversion at the third harmonic of the Nova laser,” in Laser Coherence Control: Technology and Applications, T. J. Kessler and H. T. Powell, eds., Proc. SPIE1870, 175–185 (1993).

Weiner, A. K. M.

R. N. Thurston, J. P. Heritage, A. K. M. Weiner, and J. W. J. Tomlinson, “Analysis of picosecond pulse shape synthesis by spectral masking in a grating pulse compressor,” IEEE J. Quantum Electron. 22, 682–696 (1986).
[CrossRef]

Wodkiewicz, K.

Zernike, F.

Appl. Opt. (1)

Appl. Phys. B (1)

G. Szabo and Z. Bor, “Broadband frequency doubler for femtosecond pulses,” Appl. Phys. B 50, 51–54 (1990); “Frequency conversion of ultra-short pulses,” Appl. Phys. B 58, 237–241 (1994).
[CrossRef]

Ferroelectrics (1)

D. Eimerl, “Electro-optic, linear and nonlinear optical properties of KDP and its isomorph,” Ferroelectrics 72, 95–139 (1987).
[CrossRef]

IEEE J. Quantum Electron. (6)

R. S. Craxton, “High efficiency tripling schemes for high power Nd glass lasers,” IEEE J. Quantum Electron. 17, 1771–1782 (1981).
[CrossRef]

R. C. Eckardt and J. Reintjes, “Phase matching limitations of high efficiency second harmonic generation,” IEEE J. Quantum Electron. 20, 1178–1187 (1984).
[CrossRef]

R. W. Short and S. Skupsky, “Frequency conversion of broad band bandwidth laser light,” IEEE J. Quantum Electron. 26, 580–588 (1990).
[CrossRef]

B. H. Kolner, “Space–time duality and the theory of temporal imaging,” IEEE J. Quantum Electron. 30, 1951–1963 (1994).
[CrossRef]

R. N. Thurston, J. P. Heritage, A. K. M. Weiner, and J. W. J. Tomlinson, “Analysis of picosecond pulse shape synthesis by spectral masking in a grating pulse compressor,” IEEE J. Quantum Electron. 22, 682–696 (1986).
[CrossRef]

M. D. Skeldon, R. S. Craxton, T. J. Kessler, W. Seka, R. W. Short, S. Skupsky, and J. M. Soures, “Efficient third harmonic generation with a broadband laser,” IEEE J. Quantum Electron. 28, 1389–1399 (1992).
[CrossRef]

IEEE J. Quantum. Electron. (1)

J. Paye, “The chronocycle representation of ultra-short light pulses,” IEEE J. Quantum. Electron. 28, 2262–2273 (1992).
[CrossRef]

J. Acoust. Soc. Am. (2)

A. A. Altes, “Detection, estimation and classification with spectrograms,” J. Acoust. Soc. Am. 67, 1232–1246 (1980).
[CrossRef]

W. Koenig, H. K. Dunn, and L. Y. Lacy, “The sound spectrograph,” J. Acoust. Soc. Am. 18, 19–49 (1946).
[CrossRef]

J. Appl. Phys. (3)

C. P. Page, “Instantaneous power spectra,” J. Appl. Phys. 23, 103–106 (1952).
[CrossRef]

R. H. Lehmberg, A. J. Schmitt, and S. E. Bodner, “Theory of induced spatial incoherence,” J. Appl. Phys. 62, 2680–2683 (1987); R. H. Lehmberg and S. P. Obenschain, “Use of induced spatial incoherence for uniform illumination of laser fusion targets,” Opt. Commun. 46, 27–31 (1983).
[CrossRef]

S. Skupsky, R. W. Short, T. Kessler, R. S. Craxton, S. Letzring, and J. M. Soures, “Improved laser-beam uniformity using the angular dispersion of frequency-modulated light,” J. Appl. Phys. 66, 3456–3642 (1989).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. B (1)

Opt. Commun. (3)

J. Sauteret, T. Duvillier, and A. Adolf, “Harmonic generation with noncollinear laser beams. Application to pulse stacking,” Opt. Commun. 44, 135–138 (1982).
[CrossRef]

