Abstract

We show by experiment and mathematical model that angular and frequency acceptance bandwidths for frequency mixing in a nonlinear crystal can often be improved by segmenting the crystal and reversing the spatial or temporal walk-off in alternating segments. We analyze nonlinear mixing primarily in real space, (x, t), rather than Fourier space, (k, ω), and show that acceptance bands for sum- and difference-frequency mixing can be increased by up to a factor equal to the number of crystal segments. We consider both high- and low-efficiency mixing as well as parametric gain, and show that in many cases of practical interest the increased bandwidth substantially improves conversion efficiency. We also attempt to clarify the role of acceptance bandwidths in frequency mixing.

© 1998 Optical Society of America

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  8. L. K. Samanta, T. Tanagawa, and Y. Yamamoto, “Technique for enhanced second harmonic output power,” Opt. Commun. 76, 250–252 (1990).
    [CrossRef]
  9. M. Watanabe, K. Hayasaka, H. Imajo, and S. Urabe, “Continuous-wave sum-frequency generation near 194 nm with collinear double enhancement cavity,” Opt. Commun. 97, 225–227 (1993).
    [CrossRef]
  10. W. R. Bosenberg, W. S. Pelouch, and C. L. Tang, “High-efficiency and narrow-linewidth operation of a two-crystal β-BaB-2O-4 optical parametric oscillator,” Appl. Phys. Lett. 55, 1952–1954 (1989).
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    [CrossRef]
  30. R. C. Eckardt and J. Reintjes, “Phase matching limitations of high efficiency second harmonic generation,” IEEE J. Quantum Electron. QE-20, 1178–1187 (1984).
    [CrossRef]
  31. D. R. White, E. L. Dawes, and J. H. Marburger, “Theory of second-harmonic generation with high-conversion efficiency,” IEEE J. Quantum Electron. QE-6, 793–796 (1970).
    [CrossRef]
  32. T. Ditmire, A. M. Rubenchik, D. Eimerl, and M. D. Perry, “Effects of cubic nonlinearity on frequency doubling of high-power laser pulses,” J. Opt. Soc. Am. B 13, 649–655 (1996).
    [CrossRef]

1997 (1)

1996 (3)

T. Ditmire, A. M. Rubenchik, D. Eimerl, and M. D. Perry, “Effects of cubic nonlinearity on frequency doubling of high-power laser pulses,” J. Opt. Soc. Am. B 13, 649–655 (1996).
[CrossRef]

G. T. Moore and K. Koch, “Phasing of tandem crystals for nonlinear optical frequency conversion,” Opt. Commun. 124, 292–294 (1996).
[CrossRef]

J.-J. Zondy, M. Abed, S. Khodja, C. Bonnin, B. Rainaud, H. Albrecht, and D. Lupinsky, “Walkoff-compensated type-I and type-II SHG using twin-crystal AgGaSe2 and KTiOPO4 devices,” in Nonlinear Frequency Generation and Conversion, Proc. SPIE 2700, 66–72 (1996).
[CrossRef]

1995 (6)

C. Radzewicz, Y. B. Band, G. W. Pearson, and J. S. Krasinski, “Short pulse nonlinear frequency conversion without group-velocity-mismatch broadening,” Opt. Commun. 117, 295–302 (1995).
[CrossRef]

J.-J. Zondy, “Experimental investigation of single and twin AgGaSe2 crystals for CW 10.2 μm SHG,” Opt. Commun. 119, 320–326 (1995).
[CrossRef]

D. Eimerl, J. M. Auerbach, and P. W. Milonni, “Paraxial wave theory of second and third harmonic generation in uniaxial crystals,” J. Mod. Opt. 42, 1037–1064 (1995).
[CrossRef]

M. Trippenbach and Y. B. Band, “Propagation of light pulses in nonisotropic media,” J. Opt. Soc. Am. B 13, 1403–1411 (1995).
[CrossRef]

A. V. Smith and M. S. Bowers, “Phase distortions in sum- and difference-frequency mixing in crystals,” J. Opt. Soc. Am. B 12, 49–57 (1995).
[CrossRef]

E. Sidick, A. Knoesen, and A. Dienes, “Ultrashort-pulse second-harmonic generation. I. Transform-limited fundamental pulses,” J. Opt. Soc. Am. B 12, 1704–1712 (1995).
[CrossRef]

1994 (2)

1993 (2)

K. Hayata and M. Koshiba, “Group-velocity-matched second-harmonic generation: an efficient scheme for femtosecond ultraviolet pulse generation in periodically domain-inverted β-BaB2O4,” Appl. Phys. Lett. 62, 2188–2190 (1993).
[CrossRef]

