Abstract

Ultrashort-pulse evolution inside a optical parametric oscillator is described by using a nonlinear-envelope-equation approach, eliminating the assumptions of fixed frequencies and a single χ(2) process associated with conventional solutions based on the three coupled-amplitude equations. By treating the interacting waves as a single propagating field, the experimentally-observed behaviors of singly and doubly-resonant OPOs are predicted across near-octave-spanning bandwidths, including situations where the nonlinear crystal provides simultaneous phasematching for multiple nonlinear processes.

©2011 Optical Society of America

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References

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  1. J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between Light Waves in a Nonlinear Dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
    [Crossref]
  2. M. F. Becker, D. J. Kuizenga, D. W. Phillion, and A. E. Siegman, “Analytic expression for ultrashort pulse generation in mode-locked optical parametric oscillators,” J. Appl. Phys. 45(9), 3996–4005 (1974).
    [Crossref]
  3. E. C. Cheung and J. M. Liu, “Theory of a synchronously pumped optical parametric oscillator in steady-state operation,” J. Opt. Soc. Am. B 7(8), 1385–1401 (1990).
    [Crossref]
  4. B. Ruffing, A. Nebel, and R. Wallenstein, “All-solid-state cw mode-locked picosecond KTiOAsO4 (KTA) optical parametric oscillator,” Appl. Phys. B 67(5), 537–544 (1998).
    [Crossref]
  5. J. E. Schaar, J. S. Pelc, K. L. Vodopyanov, and M. M. Fejer, “Characterization and control of pulse shapes in a doubly resonant synchronously pumped optical parametric oscillator,” Appl. Opt. 49(24), 4489–4493 (2010).
    [Crossref] [PubMed]
  6. M. Conforti, F. Baronio, and C. De Angelis, “Nonlinear envelope equation for broadband optical pulses in quadratic media,” Phys. Rev. A 81(5), 053841 (2010).
    [Crossref]
  7. J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
    [Crossref]
  8. T. Brabec and F. Krausz, “Nonlinear Optical Pulse Propagation in the Single-Cycle Regime,” Phys. Rev. Lett. 78(17), 3282–3285 (1997).
    [Crossref]
  9. C. Langrock, M. M. Fejer, I. Hartl, and M. E. Fermann, “Generation of octave-spanning spectra inside reverse-photon-exchanged periodically poled lithium niobate waveguides,” Opt. Lett. 32(17), 2478–2480 (2007).
    [Crossref] [PubMed]
  10. N. Leindecker, A. Marandi, R. L. Byer, and K. L. Vodopyanov, “Broadband degenerate OPO for mid-infrared frequency comb generation,” Opt. Express 19(7), 6296–6302 (2011).
    [Crossref] [PubMed]
  11. S. T. Wong, K. L. Vodopyanov, and R. L. Byer, “Self-phase-locked divide-by-2 optical parametric oscillator as a broadband frequency comb source,” J. Opt. Soc. Am. B 27(5), 876–882 (2010).
    [Crossref]
  12. M. Conforti, F. Baronio, C. De Angelis, M. Marangoni, and G. Cerullo, “Theory and experiments on multistep parametric processes in nonlinear optics,” J. Opt. Soc. Am. B 28(4), 892–895 (2011).
    [Crossref]
  13. J. H. Sun, B. J. S. Gale, and D. T. Reid, “Composite frequency comb spanning 0.4-2.4μm from a phase-controlled femtosecond Ti:sapphire laser and synchronously pumped optical parametric oscillator,” Opt. Lett. 32(11), 1414–1416 (2007).
    [Crossref] [PubMed]
  14. K. L. Vodopyanov, E. Sorokin, I. T. Sorokina, and P. G. Schunemann, “Mid-IR frequency comb source spanning 4.4-5.4 μm based on subharmonic GaAs optical parametric oscillator,” Opt. Lett. 36(12), 2275–2277 (2011).
    [Crossref] [PubMed]
  15. G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, San Diego, 2001).
  16. K. A. Tillman, D. T. Reid, D. Artigas, and T. Y. Jiang, “Idler-resonant femtosecond tandem optical parametric oscillator tuning from 2.1 µm to 4.2 µm,” J. Opt. Soc. Am. B 21(8), 1551–1558 (2004).
    [Crossref]
  17. D. T. Reid, J. M. Dudley, M. Ebrahimzadeh, and W. Sibbett, “Soliton formation in a femtosecond optical parametric oscillator,” Opt. Lett. 19(11), 825–827 (1994).
    [Crossref] [PubMed]

2011 (3)

2010 (3)

2007 (2)

2006 (1)

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
[Crossref]

2004 (1)

1998 (1)

