Abstract

We report on a novel scheme for generating a broad spectrum in the UV region. This scheme enables us to control the phase of the UV pulse through a frequency-mixing process in a nonlinear crystal. For group velocity matching, it is essential that a monochromatic beam should be sum-frequency mixed with an angularly dispersed beam having a broad spectrum in noncollinear geometry. We found analytically unique solutions for a noncollinear angle, for an angular dispersion of the broadband input beam, and for an angle of the beam from the optical axis in a nonlinear crystal, with the condition that there is no angular dispersion in the output beam. Based on the analysis of this scheme, we obtained UV pulses with a sufficiently broad spectrum for obtaining a sub-20-fs pulsewidths in the experiment. The improvement of conversion efficiency and compensation of chirp are also discussed.

© 2003 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  27. K. Varjú, A. P. Kovács, G. Kurdi, and K. Osvay, “High-precision measurement of angular dispersion in a cpa laser,” Appl. Phys. B [Suppl.],  74, S259–S263 (2002).
    [CrossRef]

2002 (6)

J. Degert, W. Wohlleben, B. Chatel, M. Motzkus, and B. Girard, “Realization of a Time-Domain Frensel Lens with Coherent Control,” Phys. Rev. Lett. 89, 203003-1–203003-4 (2002).
[CrossRef] [PubMed]

A. Baltŭska and T. Kobayashi, “Adaptive shaping of two-cycle visible pulses using a flexible mirror,” Appl. Phys. B 75, 427– 443 (2002).
[CrossRef]

K. Varjú, A. P. Kovács, G. Kurdi, and K. Osvay, “High-precision measurement of angular dispersion in a cpa laser,” Appl. Phys. B [Suppl.],  74, S259–S263 (2002).
[CrossRef]

H.-S. Tan, E. Schreiber, and W. S. Warren, “High-resolution indirect pulse shaping by parametric transfer,” Opt. Lett. 27, 439–441 (2002).
[CrossRef]

Y. Nabekawa, Y. Shimizu, and K. Midorikawa, “Sub-20-fs terawatt-class laser system with a mirrorless regenerative amplifier and an adaptive phase controller,” Opt. Lett. 27, 1265–1267 (2002).
[CrossRef]

I. N. Ross, P. Matousek, G. H. C. New, and K. Osvay, “Analysis and optimization of optical parametric chirped pulse amplification,” J. Opt. Soc. Am. B,  19, 2945– 2956 (2002).
[CrossRef]

2001 (5)

M. Hacker, T. Feurer, R. Sauerbrey, T. Lucza, and G. Szabó, “Programmable femtosecond laser pulses in the ultraviolet,” J. Opt. Soc. Am. B 18, 866– 871 (2001).
[CrossRef]

N. Dudovich, B. Dayan, S. M. Gallagher, and Y. Silberberg, “Transform-Limited Pulses Are Not Optimal for Resonant Mutiphoton Transition,” Phys. Rev. Lett. 86, 47–50 (2001).
[CrossRef] [PubMed]

Y. Nabekawa, D. Yoshitomi, T. Sekikawa, and S. Watanabe, “High-Average-Power Femtosecond KrF Excimer Laser,” IEEE J. Select. Topics Quantum Electron. 7, 551–558 (2001).
[CrossRef]

M. Hacker, R. Netz, M. Roth, G. Stobrawa, T. Feurer, and R. Sauerbrey, “Frequency doubling of phase-modulated, ultrashort laser pulses,”  Appl. Phys. B 73, 273– 277 (2001).

A. Suda, Y. Oishi, K. Nagasaka, P. Wang, and K. Midorikawa, “A spatial light modulator based on fused-silica plates for adaptive feedback control of intense femtosecond laser pulses,” Opt. xpress. 9, 2–6 (2001). http://www.opticsinfobase.org/ViewMedia.cfm?id=64680&seq=0.
[CrossRef]

2000 (2)

1999 (2)

T. Nakajima and K. Miyazaki, “Spectrally compensated third harmonic generation using angular dispersers,” Opt. Commun. 163, 217– 222 (1999).
[CrossRef]

B. A. Richman, S. E. Bisson, R. Trebino, E. Sidick, and A. Jacobson, “All-prism achromatic phase matching for tunable second-harmonic generation,” Appl. Opt. 38, 3316– 3323 (1999).
[CrossRef]

1997 (1)

1996 (1)

1994 (2)

1993 (1)