M. Watanabe, K. Hayasaka, H. Imajo, and S. Urabe, “Continuous-wave sum-frequency generation near 194 nm with collinear double enhancement cavity,” Opt. Commun. 97, 225–227 (1993).
[CrossRef]

1992 (1)

1991 (1)

J.-J. Zondy, “Comparative theory of walkoff-limited type-II versus type-I second harmonic generation with gaussian beams,” Opt. Commun. 81, 427–440 (1991).
[CrossRef]

1990 (4)

M. A. Dreger and J. K. McIver, “Second-harmonic generation in a nonlinear, anisotropic medium with diffraction and depletion,” J. Opt. Soc. Am. B 7, 776–784 (1990).
[CrossRef]

M. A. Norton, D. Eimerl, C. A. Ebbers, S. P. Velsko, and C. S. Petty, “KD*P frequency doubler for high average power applications,” in Solid State Lasers, Proc. SPIE 1223, 75–83 (1990).
[CrossRef]

B. Ya. Zel’dovich, Yu. E. Kapitskii, and A. N. Chudinov, “Interference between second harmonics generated into different KTP crystals,” Sov. J. Quantum Electron. 20, 1120–1121 (1990).
[CrossRef]

L. K. Samanta, T. Tanagawa, and Y. Yamamoto, “Technique for enhanced second harmonic output power,” Opt. Commun. 76, 250–252 (1990).
[CrossRef]

1989 (1)

W. R. Bosenberg, W. S. Pelouch, and C. L. Tang, “High-efficiency and narrow-linewidth operation of a two-crystal β-BaB-2O-4 optical parametric oscillator,” Appl. Phys. Lett. 55, 1952–1954 (1989).
[CrossRef]

1988 (1)

R. B. Andreev, K. V. Vetrov, V. D. Volosov, and A. G. Kalintsev, “Three-wave parametric processes in multicrystal nonlinear frequency converters,” Opt. Spectrosc. 65, 90–93 (1988).

1987 (1)

C. Xijie, D. Meilan, L. Jiapun, L. Tielxe, and Q. Wenhua, “Large-aperture high-efficiency frequency doubling using tandem KDP crystals,” Chin. Phys. 7, 1055–1060 (1987).

1984 (1)

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

1983 (1)

1970 (1)

D. R. White, E. L. Dawes, and J. H. Marburger, “Theory of second-harmonic generation with high-conversion efficiency,” IEEE J. Quantum Electron. QE-6, 793–796 (1970).
[CrossRef]

1968 (1)

G. D. Boyd and D. A. Kleinman, “Parametric interaction of focused Gaussian light beams,” J. Appl. Phys. 39, 3597–3639 (1968).
[CrossRef]

Abed, M.

J.-J. Zondy, M. Abed, S. Khodja, C. Bonnin, B. Rainaud, H. Albrecht, and D. Lupinsky, “Walkoff-compensated type-I and type-II SHG using twin-crystal AgGaSe2 and KTiOPO4 devices,” in Nonlinear Frequency Generation and Conversion, Proc. SPIE 2700, 66–72 (1996).
[CrossRef]

J. J. Zondy, M. Abed, and S. Khodja, “Twin-crystal walk-off-compensated type-II second harmonic generation: single-pass and cavity-enhanced experiments in KTiOPO4,” J. Opt. Soc. Am. B 11, 2368–2379 (1994).
[CrossRef]

Albrecht, H.

J.-J. Zondy, M. Abed, S. Khodja, C. Bonnin, B. Rainaud, H. Albrecht, and D. Lupinsky, “Walkoff-compensated type-I and type-II SHG using twin-crystal AgGaSe2 and KTiOPO4 devices,” in Nonlinear Frequency Generation and Conversion, Proc. SPIE 2700, 66–72 (1996).
[CrossRef]

Alford, W. J.

Andreev, R. B.

R. B. Andreev, K. V. Vetrov, V. D. Volosov, and A. G. Kalintsev, “Three-wave parametric processes in multicrystal nonlinear frequency converters,” Opt. Spectrosc. 65, 90–93 (1988).

Armstrong, D. J.

Auerbach, J. M.

D. Eimerl, J. M. Auerbach, and P. W. Milonni, “Paraxial wave theory of second and third harmonic generation in uniaxial crystals,” J. Mod. Opt. 42, 1037–1064 (1995).
[CrossRef]

Band, Y. B.

M. Trippenbach and Y. B. Band, “Propagation of light pulses in nonisotropic media,” J. Opt. Soc. Am. B 13, 1403–1411 (1995).
[CrossRef]

C. Radzewicz, Y. B. Band, G. W. Pearson, and J. S. Krasinski, “Short pulse nonlinear frequency conversion without group-velocity-mismatch broadening,” Opt. Commun. 117, 295–302 (1995).
[CrossRef]

Bonnin, C.

