Abstract

We investigate, both theoretically and experimentally, spectral, temporal, and coherence properties of a degenerate synchronously pumped optical parametric oscillator (SPOPO) as a divide-by-2 subharmonic generator. Periodically poled lithium niobate was used as the nonlinear gain medium and 180 fs pulses from a mode-locked Ti:Sapphire laser as the pump. A regime of stable SPOPO operation at degeneracy was achieved, where the SPOPO longitudinal modes were phase-locked to the pump, even without active cavity-length stabilization. Phase locking was confirmed by interference measurements between the pump and the frequency-doubled optical parametric oscillator output, as well as by beat frequency measurements using an independent continuous-wave laser. We have found that the stability range of such a phase-locked state, with respect to external perturbations, increased with the pump power and decreased with the cavity Q at a constant number of times above threshold, in excellent agreement with our model based on coupled nonlinear wave equations. At degeneracy (around 1550 nm), the SPOPO produced 70 fs output pulses with the full width at half-maximum spectral width of 210cm1, which manifests significant pulse compression and spectral broadening with respect to the pump laser.

© 2010 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]

2009 (2)

J. Mandon, G. Guelachvili, and N. Picque, “Fourier transform spectroscopy with a laser frequency comb,” Nat. Photonics 3, 99-102 (2009).
[CrossRef]

F. Adler, K. C. Cossel, M. J. Thorpe, I. Hartl, M. E. Fermann, and J. Ye, “Phase-stabilized, 1.5 W frequency comb at 2.8-4.8 μm,” Opt. Lett. 34, 1330-1332 (2009).
[CrossRef] [PubMed]

2008 (7)

A. Gambetta, R. Ramponi, and M. Marangoni, “Mid-infrared optical combs from a compact amplified Er-doped fiber oscillator,” Opt. Lett. 33, 2671-2673 (2008).
[CrossRef] [PubMed]

P. Malara, P. Maddaloni, G. Gagliardi, and P. De Natale, “Absolute frequency measurement of molecular transitions by a direct link to a comb generated around 3-μm,” Opt. Express 16, 8242-8249 (2008).
[CrossRef] [PubMed]

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D'Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science 321, 1335-1337 (2008).
[CrossRef] [PubMed]

M. J. Thorpe, D. Balslev-Clausen, M. S. Kirchner, and J. Ye, “Cavity-enhanced optical frequency comb spectroscopy: Application to human breath analysis,” Opt. Express 16, 2387-2397 (2008).
[CrossRef] [PubMed]

C. M. S. Sears, E. Colby, R. J. England, R. Ischebeck, C. McGuinness, J. Nelson, R. Noble, R. H. Siemann, J. Spencer, D. Walz, T. Plettner, and R. L. Byer, “Phase stable net acceleration of electrons from a two-stage optical accelerator,” Phys. Rev. Lett. 11, 101301 (2008).

B. M. Cowan, “Three-dimensional dielectric photonic crystal structures for laser-driven acceleration,” Phys. Rev. ST Accel. Beams 11, 011301 (2008).
[CrossRef]

J. Mandon, E. Sorokin, I. T. Sorokina, G. Guelachvili, and N. Picqué, “Supercontinua for high-resolution absorption multiplex infrared spectroscopy,” Opt. Lett. 33, 285-287 (2008).
[CrossRef] [PubMed]

2007 (6)

2006 (2)

C. L. Hagen, J. W. Walewski, and S. T. Sanders, “Generation of a continuum extending to the midinfrared by pumping ZBLAN fiber with an ultrafast 1550-nm source,” IEEE Photon. Technol. Lett. 18, 91-93 (2006).
[CrossRef]

C. Xia, M. Kumar, O. P. Kulkarni, M. N. Islam, F. L. Terry, M. J. Freeman, M. Poulain, and G. Mazé, “Midinfrared supercontinuum generation to 4.5 μm in ZBLAN fluoride fibers by nanosecond diode pumping,” Opt. Lett. 31, 2553-2555 (2006).
[CrossRef] [PubMed]

2005 (4)

T. Plettner, R. L. Byer, E. Colby, B. Cowan, C. M. S. Sears, J. E. Spencer, and R. H. Siemann, “Visible-laser acceleration of relativistic electrons in a semi-infinite vacuum,” Phys. Rev. Lett. 95, 134801 (2005).
[CrossRef] [PubMed]

