Abstract

The spectral and temporal characteristics and optical-conversion efficiency of 150-fs laser pulses at 400 nm generated by second-harmonic generation (SHG) of a regeneratively amplified mode-locked Ti:sapphire laser were investigated both theoretically and experimentally. The theoretical investigation was done by taking into account cubic nonlinearity, pulse walk-off, group-velocity dispersion, Kerr nonlinearity, quadratic broadening, frequency chirping of the fundamental pulse, and higher-order nonlinear mixing such as backconversion and optical parametric processing. The experimental studies of the effects of crystal length and pumping intensity on the pulse duration, the spectrum, and the optical-conversion efficiency of the SHG were carried out in BBO and LBO crystals of various thicknesses and compared with the theory. It was found that in a non-transform-limited pulse, the most significant contribution to the temporal and spectral distortion of the 150-fs SHG pulses is mainly due to the chirping of the fundamental beam and self-phase modulation at high pumping intensity and long crystal length. The optimum crystal length and pumping intensity for obtaining a high optical-conversion efficiency and a pure spectrum in SHG are also calculated and experimentally investigated. It was found that a transform-limited fundamental pulse is essential to obtain a high conversion efficiency and to preserve the temporal profile of the second-harmonic pulse. It is also found that for a non-transform-limited 150-fs pulse, a 0.5–0.6-mm BBO crystal and a modest pumping intensity of 40 GW/cm2 are the most suitable for SHG.

© 1998 Optical Society of America

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References

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  1. W. H. Knox, M. C. Downer, R. L. Fork, and C. V. Shank, “Amplified femtosecond optical pulses and continuum generation at a 5-kHz repetition rate,” Opt. Lett. 9, 552 (1984).
    [CrossRef] [PubMed]
  2. P. F. Curley, Ch. Spielmann, T. Brabec, F. Krausz, E. Wintner, and J. Schmidt, “Operation of a femtosecond Ti-sapphire solitary laser in vicinity of zero group-delay dispersion,” Opt. Lett. 18, 54 (1993).
    [CrossRef] [PubMed]
  3. M. T. Asaki, C. P. Huang, D. Garvey, J. P. Zhou, H. C. Kapteyn, and M. M. Murnane, “Generation of 11-fs pulses from a self-mode-locked Ti-sapphire laser,” Opt. Lett. 18, 977 (1993).
    [CrossRef] [PubMed]
  4. A. Stingl, C. Spiemann, F. Krausz, and R. Szipocs, “Generation of 11-fs pulses from a Ti:sapphire laser without the use of prisms,” Opt. Lett. 19, 204 (1994).
    [CrossRef] [PubMed]
  5. J. P. Zhou, G. Taft, C. P. Huang, M. M. Murnane, and H. C. Kapteyn, “Pulse evolution in broadband Ti:sapphire laser,” Opt. Lett. 19, 1149 (1994).
    [CrossRef] [PubMed]
  6. J. D. Harvey, J. M. Dudley, P. F. Curley, C. Spiemann, and F. Krausz, “Coherent effects in a self-mode-locked Ti:sapphire laser,” Opt. Lett. 19, 972 (1994).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  10. V. Krylov, A. Rebane, A. G. Kalintsev, H. Schwoerer, and U. Wild, “Second-harmonic generation of amplified femtosecond Ti:sapphire laser pulses,” Opt. Lett. 20, 198 (1995).
    [CrossRef] [PubMed]
  11. E. Sidick, A. Knoesen, and A. Dienes, “Ultrashort-pulse second-harmonic generation. I. Transform-limited fundamental pulses,” J. Opt. Soc. Am. B 12, 1704 (1995).
    [CrossRef]
  12. E. Sidick, A. Knoesen, and A. Dienes, “Ultrashort-pulse second-harmonic generation. II. Non-transform-limited fundamental pulses,” J. Opt. Soc. Am. B 12, 1713 (1995).
    [CrossRef]
  13. D. C. Edelstein, E. S. Washman, L. K. Cheng, W. R. Bosenberg, and C. L. Tang, “Femtosecond ultraviolet pulse generation in β–BaB2O4,” Appl. Phys. Lett. 52, 2211 (1988).
    [CrossRef]
  14. G. Rodriguez, J. P. Roberts, and A. J. Taylor, “Ultraviolet ultrafast pump-probe laser based on a Ti:sapphire laser system,” Opt. Lett. 19, 1146 (1994).
    [CrossRef] [PubMed]
  15. J. Y. Zhang, Z. Xu, Y. Kong, C. Yu, and Y. Wu, “10-HZ, 241 μJ widely tunable parametric generation and amplification in BBO, LBO, and CBO pumped by frequency-doubled femtosecond Ti:sapphire laser pulses,” Appl. Opt. (to be published).