J.-J. Zondy, M. Abed, S. Khodja, C. Bonnin, B. Rainaud, H. Albrecht, and D. Lupinsky, “Walkoff-compensated type-I and type-II SHG using twin-crystal AgGaSe2 and KTiOPO4 devices,” in Nonlinear Frequency Generation and Conversion, Proc. SPIE 2700, 66–72 (1996).
[CrossRef]

B. Boulanger, J. P. Feve, G. Marnier, B. Menaert, X. Cabirol, P. Villeval, and C. Bonnin, “Relative sign and absolute magnitude of d(2) nonlinear coefficients of KTP from second-harmonic-generation measurements,” J. Opt. Soc. Am. B 11, 750–757 (1994).
[CrossRef]

Bosenberg, W. R.

W. R. Bosenberg, W. S. Pelouch, and C. L. Tang, “High-efficiency and narrow-linewidth operation of a two-crystal β-BaB-2O-4 optical parametric oscillator,” Appl. Phys. Lett. 55, 1952–1954 (1989).
[CrossRef]

Boulanger, B.

Bowers, M. S.

Boyd, G. D.

G. D. Boyd and D. A. Kleinman, “Parametric interaction of focused Gaussian light beams,” J. Appl. Phys. 39, 3597–3639 (1968).
[CrossRef]

Cabirol, X.

Chudinov, A. N.

B. Ya. Zel’dovich, Yu. E. Kapitskii, and A. N. Chudinov, “Interference between second harmonics generated into different KTP crystals,” Sov. J. Quantum Electron. 20, 1120–1121 (1990).
[CrossRef]

Dawes, E. L.

D. R. White, E. L. Dawes, and J. H. Marburger, “Theory of second-harmonic generation with high-conversion efficiency,” IEEE J. Quantum Electron. QE-6, 793–796 (1970).
[CrossRef]

Dienes, A.

Ditmire, T.

Dou, S. X.

Dreger, M. A.

Ebbers, C. A.

M. A. Norton, D. Eimerl, C. A. Ebbers, S. P. Velsko, and C. S. Petty, “KD*P frequency doubler for high average power applications,” in Solid State Lasers, Proc. SPIE 1223, 75–83 (1990).
[CrossRef]

Eckardt, R. C.

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

Eimerl, D.

T. Ditmire, A. M. Rubenchik, D. Eimerl, and M. D. Perry, “Effects of cubic nonlinearity on frequency doubling of high-power laser pulses,” J. Opt. Soc. Am. B 13, 649–655 (1996).
[CrossRef]

D. Eimerl, J. M. Auerbach, and P. W. Milonni, “Paraxial wave theory of second and third harmonic generation in uniaxial crystals,” J. Mod. Opt. 42, 1037–1064 (1995).
[CrossRef]

M. A. Norton, D. Eimerl, C. A. Ebbers, S. P. Velsko, and C. S. Petty, “KD*P frequency doubler for high average power applications,” in Solid State Lasers, Proc. SPIE 1223, 75–83 (1990).
[CrossRef]

Feit, M. D.

Feve, J. P.

Fleck Jr., J. A.

Hayasaka, K.

M. Watanabe, K. Hayasaka, H. Imajo, and S. Urabe, “Continuous-wave sum-frequency generation near 194 nm with collinear double enhancement cavity,” Opt. Commun. 97, 225–227 (1993).
[CrossRef]

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 β-BaB2O4,” Appl. Phys. Lett. 62, 2188–2190 (1993).
[CrossRef]

Imajo, H.

M. Watanabe, K. Hayasaka, H. Imajo, and S. Urabe, “Continuous-wave sum-frequency generation near 194 nm with collinear double enhancement cavity,” Opt. Commun. 97, 225–227 (1993).
[CrossRef]

Jiapun, L.

C. Xijie, D. Meilan, L. Jiapun, L. Tielxe, and Q. Wenhua, “Large-aperture high-efficiency frequency doubling using tandem KDP crystals,” Chin. Phys. 7, 1055–1060 (1987).

Josse, D.

Kalintsev, A. G.

R. B. Andreev, K. V. Vetrov, V. D. Volosov, and A. G. Kalintsev, “Three-wave parametric processes in multicrystal nonlinear frequency converters,” Opt. Spectrosc. 65, 90–93 (1988).

Kapitskii, Yu. E.

B. Ya. Zel’dovich, Yu. E. Kapitskii, and A. N. Chudinov, “Interference between second harmonics generated into different KTP crystals,” Sov. J. Quantum Electron. 20, 1120–1121 (1990).
[CrossRef]

Khodja, S.

