Abstract

We compare frequency doubling of broadband light in a single nonlinear crystal with doubling in five crystals with intercrystal temporal walk-off compensation and with doubling in five crystals adjusted for offset phase-matching frequencies. Using a plane-wave dispersive numerical model of frequency doubling, we study the bandwidth of the second harmonic and the conversion efficiency as functions of crystal length and fundamental irradiance. For low irradiance, the offset phase-matching arrangement has lower efficiency than a single crystal of the same total length but gives a broader second-harmonic bandwidth. The walk-off-compensated arrangement gives both higher conversion efficiency and broader bandwidth than a single crystal. At high irradiance, both multicrystal arrangements improve on the single-crystal efficiency while maintaining a broad bandwidth.

© 2001 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
  3. D. Eimerl, J. M. Auerbach, C. E. Barker, D. Milam, and P. W. Milonni, “Multicrystal designs for efficient third-harmonic generation,” Opt. Lett. 22, 1208–1210 (1997).
    [CrossRef] [PubMed]
  4. P. W. Milonni, J. M. Auerbach, and D. Eimerl, “Frequency-conversion modeling with spatially and temporally varying beams,” in Solid State Lasers for Application to Inertial Confinement Fusion (ICF), W. F. Krupke, ed., Proc. SPIE 2633, 230–241 (1997).
    [CrossRef]
  5. A. V. Smith, D. J. Armstrong, and W. J. Alford, “Increased acceptance bandwidths in optical frequency conversion by use of multiple walk-off-compensating nonlinear crystals,” J. Opt. Soc. Am. B 15, 122–141 (1998).
    [CrossRef]
  6. R. J. Gehr, M. W. Kimmel, and A. V. Smith, “Simultaneous spatial and temporal walk-off compensation in frequency-doubling femtosecond pulses in β-BaB2O4,” Opt. Lett. 23, 1298–1300 (1998).
    [CrossRef]
  7. B. A. Richman, S. E. Bisson, R. Trebino, E. Sidick, and A. Jacobson, “Efficient broadband second-harmonic generation by dispersive achromatic nonlinear conversion using only prisms,” Opt. Lett. 23, 497–499 (1998).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  10. The function GVD is within SNLO. The SNLO nonlinear optics code is available from A. V. Smith at the following web site: http://www.sandia.gov/imrl/X1118/xxtal.htm.
  11. A. V. Smith and R. J. Gehr, “Numerical models of broad-bandwidth nanosecond optical parametric oscillators,” J. Opt. Soc. Am. B 16, 609–619 (1999).
    [CrossRef]
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    [CrossRef]
  13. S. E. Kurtz, “Measurement of nonlinear optical susceptibilities,” in Quantum Electronics, H. Rabin and C. L. Tang, eds. (Academic, New York, 1975), Vol. 1, Part, A, pp. 209–281.
  14. See Figs. 15 and 16 of Ref. 5.
  15. 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, G. Duke, ed., Proc. SPIE 1223, 75–83 (1990).
    [CrossRef]
  16. 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]
  17. 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, 460–474 (1997).
    [CrossRef]

1999 (2)

1998 (6)

1997 (4)

1990 (1)

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, G. Duke, ed., Proc. SPIE 1223, 75–83 (1990).
[CrossRef]

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]

Alford, W. J.

Andreoni, A.

R. Danielius, A. Piskarskas, P. Di Trapani, A. Andreoni, C. Solcia, and P. Foggi, “A collinearly phase-matched parametric generator/amplifier of visible femtosecond pulses,” IEEE J. Quantum Electron. 34, 459–463 (1998).
[CrossRef]

Arisholm, G.

Armstrong, D. J.

Auerbach, J. M.

D. Eimerl, J. M. Auerbach, C. E. Barker, D. Milam, and P. W. Milonni, “Multicrystal designs for efficient third-harmonic generation,” Opt. Lett. 22, 1208–1210 (1997).
[CrossRef] [PubMed]

P. W. Milonni, J. M. Auerbach, and D. Eimerl, “Frequency-conversion modeling with spatially and temporally varying beams,” in Solid State Lasers for Application to Inertial Confinement Fusion (ICF), W. F. Krupke, ed., Proc. SPIE 2633, 230–241 (1997).
[CrossRef]

Babushkin, A.

Barker, C. E.

Bisson, S. E.

Bowers, M. S.

Brown, M.

Craxton, R. S.

Danielius, R.