Y. Nabekawa, K. Kondo, N. Sarukura, K. Sajiki, and S. Watanabe, “Terrawatt KrF/Ti:sapphire hybrid laser system,” Opt. Lett. 22, 1922–1924 (1993).
[CrossRef]

1992 (3)

1990 (1)

G. Szabó and Z. Bor, “Broadband Frequency Doubler for Femtosecond Pulses,” Appl. Phys. B 50, 51– 54 (1990).
[CrossRef]

1987 (1)

D. Eimerl, L. Davis, S. Velsco, E. K. Graham, and A. Zalkin, “Optical, mechanical, and thermal properties of barium borate,” J. Appl. Phys. 62, 1968–1983 (1987).
[CrossRef]

1986 (1)

K. Kato, “Second-Harmonic Generation to 2048 Å in β-BaB2O4,” IEEE J. Quantum Electron. 22, 1013–1014 (1986).
[CrossRef]

1979 (1)

Baltuska, A.

A. Baltŭska and T. Kobayashi, “Adaptive shaping of two-cycle visible pulses using a flexible mirror,” Appl. Phys. B 75, 427– 443 (2002).
[CrossRef]

Bisson, S. E.

Bor, Z.

G. Szabó and Z. Bor, “Frequency Conversion of Ultrashort Pulses,” Appl. Phys. B 58, 237–241 (1994).
[CrossRef]

G. Szabó and Z. Bor, “Broadband Frequency Doubler for Femtosecond Pulses,” Appl. Phys. B 50, 51– 54 (1990).
[CrossRef]

Chatel, B.

J. Degert, W. Wohlleben, B. Chatel, M. Motzkus, and B. Girard, “Realization of a Time-Domain Frensel Lens with Coherent Control,” Phys. Rev. Lett. 89, 203003-1–203003-4 (2002).
[CrossRef] [PubMed]

Cheng, Z.

Cheville, R. A.

Davis, L.

D. Eimerl, L. Davis, S. Velsco, E. K. Graham, and A. Zalkin, “Optical, mechanical, and thermal properties of barium borate,” J. Appl. Phys. 62, 1968–1983 (1987).
[CrossRef]

Dayan, B.

N. Dudovich, B. Dayan, S. M. Gallagher, and Y. Silberberg, “Transform-Limited Pulses Are Not Optimal for Resonant Mutiphoton Transition,” Phys. Rev. Lett. 86, 47–50 (2001).
[CrossRef] [PubMed]

Degert, J.

J. Degert, W. Wohlleben, B. Chatel, M. Motzkus, and B. Girard, “Realization of a Time-Domain Frensel Lens with Coherent Control,” Phys. Rev. Lett. 89, 203003-1–203003-4 (2002).
[CrossRef] [PubMed]

Dubeitis, A.

A. Dubeitis, G. Jonasauskas, and A. Piskarskas, “Powerful femtosecond pulse generation by chirped and stretched pulse parametric amplification in BBO crystal,” Opt. Commun. 88, 437–440 (1992).
[CrossRef]

Dudovich, N.

N. Dudovich, B. Dayan, S. M. Gallagher, and Y. Silberberg, “Transform-Limited Pulses Are Not Optimal for Resonant Mutiphoton Transition,” Phys. Rev. Lett. 86, 47–50 (2001).
[CrossRef] [PubMed]

Eimerl, D.

D. Eimerl, L. Davis, S. Velsco, E. K. Graham, and A. Zalkin, “Optical, mechanical, and thermal properties of barium borate,” J. Appl. Phys. 62, 1968–1983 (1987).
[CrossRef]

Feurer, T.

M. Hacker, R. Netz, M. Roth, G. Stobrawa, T. Feurer, and R. Sauerbrey, “Frequency doubling of phase-modulated, ultrashort laser pulses,”  Appl. Phys. B 73, 273– 277 (2001).

M. Hacker, T. Feurer, R. Sauerbrey, T. Lucza, and G. Szabó, “Programmable femtosecond laser pulses in the ultraviolet,” J. Opt. Soc. Am. B 18, 866– 871 (2001).
[CrossRef]

Gallagher, S. M.

N. Dudovich, B. Dayan, S. M. Gallagher, and Y. Silberberg, “Transform-Limited Pulses Are Not Optimal for Resonant Mutiphoton Transition,” Phys. Rev. Lett. 86, 47–50 (2001).
[CrossRef] [PubMed]

Girard, B.