J.-J. Zondy, M. Abed, S. Khodja, C. Bonnin, B. Rainaud, H. Albrecht, and D. Lupinsky, “Walkoff-compensated type-I and type-II SHG using twin-crystal AgGaSe2 and KTiOPO4 devices,” in Nonlinear Frequency Generation and Conversion, Proc. SPIE 2700, 66–72 (1996).
[CrossRef]

J. J. Zondy, M. Abed, and S. Khodja, “Twin-crystal walk-off-compensated type-II second harmonic generation: single-pass and cavity-enhanced experiments in KTiOPO4,” J. Opt. Soc. Am. B 11, 2368–2379 (1994).
[CrossRef]

Kleinman, D. A.

G. D. Boyd and D. A. Kleinman, “Parametric interaction of focused Gaussian light beams,” J. Appl. Phys. 39, 3597–3639 (1968).
[CrossRef]

Knoesen, A.

Koch, K.

G. T. Moore and K. Koch, “Phasing of tandem crystals for nonlinear optical frequency conversion,” Opt. Commun. 124, 292–294 (1996).
[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 β-BaB2O4,” Appl. Phys. Lett. 62, 2188–2190 (1993).
[CrossRef]

Krasinski, J. S.

C. Radzewicz, Y. B. Band, G. W. Pearson, and J. S. Krasinski, “Short pulse nonlinear frequency conversion without group-velocity-mismatch broadening,” Opt. Commun. 117, 295–302 (1995).
[CrossRef]

Lupinsky, D.

J.-J. Zondy, M. Abed, S. Khodja, C. Bonnin, B. Rainaud, H. Albrecht, and D. Lupinsky, “Walkoff-compensated type-I and type-II SHG using twin-crystal AgGaSe2 and KTiOPO4 devices,” in Nonlinear Frequency Generation and Conversion, Proc. SPIE 2700, 66–72 (1996).
[CrossRef]

Marburger, J. H.

D. R. White, E. L. Dawes, and J. H. Marburger, “Theory of second-harmonic generation with high-conversion efficiency,” IEEE J. Quantum Electron. QE-6, 793–796 (1970).
[CrossRef]

Marnier, G.

McIver, J. K.

Meilan, D.

C. Xijie, D. Meilan, L. Jiapun, L. Tielxe, and Q. Wenhua, “Large-aperture high-efficiency frequency doubling using tandem KDP crystals,” Chin. Phys. 7, 1055–1060 (1987).

Menaert, B.

Milonni, P. W.

D. Eimerl, J. M. Auerbach, and P. W. Milonni, “Paraxial wave theory of second and third harmonic generation in uniaxial crystals,” J. Mod. Opt. 42, 1037–1064 (1995).
[CrossRef]

Moore, G. T.

G. T. Moore and K. Koch, “Phasing of tandem crystals for nonlinear optical frequency conversion,” Opt. Commun. 124, 292–294 (1996).
[CrossRef]

Norton, M. A.

M. A. Norton, D. Eimerl, C. A. Ebbers, S. P. Velsko, and C. S. Petty, “KD*P frequency doubler for high average power applications,” in Solid State Lasers, Proc. SPIE 1223, 75–83 (1990).
[CrossRef]

Pearson, G. W.

C. Radzewicz, Y. B. Band, G. W. Pearson, and J. S. Krasinski, “Short pulse nonlinear frequency conversion without group-velocity-mismatch broadening,” Opt. Commun. 117, 295–302 (1995).
[CrossRef]

Pelouch, W. S.

W. R. Bosenberg, W. S. Pelouch, and C. L. Tang, “High-efficiency and narrow-linewidth operation of a two-crystal β-BaB-2O-4 optical parametric oscillator,” Appl. Phys. Lett. 55, 1952–1954 (1989).
[CrossRef]

Perry, M. D.

Petty, C. S.

M. A. Norton, D. Eimerl, C. A. Ebbers, S. P. Velsko, and C. S. Petty, “KD*P frequency doubler for high average power applications,” in Solid State Lasers, Proc. SPIE 1223, 75–83 (1990).
[CrossRef]

Radzewicz, C.

C. Radzewicz, Y. B. Band, G. W. Pearson, and J. S. Krasinski, “Short pulse nonlinear frequency conversion without group-velocity-mismatch broadening,” Opt. Commun. 117, 295–302 (1995).
[CrossRef]

Rainaud, B.

J.-J. Zondy, M. Abed, S. Khodja, C. Bonnin, B. Rainaud, H. Albrecht, and D. Lupinsky, “Walkoff-compensated type-I and type-II SHG using twin-crystal AgGaSe2 and KTiOPO4 devices,” in Nonlinear Frequency Generation and Conversion, Proc. SPIE 2700, 66–72 (1996).
[CrossRef]

Raymond, T. D.

Reintjes, J.

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

Rubenchik, A. M.