R. Danielius, A. Piskarskas, P. Di Trapani, A. Andreoni, C. Solcia, and P. Foggi, “A collinearly phase-matched parametric generator/amplifier of visible femtosecond pulses,” IEEE J. Quantum Electron. 34, 459–463 (1998).
[CrossRef]

Di Trapani, P.

R. Danielius, A. Piskarskas, P. Di Trapani, A. Andreoni, C. Solcia, and P. Foggi, “A collinearly phase-matched parametric generator/amplifier of visible femtosecond pulses,” IEEE J. Quantum Electron. 34, 459–463 (1998).
[CrossRef]

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, G. Duke, ed., 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.

P. W. Milonni, J. M. Auerbach, and D. Eimerl, “Frequency-conversion modeling with spatially and temporally varying beams,” in Solid State Lasers for Application to Inertial Confinement Fusion (ICF), W. F. Krupke, ed., Proc. SPIE 2633, 230–241 (1997).
[CrossRef]

D. Eimerl, J. M. Auerbach, C. E. Barker, D. Milam, and P. W. Milonni, “Multicrystal designs for efficient third-harmonic generation,” Opt. Lett. 22, 1208–1210 (1997).
[CrossRef] [PubMed]

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, G. Duke, ed., Proc. SPIE 1223, 75–83 (1990).
[CrossRef]

Foggi, P.

R. Danielius, A. Piskarskas, P. Di Trapani, A. Andreoni, C. Solcia, and P. Foggi, “A collinearly phase-matched parametric generator/amplifier of visible femtosecond pulses,” IEEE J. Quantum Electron. 34, 459–463 (1998).
[CrossRef]

Gehr, R. J.

Guardalben, M. J.

Jacobson, A.

Keck, R. L.

Kimmel, M. W.

Milam, D.

Milonni, P. W.

D. Eimerl, J. M. Auerbach, C. E. Barker, D. Milam, and P. W. Milonni, “Multicrystal designs for efficient third-harmonic generation,” Opt. Lett. 22, 1208–1210 (1997).
[CrossRef] [PubMed]

P. W. Milonni, J. M. Auerbach, and D. Eimerl, “Frequency-conversion modeling with spatially and temporally varying beams,” in Solid State Lasers for Application to Inertial Confinement Fusion (ICF), W. F. Krupke, ed., Proc. SPIE 2633, 230–241 (1997).
[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, G. Duke, ed., Proc. SPIE 1223, 75–83 (1990).
[CrossRef]

Oskoui, S.

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, G. Duke, ed., Proc. SPIE 1223, 75–83 (1990).
[CrossRef]

Piel, J.

Piskarskas, A.

R. Danielius, A. Piskarskas, P. Di Trapani, A. Andreoni, C. Solcia, and P. Foggi, “A collinearly phase-matched parametric generator/amplifier of visible femtosecond pulses,” IEEE J. Quantum Electron. 34, 459–463 (1998).
[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]

Richman, B. A.

Riedle, E.

Schmitt, R. L.

Seka, W.

Sidick, E.

Smith, A. V.

Solcia, C.

R. Danielius, A. Piskarskas, P. Di Trapani, A. Andreoni, C. Solcia, and P. Foggi, “A collinearly phase-matched parametric generator/amplifier of visible femtosecond pulses,” IEEE J. Quantum Electron. 34, 459–463 (1998).
[CrossRef]

Trebino, R.

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, G. Duke, ed., Proc. SPIE 1223, 75–83 (1990).
[CrossRef]

Wilhelm, T.

IEEE J. Quantum Electron. (2)

R. Danielius, A. Piskarskas, P. Di Trapani, A. Andreoni, C. Solcia, and P. Foggi, “A collinearly phase-matched parametric generator/amplifier of visible femtosecond pulses,” IEEE J. Quantum Electron. 34, 459–463 (1998).
[CrossRef]

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]

J. Opt. Soc. Am. B (4)

Opt. Lett. (6)

Proc. SPIE (2)

P. W. Milonni, J. M. Auerbach, and D. Eimerl, “Frequency-conversion modeling with spatially and temporally varying beams,” in Solid State Lasers for Application to Inertial Confinement Fusion (ICF), W. F. Krupke, ed., Proc. SPIE 2633, 230–241 (1997).
[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, G. Duke, ed., Proc. SPIE 1223, 75–83 (1990).
[CrossRef]

Other (3)

S. E. Kurtz, “Measurement of nonlinear optical susceptibilities,” in Quantum Electronics, H. Rabin and C. L. Tang, eds. (Academic, New York, 1975), Vol. 1, Part, A, pp. 209–281.

