Abstract

We report on the influence of self-focusing and self-defocusing in the phase-mismatched frequency doubling crystal on the third harmonic generation (THG) efficiency in a two crystal frequency tripling scheme. By detuning the temperature of the doubling crystal, the impact of a phase-mismatch in second harmonic generation (SHG) on the subsequent sum frequency mixing process was investigated. It was found that adjusting the temperature not only affected the power ratio of the second harmonic to the fundamental but also the beam diameter of the fundamental beam in the THG crystal, which was caused by self-focusing and self-defocusing of the fundamental beam, respectively. This self-action was induced by a cascaded χ(2) : χ(2) process in the phase-mismatched SHG crystal. Self-defocusing was observable for positive detuning and self-focusing for negative detuning of the phase-matching temperature. Hence, the THG efficiency was not symmetric with respect to the point of optimum phase-matching. Optimum THG was obtained for positive detuning and the resulting self-defocusing in combination with the focusing lens in front of the THG stage was also beneficial for the beam quality of the third harmonic.

© 2015 Optical Society of America

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References

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  1. R. S. Craxton, “High efficiency frequency tripling schemes for high-power Nd:Glass lasers,” IEEE J. Quantum Electron. 17(9), 1771–1782 (1981).
    [Crossref]
  2. P. Qiu and A. Penzkofer, “Picosecond third-harmonic light generation in β-BaB2O4,” Appl. Phys. B 45, 225–236 (1988).
    [Crossref]
  3. P. S. Banks, M. D. Feit, and M. D. Perry, “High-intensity third-harmonic generation in beta barium borate through second-order and third-order susceptibilities,” Opt. Lett. 24(1), 4–6 (1999).
    [Crossref]
  4. P. S. Banks, M. D. Feit, and M. D. Perry, “High-intensity third-harmonic generation,” J. Opt. Soc. Am. B 19(1), 102–118 (2002).
    [Crossref]
  5. K. Miyata, V. Petrov, and F. Noack, “High-efficiency single-crystal third-harmonic generation in BiB3O6,” Opt. Lett. 36(18), 3627–3629 (2011).
    [Crossref] [PubMed]
  6. L. A. Ostrovskii, ”Self-action of light in crystals,” JETP Lett. 5, 272–275 (1967).
  7. R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, and E. W Van Stryland, “Self-focusing and self-defocusing by cascaded second-order effects in KTP,” Opt. Lett. 17(1), 28–30 (1992).
    [Crossref] [PubMed]
  8. G. I. Stegeman, “χ(2) cascading: nonlinear phase shifts,” Quantum Semiclass. Opt. 9, 139–153 (1997).
    [Crossref]
  9. G. I. Stegeman, D. J. Hagan, and L. Torner, “χ(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691–1740 (1996).
    [Crossref]
  10. G. Cerullo, S. De Silvestri, A. Monguzzi, D. Segala, and V. Magni, “Self-starting mode locking of a cw Nd:YAG laser using cascaded second-order nonlinearities,” Opt. Lett. 20(7), 746–748 (1995).
    [Crossref] [PubMed]
  11. K. Beckwitt, F. W. Wise, L. Qian, L. A. Walker, and E. Canto-Said, “Compensation for self-focusing by use of cascade quadratic nonlinearity,” Opt. Lett. 26(21), 1696–1698 (2001).
    [Crossref]
  12. P. Koch, J. Bartschke, and J. A. L’huillier, “All solid-state 191.7 nm deep-UV light source by seventh harmonic generation of an 888 nm pumped, Q-switched 1342 nm Nd:YVO4 laser with excellent beam quality,” Opt. Express 22(11), 13648–13658 (2014).
    [Crossref] [PubMed]
  13. M. Okada and S. Ieiri, “Influences of self-induced thermal effects on phase matching in nonlinear optical crystals,” IEEE J. Quantum Electron. QE-7(12), 560–563 (1971).
    [Crossref]
  14. R. L. Sutherland, Handbook of Nonlinear Optics (Marcel Dekker Inc, 2003)
  15. N. Umemura, K. Miyata, and K. Kato, “New data on the optical properties of BiB3O6,” Opt. Mater. 30, 532–534 (2007).
    [Crossref]
  16. SNLO nonlinear optics software from A. V. Smith, AS-Photonics, Albuquerque, NM, USA.