Samanta, L. K.

L. K. Samanta, T. Tanagawa, and Y. Yamamoto, “Technique for enhanced second harmonic output power,” Opt. Commun. 76, 250–252 (1990).
[CrossRef]

Sidick, E.

Smith, A. V.

Tanagawa, T.

L. K. Samanta, T. Tanagawa, and Y. Yamamoto, “Technique for enhanced second harmonic output power,” Opt. Commun. 76, 250–252 (1990).
[CrossRef]

Tang, C. L.

W. R. Bosenberg, W. S. Pelouch, and C. L. Tang, “High-efficiency and narrow-linewidth operation of a two-crystal β-BaB-2O-4 optical parametric oscillator,” Appl. Phys. Lett. 55, 1952–1954 (1989).
[CrossRef]

Tielxe, L.

C. Xijie, D. Meilan, L. Jiapun, L. Tielxe, and Q. Wenhua, “Large-aperture high-efficiency frequency doubling using tandem KDP crystals,” Chin. Phys. 7, 1055–1060 (1987).

Trippenbach, M.

Urabe, S.

M. Watanabe, K. Hayasaka, H. Imajo, and S. Urabe, “Continuous-wave sum-frequency generation near 194 nm with collinear double enhancement cavity,” Opt. Commun. 97, 225–227 (1993).
[CrossRef]

Velsko, S. P.

M. A. Norton, D. Eimerl, C. A. Ebbers, S. P. Velsko, and C. S. Petty, “KD*P frequency doubler for high average power applications,” in Solid State Lasers, Proc. SPIE 1223, 75–83 (1990).
[CrossRef]

Vetrov, K. V.

R. B. Andreev, K. V. Vetrov, V. D. Volosov, and A. G. Kalintsev, “Three-wave parametric processes in multicrystal nonlinear frequency converters,” Opt. Spectrosc. 65, 90–93 (1988).

Villeval, P.

Volosov, V. D.

R. B. Andreev, K. V. Vetrov, V. D. Volosov, and A. G. Kalintsev, “Three-wave parametric processes in multicrystal nonlinear frequency converters,” Opt. Spectrosc. 65, 90–93 (1988).

Watanabe, M.

M. Watanabe, K. Hayasaka, H. Imajo, and S. Urabe, “Continuous-wave sum-frequency generation near 194 nm with collinear double enhancement cavity,” Opt. Commun. 97, 225–227 (1993).
[CrossRef]

Wenhua, Q.

C. Xijie, D. Meilan, L. Jiapun, L. Tielxe, and Q. Wenhua, “Large-aperture high-efficiency frequency doubling using tandem KDP crystals,” Chin. Phys. 7, 1055–1060 (1987).

White, D. R.

D. R. White, E. L. Dawes, and J. H. Marburger, “Theory of second-harmonic generation with high-conversion efficiency,” IEEE J. Quantum Electron. QE-6, 793–796 (1970).
[CrossRef]

Xijie, C.

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[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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C. Xijie, D. Meilan, L. Jiapun, L. Tielxe, and Q. Wenhua, “Large-aperture high-efficiency frequency doubling using tandem KDP crystals,” Chin. Phys. 7, 1055–1060 (1987).

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J. J. Zondy, M. Abed, and S. Khodja, “Twin-crystal walk-off-compensated type-II second harmonic generation: single-pass and cavity-enhanced experiments in KTiOPO4,” J. Opt. Soc. Am. B 11, 2368–2379 (1994).
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S. X. Dou, D. Josse, and J. Zyss, “Comparison of collinear and one-beam noncritical noncollinear phase matching in optical parametric amplification,” J. Opt. Soc. Am. B 9, 1312–1319 (1992).
[CrossRef]

B. Boulanger, J. P. Feve, G. Marnier, B. Menaert, X. Cabirol, P. Villeval, and C. Bonnin, “Relative sign and absolute magnitude of d(2) nonlinear coefficients of KTP from second-harmonic-generation measurements,” J. Opt. Soc. Am. B 11, 750–757 (1994).
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A. V. Smith and M. S. Bowers, “Phase distortions in sum- and difference-frequency mixing in crystals,” J. Opt. Soc. Am. B 12, 49–57 (1995).
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E. Sidick, A. Knoesen, and A. Dienes, “Ultrashort-pulse second-harmonic generation. I. Transform-limited fundamental pulses,” J. Opt. Soc. Am. B 12, 1704–1712 (1995).
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T. Ditmire, A. M. Rubenchik, D. Eimerl, and M. D. Perry, “Effects of cubic nonlinearity on frequency doubling of high-power laser pulses,” J. Opt. Soc. Am. B 13, 649–655 (1996).
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D. J. Armstrong, W. J. Alford, T. D. Raymond, A. V. Smith, and M. S. Bowers, “Parametric amplification and oscillation with walkoff-compensating crystals,” J. Opt. Soc. Am. B 14, 460–464 (1997).
[CrossRef]