J. Degert, W. Wohlleben, B. Chatel, M. Motzkus, and B. Girard, “Realization of a Time-Domain Frensel Lens with Coherent Control,” Phys. Rev. Lett. 89, 203003-1–203003-4 (2002).
[CrossRef] [PubMed]

Graham, E. K.

D. Eimerl, L. Davis, S. Velsco, E. K. Graham, and A. Zalkin, “Optical, mechanical, and thermal properties of barium borate,” J. Appl. Phys. 62, 1968–1983 (1987).
[CrossRef]

Hacker, M.

M. Hacker, R. Netz, M. Roth, G. Stobrawa, T. Feurer, and R. Sauerbrey, “Frequency doubling of phase-modulated, ultrashort laser pulses,”  Appl. Phys. B 73, 273– 277 (2001).

M. Hacker, T. Feurer, R. Sauerbrey, T. Lucza, and G. Szabó, “Programmable femtosecond laser pulses in the ultraviolet,” J. Opt. Soc. Am. B 18, 866– 871 (2001).
[CrossRef]

Halas, N. J.

Hofmann, T.

Jacobson, A.

Jonasauskas, G.

A. Dubeitis, G. Jonasauskas, and A. Piskarskas, “Powerful femtosecond pulse generation by chirped and stretched pulse parametric amplification in BBO crystal,” Opt. Commun. 88, 437–440 (1992).
[CrossRef]

Kato, K.

K. Kato, “Second-Harmonic Generation to 2048 Å in β-BaB2O4,” IEEE J. Quantum Electron. 22, 1013–1014 (1986).
[CrossRef]

Kittelmann, O.

Kobayashi, T.

A. Baltŭska and T. Kobayashi, “Adaptive shaping of two-cycle visible pulses using a flexible mirror,” Appl. Phys. B 75, 427– 443 (2002).
[CrossRef]

Kondo, K.

Y. Nabekawa, K. Kondo, N. Sarukura, K. Sajiki, and S. Watanabe, “Terrawatt KrF/Ti:sapphire hybrid laser system,” Opt. Lett. 22, 1922–1924 (1993).
[CrossRef]

Kovács, A. P.

K. Varjú, A. P. Kovács, G. Kurdi, and K. Osvay, “High-precision measurement of angular dispersion in a cpa laser,” Appl. Phys. B [Suppl.],  74, S259–S263 (2002).
[CrossRef]

Kurdi, G.

K. Varjú, A. P. Kovács, G. Kurdi, and K. Osvay, “High-precision measurement of angular dispersion in a cpa laser,” Appl. Phys. B [Suppl.],  74, S259–S263 (2002).
[CrossRef]

Laude, V.

Lucza, T.

Matousek, P.

Midorikawa, K.

Y. Nabekawa, Y. Shimizu, and K. Midorikawa, “Sub-20-fs terawatt-class laser system with a mirrorless regenerative amplifier and an adaptive phase controller,” Opt. Lett. 27, 1265–1267 (2002).
[CrossRef]

A. Suda, Y. Oishi, K. Nagasaka, P. Wang, and K. Midorikawa, “A spatial light modulator based on fused-silica plates for adaptive feedback control of intense femtosecond laser pulses,” Opt. xpress. 9, 2–6 (2001). http://www.opticsinfobase.org/ViewMedia.cfm?id=64680&seq=0.
[CrossRef]

Miyazaki, K.

T. Nakajima and K. Miyazaki, “Spectrally compensated third harmonic generation using angular dispersers,” Opt. Commun. 163, 217– 222 (1999).
[CrossRef]

Mossavi, K.

Motzkus, M.

J. Degert, W. Wohlleben, B. Chatel, M. Motzkus, and B. Girard, “Realization of a Time-Domain Frensel Lens with Coherent Control,” Phys. Rev. Lett. 89, 203003-1–203003-4 (2002).
[CrossRef] [PubMed]

Nabekawa, Y.

Y. Nabekawa, Y. Shimizu, and K. Midorikawa, “Sub-20-fs terawatt-class laser system with a mirrorless regenerative amplifier and an adaptive phase controller,” Opt. Lett. 27, 1265–1267 (2002).
[CrossRef]

Y. Nabekawa, D. Yoshitomi, T. Sekikawa, and S. Watanabe, “High-Average-Power Femtosecond KrF Excimer Laser,” IEEE J. Select. Topics Quantum Electron. 7, 551–558 (2001).
[CrossRef]

Y. Nabekawa, K. Kondo, N. Sarukura, K. Sajiki, and S. Watanabe, “Terrawatt KrF/Ti:sapphire hybrid laser system,” Opt. Lett. 22, 1922–1924 (1993).
[CrossRef]

Nagasaka, K.

