Abstract

We demonstrate a high-power two-color femtosecond near-infrared optical parametric oscillator synchronously pumped by a 7.4W femtosecond Yb:KGW laser. This system is almost gap-free tunable with signal wavelengths ranging between 1445 and 1880nm, with up to 1.7W average signal output power at femtosecond pulse durations. At wavelengths near the point at which the cavity group-delay dispersion equals zero, dual-signal-wavelength operation occurs due to equal group delay at two wavelengths.

© 2011 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2011 (1)

J.-P. Negel, R. Hegenbarth, A. Steinmann, B. Metzger, F. Hoos, and H. Giessen, “Compact and cost-effective scheme for THz generation via optical rectification in GaP and GaAs using novel fs laser oscillators,” Appl. Phys. B , doi:10.1007/s00340-011-4385-7(2011).
[CrossRef]

2010 (2)

D. Brida, C. Manzoni, G. Cirmi, M. Marangoni, S. Bonora, P. Villoresi, S. De Silvestri, and G. Cerullo, “Few-optical-cycle pulses tunable from the visible to the mid-infrared by optical parametric amplifiers,” J. Opt. 12, 013001 (2010).
[CrossRef]

I. T. Lima, Jr., V. Kultavewuti, and A. Major, “Phasematching properties of congruent MgO-doped and undoped periodically poled LiNbO3 for optical parametric oscillation with ultrafast excitation at 1 μm,” Laser Phys. 20, 270–275 (2010).
[CrossRef]

2009 (3)

2008 (3)

R. Grebs, T. Dekorsy, S. A. Diddams, and A. Bartels, “1 GHzrepetition rate femtosecond OPO with stabilized offset between signal and idler frequency combs,” Opt. Express 16, 5397–5405(2008).
[CrossRef]

O. Gayer, Z. Sacks, E. Galun, and A. Arie, “Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO3,” Appl. Phys. B 91, 343–348 (2008).
[CrossRef]

A. Shapapov, V. Barzda, and A. Major, “Development of a high power femtosecond optical parametric oscillator for biomedical imaging applications,” Proc. SPIE 7099, 70992H (2008).
[CrossRef]

2007 (3)

2006 (2)

J. Sun, B. J. S. Gale, and D. T. Reid, “Dual-color operation of a femtosecond optical parametric oscillator exhibiting stable relative carrier-envelope phase-slip frequencies,” Opt. Lett. 31, 2021–2023 (2006).
[CrossRef] [PubMed]

K. L. Vodopyanov, M. M. Fejer, X. Yu, J. S. Harris, Y.-S. Lee, W. C. Hurlbut, V. G. Kozlov, D. Bliss, and C. Lynch, “Terahertz-wave generation in quasi-phase-matched GaAs,” Appl. Phys. Lett. 89, 141119 (2006).
[CrossRef]

2004 (2)

T. Südmeyer, E. Innerhofer, F. Brunner, R. Paschotta, T. Usami, H. Ito, S. Kurimura, K. Kitamura, D. C. Hanna, and U. Keller, “High-power femtosecond fiber-feedback optical parametric oscillator based on periodically poled stoichiometric LiTaO3,” Opt. Lett. 29, 1111–1113 (2004).
[CrossRef] [PubMed]

X. P. Zhang and H. Giessen, “Four-wave mixing based on cascaded second-order nonlinear processes in a femtosecond optical parametric oscillator operating near degeneracy,” Appl. Phys. B 79, 441–447 (2004).
[CrossRef]

2002 (2)

2001 (1)

2000 (2)

1999 (4)

S. Marzenell, R. Beigang, and R. Wallenstein, “Synchronously pumped femtosecond optical parametric oscillator based on AgGaSe2 tunable from 2 μm to 8 μm,” Appl. Phys. B 69, 423–428 (1999).
[CrossRef]

S. Haidar and H. Ito, “Injection-seeded optical parametric oscillator for efficient difference frequency generation in mid-IR,” Opt. Commun. 171, 171–176 (1999).
[CrossRef]

R. A. Kaindl, F. Eickemeyer, M. Woerner, and T. Elsaesser, “Broadband phase-matched difference frequency mixing of femtosecond pulses in GaSe: experiment and theory,” Appl. Phys. Lett. 75, 1060–1062 (1999).
[CrossRef]

M. Nakamura, M. Sugihara, M. Kotoh, H. Taniguchi, and K. Kadatomo, “Quasi-phase-matched optical parametric oscillator using periodically poled MgO-doped LiNbO3 crystal,” Jpn. J. Appl. Phys. 38, L1234–L1236 (1999).
[CrossRef]

1998 (3)

1997 (5)

I. Shoji, T. Kondo, A. Kitamoto, M. Shirane, and R. Ito, “Absolute scale of second-order nonlinear-optical coefficients,” J. Opt. Soc. Am. B 14, 2268–2292 (1997).
[CrossRef]

H. Li, F. Zhou, X. Zhang, and W. Ji, “Picosecond Z-scan study of bound electronic Kerr effect in LiNbO3 crystal associated with two-photon absorption,” Appl. Phys. B 64, 659–662 (1997).
[CrossRef]

K. C. Burr, C. L. Tang, M. A. Arbore, and M. M. Fejer, “High-repetition-rate femtosecond optical parametric oscillator based on periodically poled lithium niobate,” Appl. Phys. Lett. 70, 3341–3343 (1997).
[CrossRef]

T. Kartaloglu, K. G. Köprülü, and O. Aytür, “Phase-matched self-doubling optical parametric oscillator,” Opt. Lett. 22, 280–282 (1997).
[CrossRef]

J. Hebling, H. Giessen, S. Linden, and J. Kuhl, “Mirror-dispersion-compensated femtosecond optical parametric oscillator,” Opt. Commun. 141, 229–236 (1997).
[CrossRef]

1996 (1)

D. S. Butterworth, S. Girard, and D. C. Hanna, “A simple technique to achieve active cavity-length stabilization in a synchronously pumped optical parametric oscillator,” Opt. Commun. 123, 577–592 (1996).
[CrossRef]

1995 (2)

1994 (2)

J. M. Dudley, D. T. Reid, M. Ebrahim-Zadeh, and W. Sibbett, “Characteristics of a noncritically phasematched Ti:sapphire pumped femtosecond optical parametric oscillator,” Opt. Commun. 104, 419–430 (1994).
[CrossRef]

T. J. Driscoll, G. M. Gale, and F. Hache, “Ti:sapphire second-harmonic-pumped visible-range femtosecond optical parametric oscillator,” Opt. Commun. 110, 638–644 (1994).
[CrossRef]

1992 (2)

1990 (1)

1984 (1)

D. A. Bryan, R. Gerson, and H. E. Tomaschke, “Increased optical damage resistance in lithium niobate,” Appl. Phys. Lett. 44, 847–849 (1984).
[CrossRef]

Adler, F.