Opt. Commun. (6)

J.-J. Zondy, “Comparative theory of walkoff-limited type-II versus type-I second harmonic generation with gaussian beams,” Opt. Commun. 81, 427–440 (1991).
[CrossRef]

J.-J. Zondy, “Experimental investigation of single and twin AgGaSe2 crystals for CW 10.2 μm SHG,” Opt. Commun. 119, 320–326 (1995).
[CrossRef]

C. Radzewicz, Y. B. Band, G. W. Pearson, and J. S. Krasinski, “Short pulse nonlinear frequency conversion without group-velocity-mismatch broadening,” Opt. Commun. 117, 295–302 (1995).
[CrossRef]

G. T. Moore and K. Koch, “Phasing of tandem crystals for nonlinear optical frequency conversion,” Opt. Commun. 124, 292–294 (1996).
[CrossRef]

L. K. Samanta, T. Tanagawa, and Y. Yamamoto, “Technique for enhanced second harmonic output power,” Opt. Commun. 76, 250–252 (1990).
[CrossRef]

M. Watanabe, K. Hayasaka, H. Imajo, and S. Urabe, “Continuous-wave sum-frequency generation near 194 nm with collinear double enhancement cavity,” Opt. Commun. 97, 225–227 (1993).
[CrossRef]

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Proc. SPIE (2)

M. A. Norton, D. Eimerl, C. A. Ebbers, S. P. Velsko, and C. S. Petty, “KD*P frequency doubler for high average power applications,” in Solid State Lasers, Proc. SPIE 1223, 75–83 (1990).
[CrossRef]

J.-J. Zondy, M. Abed, S. Khodja, C. Bonnin, B. Rainaud, H. Albrecht, and D. Lupinsky, “Walkoff-compensated type-I and type-II SHG using twin-crystal AgGaSe2 and KTiOPO4 devices,” in Nonlinear Frequency Generation and Conversion, Proc. SPIE 2700, 66–72 (1996).
[CrossRef]

Sov. J. Quantum Electron. (1)

B. Ya. Zel’dovich, Yu. E. Kapitskii, and A. N. Chudinov, “Interference between second harmonics generated into different KTP crystals,” Sov. J. Quantum Electron. 20, 1120–1121 (1990).
[CrossRef]

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V. D. Volosov, A. G. Kalintsev, and V. N. Krylov, “Suppression of degenerate parametric processes limiting frequency-doubling efficiency of crystals,” Sov. J. Quantum Electron. 6, 1163–1167 (1976); V. D. Volosov, A. G. Kalintsev, and V. N. Krylov, “Degenerate parametric processes in three-wave interactions in tandem crystals,” Sov. Tech. Phys. Lett. 2, 32–34 (1976); V. D. Volosov and A. G. Kalintsev, “Optimum optical second-harmonic generation in tandem crystals,” Sov. Tech. Phys. Lett. STPLD2 2, 373–375 (1976); V. D. Volosov, A. G. Kalintsev, and V. N. Krylov, “Phase effects in a double-pass frequency doubler,” Sov. Tech. Phys. Lett. STPLD2 5, 5–7 (1979).
[CrossRef]

A. V. Smith, computer code SNLO, Sandia National Laboratories, Albuquerque, N. M., 1997 (available from the authors at no charge).

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Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).

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Figures (19)

Fig. 1
Fig. 1

Phasor diagrams for six walk-off–compensated crystal segments. In the upper diagram, Δk=0 for all segments. In the second diagram Δk is equal in magnitude but with alternating sign. In the third diagram, Δk=0 for all except the first crystal segment. In the fourth diagram, Δk=0 for all except the third crystal segment.

Fig. 2
Fig. 2

Effect of detuning one crystal segment of length Ln in an array of six segments. Curve 1,6 shows how low conversion-frequency doubling depends on detuning of segment 1 or segment 6. Similarly, the curves labeled 2,5 and 3,4 show the effect of detuning segments 2 or 5 and segments 3 or 4.

Fig. 3
Fig. 3

Apparatus for measuring phase-matching curves with four 7-mm-long BBO crystals by means of an injection-seeded Nd:YAG laser: λ/2, half-wave plate; R, reflectance; T, transmittance; fl, focal length.

Fig. 4
Fig. 4

Low-conversion phase-matching curves recorded with the spatially filtered Nd:YAG laser for one 7-mm BBO crystal, four 7-mm walk-off–compensating crystals, and one 28-mm crystal.

Fig. 5
Fig. 5

Beam behavior in a birefringent crystal for type A frequency doubling in a single crystal (upper) and in two walk-off–compensating segments (lower).