D. Véron, G. Thiell, and C. Gouédard, “Optical smoothing of the high power PHEBUS Nd-glass laser using the multi-mode optical fiber technique,” Opt. Commun. 97, 259–271 (1993); D. Véron, H. Ayral, C. Gouédard, D. Husson, J. Lauriou, O. Martin, B. Meyer, M. Rostaing, and C. Sauteret, “Optical smoothing of Nd-glass laser beam,” Opt. Commun. 65, 42–45 (1988).
[CrossRef]

W. Seka, S. D. Jacobs, J. E. Rizzo, R. Boni, and R. S. Craxton, “Demonstration of high efficiency third harmonic conversion of high power ND glass laser radiation,” Opt. Commun. 34, 469–473 (1980).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Phys. Rev. Lett. (1)

H. Nakatsuka, D. Grischkowsky, and A. C. Balant, “Nonlinear picosecond-pulse propagation through optical fiber with positive group-velocity dispersion,” Phys. Rev. Lett. 47, 910–913 (1981).
[CrossRef]

Sov. J. Quantum Electron. (2)

V. D. Volosov, S. G. Karpenko, N. E. Kornienko, and V. L. Strishevkii, “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 non monochromatic radiation harmonics. I. Doubling of neodymium– glass radiation frequency under free oscillation,” Sov. J. Quantum Electron. 6, 854–857 (1976).
[CrossRef]

Other (5)

M. D. Skeldon, T. J. Kessler, R. S. Craxton, S. Skupsky, W. Seka, and J. M. Soures, “Efficient third harmonic generation with a broadband laser,” in Conference on Lasers and Electro-Optics, Vol. 11 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D. C., 1989), pp. 168–170.

D. M. Pennington, M. A. Henesian, S. N. Dixit, H. T. Powell, C. E. Thompson, and T. L. Weiland, “Effect of bandwidth on beam smoothing and frequency conversion at the third harmonic of the Nova laser,” in Laser Coherence Control: Technology and Applications, T. J. Kessler and H. T. Powell, eds., Proc. SPIE1870, 175–185 (1993).

Part of this research has been presented: A. C. L. Boscheron and C. J. Sauteret, “Mixing of chirped pulses for broadband harmonic generation,” in Proceedings of the IAEA Technical Committee Meeting on Drivers for Inertial Confinement Fusion, J. Coutant, ed. (International Atomic Energy Agency, Paris, November14–18, 1994), pp. 109–120; A. C. L. Boscheron, C. Sauteret, and A. Migus, “Efficient broadband frequency mixing using phase-modulation matching,” in First Annual International Conference on Solid-State Lasers for Application to Inertial Confinement Fusion, M. André and H. T. Powell, eds., Proc. SPIE2633, 494–500 (1995).
[CrossRef]

A. Morimoto and T. Kobayashi, “Temporal coherence control by electrooptic phase modulation,” in First Annual International Conference on Solid-State Lasers for Application to Inertial Confinement Fusion, M. André and H. T. Powell, eds., Proc. SPIE2633, 622–626 (1995).
[CrossRef]

J. Paye, J.-L. Bruneau, and P. Coffin, “Protection of final optics in megajoule-class lasers by steering of UV beams using diffraction gratings,” in First Annual International Conference on Solid-State Lasers for Application to Inertial Confinement Fusion, M. André and H. T. Powell, eds., Proc. SPIE2633, 116–120 (1995).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Loci of the couple (ω1, ω2) for sum-frequency phase matching with constant angle θPM(ω1, ω2) = 59.07° for a Type II KDP tripler. The inset is a magnified portion of that curve showing the domain Dk of phase matching, with ω0 an arbitrary central frequency.

Fig. 2
Fig. 2

Experimental setup for sine PM4PM broadband frequency tripling.

Fig. 3
Fig. 3

Experimental setup for quadratic PM4PM broadband frequency tripling.

Fig. 4
Fig. 4

Quadratic PM4PM scheme with noncollinear frequency geometry and pulse-stacking technique.

Fig. 5
Fig. 5

Intensity profile at 3 ω for a 5-GW/cm2 3-ns square pulse chirped with a 1.2-nm bandwidth converted through a 1.9-cm Type I doubler and a 1-cm Type II tripler and a 3.5-GW/cm2 3-ns square pulse chirped with a 3-nm bandwidth doubled with a 1.9-cm Type I doubler and mixed for PM4PM adaptation with a 1.5-GW/cm2 3-ns square pulse chirped with a −1.2 nm bandwidth in a 1-cm Type II tripler.