Andres, T.

T. Andres, P. Haag, S. Reuter, S. Zelt, J.-P. Meyn, A. Borsutzky, R. Beigang, and R. Wallenstein, “Femtosecond optical parametric oscillators based on MgO:PPLN operating at room temperature,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (CD) (Optical Society of America, 2002), paper CTuO2.

Arbore, M. A.

K. C. Burr, C. L. Tang, M. A. Arbore, and M. M. Fejer, “High-repetition-rate femtosecond optical parametric oscillator based on periodically poled lithium niobate,” Appl. Phys. Lett. 70, 3341–3343 (1997).
[CrossRef]

Arie, A.

O. Gayer, Z. Sacks, E. Galun, and A. Arie, “Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO3,” Appl. Phys. B 91, 343–348 (2008).
[CrossRef]

Aus der Au, J.

Aytür, O.

Bartels, A.

R. Grebs, T. Dekorsy, S. A. Diddams, and A. Bartels, “1 GHzrepetition rate femtosecond OPO with stabilized offset between signal and idler frequency combs,” Opt. Express 16, 5397–5405(2008).
[CrossRef]

X. P. Zhang, J. Hebling, A. Bartels, D. Nau, J. Kuhl, W. W. Rühle, and H. Giessen, “1 GHz-repetition-rate femtosecond optical parametric oscillator,” Appl. Phys. Lett. 80, 1873–1875 (2002).
[CrossRef]

Barzda, V.

A. Shapapov, V. Barzda, and A. Major, “Development of a high power femtosecond optical parametric oscillator for biomedical imaging applications,” Proc. SPIE 7099, 70992H (2008).
[CrossRef]

Beigang, R.

S. Marzenell, R. Beigang, and R. Wallenstein, “Synchronously pumped femtosecond optical parametric oscillator based on AgGaSe2 tunable from 2 μm to 8 μm,” Appl. Phys. B 69, 423–428 (1999).
[CrossRef]

T. Andres, P. Haag, S. Reuter, S. Zelt, J.-P. Meyn, A. Borsutzky, R. Beigang, and R. Wallenstein, “Femtosecond optical parametric oscillators based on MgO:PPLN operating at room temperature,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (CD) (Optical Society of America, 2002), paper CTuO2.

Bliss, D.

K. L. Vodopyanov, M. M. Fejer, X. Yu, J. S. Harris, Y.-S. Lee, W. C. Hurlbut, V. G. Kozlov, D. Bliss, and C. Lynch, “Terahertz-wave generation in quasi-phase-matched GaAs,” Appl. Phys. Lett. 89, 141119 (2006).
[CrossRef]

Bonora, S.

D. Brida, C. Manzoni, G. Cirmi, M. Marangoni, S. Bonora, P. Villoresi, S. De Silvestri, and G. Cerullo, “Few-optical-cycle pulses tunable from the visible to the mid-infrared by optical parametric amplifiers,” J. Opt. 12, 013001 (2010).
[CrossRef]

Borsutzky, A.

T. Andres, P. Haag, S. Reuter, S. Zelt, J.-P. Meyn, A. Borsutzky, R. Beigang, and R. Wallenstein, “Femtosecond optical parametric oscillators based on MgO:PPLN operating at room temperature,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (CD) (Optical Society of America, 2002), paper CTuO2.

Brida, D.

D. Brida, C. Manzoni, G. Cirmi, M. Marangoni, S. Bonora, P. Villoresi, S. De Silvestri, and G. Cerullo, “Few-optical-cycle pulses tunable from the visible to the mid-infrared by optical parametric amplifiers,” J. Opt. 12, 013001 (2010).
[CrossRef]

Broderick, N. G. R.

Brunner, F.

Bryan, D. A.

D. A. Bryan, R. Gerson, and H. E. Tomaschke, “Increased optical damage resistance in lithium niobate,” Appl. Phys. Lett. 44, 847–849 (1984).
[CrossRef]

Burr, K. C.

K. C. Burr, C. L. Tang, M. A. Arbore, and M. M. Fejer, “High-repetition-rate femtosecond optical parametric oscillator based on periodically poled lithium niobate,” Appl. Phys. Lett. 70, 3341–3343 (1997).
[CrossRef]

Butterworth, D. S.

D. S. Butterworth, S. Girard, and D. C. Hanna, “A simple technique to achieve active cavity-length stabilization in a synchronously pumped optical parametric oscillator,” Opt. Commun. 123, 577–592 (1996).
[CrossRef]

Byer, R. L.

Cerullo, G.

D. Brida, C. Manzoni, G. Cirmi, M. Marangoni, S. Bonora, P. Villoresi, S. De Silvestri, and G. Cerullo, “Few-optical-cycle pulses tunable from the visible to the mid-infrared by optical parametric amplifiers,” J. Opt. 12, 013001 (2010).
[CrossRef]

M. Marangoni, R. Osellame, R. Ramponi, G. Cerullo, A. Steinmann, and U. Morgner, “Near-infrared optical parametric amplifier at 1 MHz directly pumped by a femtosecond oscillator,” Opt. Lett. 32, 1489–1491 (2007).
[CrossRef] [PubMed]

Cheung, E. C.

Cirmi, G.

D. Brida, C. Manzoni, G. Cirmi, M. Marangoni, S. Bonora, P. Villoresi, S. De Silvestri, and G. Cerullo, “Few-optical-cycle pulses tunable from the visible to the mid-infrared by optical parametric amplifiers,” J. Opt. 12, 013001 (2010).
[CrossRef]

Cossel, K. C.

De Silvestri, S.