1995 (4)

1994 (4)

1993 (2)

1992 (1)

J. Shen, H. He, Y. Liu, Y. Zhang, Z. Wang, and B. Wu, “Second harmonic generation by femtosecond optical pulses: theory and experiment,” Chin. Phys. 12, 413 (1992).

1990 (1)

1988 (1)

D. C. Edelstein, E. S. Washman, L. K. Cheng, W. R. Bosenberg, and C. L. Tang, “Femtosecond ultraviolet pulse generation in β–BaB2O4,” Appl. Phys. Lett. 52, 2211 (1988).
[CrossRef]

1984 (1)

Asaki, M. T.

Bosenberg, W. R.

D. C. Edelstein, E. S. Washman, L. K. Cheng, W. R. Bosenberg, and C. L. Tang, “Femtosecond ultraviolet pulse generation in β–BaB2O4,” Appl. Phys. Lett. 52, 2211 (1988).
[CrossRef]

Bowers, M. S.

Brabec, T.

Cheng, L. K.

D. C. Edelstein, E. S. Washman, L. K. Cheng, W. R. Bosenberg, and C. L. Tang, “Femtosecond ultraviolet pulse generation in β–BaB2O4,” Appl. Phys. Lett. 52, 2211 (1988).
[CrossRef]

Choo, H. R.

Curley, P. F.

Dienes, A.

Downer, M. C.

Dudley, J. M.

Edelstein, D. C.

D. C. Edelstein, E. S. Washman, L. K. Cheng, W. R. Bosenberg, and C. L. Tang, “Femtosecond ultraviolet pulse generation in β–BaB2O4,” Appl. Phys. Lett. 52, 2211 (1988).
[CrossRef]

Fork, R. L.

Garvey, D.

Harvey, J. D.

He, H.

J. Shen, H. He, Y. Liu, Y. Zhang, Z. Wang, and B. Wu, “Second harmonic generation by femtosecond optical pulses: theory and experiment,” Chin. Phys. 12, 413 (1992).

Huang, C. P.

Kalintsev, A. G.

Kapteyn, H. C.

Knoesen, A.

Knox, W. H.

Krausz, F.

Krylov, V.

Liu, Y.

J. Shen, H. He, Y. Liu, Y. Zhang, Z. Wang, and B. Wu, “Second harmonic generation by femtosecond optical pulses: theory and experiment,” Chin. Phys. 12, 413 (1992).

Murnane, M. M.

Rebane, A.

Roberts, J. P.

Rodriguez, G.

Schmidt, J.

Schwoerer, H.

Shank, C. V.

Shen, J.

J. Shen, H. He, Y. Liu, Y. Zhang, Z. Wang, and B. Wu, “Second harmonic generation by femtosecond optical pulses: theory and experiment,” Chin. Phys. 12, 413 (1992).

Sidick, E.

Smith, A. V.

Spielmann, Ch.

Spiemann, C.

Stingl, A.

Szipocs, R.

Taft, G.

Tang, C. L.

D. C. Edelstein, E. S. Washman, L. K. Cheng, W. R. Bosenberg, and C. L. Tang, “Femtosecond ultraviolet pulse generation in β–BaB2O4,” Appl. Phys. Lett. 52, 2211 (1988).
[CrossRef]

Taylor, A. J.

Wang, Z.

J. Shen, H. He, Y. Liu, Y. Zhang, Z. Wang, and B. Wu, “Second harmonic generation by femtosecond optical pulses: theory and experiment,” Chin. Phys. 12, 413 (1992).

Washman, E. S.

D. C. Edelstein, E. S. Washman, L. K. Cheng, W. R. Bosenberg, and C. L. Tang, “Femtosecond ultraviolet pulse generation in β–BaB2O4,” Appl. Phys. Lett. 52, 2211 (1988).
[CrossRef]

Wild, U.

Wintner, E.

Wu, B.

J. Shen, H. He, Y. Liu, Y. Zhang, Z. Wang, and B. Wu, “Second harmonic generation by femtosecond optical pulses: theory and experiment,” Chin. Phys. 12, 413 (1992).

Zhang, T. R.

Zhang, Y.

J. Shen, H. He, Y. Liu, Y. Zhang, Z. Wang, and B. Wu, “Second harmonic generation by femtosecond optical pulses: theory and experiment,” Chin. Phys. 12, 413 (1992).