Fig. 6
Fig. 6

(a) Fundamental and second-harmonic spectra, and (b) time profiles for type I frequency doubling as calculated by numeric integration of mixing equations ignoring diffraction, birefringent walk-off, and group-velocity dispersion. Group-velocity walk-off stretches the harmonic-pulse duration to 6.7 times that of the fundamental pulse. The spectra are Fourier transforms of the temporal-pulse shapes. Similar angular spectral narrowing is associated with spatial broadening related to birefringent walk-off.

Fig. 7
Fig. 7

Beam behavior in a birefringent crystal for type B frequency doubling in a single crystal (upper) and in two walk-off–compensating segments (lower).

Fig. 8
Fig. 8

Spectra for e- and o-polarized fundamental pulses and second-harmonic pulse in type II mixing with group-velocity walk-off σL=6.7T. The o-polarized fundamental spectrum has a dip at the midpoint of the curve, and the second-harmonic spectrum is the broadest.

Fig. 9
Fig. 9

Optimum values of phase mismatch -ΔkL, focus parameter L/2z0, and h(Δk, B, L, z0) as functions of B =ρ(Lπn/2λ1)1/2.

Fig. 10
Fig. 10

h(Δk1, Δk2, B, L, z0) dependence on (Δk1, Δk2) for frequency-doubling 800-nm light in two 5-mm-long crystal segments with 60-mrad walk-off. (a) For plane waves the beam waist is much larger than ρL/2, and the Rayleigh range is much greater than L. (b) For collimated Gaussian beams the walk-off in each segment, ρL/2, is three times the beam diameter of 100 μm (FWHM), and the Rayleigh range is 47 mm. (c) For a focused Gaussian the walk-off ρL/2 is 300 μm, and the Rayleigh range is 3.6 mm.

Fig. 11
Fig. 11

Comparison of calculated second-harmonic-generation efficiency versus Beff for a single crystal, for 1, 2, 3, 4, 8, or 60 walk-off–compensating segments of a crystal with B0=4, and for 2, 4, 6, 8, or 16 walk-off–compensating segments of a crystal with B0=8.

Fig. 12
Fig. 12

Apparatus for measuring phase-matching curves for frequency-doubling 1064-nm light from a short-cavity optical parametric oscillator in four 7-mm-long BBO crystals; R, reflectance; T, transmittance.

Fig. 13
Fig. 13

Doubling signal (solid curve) and 1064-nm pulse depletion (dashed curve) for four walk-off-compensating 7-mm-long crystals.

Fig. 14
Fig. 14

Angular acceptance, defined as the value of ΔkL/π at which parametric gain is reduced by half, versus parametric gain for a crystal of length L divided into 1, 2, or 4 walk-off–compensating segments.

Fig. 15
Fig. 15

Type I second-harmonic conversion efficiency of 1064-nm plane waves in 28 mm of BBO as a function of ΔkL/π and fundamental irradiance calculated by numeric integration (a) for a single crystal of length 28 mm, (b) for four walk-off–compensating segments of length 7 mm, and (c) for eight walk-off–compensating segments of length 3.5 mm. Note the change in the ΔkL/π scale.

Fig. 16
Fig. 16

Type I second-harmonic conversion efficiency of 1064-nm plane waves in 28 mm of BBO as a function of internal angle and fundamental pulse energy (a) for a single crystal of length 28 mm and (b) for four walk-off-compensating segments of length 7 mm. Solid curves are the second-harmonic fluence at the beam center, dotted-dashed curves are the depleted fundamental fluence at the beam center, and dashed curves are the depleted fundamental fluence integrated over the spatial profile.

Fig. 17
Fig. 17

Sensitivity of doubling to Δkn, the phase mismatch of the nth crystal (n=1, , 4), for four walk-off-compensating crystal segments at high nonlinear drive. All crystals are adjusted to Δk=0 except the one indicated.

Fig. 18
Fig. 18

Doubling efficiency of focused 800-nm beams in a 10-mm-long BBO crystal versus fundamental power for no spatial walk-off, 70-mrad walk-off in a single crystal, and 70-mrad walk-off in four walk-off–compensating crystal segments.

Fig. 19
Fig. 19

Doubling efficiency versus temporal walk-off, measured in units of pulse duration, at low power normalized to 95% at σL/τ=0, at high power for unmodulated pulse, for phase modulation with phase excursion of π/15 and period equal to 55% of the pulse duration in a single crystal, and for four walk-off-compensating crystal segments.