D. Brida, C. Manzoni, G. Cirmi, M. Marangoni, S. Bonora, P. Villoresi, S. De Silvestri, and G. Cerullo, “Few-optical-cycle pulses tunable from the visible to the mid-infrared by optical parametric amplifiers,” J. Opt. 12, 013001 (2010).
[CrossRef]

Dearborn, M. E.

Dekorsy, T.

Diddams, S. A.

Driscoll, T. J.

T. J. Driscoll, G. M. Gale, and F. Hache, “Ti:sapphire second-harmonic-pumped visible-range femtosecond optical parametric oscillator,” Opt. Commun. 110, 638–644 (1994).
[CrossRef]

Dudley, J. M.

J. M. Dudley, D. T. Reid, M. Ebrahim-Zadeh, and W. Sibbett, “Characteristics of a noncritically phasematched Ti:sapphire pumped femtosecond optical parametric oscillator,” Opt. Commun. 104, 419–430 (1994).
[CrossRef]

Ebrahim-Zadeh, M.

Eckardt, R. C.

Eickemeyer, F.

R. A. Kaindl, F. Eickemeyer, M. Woerner, and T. Elsaesser, “Broadband phase-matched difference frequency mixing of femtosecond pulses in GaSe: experiment and theory,” Appl. Phys. Lett. 75, 1060–1062 (1999).
[CrossRef]

Elsaesser, T.

R. A. Kaindl, F. Eickemeyer, M. Woerner, and T. Elsaesser, “Broadband phase-matched difference frequency mixing of femtosecond pulses in GaSe: experiment and theory,” Appl. Phys. Lett. 75, 1060–1062 (1999).
[CrossRef]

Esteban-Martin, A.

Fejer, M. M.

J. E. Schaar, K. L. Vodopyanov, and M. M. Fejer, “Intracavity terahertz-wave generation in a synchronously pumped optical parametric oscillator using quasi-phase-matched GaAs,” Opt. Lett. 32, 1284–1286 (2007).
[CrossRef] [PubMed]

K. L. Vodopyanov, M. M. Fejer, X. Yu, J. S. Harris, Y.-S. Lee, W. C. Hurlbut, V. G. Kozlov, D. Bliss, and C. Lynch, “Terahertz-wave generation in quasi-phase-matched GaAs,” Appl. Phys. Lett. 89, 141119 (2006).
[CrossRef]

K. C. Burr, C. L. Tang, M. A. Arbore, and M. M. Fejer, “High-repetition-rate femtosecond optical parametric oscillator based on periodically poled lithium niobate,” Appl. Phys. Lett. 70, 3341–3343 (1997).
[CrossRef]

L. E. Myers, R. C. Eckardt, M. M. Fejer, R. L. Byer, W. R. Rosenberg, and J. W. Pierce, “Quasi-phase-matched optical parametric oscillators in bulk periodically poled LiNbO3,” J. Opt. Soc. Am. B 12, 2102–2116 (1995).
[CrossRef]

Fermann, M. E.

Fu, Q.

Gale, B. J. S.

Gale, G. M.

T. J. Driscoll, G. M. Gale, and F. Hache, “Ti:sapphire second-harmonic-pumped visible-range femtosecond optical parametric oscillator,” Opt. Commun. 110, 638–644 (1994).
[CrossRef]

Galun, E.

O. Gayer, Z. Sacks, E. Galun, and A. Arie, “Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO3,” Appl. Phys. B 91, 343–348 (2008).
[CrossRef]

Gayer, O.

O. Gayer, Z. Sacks, E. Galun, and A. Arie, “Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO3,” Appl. Phys. B 91, 343–348 (2008).
[CrossRef]

Gerson, R.

D. A. Bryan, R. Gerson, and H. E. Tomaschke, “Increased optical damage resistance in lithium niobate,” Appl. Phys. Lett. 44, 847–849 (1984).
[CrossRef]

Giessen, H.

J.-P. Negel, R. Hegenbarth, A. Steinmann, B. Metzger, F. Hoos, and H. Giessen, “Compact and cost-effective scheme for THz generation via optical rectification in GaP and GaAs using novel fs laser oscillators,” Appl. Phys. B , doi:10.1007/s00340-011-4385-7(2011).
[CrossRef]

X. P. Zhang and H. Giessen, “Four-wave mixing based on cascaded second-order nonlinear processes in a femtosecond optical parametric oscillator operating near degeneracy,” Appl. Phys. B 79, 441–447 (2004).
[CrossRef]

X. P. Zhang, J. Hebling, A. Bartels, D. Nau, J. Kuhl, W. W. Rühle, and H. Giessen, “1 GHz-repetition-rate femtosecond optical parametric oscillator,” Appl. Phys. Lett. 80, 1873–1875 (2002).
[CrossRef]

J. Hebling, X. P. Zhang, H. Giessen, J. Kuhl, and J. Seres, “Pulse-characteristics of an optical parametric oscillator pumped by sub-30 fs light pulses,” Opt. Lett. 25, 1055–1057 (2000).
[CrossRef]

J. Hebling, H. Giessen, S. Linden, and J. Kuhl, “Mirror-dispersion-compensated femtosecond optical parametric oscillator,” Opt. Commun. 141, 229–236 (1997).
[CrossRef]

A. Steinmann, B. Metzger, R. Hegenbarth, and H. Giessen, “Compact 7.4 W femtosecond oscillator for white-light generation and nonlinear microscopy,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (CD) (Optical Society of America, 2011), paper CThAA5.

Girard, S.

D. S. Butterworth, S. Girard, and D. C. Hanna, “A simple technique to achieve active cavity-length stabilization in a synchronously pumped optical parametric oscillator,” Opt. Commun. 123, 577–592 (1996).
[CrossRef]

Grebs, R.

Haag, P.

T. Andres, P. Haag, S. Reuter, S. Zelt, J.-P. Meyn, A. Borsutzky, R. Beigang, and R. Wallenstein, “Femtosecond optical parametric oscillators based on MgO:PPLN operating at room temperature,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (CD) (Optical Society of America, 2002), paper CTuO2.

Hache, F.

T. J. Driscoll, G. M. Gale, and F. Hache, “Ti:sapphire second-harmonic-pumped visible-range femtosecond optical parametric oscillator,” Opt. Commun. 110, 638–644 (1994).
[CrossRef]

Haidar, S.