Zhou, J. P.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

D. C. Edelstein, E. S. Washman, L. K. Cheng, W. R. Bosenberg, and C. L. Tang, “Femtosecond ultraviolet pulse generation in β–BaB2O4,” Appl. Phys. Lett. 52, 2211 (1988).
[CrossRef]

Chin. Phys. (1)

J. Shen, H. He, Y. Liu, Y. Zhang, Z. Wang, and B. Wu, “Second harmonic generation by femtosecond optical pulses: theory and experiment,” Chin. Phys. 12, 413 (1992).

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

Opt. Lett. (8)

V. Krylov, A. Rebane, A. G. Kalintsev, H. Schwoerer, and U. Wild, “Second-harmonic generation of amplified femtosecond Ti:sapphire laser pulses,” Opt. Lett. 20, 198 (1995).
[CrossRef] [PubMed]

W. H. Knox, M. C. Downer, R. L. Fork, and C. V. Shank, “Amplified femtosecond optical pulses and continuum generation at a 5-kHz repetition rate,” Opt. Lett. 9, 552 (1984).
[CrossRef] [PubMed]

P. F. Curley, Ch. Spielmann, T. Brabec, F. Krausz, E. Wintner, and J. Schmidt, “Operation of a femtosecond Ti-sapphire solitary laser in vicinity of zero group-delay dispersion,” Opt. Lett. 18, 54 (1993).
[CrossRef] [PubMed]

M. T. Asaki, C. P. Huang, D. Garvey, J. P. Zhou, H. C. Kapteyn, and M. M. Murnane, “Generation of 11-fs pulses from a self-mode-locked Ti-sapphire laser,” Opt. Lett. 18, 977 (1993).
[CrossRef] [PubMed]

A. Stingl, C. Spiemann, F. Krausz, and R. Szipocs, “Generation of 11-fs pulses from a Ti:sapphire laser without the use of prisms,” Opt. Lett. 19, 204 (1994).
[CrossRef] [PubMed]

J. D. Harvey, J. M. Dudley, P. F. Curley, C. Spiemann, and F. Krausz, “Coherent effects in a self-mode-locked Ti:sapphire laser,” Opt. Lett. 19, 972 (1994).
[CrossRef] [PubMed]

G. Rodriguez, J. P. Roberts, and A. J. Taylor, “Ultraviolet ultrafast pump-probe laser based on a Ti:sapphire laser system,” Opt. Lett. 19, 1146 (1994).
[CrossRef] [PubMed]

J. P. Zhou, G. Taft, C. P. Huang, M. M. Murnane, and H. C. Kapteyn, “Pulse evolution in broadband Ti:sapphire laser,” Opt. Lett. 19, 1149 (1994).
[CrossRef] [PubMed]

Other (1)

J. Y. Zhang, Z. Xu, Y. Kong, C. Yu, and Y. Wu, “10-HZ, 241 μJ widely tunable parametric generation and amplification in BBO, LBO, and CBO pumped by frequency-doubled femtosecond Ti:sapphire laser pulses,” Appl. Opt. (to be published).

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Figures (12)

Fig. 1
Fig. 1

Experimental arrangement for the study of temporal and spectral characteristics of the SHG of ultrashort pulses.

Fig. 2
Fig. 2

Calculated results of optical-conversion efficiency as a function of (a) crystal length and cross-correlation profiles of the SHG pulse with a transform-limited femtosecond laser with a pulse duration of 150 fs at three pumping intensities: 7 GW/cm2 (short-dashed curve), 40 GW/cm2 (dashed curve), and 120 GW/cm2 (solid curve) in (b) 0.5-mm BBO, (c) 1.0-mm BBO, and (d) 2.0-mm BBO.

Fig. 3
Fig. 3

Calculated results of optical-conversion efficiency as a function of (a) crystal length and cross-correlation profiles of SHG pulse with a non-transform-limited femtosecond laser with a pulse duration of 150 fs at three pumping intensities: 7 GW/cm2 (short-dashed curve), 40 GW/cm2 (dashed curve), and 120 GW/cm2 (solid curve) in (b) 0.5-mm BBO, (c) 1.0-mm BBO, and (d) 2.0-mm BBO.

Fig. 4
Fig. 4

Experimental cross-correlation profiles of SHG pulses at various pumping intensities obtained from a BBO crystal with various thicknesses: (a) 0.5 mm, (b) 1.0 mm, and (c) 2.0 mm. The pumping intensities (from bottom up) are 8.6, 14.9, 45.6, 81.6, 110, and 132 GW/cm2. Also shown are experimental cross-correlation profiles of SHG pulses obtained at various pumping intensities from LBO crystal with different thickness: (d) 1.0 mm and (e) 3.0 mm. The pumping intensities (from bottom up) are 8.6, 14.9, 45.6, 81.6, 110, and 132 GW/cm2.