P. Groβ and K. J. Boller, “Stability analysis of the self-phase-locked divide-by-2 optical parametric oscillator,” Phys. Rev. A 71, 033801 (2005).
[CrossRef]

P. Groβ, K. J. Boller, and M. E. Klein, “High-precision wavelength-flexible frequency division for metrology,” Phys. Rev. A 71, 043824 (2005).
[CrossRef]

G. Kalmani, A. Arie, P. Blau, S. Pearl, and A. V. Smith, “Polarization-mixing optical parametric oscillator,” Opt. Lett. 30, 2146-2148 (2005).
[CrossRef] [PubMed]

2004 (1)

2003 (2)

2002 (1)

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416, 233-237 (2002).
[CrossRef] [PubMed]

2001 (2)

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414, 509-513 (2001).
[CrossRef] [PubMed]

J. Zondy, A. Douillet, A. Tallet, E. Ressayre, and M. Le Berre, “Theory of self-phase-locked optical parametric oscillator,” Phys. Rev. A 63, 023814 (2001).
[CrossRef]

2000 (1)

1999 (2)

C. Fabre, E. J. Mason, and N. C. Wong, “Theoretical analysis of self-phase-locking in a type II phase-matched optical parametric oscillator,” Opt. Commun. 170, 299-307 (1999).
[CrossRef]

D. H. Lee, M. E. Klein, J. P. Meyn, P. Groβ, R. Wallenstein, and K. J. Boller, “Self-injection-locking of a CW-OPO by intracavity frequency-doubling the idler wave,” Opt. Express 5, 114-119 (1999).
[CrossRef] [PubMed]

1998 (1)

1995 (1)

A. Bonvalet, M. Joffre, J. L. Martin, and A. Migus, “Generation of ultrabroadband femtosecond pulses in the mid-infrared by optical rectification of 15 fs light pulses at 100 MHz repetition rate,” Appl. Phys. Lett. 67, 2907-2909 (1995).
[CrossRef]

1990 (2)

Adler, F.

Araujo-Hauck, C.

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D'Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science 321, 1335-1337 (2008).
[CrossRef] [PubMed]

Arie, A.

Balslev-Clausen, D.

Biegert, J.

Blau, P.

Boller, K. J.

P. Groβ, K. J. Boller, and M. E. Klein, “High-precision wavelength-flexible frequency division for metrology,” Phys. Rev. A 71, 043824 (2005).
[CrossRef]

P. Groβ and K. J. Boller, “Stability analysis of the self-phase-locked divide-by-2 optical parametric oscillator,” Phys. Rev. A 71, 033801 (2005).
[CrossRef]

D. H. Lee, M. E. Klein, J. P. Meyn, P. Groβ, R. Wallenstein, and K. J. Boller, “Self-injection-locking of a CW-OPO by intracavity frequency-doubling the idler wave,” Opt. Express 5, 114-119 (1999).
[CrossRef] [PubMed]

Bonvalet, A.

A. Bonvalet, M. Joffre, J. L. Martin, and A. Migus, “Generation of ultrabroadband femtosecond pulses in the mid-infrared by optical rectification of 15 fs light pulses at 100 MHz repetition rate,” Appl. Phys. Lett. 67, 2907-2909 (1995).
[CrossRef]

Brabec, T.

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414, 509-513 (2001).
[CrossRef] [PubMed]

Brida, D.

Byer, R. L.

C. M. S. Sears, E. Colby, R. J. England, R. Ischebeck, C. McGuinness, J. Nelson, R. Noble, R. H. Siemann, J. Spencer, D. Walz, T. Plettner, and R. L. Byer, “Phase stable net acceleration of electrons from a two-stage optical accelerator,” Phys. Rev. Lett. 11, 101301 (2008).

T. Plettner, R. L. Byer, E. Colby, B. Cowan, C. M. S. Sears, J. E. Spencer, and R. H. Siemann, “Visible-laser acceleration of relativistic electrons in a semi-infinite vacuum,” Phys. Rev. Lett. 95, 134801 (2005).
[CrossRef] [PubMed]

C. D. Nabors, S. T. Yang, T. Day, and R. L. Byer, “Coherence properties of a doubly-resonant monolithic optical parametric oscillator,” J. Opt. Soc. Am. B 7, 815-820 (1990).
[CrossRef]

Cerullo, G.