A. Suda, Y. Oishi, K. Nagasaka, P. Wang, and K. Midorikawa, “A spatial light modulator based on fused-silica plates for adaptive feedback control of intense femtosecond laser pulses,” Opt. xpress. 9, 2–6 (2001). http://www.opticsinfobase.org/ViewMedia.cfm?id=64680&seq=0.
[CrossRef]

Nakajima, T.

T. Nakajima and K. Miyazaki, “Spectrally compensated third harmonic generation using angular dispersers,” Opt. Commun. 163, 217– 222 (1999).
[CrossRef]

Netz, R.

M. Hacker, R. Netz, M. Roth, G. Stobrawa, T. Feurer, and R. Sauerbrey, “Frequency doubling of phase-modulated, ultrashort laser pulses,”  Appl. Phys. B 73, 273– 277 (2001).

New, G. H. C.

Noack, F.

Oishi, Y.

A. Suda, Y. Oishi, K. Nagasaka, P. Wang, and K. Midorikawa, “A spatial light modulator based on fused-silica plates for adaptive feedback control of intense femtosecond laser pulses,” Opt. xpress. 9, 2–6 (2001). http://www.opticsinfobase.org/ViewMedia.cfm?id=64680&seq=0.
[CrossRef]

Osvay, K.

Ouw, D.

Petrov, V.

Piel, J.

Piskarskas, A.

A. Dubeitis, G. Jonasauskas, and A. Piskarskas, “Powerful femtosecond pulse generation by chirped and stretched pulse parametric amplification in BBO crystal,” Opt. Commun. 88, 437–440 (1992).
[CrossRef]

Reiten, M. T.

Richman, B. A.

Riedle, E.

Ringling, J.

Ross, I. N.

Roth, M.

M. Hacker, R. Netz, M. Roth, G. Stobrawa, T. Feurer, and R. Sauerbrey, “Frequency doubling of phase-modulated, ultrashort laser pulses,”  Appl. Phys. B 73, 273– 277 (2001).

Saikan, S.

Sajiki, K.

Y. Nabekawa, K. Kondo, N. Sarukura, K. Sajiki, and S. Watanabe, “Terrawatt KrF/Ti:sapphire hybrid laser system,” Opt. Lett. 22, 1922–1924 (1993).
[CrossRef]

Sarukura, N.

Y. Nabekawa, K. Kondo, N. Sarukura, K. Sajiki, and S. Watanabe, “Terrawatt KrF/Ti:sapphire hybrid laser system,” Opt. Lett. 22, 1922–1924 (1993).
[CrossRef]

Sauerbrey, R.

M. Hacker, R. Netz, M. Roth, G. Stobrawa, T. Feurer, and R. Sauerbrey, “Frequency doubling of phase-modulated, ultrashort laser pulses,”  Appl. Phys. B 73, 273– 277 (2001).

M. Hacker, T. Feurer, R. Sauerbrey, T. Lucza, and G. Szabó, “Programmable femtosecond laser pulses in the ultraviolet,” J. Opt. Soc. Am. B 18, 866– 871 (2001).
[CrossRef]

Schäfer, F. P.

Schreiber, E.

Seifert, F.

Sekikawa, T.

Y. Nabekawa, D. Yoshitomi, T. Sekikawa, and S. Watanabe, “High-Average-Power Femtosecond KrF Excimer Laser,” IEEE J. Select. Topics Quantum Electron. 7, 551–558 (2001).
[CrossRef]

Shimizu, Y.

Sidick, E.

Silberberg, Y.

N. Dudovich, B. Dayan, S. M. Gallagher, and Y. Silberberg, “Transform-Limited Pulses Are Not Optimal for Resonant Mutiphoton Transition,” Phys. Rev. Lett. 86, 47–50 (2001).
[CrossRef] [PubMed]

Spielmann, C.

Stobrawa, G.

M. Hacker, R. Netz, M. Roth, G. Stobrawa, T. Feurer, and R. Sauerbrey, “Frequency doubling of phase-modulated, ultrashort laser pulses,”  Appl. Phys. B 73, 273– 277 (2001).