2014 (1)

2011 (1)

2007 (1)

N. Umemura, K. Miyata, and K. Kato, “New data on the optical properties of BiB3O6,” Opt. Mater. 30, 532–534 (2007).
[Crossref]

2002 (1)

2001 (1)

1999 (1)

1997 (1)

G. I. Stegeman, “χ(2) cascading: nonlinear phase shifts,” Quantum Semiclass. Opt. 9, 139–153 (1997).
[Crossref]

1996 (1)

G. I. Stegeman, D. J. Hagan, and L. Torner, “χ(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691–1740 (1996).
[Crossref]

1995 (1)

1992 (1)

1988 (1)

P. Qiu and A. Penzkofer, “Picosecond third-harmonic light generation in β-BaB2O4,” Appl. Phys. B 45, 225–236 (1988).
[Crossref]

1981 (1)

R. S. Craxton, “High efficiency frequency tripling schemes for high-power Nd:Glass lasers,” IEEE J. Quantum Electron. 17(9), 1771–1782 (1981).
[Crossref]

1971 (1)

M. Okada and S. Ieiri, “Influences of self-induced thermal effects on phase matching in nonlinear optical crystals,” IEEE J. Quantum Electron. QE-7(12), 560–563 (1971).
[Crossref]

1967 (1)

L. A. Ostrovskii, ”Self-action of light in crystals,” JETP Lett. 5, 272–275 (1967).

Banks, P. S.

Bartschke, J.

Beckwitt, K.

Canto-Said, E.

Cerullo, G.

Craxton, R. S.

R. S. Craxton, “High efficiency frequency tripling schemes for high-power Nd:Glass lasers,” IEEE J. Quantum Electron. 17(9), 1771–1782 (1981).
[Crossref]

De Silvestri, S.

DeSalvo, R.

Feit, M. D.

Hagan, D. J.

G. I. Stegeman, D. J. Hagan, and L. Torner, “χ(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691–1740 (1996).
[Crossref]

R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, and E. W Van Stryland, “Self-focusing and self-defocusing by cascaded second-order effects in KTP,” Opt. Lett. 17(1), 28–30 (1992).
[Crossref] [PubMed]

Ieiri, S.

M. Okada and S. Ieiri, “Influences of self-induced thermal effects on phase matching in nonlinear optical crystals,” IEEE J. Quantum Electron. QE-7(12), 560–563 (1971).
[Crossref]

Kato, K.

N. Umemura, K. Miyata, and K. Kato, “New data on the optical properties of BiB3O6,” Opt. Mater. 30, 532–534 (2007).
[Crossref]

Koch, P.

L’huillier, J. A.

Magni, V.

Miyata, K.

K. Miyata, V. Petrov, and F. Noack, “High-efficiency single-crystal third-harmonic generation in BiB3O6,” Opt. Lett. 36(18), 3627–3629 (2011).
[Crossref] [PubMed]

N. Umemura, K. Miyata, and K. Kato, “New data on the optical properties of BiB3O6,” Opt. Mater. 30, 532–534 (2007).
[Crossref]

Monguzzi, A.

Noack, F.

Okada, M.

M. Okada and S. Ieiri, “Influences of self-induced thermal effects on phase matching in nonlinear optical crystals,” IEEE J. Quantum Electron. QE-7(12), 560–563 (1971).
[Crossref]

Ostrovskii, L. A.

L. A. Ostrovskii, ”Self-action of light in crystals,” JETP Lett. 5, 272–275 (1967).

Penzkofer, A.

P. Qiu and A. Penzkofer, “Picosecond third-harmonic light generation in β-BaB2O4,” Appl. Phys. B 45, 225–236 (1988).
[Crossref]

Perry, M. D.

Petrov, V.

Qian, L.

Qiu, P.

P. Qiu and A. Penzkofer, “Picosecond third-harmonic light generation in β-BaB2O4,” Appl. Phys. B 45, 225–236 (1988).
[Crossref]

Segala, D.

Sheik-Bahae, M.

Stegeman, G.

Stegeman, G. I.

G. I. Stegeman, “χ(2) cascading: nonlinear phase shifts,” Quantum Semiclass. Opt. 9, 139–153 (1997).
[Crossref]

G. I. Stegeman, D. J. Hagan, and L. Torner, “χ(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691–1740 (1996).
[Crossref]

Sutherland, R. L.

R. L. Sutherland, Handbook of Nonlinear Optics (Marcel Dekker Inc, 2003)

Torner, L.

G. I. Stegeman, D. J. Hagan, and L. Torner, “χ(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691–1740 (1996).
[Crossref]

Umemura, N.

N. Umemura, K. Miyata, and K. Kato, “New data on the optical properties of BiB3O6,” Opt. Mater. 30, 532–534 (2007).
[Crossref]

Van Stryland, E. W

Walker, L. A.

Wise, F. W.

