Abstract

The timing jitter of optical pulse trains from diode-pumped, semiconductor saturable absorber mode-locked femtosecond Cr:LiSAF lasers is characterized by a single-crystal balanced optical cross-correlator with an equivalent sensitivity in phase noise of −235 dBc/Hz. The RMS timing jitter is 30 attoseconds integrated from 10 kHz to 50 MHz, the Nyquist frequency of the 100 MHz repetition rate oscillator. The AM-to-PM conversion induced excess phase noise is calculated and compared with experiment. The self-steepening effect is proven to be the dominant AM-to-PM coupling mechanism, whereas the semiconductor saturable absorber operation does not adversely affect timing jitter. The results show that ultrafast Cr:LiSAF lasers are promising compact and efficient ultralow-jitter sources.

© 2012 OSA

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2012

A. J. Benedick, J. G. Fujimoto, and F. X. Kärtner, “Optical flywheels with attosecond jitter,” Nat. Photonics6(2), 97–100 (2012).
[CrossRef]

2011

T. K. Kim, Y. Song, K. Jung, C. Kim, H. Kim, C. H. Nam, and J. Kim, “Sub-100-as timing jitter optical pulse trains from mode-locked Er-fiber lasers,” Opt. Lett.36(22), 4443–4445 (2011).
[CrossRef] [PubMed]

Y. Song, K. Jung, and J. Kim, “Impact of pulse dynamics on timing jitter in mode-locked fiber lasers,” Opt. Lett.36(10), 1761–1763 (2011).
[CrossRef] [PubMed]

Y. Song, C. Kim, K. Jung, H. Kim, and J. Kim, “Timing jitter optimization of mode-locked Yb-fiber lasers toward the attosecond regime,” Opt. Express19(15), 14518–14525 (2011).
[CrossRef] [PubMed]

U. Demirbas, G. S. Petrich, D. Li, A. Sennaroglu, L. A. Kolodziejski, F. X. Kärtner, and J. G. Fujimoto, “Femtosecond tuning of Cr:colquiriite lasers with AlGaAs-based saturable Bragg reflectors,” J. Opt. Soc. Am. B28(5), 986–993 (2011).
[CrossRef]

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics5(7), 425–429 (2011).
[CrossRef]

B. Sumpf, P. Adamiec, M. Zorn, H. Wenzel, and G. Erbert, “Nearly diffraction-limited tapered lasers at 675 nm with 1-W output power and conversion efficiencies above 30%,” IEEE Photon. Technol. Lett.23(4), 266–268 (2011).
[CrossRef]

U. Demirbas, M. Schmalz, B. Sumpf, G. Erbert, G. S. Petrich, L. A. Kolodziejski, J. G. Fujimoto, F. X. Kärtner, and A. Leitenstorfer, “Femtosecond Cr:LiSAF and Cr:LiCAF lasers pumped by tapered diode lasers,” Opt. Express19(21), 20444–20461 (2011).
[CrossRef] [PubMed]

2010

2009

2008

2007

2006

2004

R. Paschotta, “Noise of mode-locked lasers (Part I): numerical model,” Appl. Phys. B79(2), 153–162 (2004).
[CrossRef]

R. Paschotta, “Noise of mode-locked lasers (Part II): timing jitter and other fluctuations,” Appl. Phys. B79(2), 163–173 (2004).
[CrossRef]

2003

2001

R. P. Scott, C. Langrock, and B. H. Kolner, “High-dynamic-range laser amplitude and phase noise measurement techniques,” IEEE J. Sel. Top. Quantum Electron.7(4), 641–655 (2001).
[CrossRef]

H. A. Haus and E. P. Ippen, “Group velocity of solitons,” Opt. Lett.26(21), 1654–1656 (2001).
[CrossRef] [PubMed]

1996

F. X. Kärtner, I. D. Jung, and U. Keller, “Soliton mode-locking with saturable absorbers,” IEEE J. Sel. Top. Quantum Electron.2(3), 540–556 (1996).
[CrossRef]