S. Haidar and H. Ito, “Injection-seeded optical parametric oscillator for efficient difference frequency generation in mid-IR,” Opt. Commun. 171, 171–176 (1999).
[CrossRef]

Hanna, D. C.

Harris, J. S.

K. L. Vodopyanov, M. M. Fejer, X. Yu, J. S. Harris, Y.-S. Lee, W. C. Hurlbut, V. G. Kozlov, D. Bliss, and C. Lynch, “Terahertz-wave generation in quasi-phase-matched GaAs,” Appl. Phys. Lett. 89, 141119 (2006).
[CrossRef]

Hartl, I.

Hebling, J.

X. P. Zhang, J. Hebling, A. Bartels, D. Nau, J. Kuhl, W. W. Rühle, and H. Giessen, “1 GHz-repetition-rate femtosecond optical parametric oscillator,” Appl. Phys. Lett. 80, 1873–1875 (2002).
[CrossRef]

J. Hebling, X. P. Zhang, H. Giessen, J. Kuhl, and J. Seres, “Pulse-characteristics of an optical parametric oscillator pumped by sub-30 fs light pulses,” Opt. Lett. 25, 1055–1057 (2000).
[CrossRef]

J. Seres and J. Hebling, “Nonstationary theory of synchronously pumped femtosecond optical parametric oscillators,” J. Opt. Soc. Am. B 17, 741–750 (2000).
[CrossRef]

J. Hebling, H. Giessen, S. Linden, and J. Kuhl, “Mirror-dispersion-compensated femtosecond optical parametric oscillator,” Opt. Commun. 141, 229–236 (1997).
[CrossRef]

Hegenbarth, R.

J.-P. Negel, R. Hegenbarth, A. Steinmann, B. Metzger, F. Hoos, and H. Giessen, “Compact and cost-effective scheme for THz generation via optical rectification in GaP and GaAs using novel fs laser oscillators,” Appl. Phys. B , doi:10.1007/s00340-011-4385-7(2011).
[CrossRef]

A. Steinmann, B. Metzger, R. Hegenbarth, and H. Giessen, “Compact 7.4 W femtosecond oscillator for white-light generation and nonlinear microscopy,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (CD) (Optical Society of America, 2011), paper CThAA5.

Hoos, F.

J.-P. Negel, R. Hegenbarth, A. Steinmann, B. Metzger, F. Hoos, and H. Giessen, “Compact and cost-effective scheme for THz generation via optical rectification in GaP and GaAs using novel fs laser oscillators,” Appl. Phys. B , doi:10.1007/s00340-011-4385-7(2011).
[CrossRef]

Hurlbut, W. C.

K. L. Vodopyanov, M. M. Fejer, X. Yu, J. S. Harris, Y.-S. Lee, W. C. Hurlbut, V. G. Kozlov, D. Bliss, and C. Lynch, “Terahertz-wave generation in quasi-phase-matched GaAs,” Appl. Phys. Lett. 89, 141119 (2006).
[CrossRef]

Innerhofer, E.

Ito, H.

Ito, R.

Ji, W.

H. Li, F. Zhou, X. Zhang, and W. Ji, “Picosecond Z-scan study of bound electronic Kerr effect in LiNbO3 crystal associated with two-photon absorption,” Appl. Phys. B 64, 659–662 (1997).
[CrossRef]

Jundt, D. H.

Kadatomo, K.

M. Nakamura, M. Sugihara, M. Kotoh, H. Taniguchi, and K. Kadatomo, “Quasi-phase-matched optical parametric oscillator using periodically poled MgO-doped LiNbO3 crystal,” Jpn. J. Appl. Phys. 38, L1234–L1236 (1999).
[CrossRef]

Kaindl, R. A.

R. A. Kaindl, F. Eickemeyer, M. Woerner, and T. Elsaesser, “Broadband phase-matched difference frequency mixing of femtosecond pulses in GaSe: experiment and theory,” Appl. Phys. Lett. 75, 1060–1062 (1999).
[CrossRef]

Kartaloglu, T.

Keller, U.

Kitamoto, A.

Kitamura, K.

Koch, K.

Kokabee, O.

Kondo, T.

Köprülü, K. G.

Kornaszewski, L.

Kotoh, M.

M. Nakamura, M. Sugihara, M. Kotoh, H. Taniguchi, and K. Kadatomo, “Quasi-phase-matched optical parametric oscillator using periodically poled MgO-doped LiNbO3 crystal,” Jpn. J. Appl. Phys. 38, L1234–L1236 (1999).
[CrossRef]

Kozlov, V. G.

K. L. Vodopyanov, M. M. Fejer, X. Yu, J. S. Harris, Y.-S. Lee, W. C. Hurlbut, V. G. Kozlov, D. Bliss, and C. Lynch, “Terahertz-wave generation in quasi-phase-matched GaAs,” Appl. Phys. Lett. 89, 141119 (2006).
[CrossRef]

Kuhl, J.

X. P. Zhang, J. Hebling, A. Bartels, D. Nau, J. Kuhl, W. W. Rühle, and H. Giessen, “1 GHz-repetition-rate femtosecond optical parametric oscillator,” Appl. Phys. Lett. 80, 1873–1875 (2002).
[CrossRef]

J. Hebling, X. P. Zhang, H. Giessen, J. Kuhl, and J. Seres, “Pulse-characteristics of an optical parametric oscillator pumped by sub-30 fs light pulses,” Opt. Lett. 25, 1055–1057 (2000).
[CrossRef]

J. Hebling, H. Giessen, S. Linden, and J. Kuhl, “Mirror-dispersion-compensated femtosecond optical parametric oscillator,” Opt. Commun. 141, 229–236 (1997).
[CrossRef]

Kultavewuti, V.

I. T. Lima, Jr., V. Kultavewuti, and A. Major, “Phasematching properties of congruent MgO-doped and undoped periodically poled LiNbO3 for optical parametric oscillation with ultrafast excitation at 1 μm,” Laser Phys. 20, 270–275 (2010).
[CrossRef]

Kurimura, S.

Lamour, T.

Lee, Y.-S.

K. L. Vodopyanov, M. M. Fejer, X. Yu, J. S. Harris, Y.-S. Lee, W. C. Hurlbut, V. G. Kozlov, D. Bliss, and C. Lynch, “Terahertz-wave generation in quasi-phase-matched GaAs,” Appl. Phys. Lett. 89, 141119 (2006).
[CrossRef]

Li, H.