Fig. 5
Fig. 5

Calculated spectral profiles of SHG obtained by a transform-limited femtosecond laser at 800 nm at various pumping intensities: (a) 7 GW/cm2 (short-dashed curve), (b) 40 GW/cm2 (dashed curve), and (c) 120 GW/cm2 (solid curve).

Fig. 6
Fig. 6

Calculated spectral profiles of SHG obtained by a non-transform-limited femtosecond laser at 800 nm at various pumping intensities: (a) 7 GW/cm2 (short-dashed curve), (b) 40 GW/cm2 (dashed curve), and (c) 120 GW/cm2 (solid curve).

Fig. 7
Fig. 7

Experimental spectra of SHG obtained at various pumping intensities from BBO crystals with various thicknesses: (a) 0.5 mm, (b) 1.0 mm, and (c) 2.0 mm. The pumping intensities (from bottom up) are 8.6, 14.9, 45.6, 81.6, 110, and 132 GW/cm2, respectively. Also shown are experimentally measured spectra of SHG obtained at various pumping intensities from LBO crystals with different thicknesses: (d) 1.0 mm and (e) 3.0 mm. The pumping intensities (from bottom up) are 8.6, 14.9, 45.6, 81.6, 110, and 132 GW/cm2.

Fig. 8
Fig. 8

Theoretical calculation of optical-conversion efficiency of SHG as a function of the crystal length and the laser pumping intensity with a non-transform-limited laser pulse with f2 =0.2.

Fig. 9
Fig. 9

Theoretical prediction of optical-conversion efficiency of SHG in BBO as a function of the crystal length at various degrees of frequency chirping.

Fig. 10
Fig. 10

(a) Experimental measurement of optical-conversion efficiency of SHG in three BBO crystals with different thicknesses as a function of laser pumping intensity. (b) Experimental measurement of optical-conversion efficiency of SHG in LBO as a function of laser pumping intensity.

Fig. 11
Fig. 11

Experimental spectra of conical parametric superfluorescence in (a) the high-frequency region and in (b) the low-frequency region. The fundamental pumping beam and the generated SHG are spatially filtered out.

Fig. 12
Fig. 12

Calculated SHG spectral profile from a 1-mm BBO at very high pumping intensity with different nonlinear indices of refraction n2 showing the effect of Kerr nonlinearity. Filled symbols are the result with n2=0 and f2=0, the dashed curve indicates the result with n2=0.45×10-15 cm2/W and f2 =0, and the solid curve denotes the result with n2=0.45 ×10-15 cm2/W and f2=0.2.

Equations (20)

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2Ez2-μ00 2Et2-μ0 2PLt2=μ0 2PNLt2,
E1(z, t)=12 E¯1 exp[i(ω1t-k1z)]+c.c.,
E2(z, t)=12 E¯2 exp[i(2ω1t-k2z)]+c.c..
E¯1z+1v1g E¯1t+igω 2E¯1t2
=iωχ(2)2nωc E¯1*E¯2+iωχ(3)2nωc×34 |E¯1|2+32 |E¯2|2E¯1,
E¯2z+1v2g E¯2t+ig2ω 2E¯2t2
=iωχ(2)2n2ωc E¯12+iωχ(3)n2ωc 32 |E¯1|2+34 |E¯2|2E¯2,
E˜1l+zIlw E˜1τ¯+izI4ld1 2E˜1τ¯2
=iE˜1*E˜2+2πi(n2E102)(zI/λ)34 |E˜1|2+32 |E˜2|2E¯1,
E˜2l+izI4ld2 2E˜2τ¯2
=i nωn2ω E˜12+4πi(n2E102)(zI/λ)34 |E˜2|2+32 |E˜1|2E˜2,
E˜1l+zIlw E˜1τ¯+izI4ld1 2E˜1τ¯2=0,
E˜2l+izI4ld2 2E˜2τ¯2=0,
E˜1l=iE˜1*E˜2+2πi(n2E102)(zI/λ)×34 |E˜1|2+32 |E˜2|2E˜1,
E˜2l=i nωn2ω E˜12+4πi(n2E102)(zI/λ)×34 |E˜2|2+32 |E˜1|2E˜2,
Ȇ1(l+dl, f )=Ȇ1(l, f )exp2πifzIlw+πfzI2ld1dl,
Ȇ2(l+dl, f )=Ȇ2(l, f )exp2πifπfzI2ld2dl.
E¯1(0, τ¯)=E10 exp-τ¯2(1+i4f2).
τ0ΔfB=2 ln 2π 1+(4f2)2,
τ0 Δλλ0=2λ0 ln 2cπ 1+(4f2)2.

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