Appl. Phys. B (1)

P. Qiu and A. Penzkofer, “Picosecond third-harmonic light generation in β-BaB2O4,” Appl. Phys. B 45, 225–236 (1988).
[Crossref]

IEEE J. Quantum Electron. (2)

R. S. Craxton, “High efficiency frequency tripling schemes for high-power Nd:Glass lasers,” IEEE J. Quantum Electron. 17(9), 1771–1782 (1981).
[Crossref]

M. Okada and S. Ieiri, “Influences of self-induced thermal effects on phase matching in nonlinear optical crystals,” IEEE J. Quantum Electron. QE-7(12), 560–563 (1971).
[Crossref]

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

JETP Lett. (1)

L. A. Ostrovskii, ”Self-action of light in crystals,” JETP Lett. 5, 272–275 (1967).

Opt. Express (1)

Opt. Lett. (5)

Opt. Mater. (1)

N. Umemura, K. Miyata, and K. Kato, “New data on the optical properties of BiB3O6,” Opt. Mater. 30, 532–534 (2007).
[Crossref]

Opt. Quantum Electron. (1)

G. I. Stegeman, D. J. Hagan, and L. Torner, “χ(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691–1740 (1996).
[Crossref]

Quantum Semiclass. Opt. (1)

G. I. Stegeman, “χ(2) cascading: nonlinear phase shifts,” Quantum Semiclass. Opt. 9, 139–153 (1997).
[Crossref]

Other (2)

SNLO nonlinear optics software from A. V. Smith, AS-Photonics, Albuquerque, NM, USA.

R. L. Sutherland, Handbook of Nonlinear Optics (Marcel Dekker Inc, 2003)

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Figures (6)

Fig. 1
Fig. 1 Experimental setup. For details see text.

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Fig. 2
Fig. 2 Dependence of the sum frequency power at 447 nm (blue) and the SHG power without THG (red) from the phase-matching temperature of the SHG crystal for different setups. The total pump power of the conversion units is kept constant at 13.3 W. Decreasing beam radii of the 1342 nm beam inside the SHG crystal were used for measurements (b)–(e) resulting in an increasing peak fluence. The summarized fluence of the 671 nm beam and the 1342 nm beam inside the THG crystal is approximately constant for measurements (b)–(e). Measurement (a) is conducted without lens L4 resulting in a lower fluence in the THG crystal. Beam radii and fluences F in the SHG crystal for the different setups (geometric mean of both axis): (a) 265 μm (F = 1.21 J/cm2), (b) 265 μm, (c) 231 μm (F = 1.59 J/cm2), (d) 201 μm (F = 2.1 J/cm2) and (e) 179 μm (F = 2.64 J/cm2). See text for further details. The THG data of part (e) has already been published in our prior work [12].

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Fig. 3
Fig. 3 (a) Dependence of the beam radii of the 1342 nm beam and the 671 nm beam inside the THG crystal from the phase-matching temperature for a beam radius of 179 μm in the SHG crystal. (b) Dioptric power of an effective Kerr lens inside the SHG crystal calculated from the beam radius at 1342 nm inside the THG crystal with the ABCD-matrix formalism using a thin lens inside the SHG crystal. Shifting the measured data by ΔT = 0.132 °C would lead to a vanishing lens for zero detuning.

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Fig. 4
Fig. 4 (a) Asymmetry of the measured phase-matching curve of the SHG stage. The deviation of the phase-matching peak from the mean value of the FWHM positions is ΔT = 0.147 °C. (b) Influence of the effective Kerr lens inside the SHG crystal on the propagation of the 1342 nm beam and its beam radius inside the THG crystal. The beam radii are calculated with the ABCD-matrix formalism.

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Fig. 5
Fig. 5 (Top) Beam profiles of the 447 nm beam for different phase-mismatches of the SHG process. (Bottom) Profiles in x-direction (black) with the corresponding Gaussian fit (green) and percentage of match. (a) ΔT ≈ −0.612 °C (Match of Gaussian fit: 79.9 %). (b) ΔT = 0 °C (SHG phase-matching peak, match of Gaussian fit: 88.3 %). (c) ΔT ≈ 0.186 °C (Match of Gaussian fit: 96.2 %).

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Fig. 6
Fig. 6 (a) Numerically calculated SHG phase-matching curve for a radius of 179 μm and 13.3 W fundamental power (green) and the phase-matching curve for the non-depleted pump approximation (black). (b) Numerically calculated nonlinear phase-shift per optical intensity η in dependence from the phase-mismatch of the SHG process at 13.3 W pump power (green). η is equivalent to the effective nonlinear refractive index n 2 eff in the limiting case of non-depleted pump approximation (black). The experimental data on the dioptric power of the Kerr lens is overlaid for comparison (blue). The experimental data is shifted by ΔT = 0.132 °C for better comparability resulting in zero-crossing for vanishing dioptric power.

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Equations (5)

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d A 2 ω d z = i 2 ω c n 2 ω d eff A ω 2 exp ( i Δ k z )
d A ω d z = i 2 ω c n ω d eff A ω * A 2 ω exp ( − i Δ k z ) .
Δ Φ NL ( L ) = arctan ( Im [ A ω ( z = L ) ] Re [ A ω ( z = L ) ] ) .
Δ Φ NDPA ( L ) = 2 ω 2 d eff 2 I ω L ε 0 c 3 n ω 2 n 2 ω Δ k [ 1 − sinc ( Δ k L ) ]
η = λ 2 π L Δ Φ NL ( L ) I ω .

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