H. Li, F. Zhou, X. Zhang, and W. Ji, “Picosecond Z-scan study of bound electronic Kerr effect in LiNbO3 crystal associated with two-photon absorption,” Appl. Phys. B 64, 659–662 (1997).
[CrossRef]

Linden, S.

J. Hebling, H. Giessen, S. Linden, and J. Kuhl, “Mirror-dispersion-compensated femtosecond optical parametric oscillator,” Opt. Commun. 141, 229–236 (1997).
[CrossRef]

Liu, J. M.

Lynch, C.

K. L. Vodopyanov, M. M. Fejer, X. Yu, J. S. Harris, Y.-S. Lee, W. C. Hurlbut, V. G. Kozlov, D. Bliss, and C. Lynch, “Terahertz-wave generation in quasi-phase-matched GaAs,” Appl. Phys. Lett. 89, 141119 (2006).
[CrossRef]

Major, A.

I. T. Lima, Jr., V. Kultavewuti, and A. Major, “Phasematching properties of congruent MgO-doped and undoped periodically poled LiNbO3 for optical parametric oscillation with ultrafast excitation at 1 μm,” Laser Phys. 20, 270–275 (2010).
[CrossRef]

A. Shapapov, V. Barzda, and A. Major, “Development of a high power femtosecond optical parametric oscillator for biomedical imaging applications,” Proc. SPIE 7099, 70992H (2008).
[CrossRef]

Mak, G.

Malinowski, A.

Manzoni, C.

D. Brida, C. Manzoni, G. Cirmi, M. Marangoni, S. Bonora, P. Villoresi, S. De Silvestri, and G. Cerullo, “Few-optical-cycle pulses tunable from the visible to the mid-infrared by optical parametric amplifiers,” J. Opt. 12, 013001 (2010).
[CrossRef]

Marangoni, M.

D. Brida, C. Manzoni, G. Cirmi, M. Marangoni, S. Bonora, P. Villoresi, S. De Silvestri, and G. Cerullo, “Few-optical-cycle pulses tunable from the visible to the mid-infrared by optical parametric amplifiers,” J. Opt. 12, 013001 (2010).
[CrossRef]

M. Marangoni, R. Osellame, R. Ramponi, G. Cerullo, A. Steinmann, and U. Morgner, “Near-infrared optical parametric amplifier at 1 MHz directly pumped by a femtosecond oscillator,” Opt. Lett. 32, 1489–1491 (2007).
[CrossRef] [PubMed]

Marzenell, S.

S. Marzenell, R. Beigang, and R. Wallenstein, “Synchronously pumped femtosecond optical parametric oscillator based on AgGaSe2 tunable from 2 μm to 8 μm,” Appl. Phys. B 69, 423–428 (1999).
[CrossRef]

McGowan, C.

Metzger, B.

J.-P. Negel, R. Hegenbarth, A. Steinmann, B. Metzger, F. Hoos, and H. Giessen, “Compact and cost-effective scheme for THz generation via optical rectification in GaP and GaAs using novel fs laser oscillators,” Appl. Phys. B , doi:10.1007/s00340-011-4385-7(2011).
[CrossRef]

A. Steinmann, B. Metzger, R. Hegenbarth, and H. Giessen, “Compact 7.4 W femtosecond oscillator for white-light generation and nonlinear microscopy,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (CD) (Optical Society of America, 2011), paper CThAA5.

Meyn, J.-P.

T. Andres, P. Haag, S. Reuter, S. Zelt, J.-P. Meyn, A. Borsutzky, R. Beigang, and R. Wallenstein, “Femtosecond optical parametric oscillators based on MgO:PPLN operating at room temperature,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (CD) (Optical Society of America, 2002), paper CTuO2.

Moore, G. T.

Morgner, U.

Motzouris, K.

Myers, L. E.

Nakamura, M.

M. Nakamura, M. Sugihara, M. Kotoh, H. Taniguchi, and K. Kadatomo, “Quasi-phase-matched optical parametric oscillator using periodically poled MgO-doped LiNbO3 crystal,” Jpn. J. Appl. Phys. 38, L1234–L1236 (1999).
[CrossRef]

Nau, D.

X. P. Zhang, J. Hebling, A. Bartels, D. Nau, J. Kuhl, W. W. Rühle, and H. Giessen, “1 GHz-repetition-rate femtosecond optical parametric oscillator,” Appl. Phys. Lett. 80, 1873–1875 (2002).
[CrossRef]

Negel, J.-P.

J.-P. Negel, R. Hegenbarth, A. Steinmann, B. Metzger, F. Hoos, and H. Giessen, “Compact and cost-effective scheme for THz generation via optical rectification in GaP and GaAs using novel fs laser oscillators,” Appl. Phys. B , doi:10.1007/s00340-011-4385-7(2011).
[CrossRef]

Nilsson, J.

O’Connor, M. V.

Osellame, R.

Paschotta, R.

Pelouch, W. S.

Penman, Z. E.

Pierce, J. W.

Powers, P. E.

Price, J. H. V.

Ramponi, R.

Reid, D. T.

Reuter, S.

T. Andres, P. Haag, S. Reuter, S. Zelt, J.-P. Meyn, A. Borsutzky, R. Beigang, and R. Wallenstein, “Femtosecond optical parametric oscillators based on MgO:PPLN operating at room temperature,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (CD) (Optical Society of America, 2002), paper CTuO2.

Richardson, D. J.

Risk, W. P.

Rosenberg, W. R.

Ross, G. W.

Rühle, W. W.

X. P. Zhang, J. Hebling, A. Bartels, D. Nau, J. Kuhl, W. W. Rühle, and H. Giessen, “1 GHz-repetition-rate femtosecond optical parametric oscillator,” Appl. Phys. Lett. 80, 1873–1875 (2002).
[CrossRef]

Sacks, Z.

O. Gayer, Z. Sacks, E. Galun, and A. Arie, “Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO3,” Appl. Phys. B 91, 343–348 (2008).
[CrossRef]

Schaar, J. E.

Seres, J.

Shapapov, A.

A. Shapapov, V. Barzda, and A. Major, “Development of a high power femtosecond optical parametric oscillator for biomedical imaging applications,” Proc. SPIE 7099, 70992H (2008).
[CrossRef]

Shepherd, D. P.