Fig. 6
Fig. 6

Frequency-tripling efficiency comparison of monochromatic, chirped, and quadratic PM4PM adapted pulses.

Tables (4)

Tables Icon

Table 1 Type I KDP Doubler Data for PM4PM

Tables Icon

Table 2 Type II KDP Doubler Data for PM4PM

Tables Icon

Table 3 Type I KDP Tripler Data for PM4PM

Tables Icon

Table 4 Type II KDP Tripler Data for PM4PM

Equations (27)

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Δ k ( t ) = k 3 [ ω 3 ( t ) ] k 1 [ ω 1 ( t ) ] k 2 [ ω 2 ( t ) ] ,
ω 3 ( t ) = ω 1 ( t ) + ω 2 ( t ) .
Δ k ( t ) = k 3 Δ ω 3 k 1 Δ ω 1 k 2 Δ ω 2 = Δ ω 2 ( k 3 k 2 ) + Δ ω 1 ( k 3 k 1 ) ,
Δ ω 1 Δ ω 2 = k 3 k 2 k 3 k 1 ,
Δ ϕ ( t ) = L 2 Δ k ( t ) = ½ ( Δ t 31 Δ ω 1 + Δ t 32 Δ ω 2 ) ,
Δ t 3 i = L ( k 3 k i ) , i = 1 , 2
Δ ϕ ( t ) = ½ [ Δ t 31 δ ω 1 ( t ) + Δ t 32 δ ω 2 ( t ) ] .
| Δ t 31 Δ T δ ω 1 ( t ) + Δ t 32 Δ T δ ω 2 ( t ) | < K Δ T ,
Δ T = ( Δ t 31 2 + Δ t 32 2 ) 1 / 2
i ( z , t ) = Re { E i ( z , t ) exp [ i Φ i ( z , t ) ] exp [ i ( ω i t k i z ) ] } ,
Φ i ( z , t ) = b i f ( t k i z ) .
E 1 * z + k 1 E 1 * t i E 1 * ( Φ 1 z + k 1 Φ 1 t ) = i ω 1 c n 1 d eff E 2 E 3 * exp [ i Δ Φ ( z , t ) ] , E 2 * z + k 2 E 2 * t i E 2 * ( Φ 2 z + k 2 Φ 2 t ) = i ω 2 c n 2 d eff E 1 E 3 * exp [ i Δ Φ ( z , t ) ] , E 3 z + k 3 E 3 t + i E 3 ( Φ 3 z + k 3 Φ 3 t ) = i ω 3 c n 3 d eff E 1 E 2 exp [ i Δ Φ ( z , t ) ] .
ω i ( t ) ω i 0 = Φ i t | t = 0 ,
b 3 = b 1 + b 2 ,
k i ( t ) k i 0 = Φ i z | t = 0 ,
k 3 b 3 = k 1 b 1 + k 2 b 2 .
b 1 b 2 = k 3 k 2 k 3 k 1 ,
Δ Φ ( z , t ) Δ Φ ( 0 , t ) + d Δ Φ d z | z = 0 z + 1 2 d 2 Δ Φ d 2 z | z = 0 z 2 .
Δ Φ ( z , t ) z 2 2 b 1 ( k 3 k 1 ) ( k 1 k 2 ) d 2 f ( x ) d x 2 | x = t + ( k 3 k 1 ) z .
Φ j ( z , t ) = b j sin [ Ω ( t k j z ) ] .
Ω L 2 π { 1 [ ( k 3 k 1 ) 2 + ( k 3 k 2 ) 2 ] } 1 / 2 ,
Ω L b i 1 / 2 | 4 π ( k 3 k 1 ) ( k 3 k 2 ) | 1 / 2 .
Δ Φ ( z , t ) z 2 2 Ω 2 b 1 ( k 3 k 1 ) ( k 1 k 2 ) × sin { Ω [ t + ( k 3 k 1 ) z ] } .
Φ j ( z , t ) = b j ( t k j z ) 2 .
E ˜ ( ω ω 0 ) = + E ( t ) exp [ i Φ ( z , t ) ] exp [ i ( ω ω 0 ) t ] d t ,
ω j ( t ) ω j 0 = Φ ( z , t ) t | z = 0 = 2 b j t ,
Δ Φ ( L , t ) b 1 ( k 3 k 1 ) ( k 1 k 2 ) L 2 2 π ,

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