Equations (48)

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z+i2k1 (kx2+ky2)+iα1(Δω)2+iΔωv1+ikxρ11(kx, ky, z, Δω)=P1(kx, ky, z, Δω),
z+i2k2 (kx2+ky2)+iα2(Δω)2+iΔωv2+ikxρ22(kx, ky, z, Δω)=P2(kx, ky, z, Δω),
z+i2k3 (kx2+ky2)+iα3(Δω)2+iΔωv3+ikxρ33(kx, ky, z, Δω)=P3(kx, ky, z, Δω),
P1(kx, ky, z, Δω)
=i deffω1cn1 exp(iΔkz)2*(kx, ky, z, δ)×3(kx+kx, ky+ky, z, Δω+δ)dkxdkydδ,
P2(kx, ky, z, Δω)
=i deffω2cn2 exp(iΔkz)1*(kx, ky, z, δ)×3(kx+kx, ky+ky, z, Δω+δ)dkxdkydδ,
P3(kx, ky, z, δω)
=i deffω3cn3 exp(-iΔkz)2(kx-kx, ky-ky, z, Δω-δ)1(kx, ky, z, δ)dkxdkydδ,
z-i2k1 2x2+2y2+iα1 2t2+1v1 t+ρ1 x×1(x, y, z, t)
=iω1deffn1c 3(x, y, z, t)2*(x, y, z, t)exp(iΔk0z),
z-i2k2 2x2+2y2+iα2 2t2+1v2 t+ρ2 x×2(x, y, z, t)
=iω2deffn2c 3(x, y, z, t)1*(x, y, z, t)exp(iΔk0z),
z-i2k3 2x2+2y2+iα3 2t2+1v3 t+ρ3 x×3(x, y, z, t)
=iω3deffn3c 2(x, y, z, t)1(x, y, z, t)exp(-iΔk0z).
ρ=-1ne dnedθ.
1v=nc+ωc dndω=dkdω.
2ω=i ωdeffnc ω2L sin(ΔkL/2)(ΔkL/2) exp(iΔkL/2).
Δθpw=0.866(2π)L(k3ρ3-k2ρ2-k1ρ1).
2ωa=i ωdeffnc ω2 L2 sin(ΔkL/4)(ΔkL/4) exp(iΔkL/4)×exp(-iΔkL/2),
2ωb=i ωdeffnc ω2 L2 sin(ΔkL/4)(ΔkL/4) exp(-iΔkL/4).
2ω=2ωa+2ωb=i ωdeffnc ω2L sin(ΔkL/4)(ΔkL/4) exp(-iΔkL/4).
2ω=i ωdeffnc ω2L sin(ΔkL/2N)(ΔkL/2N) exp[(-1)N+1iΔkL/2N],
P3=(1.31×10-2)deff2P1P2L2WHλ32n1n2n3 11+0.51(ρL/W)2,
U3=(8.71×10-3)deff2U1U2L2TWHλ32n1n2n3 11+0.51(ρL/W)2.
σ=1v3-1v1.
P(θ)exp-W2πθλ8 ln(0.5)2sinc2(πθρL/λ),
δθ=0.624λW,
δθ=0.886λρL.
Δkl=0.886×2π,
Δθ=0.886λ/W,
Δθ=0.443λLρn,
P2=5.99×104deff2P12Lh(Δk, B, l, z0)n2λ13,
h(Δk, B, L, z0)
=z02L -L/2z0L/2z0-L/2z0L/2z0dτdτ×exp[i(z0Δk)(τ-τ)-(2z0B2/L)(τ-τ)2](1+iτ)(1-iτ),
B=ρLπn2λ1.
h(Δk1, Δk2, B, L, z0)
=z02L 0L/2z00L/2z0dτdτ exp[-2z0B2/L(τ-τ)2](1+τ2)(1+τ2)×{(1+ττ)cos[z0Δk2(τ-τ)]-(τ-τ)sin[z0Δk2(τ-τ)]+(1+ττ)cos[z0Δk1(τ-τ)]-(τ-τ)sin[z0Δk1(τ-τ)]±2(1-ττ)cos[z0Δk1τ+z0Δk2τ]2(τ+τ)sin[z0Δk1τ+z0Δk2τ]}.
P3P1P2l2SH(ρL+W)H2W2=P1P2L(ρL+W)HWMρ,
U3U1U2L(στ+T)HWTMσ,
P3P1P2LHρM,
s(z)=s(0)cosh γz-iΔk2γ sinh γzexpiΔkz2+i Aγ i*(0)sinh γz expiΔkz2,
i*(z)=i*(0)cosh γz+iΔk2γ sinh γzexp-iΔkz2-i Bγ s(0)sinh γz exp-iΔkz2,
A=deffωspcns,
B=deffωip*cni,
γ=12 4AB-Δk2.
γL=2deff2ωsωiIp0c3nsninp1/2L,
γL=0.172deffLIpλsλinsninp1/2

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