Shirane, M.

Shoji, I.

Sibbett, W.

C. McGowan, D. T. Reid, Z. E. Penman, M. Ebrahim-Zadeh, W. Sibbett, and D. H. Jundt, “Femtosecond optical parametric oscillator based on periodically poled lithium niobate,” J. Opt. Soc. Am. B 15, 694–701 (1998).
[CrossRef]

J. M. Dudley, D. T. Reid, M. Ebrahim-Zadeh, and W. Sibbett, “Characteristics of a noncritically phasematched Ti:sapphire pumped femtosecond optical parametric oscillator,” Opt. Commun. 104, 419–430 (1994).
[CrossRef]

Smith, P. G. R.

Steinmann, A.

J.-P. Negel, R. Hegenbarth, A. Steinmann, B. Metzger, F. Hoos, and H. Giessen, “Compact and cost-effective scheme for THz generation via optical rectification in GaP and GaAs using novel fs laser oscillators,” Appl. Phys. B , doi:10.1007/s00340-011-4385-7(2011).
[CrossRef]

M. Marangoni, R. Osellame, R. Ramponi, G. Cerullo, A. Steinmann, and U. Morgner, “Near-infrared optical parametric amplifier at 1 MHz directly pumped by a femtosecond oscillator,” Opt. Lett. 32, 1489–1491 (2007).
[CrossRef] [PubMed]

A. Steinmann, B. Metzger, R. Hegenbarth, and H. Giessen, “Compact 7.4 W femtosecond oscillator for white-light generation and nonlinear microscopy,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (CD) (Optical Society of America, 2011), paper CThAA5.

Südmeyer, T.

Sugihara, M.

M. Nakamura, M. Sugihara, M. Kotoh, H. Taniguchi, and K. Kadatomo, “Quasi-phase-matched optical parametric oscillator using periodically poled MgO-doped LiNbO3 crystal,” Jpn. J. Appl. Phys. 38, L1234–L1236 (1999).
[CrossRef]

Sun, J.

Sun, J. H.

Sundheimer, M.

Sutherland, R. L.

R. L. Sutherland, “Handbook of Nonlinear Optics,” 2nd ed. (Dekker, 2003).
[CrossRef]

Tang, C. L.

K. C. Burr, C. L. Tang, M. A. Arbore, and M. M. Fejer, “High-repetition-rate femtosecond optical parametric oscillator based on periodically poled lithium niobate,” Appl. Phys. Lett. 70, 3341–3343 (1997).
[CrossRef]

W. S. Pelouch, P. E. Powers, and C. L. Tang, “Ti:sapphire-pumped, high-repetition-rate femtosecond optical parametric oscillator,” Opt. Lett. 17, 1070–1072 (1992).
[CrossRef] [PubMed]

Taniguchi, H.

M. Nakamura, M. Sugihara, M. Kotoh, H. Taniguchi, and K. Kadatomo, “Quasi-phase-matched optical parametric oscillator using periodically poled MgO-doped LiNbO3 crystal,” Jpn. J. Appl. Phys. 38, L1234–L1236 (1999).
[CrossRef]

Tartara, L.

Thorpe, M. J.

Tomaschke, H. E.

D. A. Bryan, R. Gerson, and H. E. Tomaschke, “Increased optical damage resistance in lithium niobate,” Appl. Phys. Lett. 44, 847–849 (1984).
[CrossRef]

Usami, T.

van Driel, H. M.

Villoresi, P.

D. Brida, C. Manzoni, G. Cirmi, M. Marangoni, S. Bonora, P. Villoresi, S. De Silvestri, and G. Cerullo, “Few-optical-cycle pulses tunable from the visible to the mid-infrared by optical parametric amplifiers,” J. Opt. 12, 013001 (2010).
[CrossRef]

Vodopyanov, K. L.

J. E. Schaar, K. L. Vodopyanov, and M. M. Fejer, “Intracavity terahertz-wave generation in a synchronously pumped optical parametric oscillator using quasi-phase-matched GaAs,” Opt. Lett. 32, 1284–1286 (2007).
[CrossRef] [PubMed]

K. L. Vodopyanov, M. M. Fejer, X. Yu, J. S. Harris, Y.-S. Lee, W. C. Hurlbut, V. G. Kozlov, D. Bliss, and C. Lynch, “Terahertz-wave generation in quasi-phase-matched GaAs,” Appl. Phys. Lett. 89, 141119 (2006).
[CrossRef]

Wallenstein, R.

S. Marzenell, R. Beigang, and R. Wallenstein, “Synchronously pumped femtosecond optical parametric oscillator based on AgGaSe2 tunable from 2 μm to 8 μm,” Appl. Phys. B 69, 423–428 (1999).
[CrossRef]

T. Andres, P. Haag, S. Reuter, S. Zelt, J.-P. Meyn, A. Borsutzky, R. Beigang, and R. Wallenstein, “Femtosecond optical parametric oscillators based on MgO:PPLN operating at room temperature,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (CD) (Optical Society of America, 2002), paper CTuO2.

Watson, M. A.

Woerner, M.

R. A. Kaindl, F. Eickemeyer, M. Woerner, and T. Elsaesser, “Broadband phase-matched difference frequency mixing of femtosecond pulses in GaSe: experiment and theory,” Appl. Phys. Lett. 75, 1060–1062 (1999).
[CrossRef]

Ye, J.

Yu, X.

K. L. Vodopyanov, M. M. Fejer, X. Yu, J. S. Harris, Y.-S. Lee, W. C. Hurlbut, V. G. Kozlov, D. Bliss, and C. Lynch, “Terahertz-wave generation in quasi-phase-matched GaAs,” Appl. Phys. Lett. 89, 141119 (2006).
[CrossRef]

Zelt, S.

T. Andres, P. Haag, S. Reuter, S. Zelt, J.-P. Meyn, A. Borsutzky, R. Beigang, and R. Wallenstein, “Femtosecond optical parametric oscillators based on MgO:PPLN operating at room temperature,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (CD) (Optical Society of America, 2002), paper CTuO2.

Zhang, X.

H. Li, F. Zhou, X. Zhang, and W. Ji, “Picosecond Z-scan study of bound electronic Kerr effect in LiNbO3 crystal associated with two-photon absorption,” Appl. Phys. B 64, 659–662 (1997).
[CrossRef]

Zhang, X. P.