Cirmi, G.

Colby, E.

C. M. S. Sears, E. Colby, R. J. England, R. Ischebeck, C. McGuinness, J. Nelson, R. Noble, R. H. Siemann, J. Spencer, D. Walz, T. Plettner, and R. L. Byer, “Phase stable net acceleration of electrons from a two-stage optical accelerator,” Phys. Rev. Lett. 11, 101301 (2008).

T. Plettner, R. L. Byer, E. Colby, B. Cowan, C. M. S. Sears, J. E. Spencer, and R. H. Siemann, “Visible-laser acceleration of relativistic electrons in a semi-infinite vacuum,” Phys. Rev. Lett. 95, 134801 (2005).
[CrossRef] [PubMed]

Corkum, P.

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414, 509-513 (2001).
[CrossRef] [PubMed]

Corkum, P. B.

P. B. Corkum and F. Krausz, “Attosecond science,” Nat. Phys. 3, 381-387 (2007).
[CrossRef]

Cossel, K. C.

Cowan, B.

T. Plettner, R. L. Byer, E. Colby, B. Cowan, C. M. S. Sears, J. E. Spencer, and R. H. Siemann, “Visible-laser acceleration of relativistic electrons in a semi-infinite vacuum,” Phys. Rev. Lett. 95, 134801 (2005).
[CrossRef] [PubMed]

Cowan, B. M.

B. M. Cowan, “Three-dimensional dielectric photonic crystal structures for laser-driven acceleration,” Phys. Rev. ST Accel. Beams 11, 011301 (2008).
[CrossRef]

Cundiff, S. T.

S. T. Cundiff and J. Ye, “Colloquium: femtosecond optical frequency combs,” Rev. Mod. Phys. 75, 325-342 (2003).
[CrossRef]

Day, T.

De Natale, P.

De Silvestri, S.

D'Odorico, S.

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D'Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science 321, 1335-1337 (2008).
[CrossRef] [PubMed]

Drescher, M.

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414, 509-513 (2001).
[CrossRef] [PubMed]

England, R. J.

C. M. S. Sears, E. Colby, R. J. England, R. Ischebeck, C. McGuinness, J. Nelson, R. Noble, R. H. Siemann, J. Spencer, D. Walz, T. Plettner, and R. L. Byer, “Phase stable net acceleration of electrons from a two-stage optical accelerator,” Phys. Rev. Lett. 11, 101301 (2008).

Erny, C.

Fabre, C.

C. Fabre, E. J. Mason, and N. C. Wong, “Theoretical analysis of self-phase-locking in a type II phase-matched optical parametric oscillator,” Opt. Commun. 170, 299-307 (1999).
[CrossRef]

Fedorov, V. V.

I. S. Moskalev, V. V. Fedorov, and S. B. Mirov, “Self-starting Kerr-mode-locked polycrystalline Cr2+:ZnSe laser,” in The CLEO/QELS Conference (Optical Society of America, 2008), paper CF13.

Fejer, M. M.

Fermann, M. E.

Foreman, S. M.

Freeman, M. J.

Gagliardi, G.

Gale, B. J. S.

Gambetta, A.

Gohle, C.

Groß, P.

P. Groβ and K. J. Boller, “Stability analysis of the self-phase-locked divide-by-2 optical parametric oscillator,” Phys. Rev. A 71, 033801 (2005).
[CrossRef]

P. Groβ, K. J. Boller, and M. E. Klein, “High-precision wavelength-flexible frequency division for metrology,” Phys. Rev. A 71, 043824 (2005).
[CrossRef]

D. H. Lee, M. E. Klein, J. P. Meyn, P. Groβ, R. Wallenstein, and K. J. Boller, “Self-injection-locking of a CW-OPO by intracavity frequency-doubling the idler wave,” Opt. Express 5, 114-119 (1999).
[CrossRef] [PubMed]

Guelachvili, G.

Hagen, C. L.

C. L. Hagen, J. W. Walewski, and S. T. Sanders, “Generation of a continuum extending to the midinfrared by pumping ZBLAN fiber with an ultrafast 1550-nm source,” IEEE Photon. Technol. Lett. 18, 91-93 (2006).
[CrossRef]

Hamm, P.

Hänsch, T. W.