S. Tsuda, W. H. Knox, S. T. Cundiff, W. Y. Jan, and J. E. Cunningham, “Mode-locking ultrafast solid-state lasers with saturable Bragg reflectors,” IEEE J. Sel. Top. Quantum Electron.2(3), 454–464 (1996).
[CrossRef]

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Honninger, N. Matuschek, and J. Aus der Au, “Semiconductor saturable absorber mirrors (SESAM's) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Top. Quantum Electron.2(3), 435–453 (1996).
[CrossRef]

1993

H. A. Haus and A. Mecozzi, “Noise of Mode-Locked Lasers,” IEEE J. Quantum Electron.29(3), 983–996 (1993).
[CrossRef]

1986

1967

F. DeMartini, C. H. Townes, T. K. Gustafson, and P. L. Kelley, “Self-Steepening of Light Pulses,” Phys. Rev.164(2), 312–323 (1967).
[CrossRef]

Adamiec, P.

B. Sumpf, P. Adamiec, M. Zorn, H. Wenzel, and G. Erbert, “Nearly diffraction-limited tapered lasers at 675 nm with 1-W output power and conversion efficiencies above 30%,” IEEE Photon. Technol. Lett.23(4), 266–268 (2011).
[CrossRef]

Aus der Au, J.

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Honninger, N. Matuschek, and J. Aus der Au, “Semiconductor saturable absorber mirrors (SESAM's) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Top. Quantum Electron.2(3), 435–453 (1996).
[CrossRef]

Benedick, A. J.

A. J. Benedick, J. G. Fujimoto, and F. X. Kärtner, “Optical flywheels with attosecond jitter,” Nat. Photonics6(2), 97–100 (2012).
[CrossRef]

Bergquist, J. C.

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics5(7), 425–429 (2011).
[CrossRef]

Birge, J. R.

Boudot, R.

Bourgeois, P. Y.

Braun, B.

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Honninger, N. Matuschek, and J. Aus der Au, “Semiconductor saturable absorber mirrors (SESAM's) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Top. Quantum Electron.2(3), 435–453 (1996).
[CrossRef]

Chen, J.

Coq, Y. L.

Cox, J.

Cox, J. A.

Cundiff, S. T.

S. Tsuda, W. H. Knox, S. T. Cundiff, W. Y. Jan, and J. E. Cunningham, “Mode-locking ultrafast solid-state lasers with saturable Bragg reflectors,” IEEE J. Sel. Top. Quantum Electron.2(3), 454–464 (1996).
[CrossRef]

Cunningham, J. E.

S. Tsuda, W. H. Knox, S. T. Cundiff, W. Y. Jan, and J. E. Cunningham, “Mode-locking ultrafast solid-state lasers with saturable Bragg reflectors,” IEEE J. Sel. Top. Quantum Electron.2(3), 454–464 (1996).
[CrossRef]

DeMartini, F.

F. DeMartini, C. H. Townes, T. K. Gustafson, and P. L. Kelley, “Self-Steepening of Light Pulses,” Phys. Rev.164(2), 312–323 (1967).
[CrossRef]

Demirbas, U.

Diddams, S. A.

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics5(7), 425–429 (2011).
[CrossRef]

E. N. Ivanov, J. J. McFerran, S. A. Diddams, and L. Hollberg, “Noise properties of microwave signals synthesized with femtosecond lasers,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control54(4), 736–745 (2007).
[CrossRef] [PubMed]

Erbert, G.

U. Demirbas, M. Schmalz, B. Sumpf, G. Erbert, G. S. Petrich, L. A. Kolodziejski, J. G. Fujimoto, F. X. Kärtner, and A. Leitenstorfer, “Femtosecond Cr:LiSAF and Cr:LiCAF lasers pumped by tapered diode lasers,” Opt. Express19(21), 20444–20461 (2011).
[CrossRef] [PubMed]

B. Sumpf, P. Adamiec, M. Zorn, H. Wenzel, and G. Erbert, “Nearly diffraction-limited tapered lasers at 675 nm with 1-W output power and conversion efficiencies above 30%,” IEEE Photon. Technol. Lett.23(4), 266–268 (2011).
[CrossRef]

Felber, M.