Suda, A.

A. Suda, Y. Oishi, K. Nagasaka, P. Wang, and K. Midorikawa, “A spatial light modulator based on fused-silica plates for adaptive feedback control of intense femtosecond laser pulses,” Opt. xpress. 9, 2–6 (2001). http://www.opticsinfobase.org/ViewMedia.cfm?id=64680&seq=0.
[CrossRef]

Szabó, G.

Tan, H.-S.

Tittel, F. K.

Tournois, P.

Trebino, R.

Varjú, K.

K. Varjú, A. P. Kovács, G. Kurdi, and K. Osvay, “High-precision measurement of angular dispersion in a cpa laser,” Appl. Phys. B [Suppl.],  74, S259–S263 (2002).
[CrossRef]

Velsco, S.

D. Eimerl, L. Davis, S. Velsco, E. K. Graham, and A. Zalkin, “Optical, mechanical, and thermal properties of barium borate,” J. Appl. Phys. 62, 1968–1983 (1987).
[CrossRef]

Verluise, F.

Wang, P.

A. Suda, Y. Oishi, K. Nagasaka, P. Wang, and K. Midorikawa, “A spatial light modulator based on fused-silica plates for adaptive feedback control of intense femtosecond laser pulses,” Opt. xpress. 9, 2–6 (2001). http://www.opticsinfobase.org/ViewMedia.cfm?id=64680&seq=0.
[CrossRef]

Warren, W. S.

Watanabe, S.

Y. Nabekawa, D. Yoshitomi, T. Sekikawa, and S. Watanabe, “High-Average-Power Femtosecond KrF Excimer Laser,” IEEE J. Select. Topics Quantum Electron. 7, 551–558 (2001).
[CrossRef]

Y. Nabekawa, K. Kondo, N. Sarukura, K. Sajiki, and S. Watanabe, “Terrawatt KrF/Ti:sapphire hybrid laser system,” Opt. Lett. 22, 1922–1924 (1993).
[CrossRef]

Weiner, A. M.

A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum. 71, 1929–1960 (2000).
[CrossRef]

Wilhelm, T.

Wohlleben, W.

J. Degert, W. Wohlleben, B. Chatel, M. Motzkus, and B. Girard, “Realization of a Time-Domain Frensel Lens with Coherent Control,” Phys. Rev. Lett. 89, 203003-1–203003-4 (2002).
[CrossRef] [PubMed]

Yoshitomi, D.

Y. Nabekawa, D. Yoshitomi, T. Sekikawa, and S. Watanabe, “High-Average-Power Femtosecond KrF Excimer Laser,” IEEE J. Select. Topics Quantum Electron. 7, 551–558 (2001).
[CrossRef]

Zalkin, A.

D. Eimerl, L. Davis, S. Velsco, E. K. Graham, and A. Zalkin, “Optical, mechanical, and thermal properties of barium borate,” J. Appl. Phys. 62, 1968–1983 (1987).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. B (4)

A. Baltŭska and T. Kobayashi, “Adaptive shaping of two-cycle visible pulses using a flexible mirror,” Appl. Phys. B 75, 427– 443 (2002).
[CrossRef]

G. Szabó and Z. Bor, “Frequency Conversion of Ultrashort Pulses,” Appl. Phys. B 58, 237–241 (1994).
[CrossRef]

G. Szabó and Z. Bor, “Broadband Frequency Doubler for Femtosecond Pulses,” Appl. Phys. B 50, 51– 54 (1990).
[CrossRef]

K. Varjú, A. P. Kovács, G. Kurdi, and K. Osvay, “High-precision measurement of angular dispersion in a cpa laser,” Appl. Phys. B [Suppl.],  74, S259–S263 (2002).
[CrossRef]

IEEE J. Quantum Electron. (1)

K. Kato, “Second-Harmonic Generation to 2048 Å in β-BaB2O4,” IEEE J. Quantum Electron. 22, 1013–1014 (1986).
[CrossRef]

IEEE J. Select. Topics Quantum Electron. (1)

Y. Nabekawa, D. Yoshitomi, T. Sekikawa, and S. Watanabe, “High-Average-Power Femtosecond KrF Excimer Laser,” IEEE J. Select. Topics Quantum Electron. 7, 551–558 (2001).
[CrossRef]

J. Appl. Phys. (1)

D. Eimerl, L. Davis, S. Velsco, E. K. Graham, and A. Zalkin, “Optical, mechanical, and thermal properties of barium borate,” J. Appl. Phys. 62, 1968–1983 (1987).
[CrossRef]