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D'Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science 321, 1335-1337 (2008).
[CrossRef] [PubMed]

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416, 233-237 (2002).
[CrossRef] [PubMed]

Hartl, I.

Heinzmann, U.

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414, 509-513 (2001).
[CrossRef] [PubMed]

Hentschel, M.

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414, 509-513 (2001).
[CrossRef] [PubMed]

Holzwarth, R.

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D'Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science 321, 1335-1337 (2008).
[CrossRef] [PubMed]

F. Keilmann, C. Gohle, and R. Holzwarth, “Time-domain mid-infrared frequency-comb spectrometer,” Opt. Lett. 29, 1542-1544 (2004).
[CrossRef] [PubMed]

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416, 233-237 (2002).
[CrossRef] [PubMed]

Ischebeck, R.

C. M. S. Sears, E. Colby, R. J. England, R. Ischebeck, C. McGuinness, J. Nelson, R. Noble, R. H. Siemann, J. Spencer, D. Walz, T. Plettner, and R. L. Byer, “Phase stable net acceleration of electrons from a two-stage optical accelerator,” Phys. Rev. Lett. 11, 101301 (2008).

Islam, M. N.

Joffre, M.

A. Bonvalet, M. Joffre, J. L. Martin, and A. Migus, “Generation of ultrabroadband femtosecond pulses in the mid-infrared by optical rectification of 15 fs light pulses at 100 MHz repetition rate,” Appl. Phys. Lett. 67, 2907-2909 (1995).
[CrossRef]

Jones, D. J.

Kaindl, R. A.

Kalmani, G.

Keilmann, F.

Keller, U.

Kentischer, T.

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D'Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science 321, 1335-1337 (2008).
[CrossRef] [PubMed]

Kienberger, R.

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414, 509-513 (2001).
[CrossRef] [PubMed]

Kirchner, M. S.

Klein, M. E.

Krausz, F.

P. B. Corkum and F. Krausz, “Attosecond science,” Nat. Phys. 3, 381-387 (2007).
[CrossRef]

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414, 509-513 (2001).
[CrossRef] [PubMed]

Kühlke, D.

Kulkarni, O. P.

Kumar, M.

Langrock, C.

Lee, D. H.

Leitenstorfer, A.

Maddaloni, P.

Malara, P.

Mandon, J.

Manescau, A.

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D'Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science 321, 1335-1337 (2008).
[CrossRef] [PubMed]

Manzoni, C.

Marangoni, M.

Martin, J. L.

A. Bonvalet, M. Joffre, J. L. Martin, and A. Migus, “Generation of ultrabroadband femtosecond pulses in the mid-infrared by optical rectification of 15 fs light pulses at 100 MHz repetition rate,” Appl. Phys. Lett. 67, 2907-2909 (1995).
[CrossRef]

Mason, E. J.

C. Fabre, E. J. Mason, and N. C. Wong, “Theoretical analysis of self-phase-locking in a type II phase-matched optical parametric oscillator,” Opt. Commun. 170, 299-307 (1999).
[CrossRef]

E. J. Mason and N. C. Wong, “Observation of two distinct phase states in a self-phase-locked type II phase-matched optical parametric oscillator,” Opt. Lett. 23, 1733-1735 (1998).
[CrossRef]

Mazé, G.

McGuinness, C.

C. M. S. Sears, E. Colby, R. J. England, R. Ischebeck, C. McGuinness, J. Nelson, R. Noble, R. H. Siemann, J. Spencer, D. Walz, T. Plettner, and R. L. Byer, “Phase stable net acceleration of electrons from a two-stage optical accelerator,” Phys. Rev. Lett. 11, 101301 (2008).

Meyn, J. P.

Migus, A.

A. Bonvalet, M. Joffre, J. L. Martin, and A. Migus, “Generation of ultrabroadband femtosecond pulses in the mid-infrared by optical rectification of 15 fs light pulses at 100 MHz repetition rate,” Appl. Phys. Lett. 67, 2907-2909 (1995).
[CrossRef]

Milosevic, N.

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414, 509-513 (2001).
[CrossRef] [PubMed]

Mirov, S. B.

I. S. Moskalev, V. V. Fedorov, and S. B. Mirov, “Self-starting Kerr-mode-locked polycrystalline Cr2+:ZnSe laser,” in The CLEO/QELS Conference (Optical Society of America, 2008), paper CF13.