B. Ruffing, A. Nebel, and R. Wallenstein, “All-solid-state cw mode-locked picosecond KTiOAsO4 (KTA) optical parametric oscillator,” Appl. Phys. B 67(5), 537–544 (1998).
[Crossref]

1997 (1)

T. Brabec and F. Krausz, “Nonlinear Optical Pulse Propagation in the Single-Cycle Regime,” Phys. Rev. Lett. 78(17), 3282–3285 (1997).
[Crossref]

1994 (1)

1990 (1)

1974 (1)

M. F. Becker, D. J. Kuizenga, D. W. Phillion, and A. E. Siegman, “Analytic expression for ultrashort pulse generation in mode-locked optical parametric oscillators,” J. Appl. Phys. 45(9), 3996–4005 (1974).
[Crossref]

1962 (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between Light Waves in a Nonlinear Dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
[Crossref]

Armstrong, J. A.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between Light Waves in a Nonlinear Dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
[Crossref]

Artigas, D.

Baronio, F.

M. Conforti, F. Baronio, C. De Angelis, M. Marangoni, and G. Cerullo, “Theory and experiments on multistep parametric processes in nonlinear optics,” J. Opt. Soc. Am. B 28(4), 892–895 (2011).
[Crossref]

M. Conforti, F. Baronio, and C. De Angelis, “Nonlinear envelope equation for broadband optical pulses in quadratic media,” Phys. Rev. A 81(5), 053841 (2010).
[Crossref]

Becker, M. F.

M. F. Becker, D. J. Kuizenga, D. W. Phillion, and A. E. Siegman, “Analytic expression for ultrashort pulse generation in mode-locked optical parametric oscillators,” J. Appl. Phys. 45(9), 3996–4005 (1974).
[Crossref]

Bloembergen, N.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between Light Waves in a Nonlinear Dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
[Crossref]

Brabec, T.

T. Brabec and F. Krausz, “Nonlinear Optical Pulse Propagation in the Single-Cycle Regime,” Phys. Rev. Lett. 78(17), 3282–3285 (1997).
[Crossref]

Byer, R. L.

Cerullo, G.

Cheung, E. C.

Coen, S.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
[Crossref]

Conforti, M.

M. Conforti, F. Baronio, C. De Angelis, M. Marangoni, and G. Cerullo, “Theory and experiments on multistep parametric processes in nonlinear optics,” J. Opt. Soc. Am. B 28(4), 892–895 (2011).
[Crossref]

M. Conforti, F. Baronio, and C. De Angelis, “Nonlinear envelope equation for broadband optical pulses in quadratic media,” Phys. Rev. A 81(5), 053841 (2010).
[Crossref]

De Angelis, C.

M. Conforti, F. Baronio, C. De Angelis, M. Marangoni, and G. Cerullo, “Theory and experiments on multistep parametric processes in nonlinear optics,” J. Opt. Soc. Am. B 28(4), 892–895 (2011).
[Crossref]

M. Conforti, F. Baronio, and C. De Angelis, “Nonlinear envelope equation for broadband optical pulses in quadratic media,” Phys. Rev. A 81(5), 053841 (2010).
[Crossref]

Ducuing, J.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between Light Waves in a Nonlinear Dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
[Crossref]

Dudley, J. M.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
[Crossref]

D. T. Reid, J. M. Dudley, M. Ebrahimzadeh, and W. Sibbett, “Soliton formation in a femtosecond optical parametric oscillator,” Opt. Lett. 19(11), 825–827 (1994).
[Crossref] [PubMed]

Ebrahimzadeh, M.

Fejer, M. M.

Fermann, M. E.

Gale, B. J. S.

Genty, G.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
[Crossref]

Hartl, I.

Jiang, T. Y.

Krausz, F.

T. Brabec and F. Krausz, “Nonlinear Optical Pulse Propagation in the Single-Cycle Regime,” Phys. Rev. Lett. 78(17), 3282–3285 (1997).
[Crossref]

Kuizenga, D. J.

M. F. Becker, D. J. Kuizenga, D. W. Phillion, and A. E. Siegman, “Analytic expression for ultrashort pulse generation in mode-locked optical parametric oscillators,” J. Appl. Phys. 45(9), 3996–4005 (1974).
[Crossref]

Langrock, C.

Leindecker, N.

Liu, J. M.

Marandi, A.

Marangoni, M.

Nebel, A.

B. Ruffing, A. Nebel, and R. Wallenstein, “All-solid-state cw mode-locked picosecond KTiOAsO4 (KTA) optical parametric oscillator,” Appl. Phys. B 67(5), 537–544 (1998).
[Crossref]

Pelc, J. S.

Pershan, P. S.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between Light Waves in a Nonlinear Dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
[Crossref]

Phillion, D. W.