X. P. Zhang and H. Giessen, “Four-wave mixing based on cascaded second-order nonlinear processes in a femtosecond optical parametric oscillator operating near degeneracy,” Appl. Phys. B 79, 441–447 (2004).
[CrossRef]

X. P. Zhang, J. Hebling, A. Bartels, D. Nau, J. Kuhl, W. W. Rühle, and H. Giessen, “1 GHz-repetition-rate femtosecond optical parametric oscillator,” Appl. Phys. Lett. 80, 1873–1875 (2002).
[CrossRef]

J. Hebling, X. P. Zhang, H. Giessen, J. Kuhl, and J. Seres, “Pulse-characteristics of an optical parametric oscillator pumped by sub-30 fs light pulses,” Opt. Lett. 25, 1055–1057 (2000).
[CrossRef]

X. P. Zhang, “High-repetition-rate femtosecond optical parametric oscillators based on KTP and PPLN,” Ph.D. dissertation (University of Marburg, 2002).

Zhou, F.

H. Li, F. Zhou, X. Zhang, and W. Ji, “Picosecond Z-scan study of bound electronic Kerr effect in LiNbO3 crystal associated with two-photon absorption,” Appl. Phys. B 64, 659–662 (1997).
[CrossRef]

Appl. Phys. B (6)

S. Marzenell, R. Beigang, and R. Wallenstein, “Synchronously pumped femtosecond optical parametric oscillator based on AgGaSe2 tunable from 2 μm to 8 μm,” Appl. Phys. B 69, 423–428 (1999).
[CrossRef]

J.-P. Negel, R. Hegenbarth, A. Steinmann, B. Metzger, F. Hoos, and H. Giessen, “Compact and cost-effective scheme for THz generation via optical rectification in GaP and GaAs using novel fs laser oscillators,” Appl. Phys. B , doi:10.1007/s00340-011-4385-7(2011).
[CrossRef]

H. M. van Driel, “Synchronously pumped optical parametric oscillators,” Appl. Phys. B 60, 411–420 (1995).
[CrossRef]

H. Li, F. Zhou, X. Zhang, and W. Ji, “Picosecond Z-scan study of bound electronic Kerr effect in LiNbO3 crystal associated with two-photon absorption,” Appl. Phys. B 64, 659–662 (1997).
[CrossRef]

O. Gayer, Z. Sacks, E. Galun, and A. Arie, “Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO3,” Appl. Phys. B 91, 343–348 (2008).
[CrossRef]

X. P. Zhang and H. Giessen, “Four-wave mixing based on cascaded second-order nonlinear processes in a femtosecond optical parametric oscillator operating near degeneracy,” Appl. Phys. B 79, 441–447 (2004).
[CrossRef]

Appl. Phys. Lett. (5)

D. A. Bryan, R. Gerson, and H. E. Tomaschke, “Increased optical damage resistance in lithium niobate,” Appl. Phys. Lett. 44, 847–849 (1984).
[CrossRef]

X. P. Zhang, J. Hebling, A. Bartels, D. Nau, J. Kuhl, W. W. Rühle, and H. Giessen, “1 GHz-repetition-rate femtosecond optical parametric oscillator,” Appl. Phys. Lett. 80, 1873–1875 (2002).
[CrossRef]

K. C. Burr, C. L. Tang, M. A. Arbore, and M. M. Fejer, “High-repetition-rate femtosecond optical parametric oscillator based on periodically poled lithium niobate,” Appl. Phys. Lett. 70, 3341–3343 (1997).
[CrossRef]

K. L. Vodopyanov, M. M. Fejer, X. Yu, J. S. Harris, Y.-S. Lee, W. C. Hurlbut, V. G. Kozlov, D. Bliss, and C. Lynch, “Terahertz-wave generation in quasi-phase-matched GaAs,” Appl. Phys. Lett. 89, 141119 (2006).
[CrossRef]

R. A. Kaindl, F. Eickemeyer, M. Woerner, and T. Elsaesser, “Broadband phase-matched difference frequency mixing of femtosecond pulses in GaSe: experiment and theory,” Appl. Phys. Lett. 75, 1060–1062 (1999).
[CrossRef]

J. Opt. (1)

D. Brida, C. Manzoni, G. Cirmi, M. Marangoni, S. Bonora, P. Villoresi, S. De Silvestri, and G. Cerullo, “Few-optical-cycle pulses tunable from the visible to the mid-infrared by optical parametric amplifiers,” J. Opt. 12, 013001 (2010).
[CrossRef]

J. Opt. Soc. Am. B (5)

Jpn. J. Appl. Phys. (1)

M. Nakamura, M. Sugihara, M. Kotoh, H. Taniguchi, and K. Kadatomo, “Quasi-phase-matched optical parametric oscillator using periodically poled MgO-doped LiNbO3 crystal,” Jpn. J. Appl. Phys. 38, L1234–L1236 (1999).
[CrossRef]

Laser Phys. (1)

I. T. Lima, Jr., V. Kultavewuti, and A. Major, “Phasematching properties of congruent MgO-doped and undoped periodically poled LiNbO3 for optical parametric oscillation with ultrafast excitation at 1 μm,” Laser Phys. 20, 270–275 (2010).
[CrossRef]

Opt. Commun. (5)

J. M. Dudley, D. T. Reid, M. Ebrahim-Zadeh, and W. Sibbett, “Characteristics of a noncritically phasematched Ti:sapphire pumped femtosecond optical parametric oscillator,” Opt. Commun. 104, 419–430 (1994).
[CrossRef]

S. Haidar and H. Ito, “Injection-seeded optical parametric oscillator for efficient difference frequency generation in mid-IR,” Opt. Commun. 171, 171–176 (1999).
[CrossRef]

T. J. Driscoll, G. M. Gale, and F. Hache, “Ti:sapphire second-harmonic-pumped visible-range femtosecond optical parametric oscillator,” Opt. Commun. 110, 638–644 (1994).
[CrossRef]

J. Hebling, H. Giessen, S. Linden, and J. Kuhl, “Mirror-dispersion-compensated femtosecond optical parametric oscillator,” Opt. Commun. 141, 229–236 (1997).
[CrossRef]

D. S. Butterworth, S. Girard, and D. C. Hanna, “A simple technique to achieve active cavity-length stabilization in a synchronously pumped optical parametric oscillator,” Opt. Commun. 123, 577–592 (1996).
[CrossRef]

Opt. Express (2)

Opt. Lett. (15)

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]

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[CrossRef]

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Proc. SPIE (1)

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Other (4)

T. Andres, P. Haag, S. Reuter, S. Zelt, J.-P. Meyn, A. Borsutzky, R. Beigang, and R. Wallenstein, “Femtosecond optical parametric oscillators based on MgO:PPLN operating at room temperature,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (CD) (Optical Society of America, 2002), paper CTuO2.