Moskalev, I. S.

I. S. Moskalev, V. V. Fedorov, and S. B. Mirov, “Self-starting Kerr-mode-locked polycrystalline Cr2+:ZnSe laser,” in The CLEO/QELS Conference (Optical Society of America, 2008), paper CF13.

Moutzouris, K.

Murphy, M. T.

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D'Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science 321, 1335-1337 (2008).
[CrossRef] [PubMed]

Nabors, C. D.

Nelson, J.

C. M. S. Sears, E. Colby, R. J. England, R. Ischebeck, C. McGuinness, J. Nelson, R. Noble, R. H. Siemann, J. Spencer, D. Walz, T. Plettner, and R. L. Byer, “Phase stable net acceleration of electrons from a two-stage optical accelerator,” Phys. Rev. Lett. 11, 101301 (2008).

Noble, R.

C. M. S. Sears, E. Colby, R. J. England, R. Ischebeck, C. McGuinness, J. Nelson, R. Noble, R. H. Siemann, J. Spencer, D. Walz, T. Plettner, and R. L. Byer, “Phase stable net acceleration of electrons from a two-stage optical accelerator,” Phys. Rev. Lett. 11, 101301 (2008).

Pasquini, L.

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D'Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science 321, 1335-1337 (2008).
[CrossRef] [PubMed]

Pearl, S.

Picque, N.

J. Mandon, G. Guelachvili, and N. Picque, “Fourier transform spectroscopy with a laser frequency comb,” Nat. Photonics 3, 99-102 (2009).
[CrossRef]

Picqué, N.

Plettner, T.

C. M. S. Sears, E. Colby, R. J. England, R. Ischebeck, C. McGuinness, J. Nelson, R. Noble, R. H. Siemann, J. Spencer, D. Walz, T. Plettner, and R. L. Byer, “Phase stable net acceleration of electrons from a two-stage optical accelerator,” Phys. Rev. Lett. 11, 101301 (2008).

T. Plettner, R. L. Byer, E. Colby, B. Cowan, C. M. S. Sears, J. E. Spencer, and R. H. Siemann, “Visible-laser acceleration of relativistic electrons in a semi-infinite vacuum,” Phys. Rev. Lett. 95, 134801 (2005).
[CrossRef] [PubMed]

Poulain, M.

Ramponi, R.

Reid, D. T.

Reider, G. A.

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414, 509-513 (2001).
[CrossRef] [PubMed]

Reimann, K.

Sanders, S. T.

C. L. Hagen, J. W. Walewski, and S. T. Sanders, “Generation of a continuum extending to the midinfrared by pumping ZBLAN fiber with an ultrafast 1550-nm source,” IEEE Photon. Technol. Lett. 18, 91-93 (2006).
[CrossRef]

Schmidt, W.

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D'Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science 321, 1335-1337 (2008).
[CrossRef] [PubMed]

Sears, C. M. S.

C. M. S. Sears, E. Colby, R. J. England, R. Ischebeck, C. McGuinness, J. Nelson, R. Noble, R. H. Siemann, J. Spencer, D. Walz, T. Plettner, and R. L. Byer, “Phase stable net acceleration of electrons from a two-stage optical accelerator,” Phys. Rev. Lett. 11, 101301 (2008).

T. Plettner, R. L. Byer, E. Colby, B. Cowan, C. M. S. Sears, J. E. Spencer, and R. H. Siemann, “Visible-laser acceleration of relativistic electrons in a semi-infinite vacuum,” Phys. Rev. Lett. 95, 134801 (2005).
[CrossRef] [PubMed]

Siemann, R. H.

C. M. S. Sears, E. Colby, R. J. England, R. Ischebeck, C. McGuinness, J. Nelson, R. Noble, R. H. Siemann, J. Spencer, D. Walz, T. Plettner, and R. L. Byer, “Phase stable net acceleration of electrons from a two-stage optical accelerator,” Phys. Rev. Lett. 11, 101301 (2008).

T. Plettner, R. L. Byer, E. Colby, B. Cowan, C. M. S. Sears, J. E. Spencer, and R. H. Siemann, “Visible-laser acceleration of relativistic electrons in a semi-infinite vacuum,” Phys. Rev. Lett. 95, 134801 (2005).
[CrossRef] [PubMed]

Smith, A. V.

Sorokin, E.

Sorokina, I. T.