M. F. Becker, D. J. Kuizenga, D. W. Phillion, and A. E. Siegman, “Analytic expression for ultrashort pulse generation in mode-locked optical parametric oscillators,” J. Appl. Phys. 45(9), 3996–4005 (1974).
[Crossref]

Reid, D. T.

Ruffing, B.

B. Ruffing, A. Nebel, and R. Wallenstein, “All-solid-state cw mode-locked picosecond KTiOAsO4 (KTA) optical parametric oscillator,” Appl. Phys. B 67(5), 537–544 (1998).
[Crossref]

Schaar, J. E.

Schunemann, P. G.

Sibbett, W.

Siegman, A. E.

M. F. Becker, D. J. Kuizenga, D. W. Phillion, and A. E. Siegman, “Analytic expression for ultrashort pulse generation in mode-locked optical parametric oscillators,” J. Appl. Phys. 45(9), 3996–4005 (1974).
[Crossref]

Sorokin, E.

Sorokina, I. T.

Sun, J. H.

Tillman, K. A.

Vodopyanov, K. L.

Wallenstein, R.

B. Ruffing, A. Nebel, and R. Wallenstein, “All-solid-state cw mode-locked picosecond KTiOAsO4 (KTA) optical parametric oscillator,” Appl. Phys. B 67(5), 537–544 (1998).
[Crossref]

Wong, S. T.

Appl. Opt. (1)

Appl. Phys. B (1)

B. Ruffing, A. Nebel, and R. Wallenstein, “All-solid-state cw mode-locked picosecond KTiOAsO4 (KTA) optical parametric oscillator,” Appl. Phys. B 67(5), 537–544 (1998).
[Crossref]

J. Appl. Phys. (1)

M. F. Becker, D. J. Kuizenga, D. W. Phillion, and A. E. Siegman, “Analytic expression for ultrashort pulse generation in mode-locked optical parametric oscillators,” J. Appl. Phys. 45(9), 3996–4005 (1974).
[Crossref]

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

Opt. Express (1)

Opt. Lett. (4)

Phys. Rev. (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between Light Waves in a Nonlinear Dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
[Crossref]

Phys. Rev. A (1)

M. Conforti, F. Baronio, and C. De Angelis, “Nonlinear envelope equation for broadband optical pulses in quadratic media,” Phys. Rev. A 81(5), 053841 (2010).
[Crossref]

Phys. Rev. Lett. (1)

T. Brabec and F. Krausz, “Nonlinear Optical Pulse Propagation in the Single-Cycle Regime,” Phys. Rev. Lett. 78(17), 3282–3285 (1997).
[Crossref]

Rev. Mod. Phys. (1)

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
[Crossref]

Other (1)

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, San Diego, 2001).

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Figures (4)

Fig. 1
Fig. 1 (a) Output spectrum of the tandem OPO, expressed as a logarithmic density plot, showing its evolution from a weak 50-fs seed pulse, centered at 2.3 µm, into a steady-state output after ~30 cavity roundtrips. (b) Spectral evolution of the field in the tandem OPO crystal once steady-state has been reached, showing the origin of additional waves due to multiple simultaneous sum- and difference-frequency processes (for details, see text).

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Fig. 2
Fig. 2 Comparison of the experimental and simulated output-coupled spectra for the tandem OPO described in [16] for a 1-mm grating period of 22.94 µm and a 1.6-mm grating period of 34.71 µm. Sharp features in the simulation result (solid lines) have been filtered (dashed lines) for comparison with the experimental spectrum acquired using a low-resolution spectrometer.

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Fig. 3
Fig. 3 (a) Simulated spectrum of the degenerate MgO:PPLN OPO reported in [10], presented on axes allowing a comparison with the previously published experimental data. (b) Spectral evolution of the resonant pulse showing steady-state behavior after 20 cavity roundtrips.

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Fig. 4
Fig. 4 Spectral evolution of the resonant pulse in a degenerate OPO similar to that reported in [10], in which the cavity length is detuned from the position corresponding to perfect synchronization of the exactly-phasematched pulse with the pump pulse. The OPO displays spectral oscillations with a period of around 26 cavity roundtrips.

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Equations (3)

Equations on this page are rendered with MathJax. Learn more.

∂ A ∂ z + i D A = − i χ ( 2 ) ω 0 2 4 β 0 c 2 ( 1 − i ω 0 ∂ ∂ τ ) [ A 2 e i ω 0 τ − i ( β 0 − β 1 ω 0 ) z + 2 | A | 2 e − i ω 0 τ + i ( β 0 − β 1 ω 0 ) z ]
χ ( 2 ) ( z ) = χ e f f ( 2 ) sin ( 2 π z / Λ ) / | sin ( 2 π z / Λ ) |
H ( ω ) = R e − ln 2 [ 2 ( ω − ω 0 ) / Δ ω ] 10 − i ( ω − ω 0 ) T

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