Fluck, R.

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Honninger, N. Matuschek, and J. Aus der Au, “Semiconductor saturable absorber mirrors (SESAM's) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Top. Quantum Electron.2(3), 435–453 (1996).
[CrossRef]

Fortier, T. M.

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics5(7), 425–429 (2011).
[CrossRef]

Fujimoto, J. G.

A. J. Benedick, J. G. Fujimoto, and F. X. Kärtner, “Optical flywheels with attosecond jitter,” Nat. Photonics6(2), 97–100 (2012).
[CrossRef]

U. Demirbas, G. S. Petrich, D. Li, A. Sennaroglu, L. A. Kolodziejski, F. X. Kärtner, and J. G. Fujimoto, “Femtosecond tuning of Cr:colquiriite lasers with AlGaAs-based saturable Bragg reflectors,” J. Opt. Soc. Am. B28(5), 986–993 (2011).
[CrossRef]

U. Demirbas, M. Schmalz, B. Sumpf, G. Erbert, G. S. Petrich, L. A. Kolodziejski, J. G. Fujimoto, F. X. Kärtner, and A. Leitenstorfer, “Femtosecond Cr:LiSAF and Cr:LiCAF lasers pumped by tapered diode lasers,” Opt. Express19(21), 20444–20461 (2011).
[CrossRef] [PubMed]

D. Li, U. Demirbas, J. R. Birge, G. S. Petrich, L. A. Kolodziejski, A. Sennaroglu, F. X. Kärtner, and J. G. Fujimoto, “Diode-pumped passively mode-locked GHz femtosecond Cr:LiSAF laser with kW peak power,” Opt. Lett.35(9), 1446–1448 (2010).
[CrossRef] [PubMed]

U. Demirbas, D. Li, J. R. Birge, A. Sennaroglu, G. S. Petrich, L. A. Kolodziejski, F. X. Kaertner, and J. G. Fujimoto, “Low-cost, single-mode diode-pumped Cr:Colquiriite lasers,” Opt. Express17(16), 14374–14388 (2009).
[CrossRef] [PubMed]

T. R. Schibli, J. Kim, O. Kuzucu, J. T. Gopinath, S. N. Tandon, G. S. Petrich, L. A. Kolodziejski, J. G. Fujimoto, E. P. Ippen, and F. X. Kaertner, “Attosecond active synchronization of passively mode-locked lasers by balanced cross correlation,” Opt. Lett.28(11), 947–949 (2003).
[CrossRef] [PubMed]

T. R. Schibli, J. Kim, O. Kuzucu, J. T. Gopinath, S. N. Tandon, G. S. Petrich, L. A. Kolodziejski, J. G. Fujimoto, E. P. Ippen, and F. X. Kaertner, “Attosecond active synchronization of passively mode-locked lasers by balanced cross correlation,” Opt. Lett.28(11), 947–949 (2003).
[CrossRef] [PubMed]

Gopinath, J. T.

Gordon, J. P.

Gustafson, T. K.

F. DeMartini, C. H. Townes, T. K. Gustafson, and P. L. Kelley, “Self-Steepening of Light Pulses,” Phys. Rev.164(2), 312–323 (1967).
[CrossRef]

Haus, H. A.

Hollberg, L.

E. N. Ivanov, J. J. McFerran, S. A. Diddams, and L. Hollberg, “Noise properties of microwave signals synthesized with femtosecond lasers,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control54(4), 736–745 (2007).
[CrossRef] [PubMed]

Honninger, C.

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Honninger, N. Matuschek, and J. Aus der Au, “Semiconductor saturable absorber mirrors (SESAM's) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Top. Quantum Electron.2(3), 435–453 (1996).
[CrossRef]

Ippen, E. P.

Ivanov, E. N.