Spencer, J.

C. M. S. Sears, E. Colby, R. J. England, R. Ischebeck, C. McGuinness, J. Nelson, R. Noble, R. H. Siemann, J. Spencer, D. Walz, T. Plettner, and R. L. Byer, “Phase stable net acceleration of electrons from a two-stage optical accelerator,” Phys. Rev. Lett. 11, 101301 (2008).

Spencer, J. E.

T. Plettner, R. L. Byer, E. Colby, B. Cowan, C. M. S. Sears, J. E. Spencer, and R. H. Siemann, “Visible-laser acceleration of relativistic electrons in a semi-infinite vacuum,” Phys. Rev. Lett. 95, 134801 (2005).
[CrossRef] [PubMed]

Spielmann, C.

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414, 509-513 (2001).
[CrossRef] [PubMed]

Steinmetz, T.

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D'Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science 321, 1335-1337 (2008).
[CrossRef] [PubMed]

Sun, J. H.

Terry, F. L.

Thorpe, M. J.

Udem, T.

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D'Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science 321, 1335-1337 (2008).
[CrossRef] [PubMed]

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416, 233-237 (2002).
[CrossRef] [PubMed]

Walewski, J. W.

C. L. Hagen, J. W. Walewski, and S. T. Sanders, “Generation of a continuum extending to the midinfrared by pumping ZBLAN fiber with an ultrafast 1550-nm source,” IEEE Photon. Technol. Lett. 18, 91-93 (2006).
[CrossRef]

Wallenstein, R.

Walz, D.

C. M. S. Sears, E. Colby, R. J. England, R. Ischebeck, C. McGuinness, J. Nelson, R. Noble, R. H. Siemann, J. Spencer, D. Walz, T. Plettner, and R. L. Byer, “Phase stable net acceleration of electrons from a two-stage optical accelerator,” Phys. Rev. Lett. 11, 101301 (2008).

Weiner, A. M.

Wilken, T.

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D'Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science 321, 1335-1337 (2008).
[CrossRef] [PubMed]

Woerner, M.

Wong, N. C.

Wurm, M.

Xia, C.

Yang, S. T.

Ye, J.

Zondy, J.

J. Zondy, A. Douillet, A. Tallet, E. Ressayre, and M. Le Berre, “Theory of self-phase-locked optical parametric oscillator,” Phys. Rev. A 63, 023814 (2001).
[CrossRef]

Appl. Phys. Lett. (1)

A. Bonvalet, M. Joffre, J. L. Martin, and A. Migus, “Generation of ultrabroadband femtosecond pulses in the mid-infrared by optical rectification of 15 fs light pulses at 100 MHz repetition rate,” Appl. Phys. Lett. 67, 2907-2909 (1995).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

C. L. Hagen, J. W. Walewski, and S. T. Sanders, “Generation of a continuum extending to the midinfrared by pumping ZBLAN fiber with an ultrafast 1550-nm source,” IEEE Photon. Technol. Lett. 18, 91-93 (2006).
[CrossRef]

J. Opt. Soc. Am. B (2)

Nat. Photonics (1)

J. Mandon, G. Guelachvili, and N. Picque, “Fourier transform spectroscopy with a laser frequency comb,” Nat. Photonics 3, 99-102 (2009).
[CrossRef]

Nat. Phys. (1)

P. B. Corkum and F. Krausz, “Attosecond science,” Nat. Phys. 3, 381-387 (2007).
[CrossRef]

Nature (2)

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416, 233-237 (2002).
[CrossRef] [PubMed]

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414, 509-513 (2001).
[CrossRef] [PubMed]

Opt. Commun. (1)

C. Fabre, E. J. Mason, and N. C. Wong, “Theoretical analysis of self-phase-locking in a type II phase-matched optical parametric oscillator,” Opt. Commun. 170, 299-307 (1999).
[CrossRef]

Opt. Express (5)

Opt. Lett. (12)

F. Keilmann, C. Gohle, and R. Holzwarth, “Time-domain mid-infrared frequency-comb spectrometer,” Opt. Lett. 29, 1542-1544 (2004).
[CrossRef] [PubMed]

S. M. Foreman, D. J. Jones, and J. Ye, “Flexible and rapidly configurable femtosecond pulse generation in the mid-IR,” Opt. Lett. 28, 370-372 (2003).
[CrossRef] [PubMed]