J. Opt. Soc. Am. B (3)

Opt. Commun. (2)

T. Nakajima and K. Miyazaki, “Spectrally compensated third harmonic generation using angular dispersers,” Opt. Commun. 163, 217– 222 (1999).
[CrossRef]

A. Dubeitis, G. Jonasauskas, and A. Piskarskas, “Powerful femtosecond pulse generation by chirped and stretched pulse parametric amplification in BBO crystal,” Opt. Commun. 88, 437–440 (1992).
[CrossRef]

Opt. Lett. (8)

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[CrossRef]

F. Verluise, V. Laude, Z. Cheng, C. Spielmann, and P. Tournois, “Amplitude and phase control of ultrashort pulses by use of an acousto-optic programmable dispersive filter: pulse compression and shaping,” Opt. Lett. 25, 575–577 (2000).
[CrossRef]

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[CrossRef] [PubMed]

F. Seifert, J. Ringling, F. Noack, V. Petrov, and O. Kittelmann, “Generation of tunable femtosecond pulses to as low as 172.7 nm by sum-frequency mixing in lithium triborate,” Opt. Lett. 19, 1538–1540 (1994).
[CrossRef] [PubMed]

T. Wilhelm, J. Piel, and E. Riedle, “Sub-20-fs pulses tunable across the visible from a blue-pumped single-pass noncollinear parametric converter,” Opt. Lett. 22, 1494– 1496 (1997).
[CrossRef]

T. Hofmann, K. Mossavi, F. K. Tittel, and G. Szabó, “Spectrally compensated sum-frequency mixing scheme for generation of broadband radiation at 193 nm,” Opt. Lett. 17, 1691– 1693 (1992).
[CrossRef]

H.-S. Tan, E. Schreiber, and W. S. Warren, “High-resolution indirect pulse shaping by parametric transfer,” Opt. Lett. 27, 439–441 (2002).
[CrossRef]

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[CrossRef]

Opt. xpress. (1)

A. Suda, Y. Oishi, K. Nagasaka, P. Wang, and K. Midorikawa, “A spatial light modulator based on fused-silica plates for adaptive feedback control of intense femtosecond laser pulses,” Opt. xpress. 9, 2–6 (2001). http://www.opticsinfobase.org/ViewMedia.cfm?id=64680&seq=0.
[CrossRef]

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[CrossRef] [PubMed]

Rev. Sci. Instrum. (1)

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[CrossRef]

Other (1)

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Figures (7)

Fig. 1.
Fig. 1.

(a) Phase matching (wave-vector matching) in NOPA. (b) Noncollinear angularly dispersed wave-vector matching in sum-frequency mixing.

Fig. 2.
Fig. 2.

Definitions of angles. An angle of κ b and that of κ c from κ a0 are defined as α ab and α ac , respectively. A sign of the angle is plus when the direction of the angle is the same as that of the angle of κ a0 vector from z-(optical) axis. This figure shows these angles at the center angular frequencies of ω b0 and ω c0 . Angularly dispersed wave-vector components in beam B are schematically shown as three arrows with different directions and lengths. The wave-vector of the monochromatic beam, κ a0 , and that of the generated beam at the center angular frequency, κ c0 , are far from the optical axis with the angles θ a0 and θ c0 , respectively. The direction of the wave vector of the generated beam, κ c , generally depends on the angular frequency, ω c , although in this figure we depict the ends of the three arrows for κ c c ) as being aligned.

Fig. 3.
Fig. 3.

Wave-vector mismatches to the wavelength of Ti:sapphire laser, Δκ b )L, in collinear (brown dotted curve) and noncollinear angularly dispersed geometries (red dot-dashed curve and blue solid curve) for Type I (a) and for Type II (b) SFM in a BBO crystal. Wavelength of the monochromatic beam is set to be 532 nm. The acceptable power spectra as the functions of the wavelength of the Ti:sapphire laser, |η(λ b )|2, are also shown below the wave-vector mismatches. The slight tilt of the crystal from the complete WVMC (blue solid curves) broadened the bandwidth in spite of a central dip.

Fig. 4.
Fig. 4.

Experimental setup for NADG for GVMC.

Fig. 5.
Fig. 5.

Spectra of the input Ti:sapphire laser pulse (a) and the UV pulse (b) with respect to wavelengths of λ b and λ c .