E. N. Ivanov, J. J. McFerran, S. A. Diddams, and L. Hollberg, “Noise properties of microwave signals synthesized with femtosecond lasers,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control54(4), 736–745 (2007).
[CrossRef] [PubMed]

Jan, W. Y.

S. Tsuda, W. H. Knox, S. T. Cundiff, W. Y. Jan, and J. E. Cunningham, “Mode-locking ultrafast solid-state lasers with saturable Bragg reflectors,” IEEE J. Sel. Top. Quantum Electron.2(3), 454–464 (1996).
[CrossRef]

Jiang, Y.

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics5(7), 425–429 (2011).
[CrossRef]

Jung, I. D.

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Honninger, N. Matuschek, and J. Aus der Au, “Semiconductor saturable absorber mirrors (SESAM's) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Top. Quantum Electron.2(3), 435–453 (1996).
[CrossRef]

F. X. Kärtner, I. D. Jung, and U. Keller, “Soliton mode-locking with saturable absorbers,” IEEE J. Sel. Top. Quantum Electron.2(3), 540–556 (1996).
[CrossRef]

Jung, K.

Kaertner, F. X.

Kärtner, F. X.

A. J. Benedick, J. G. Fujimoto, and F. X. Kärtner, “Optical flywheels with attosecond jitter,” Nat. Photonics6(2), 97–100 (2012).
[CrossRef]

U. Demirbas, G. S. Petrich, D. Li, A. Sennaroglu, L. A. Kolodziejski, F. X. Kärtner, and J. G. Fujimoto, “Femtosecond tuning of Cr:colquiriite lasers with AlGaAs-based saturable Bragg reflectors,” J. Opt. Soc. Am. B28(5), 986–993 (2011).
[CrossRef]

U. Demirbas, M. Schmalz, B. Sumpf, G. Erbert, G. S. Petrich, L. A. Kolodziejski, J. G. Fujimoto, F. X. Kärtner, and A. Leitenstorfer, “Femtosecond Cr:LiSAF and Cr:LiCAF lasers pumped by tapered diode lasers,” Opt. Express19(21), 20444–20461 (2011).
[CrossRef] [PubMed]

D. Li, U. Demirbas, J. R. Birge, G. S. Petrich, L. A. Kolodziejski, A. Sennaroglu, F. X. Kärtner, and J. G. Fujimoto, “Diode-pumped passively mode-locked GHz femtosecond Cr:LiSAF laser with kW peak power,” Opt. Lett.35(9), 1446–1448 (2010).
[CrossRef] [PubMed]

J. A. Cox, A. H. Nejadmalayeri, J. Kim, and F. X. Kärtner, “Complete characterization of quantum-limited timing jitter in passively mode-locked fiber lasers,” Opt. Lett.35(20), 3522–3524 (2010).
[CrossRef] [PubMed]

J. Kim and F. X. Kärtner, “Attosecond-precision ultrafast photonics,” Laser Photon. Rev.4(3), 432–456 (2010).
[CrossRef]

J. Kim, M. J. Park, M. H. Perrott, and F. X. Kärtner, “Photonic subsampling analog-to-digital conversion of microwave signals at 40-GHz with higher than 7-ENOB resolution,” Opt. Express16(21), 16509–16515 (2008).
[CrossRef] [PubMed]

J. Kim, F. Ludwig, M. Felber, and F. X. Kärtner, “Long-term stable microwave signal extraction from mode-locked lasers,” Opt. Express15(14), 8951–8959 (2007).
[CrossRef] [PubMed]

J. R. Birge and F. X. Kärtner, “Efficient optimization of multilayer coatings for ultrafast optics using analytic gradients of dispersion,” Appl. Opt.46(14), 2656–2662 (2007).
[CrossRef] [PubMed]

J. Kim, J. Chen, J. Cox, and F. X. Kärtner, “Attosecond-resolution timing jitter characterization of free-running mode-locked lasers,” Opt. Lett.32(24), 3519–3521 (2007).
[CrossRef] [PubMed]