C. Erny, K. Moutzouris, J. Biegert, D. Kühlke, F. Adler, A. Leitenstorfer, and U. Keller, “Mid-infrared difference-frequency generation of ultrashort pulses tunable between 3.2 and 4.8 μm from a compact fiber source,” Opt. Lett. 32, 1138-1140 (2007).
[CrossRef] [PubMed]

A. Gambetta, R. Ramponi, and M. Marangoni, “Mid-infrared optical combs from a compact amplified Er-doped fiber oscillator,” Opt. Lett. 33, 2671-2673 (2008).
[CrossRef] [PubMed]

C. Xia, M. Kumar, O. P. Kulkarni, M. N. Islam, F. L. Terry, M. J. Freeman, M. Poulain, and G. Mazé, “Midinfrared supercontinuum generation to 4.5 μm in ZBLAN fluoride fibers by nanosecond diode pumping,” Opt. Lett. 31, 2553-2555 (2006).
[CrossRef] [PubMed]

J. Mandon, E. Sorokin, I. T. Sorokina, G. Guelachvili, and N. Picqué, “Supercontinua for high-resolution absorption multiplex infrared spectroscopy,” Opt. Lett. 33, 285-287 (2008).
[CrossRef] [PubMed]

C. Langrock, M. M. Fejer, I. Hartl, and M. E. Fermann, “Generation of octave-spanning spectra inside reverse-proton-exchanged periodically poled lithium niobate waveguides,” Opt. Lett. 32, 2478-2480 (2007).
[CrossRef] [PubMed]

N. C. Wong, “Optical frequency division using an optical parametric oscillator,” Opt. Lett. 15, 1129-1131 (1990).
[CrossRef] [PubMed]

E. J. Mason and N. C. Wong, “Observation of two distinct phase states in a self-phase-locked type II phase-matched optical parametric oscillator,” Opt. Lett. 23, 1733-1735 (1998).
[CrossRef]

J. H. Sun, B. J. S. Gale, and D. T. Reid, “Composite frequency comb spanning 0.4-2.4 μm from a phase-controlled femtosecond Ti:sapphire laser and synchronously pumped optical parametric oscillator,” Opt. Lett. 32, 1414-1416 (2007).
[CrossRef] [PubMed]

F. Adler, K. C. Cossel, M. J. Thorpe, I. Hartl, M. E. Fermann, and J. Ye, “Phase-stabilized, 1.5 W frequency comb at 2.8-4.8 μm,” Opt. Lett. 34, 1330-1332 (2009).
[CrossRef] [PubMed]

G. Kalmani, A. Arie, P. Blau, S. Pearl, and A. V. Smith, “Polarization-mixing optical parametric oscillator,” Opt. Lett. 30, 2146-2148 (2005).
[CrossRef] [PubMed]

Phys. Rev. A (3)

J. Zondy, A. Douillet, A. Tallet, E. Ressayre, and M. Le Berre, “Theory of self-phase-locked optical parametric oscillator,” Phys. Rev. A 63, 023814 (2001).
[CrossRef]

P. Groβ and K. J. Boller, “Stability analysis of the self-phase-locked divide-by-2 optical parametric oscillator,” Phys. Rev. A 71, 033801 (2005).
[CrossRef]

P. Groβ, K. J. Boller, and M. E. Klein, “High-precision wavelength-flexible frequency division for metrology,” Phys. Rev. A 71, 043824 (2005).
[CrossRef]

Phys. Rev. Lett. (2)

T. Plettner, R. L. Byer, E. Colby, B. Cowan, C. M. S. Sears, J. E. Spencer, and R. H. Siemann, “Visible-laser acceleration of relativistic electrons in a semi-infinite vacuum,” Phys. Rev. Lett. 95, 134801 (2005).
[CrossRef] [PubMed]

C. M. S. Sears, E. Colby, R. J. England, R. Ischebeck, C. McGuinness, J. Nelson, R. Noble, R. H. Siemann, J. Spencer, D. Walz, T. Plettner, and R. L. Byer, “Phase stable net acceleration of electrons from a two-stage optical accelerator,” Phys. Rev. Lett. 11, 101301 (2008).