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[CrossRef]

X. P. Zhang, “High-repetition-rate femtosecond optical parametric oscillators based on KTP and PPLN,” Ph.D. dissertation (University of Marburg, 2002).

A. Steinmann, B. Metzger, R. Hegenbarth, and H. Giessen, “Compact 7.4 W femtosecond oscillator for white-light generation and nonlinear microscopy,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (CD) (Optical Society of America, 2011), paper CThAA5.

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Figures (13)

Fig. 1
Fig. 1

Simulation of the average signal output power (red circles) and conversion efficiency (black squares) versus pump power/threshold power ratio of the OPO at 1462 nm wavelength and 63% output coupling rate. The conversion efficiency reaches a maximum at approximately two times threshold.

Fig. 2
Fig. 2

Simulation of the signal wavelength versus relative change of cavity length (signal delay) at a 29.5 μm poling period.

Fig. 3
Fig. 3

(a) Simulation of the signal wavelength versus relative change of cavity length (signal delay) at 30.5 μm poling period. Dual- wavelength operation is expected at a certain cavity delay range. (b) Signal wavelength versus poling period at zero cavity delay and no GDD compensation.

Fig. 4
Fig. 4

Experimental setup of the OPO pumped by an Yb:KGW laser: FI, Faraday isolator; FL, f = 150 mm focusing lens; CM, curved mirror ( 300 mm radius of curvature); MgO:cPPLN, 5% MgO-doped congruent PPLN crystal. OC, output coupling mirror; PS, piezo stage; RP, residual pump; ID, idler.

Fig. 5
Fig. 5

(a) Autocorrelation of the Yb:KGW pump laser. The FWHM pump pulse duration is 530 fs . (b) Spectrum of the Yb:KGW laser.

Fig. 6
Fig. 6

(a) Transmittivity versus wavelength for different output coupling mirrors A, B, and C. (b) Total intracavity GDD (black solid curve) and group delay (gray dashed curve) including the crystal, 11 highly reflective mirrors, and output coupling mirror A.

Fig. 7
Fig. 7

Average signal output power versus wavelength for several combinations of poling periods and output coupling mirrors. Transmittivity curves of the output coupling mirrors are shown in Fig. 6a.

Fig. 8
Fig. 8

(a) Signal wavelength and (b) average signal output power (black curves) and FWHM signal pulse duration (red curves) versus relative change of cavity length at 29.5 μm poling period. Squares denote measurements with output coupling mirror A (15% transmission at the 1462 nm wavelength). Circles denote measurements with output coupling mirror B (63% transmission at 1462 nm wavelength).

Fig. 9
Fig. 9

(a) Average signal output power and (b) conversion efficiency versus average pump power at the 1482 nm wavelength (red circles, 12% output coupling rate) and at 1462 nm (blue triangles, 63% output coupling rate). (c) Signal spectrum and (d) autocorrelation at the 1462 nm wavelength with a 63% output coupling rate. In this case, the average signal output power is 1.52 W .

Fig. 10
Fig. 10

(a) Signal wavelength, (b) average signal output power, and (c) FWHM signal pulse duration versus relative change of cavity length at a 30.5 μm poling period. Dual-wavelength operation occurs in a certain cavity delay range. Output coupling mirror B is used in this case.

Fig. 11
Fig. 11

Signal spectra at various relative change of cavity length values. When the OPO is operated in the regime of the signal power peak shown in Fig. 10b, most of the power is concentrated at the smaller wavelength peak (spectra at 310 to 356 μm relative change of cavity delay, maximum power at 338 μm ).

Fig. 12
Fig. 12

(a) Average signal output power and (b) conversion efficiency versus average pump power for dual-wavelength operation. The peak wavelengths (output coupling rates) are 1530 nm (8%) and 1880 nm (15%)—black squares—with output coupling mirror A, 1566 nm (31%) and 1809 nm (10%)—red circles—with output coupling mirror B.

Fig. 13
Fig. 13

(a) Average signal output power and (b) conversion efficiency versus average pump power at the 1785 nm wavelength (21% output coupling rate).

Equations (14)

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2 E ( t , z ) z 2 μ ε 2 E ( t , z ) t 2 = μ 2 P NL ( t , z ) t 2 ,
a s z + i κ s a s = i ω s d 4 π c n s a p a i i ω s n NL 2 π c j s a s a i z + i κ i a i = i ω i d 4 π c n i a p a s i ω i n NL 2 π c j i a i a p z + i κ p a p = i ω p d 4 π c n p a s a i i ω p n NL 2 π c j p a p ,
j l = 1 2 π m = s , i , p ( 2 δ l , m ) γ m a m a m
a s ( Ω , z = 0 ) = a s ( Ω , z = L ) R ( ω ) exp [ i Ω ( Δ T M L v s ) ] exp ( i GDD mir 2 Ω 2 ) .
ω p = ω s + ω i
k p = k s + k i + 2 π Λ ,
1 λ p = 1 λ s + 1 λ i n p ( λ p ) λ p = n s ( λ s ) λ s + n i ( λ i ) λ i + 1 Λ ,
GDD ( λ ) = d τ d ω = λ 2 2 π c d τ d λ .
d l = c d τ .
d l = 2 π c 2 λ 2 GDD ( λ ) d λ .
Δ l = 2 π c 2 λ 0 λ 1 GDD ( λ ) λ 2 d λ
Δ ν s ( Δ ν 1 ) 2 + ( Δ ν 2 ) 2 ,
Δ ν 1 = 1 L [ 1 v i 1 v s ] ,
Δ ν 2 = Δ ν p 1 v i 1 v p 1 v i 1 v s ,

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