L. Matos, O. D. Mücke, J. Chen, and F. X. Kärtner, “Carrier-envelope phase dynamics and noise analysis in octave-spanning Ti:sapphire lasers,” Opt. Express14(6), 2497–2511 (2006).
[CrossRef] [PubMed]

F. X. Kärtner, I. D. Jung, and U. Keller, “Soliton mode-locking with saturable absorbers,” IEEE J. Sel. Top. Quantum Electron.2(3), 540–556 (1996).
[CrossRef]

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Honninger, N. Matuschek, and J. Aus der Au, “Semiconductor saturable absorber mirrors (SESAM's) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Top. Quantum Electron.2(3), 435–453 (1996).
[CrossRef]

Keller, U.

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Honninger, N. Matuschek, and J. Aus der Au, “Semiconductor saturable absorber mirrors (SESAM's) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Top. Quantum Electron.2(3), 435–453 (1996).
[CrossRef]

F. X. Kärtner, I. D. Jung, and U. Keller, “Soliton mode-locking with saturable absorbers,” IEEE J. Sel. Top. Quantum Electron.2(3), 540–556 (1996).
[CrossRef]

Kelley, P. L.

F. DeMartini, C. H. Townes, T. K. Gustafson, and P. L. Kelley, “Self-Steepening of Light Pulses,” Phys. Rev.164(2), 312–323 (1967).
[CrossRef]

Kersalé, Y.

Kim, C.

Kim, H.

Kim, J.

Y. Song, C. Kim, K. Jung, H. Kim, and J. Kim, “Timing jitter optimization of mode-locked Yb-fiber lasers toward the attosecond regime,” Opt. Express19(15), 14518–14525 (2011).
[CrossRef] [PubMed]

T. K. Kim, Y. Song, K. Jung, C. Kim, H. Kim, C. H. Nam, and J. Kim, “Sub-100-as timing jitter optical pulse trains from mode-locked Er-fiber lasers,” Opt. Lett.36(22), 4443–4445 (2011).
[CrossRef] [PubMed]

Y. Song, K. Jung, and J. Kim, “Impact of pulse dynamics on timing jitter in mode-locked fiber lasers,” Opt. Lett.36(10), 1761–1763 (2011).
[CrossRef] [PubMed]

J. A. Cox, A. H. Nejadmalayeri, J. Kim, and F. X. Kärtner, “Complete characterization of quantum-limited timing jitter in passively mode-locked fiber lasers,” Opt. Lett.35(20), 3522–3524 (2010).
[CrossRef] [PubMed]

J. Kim and F. X. Kärtner, “Attosecond-precision ultrafast photonics,” Laser Photon. Rev.4(3), 432–456 (2010).
[CrossRef]

J. Kim, M. J. Park, M. H. Perrott, and F. X. Kärtner, “Photonic subsampling analog-to-digital conversion of microwave signals at 40-GHz with higher than 7-ENOB resolution,” Opt. Express16(21), 16509–16515 (2008).
[CrossRef] [PubMed]

J. Kim, F. Ludwig, M. Felber, and F. X. Kärtner, “Long-term stable microwave signal extraction from mode-locked lasers,” Opt. Express15(14), 8951–8959 (2007).
[CrossRef] [PubMed]

J. Kim, J. Chen, J. Cox, and F. X. Kärtner, “Attosecond-resolution timing jitter characterization of free-running mode-locked lasers,” Opt. Lett.32(24), 3519–3521 (2007).
[CrossRef] [PubMed]

T. R. Schibli, J. Kim, O. Kuzucu, J. T. Gopinath, S. N. Tandon, G. S. Petrich, L. A. Kolodziejski, J. G. Fujimoto, E. P. Ippen, and F. X. Kaertner, “Attosecond active synchronization of passively mode-locked lasers by balanced cross correlation,” Opt. Lett.28(11), 947–949 (2003).
[CrossRef] [PubMed]

T. R. Schibli, J. Kim, O. Kuzucu, J. T. Gopinath, S. N. Tandon, G. S. Petrich, L. A. Kolodziejski, J. G. Fujimoto, E. P. Ippen, and F. X. Kaertner, “Attosecond active synchronization of passively mode-locked lasers by balanced cross correlation,” Opt. Lett.28(11), 947–949 (2003).
[CrossRef] [PubMed]

Kim, T. K.