See Figs. 15 and 16 of Ref. 5.

The function GVD is within SNLO. The SNLO nonlinear optics code is available from A. V. Smith at the following web site: http://www.sandia.gov/imrl/X1118/xxtal.htm.

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Figures (13)

Fig. 1
Fig. 1

Normalized irradiance of the fundamental and second-harmonic output from a 10-mm-long BBO crystal in the low-conversion regime. The input fundamental is a 1-ps (FWHM) Gaussian pulse. The second harmonic is stretched by 12 ps because of the group-velocity difference between the fundamental and the harmonic waves.

Fig. 2
Fig. 2

Normalized spectra of the pulses of Fig. 1. The fundamental is a Gaussian of width (FWHM) 440 GHz (14.7 cm-1). The harmonic is the product of a Gaussian and a |sinc(Δωt)|2 function with its first nulls at ±83 GHz (2.8 cm-1).

Fig. 3
Fig. 3

Low-conversion efficiency normalized spectra of 210-nm second-harmonic (a) for a single crystal with matched fundamental and harmonic group velocities (GVM), (b) for a single crystal with actual BBO group-velocity difference (SCW) (c) for five WOC crystals; and (d) for five crystals with phase-matched frequencies at Δω=-13.9, -6.94, 0, 6.94, and 13.9 cm-1 (DDK). The fundamental input energy is 10 µJ, resulting in a fluence of 2 mJ/cm2. The fundamental has a FWHM bandwidth of 419 GHz (14 cm-1). The spectra are smoothed by use of a running average over 0.14 cm-1 to reduce the fine structure of the spectra for better readability. The spectrum of the input fundamental light is the same in each case. The η’s are doubling efficiencies.

Fig. 4
Fig. 4

Expanded view of the spectra of Fig. 3 showing that the harmonic spectra are similar in each case.

Fig. 5
Fig. 5

Envelope function for five crystals with detunings Δω=-13.9, -6.94, 0, 6.94, and 13.9 cm-1.

Fig. 6
Fig. 6

High-conversion efficiency normalized harmonic spectra under the same conditions as Fig. 3 except the fundamental pulse energy is increased from 10 µJ to 10 mJ.

Fig. 7
Fig. 7

Expanded view of the spectra of Fig. 6 showing that the harmonic spectra are altered significantly for strong doubling, in contrast to the weak doubling case shown in Fig. 4.

Fig. 8
Fig. 8

Doubling efficiency versus crystal length and fundamental pulse energy for a crystal with no group-velocity walk-off (GVM).

Fig. 9
Fig. 9

Doubling efficiency versus crystal length and fundamental pulse energy for a crystal with BBO’s group-velocity walk-off (SCW).

Fig. 10
Fig. 10

Doubling efficiency versus total crystal length and fundamental pulse energy for five WOC crystals.

Fig. 11
Fig. 11

Doubling efficiency versus total crystal length and fundamental pulse energy for five crystals with detunings Δω=-13.9, -6.94, 0, 6.94, and 13.9 cm-1 (DDK).

Fig. 12
Fig. 12

Doubling efficiency versus fundamental pulse energy for a total crystal length of 10.54 mm for a single crystal with no walk-off (GVM) (filled circles), for a single crystal with walk-off (SCW) (open circles), for five WOC crystals (open squares), and for five crystals with phase-matching frequencies separated by half of the crystal acceptance bandwidth (DDK) (crosses).

Fig. 13
Fig. 13

Doubling efficiency versus fundamental pulse energy for a total crystal length of 10.54 mm for a single crystal with no walk-off (filled circles), for a single crystal with no walk-off and uncorrelated chaotic inputs (open triangles), and for a monochromatic input pulse (crosses).

Tables (1)

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Table 1 Properties of BBO for Doubling 420-nm Light

Equations (10)

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εharm(t)=κdtεfund2(t-t)Sτ(t)/τ,
Sτ(t)=1for|t|<(τ/2)0for|t|>(τ/2),
Sharm(ω)=F{εfund2(t)}F{Sτ(t)/τ},
F{Sτ(t)/τ}=12π sinc(Δωτ/2).
F{S12ps(t)/12ps}=12π sinc(6psΔω).
1vω=dkωdω,
Δk=dk2ωdωΔω-dkωdωΔω=1v2ω-1vωΔω,
sinc(ΔkL/2)=sinc(τΔω/2).
fharmd(Δω)|S(Δω)|2.
F{S2.4ps(t)/2.4ps}=12π sinc(1.2psΔω).

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