Fig. 6.
Fig. 6.

Power spectra of the input Ti:sapphire laser pulse (red, dotted curve) and UV pulse (blue, solid curve). Bottom and top axes correspond to the optical frequency of UV, νUV=c c , and the Ti:sapphire laser, νTiS=c b , respectively. A brown, dotdashed curve is the spectrum of the Ti:sapphire laser filtered with an acceptable power spectrum.

Fig. 7.
Fig. 7.

Energy of UV pulse (solid circles) and pulse shape of the second harmonic of the Nd:YAG laser.

Equations (32)

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E ˜ 3 ( ω ) d ω E ˜ 1 ( ω ) E ˜ 2 ( ω ω ) .
E ˜ 1 ( ω ) A 1 δ ( ω ω 1 0 ) ,
E ˜ 3 ( ω ) E ˜ 2 ( ω ω 1 0 ) ,
Δ k k c ( ω c ) { k a ( ω a ) + k b ( ω b ) } ,
ω c = ω a + ω b .
Δ k = k c ( ω c 0 ) { k a ( ω a 0 ) + k b ( ω b 0 ) }
+ { d k c d ω c | 0 d k b d ω b | 0 } Δ ω + O ( Δ ω 2 ) .
0 = k c ( ω c 0 ) { k a ( ω a 0 ) + k b ( ω b 0 ) } ,
0 = d k c d ω c | 0 d k b d ω b | 0 ,
k a ( ω a ) = k a ( ω a 0 ) = k a 0 e a 0 ,
k b ( ω b ) = k b ( ω b ) cos { α ab ( ω b ) } e a 0 + k b ( ω b ) sin { α ab ( ω b ) } e b 0 ,
k c ( ω c ) = k c ( ω c ) cos { α ac ( ω c ) } e a 0 + k c ( ω c ) sin { α ac ( ω c ) } e b 0 ,
k c 0 cos ( α ac 0 ) { k a 0 + k b 0 cos ( α ab 0 ) } = 0 ,
k c 0 sin ( α ac 0 ) k b 0 sin ( α ab 0 ) = 0 ,
d k b d ω b | 0 cos ( α ab 0 ) k b 0 sin ( α ab 0 ) d α ab d ω b | 0
{ d k c d ω c | 0 cos ( α ac 0 ) k c 0 sin ( α ac 0 ) d α ac d ω c | 0 } = 0 ,
d k b d ω b | 0 sin ( α ab 0 ) + k b 0 cos ( α ab 0 ) d α ab d ω b | 0
{ d k c d ω c | 0 sin ( α ac 0 ) + k c 0 cos ( α ac 0 ) d α ac d ω c | 0 } = 0 ,
d α ac d ω c | 0 0 ,
υ g 0 b cos ( α ab 0 α ac 0 ) = υ g 0 c ,
υ g 0 b = ( d k b d ω b | 0 ) −1 ,
υ g 0 c = ( d k c d ω c | 0 ) −1 .
d α ab d ω b | 0 gvm = tan ( α ab 0 gvm α ac 0 gvm ) 1 k b 0 d k b d ω b | 0 gvm ,
sin θ c 0 = { [ n o ( ω c 0 ) n ¯ ab 0 ( α ab 0 ) ] 2 1 [ n o ( ω c 0 ) n e ( ω c 0 ) ] 2 1 } 1 2 ,
n ¯ ab 0 ( α ab 0 )
{ [ ω bc 0 n o ( ω b 0 ) sin α ab 0 ] 2 + [ ω ac 0 n o ( ω a 0 ) + ω bc 0 n o ( ω b 0 ) cos α ab 0 ] 2 } 1 2 ,
η ( ω a 0 , ω b ) L −1 0 L d ζ e i Δ k ( ω a 0 , ω b ) ζ
= e i Δ k ( ω a 0 , ω b ) L 2 sinc { Δ k ( ω a 0 , ω b ) L 2 } ,
d eff I = [ d 11 cos ( 3 φ ) d 22 sin ( 3 φ ) ] cos θ c 0 + d 31 sin θ c 0
d 11 cos ( 3 φ ) cos θ c 0 ,
d eff II = d 11 cos θ a 0 cos θ c 0 sin ( 3 φ ) + d 22 cos θ a 0 cos θ c 0 cos ( 3 φ )
d 11 cos θ a 0 cos θ c 0 sin ( 3 φ ) ,

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