Phys. Rev. ST Accel. Beams (1)

B. M. Cowan, “Three-dimensional dielectric photonic crystal structures for laser-driven acceleration,” Phys. Rev. ST Accel. Beams 11, 011301 (2008).
[CrossRef]

Rev. Mod. Phys. (1)

S. T. Cundiff and J. Ye, “Colloquium: femtosecond optical frequency combs,” Rev. Mod. Phys. 75, 325-342 (2003).
[CrossRef]

Science (1)

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D'Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science 321, 1335-1337 (2008).
[CrossRef] [PubMed]

Other (1)

I. S. Moskalev, V. V. Fedorov, and S. B. Mirov, “Self-starting Kerr-mode-locked polycrystalline Cr2+:ZnSe laser,” in The CLEO/QELS Conference (Optical Society of America, 2008), paper CF13.

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Figures (11)

Fig. 1
Fig. 1

Longitudinal modes of (a) non-degenerate, (b) partly degenerate, and (c) degenerate SPOPO. Dashed line corresponds to the half of the pump center frequency.

Fig. 2
Fig. 2

Longitudinal modes of the pump and a degenerate doubly resonant SPOPO, which has two possible sets of modes.

Fig. 3
Fig. 3

Phase coherence between neighboring OPO modes is established via cross-coupling between the pump, signal, and idler, e.g., via a b c d path.

Fig. 4
Fig. 4

SPOPO cavity resonances and SPOPO frequencies in the degenerate phase-locked regime.

Fig. 5
Fig. 5

Schematic diagram of the degenerate type 0 SPOPO. Mirrors M 1 M 4 are highly reflective at 1550 nm, and M 5 is an OC mirror.

Fig. 6
Fig. 6

Spectra of the non-degenerate (dotted line) and degenerate (solid line) SPOPOs.

Fig. 7
Fig. 7

Background-free autocorrelation traces obtained using SH generation. Degenerate phase-locked SPOPO pulses (solid line) are transformed-limited with pulse duration of 70 fs. The pulse profile is distorted for non-degenerate (unlocked) SPOPO output (dashed line).

Fig. 8
Fig. 8

Results from interference measurements between the pump and the OPO SH transmitted through a narrowband 750 nm filter. (a) Degenerate (phase-locked) SPOPO. Presence of strongly visible fringes and absence of satellite RF beat frequencies can be seen; (b) non-degenerate (unlocked) SPOPO. There is an absence of fringe pattern and a presence of RF satellite beat notes.

Fig. 9
Fig. 9

Results from interference between the pump and the OPO SH using a 1600 nm filter before the SH crystal for (a) degenerate (phase-locked) and (b) non-degenerate (unlocked) SPOPOs. The data are consistent with those in Fig. 8.

Fig. 10
Fig. 10

Scatter plot of beat notes between the phase-locked SPOPO and a CW laser at 1550 nm versus beat notes between the pump and frequency-doubled CW laser (at 775 nm). The slopes for the two sets of beat notes are both one half.

Fig. 11
Fig. 11

Measured data and calculated curves of the frequency locking range Δ f as a function of number of times above pump threshold for the 50% and 25% output coupling.

Equations (15)

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

ν p = ν s + ν i ,
ϕ p = ϕ s + ϕ i + π / 2 ,
ϕ p = 2 ϕ s , i + π / 2 ,
ν n = f CEO + n f rep ,
ν m = f CEO 2 + m f rep ,
ν m = f CEO 2 + ( m + 1 2 ) f rep ,
ϕ n = 2 ϕ m + π / 2.
[ A s ( z = l ) A i ( z = l ) ] = | cosh ( g l ) i   sinh ( g l ) i   sinh ( g l ) cosh ( g l ) | [ A s ( z = 0 ) A i ( z = 0 ) ] .
M = | t 0 0 t | | e i φ 0 0 e i φ | | cosh ( g l ) i   sinh ( g l ) i   sinh ( g l ) cosh ( g l ) | = | t e i φ   cosh ( g l ) i t e i φ   sinh ( g l ) i t e i φ   sinh ( g l ) t e i φ   cosh ( g l ) | .
A = M A ,
det | M I | = 0 ,
t 2 2 t   cosh ( g l ) cos   φ + 1 = 0.
( g l ) 2 = ( loss / 2 ) 2 + φ 2 .
φ = ( g l ) 0 N 1 = loss 2 N 1 .
Δ f f rep = φ 2 π = loss 4 π N 1 .

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