Kirchner, M. S.

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics5(7), 425–429 (2011).
[CrossRef]

Knox, W. H.

S. Tsuda, W. H. Knox, S. T. Cundiff, W. Y. Jan, and J. E. Cunningham, “Mode-locking ultrafast solid-state lasers with saturable Bragg reflectors,” IEEE J. Sel. Top. Quantum Electron.2(3), 454–464 (1996).
[CrossRef]

Kolner, B. H.

R. P. Scott, C. Langrock, and B. H. Kolner, “High-dynamic-range laser amplitude and phase noise measurement techniques,” IEEE J. Sel. Top. Quantum Electron.7(4), 641–655 (2001).
[CrossRef]

Kolodziejski, L. A.

U. Demirbas, G. S. Petrich, D. Li, A. Sennaroglu, L. A. Kolodziejski, F. X. Kärtner, and J. G. Fujimoto, “Femtosecond tuning of Cr:colquiriite lasers with AlGaAs-based saturable Bragg reflectors,” J. Opt. Soc. Am. B28(5), 986–993 (2011).
[CrossRef]

U. Demirbas, M. Schmalz, B. Sumpf, G. Erbert, G. S. Petrich, L. A. Kolodziejski, J. G. Fujimoto, F. X. Kärtner, and A. Leitenstorfer, “Femtosecond Cr:LiSAF and Cr:LiCAF lasers pumped by tapered diode lasers,” Opt. Express19(21), 20444–20461 (2011).
[CrossRef] [PubMed]

D. Li, U. Demirbas, J. R. Birge, G. S. Petrich, L. A. Kolodziejski, A. Sennaroglu, F. X. Kärtner, and J. G. Fujimoto, “Diode-pumped passively mode-locked GHz femtosecond Cr:LiSAF laser with kW peak power,” Opt. Lett.35(9), 1446–1448 (2010).
[CrossRef] [PubMed]

U. Demirbas, D. Li, J. R. Birge, A. Sennaroglu, G. S. Petrich, L. A. Kolodziejski, F. X. Kaertner, and J. G. Fujimoto, “Low-cost, single-mode diode-pumped Cr:Colquiriite lasers,” Opt. Express17(16), 14374–14388 (2009).
[CrossRef] [PubMed]

T. R. Schibli, J. Kim, O. Kuzucu, J. T. Gopinath, S. N. Tandon, G. S. Petrich, L. A. Kolodziejski, J. G. Fujimoto, E. P. Ippen, and F. X. Kaertner, “Attosecond active synchronization of passively mode-locked lasers by balanced cross correlation,” Opt. Lett.28(11), 947–949 (2003).
[CrossRef] [PubMed]

T. R. Schibli, J. Kim, O. Kuzucu, J. T. Gopinath, S. N. Tandon, G. S. Petrich, L. A. Kolodziejski, J. G. Fujimoto, E. P. Ippen, and F. X. Kaertner, “Attosecond active synchronization of passively mode-locked lasers by balanced cross correlation,” Opt. Lett.28(11), 947–949 (2003).
[CrossRef] [PubMed]

Kopf, D.

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Honninger, N. Matuschek, and J. Aus der Au, “Semiconductor saturable absorber mirrors (SESAM's) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Top. Quantum Electron.2(3), 435–453 (1996).
[CrossRef]

Kuzucu, O.

Langrock, C.

R. P. Scott, C. Langrock, and B. H. Kolner, “High-dynamic-range laser amplitude and phase noise measurement techniques,” IEEE J. Sel. Top. Quantum Electron.7(4), 641–655 (2001).
[CrossRef]

Leitenstorfer, A.

Lemke, N.

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics5(7), 425–429 (2011).
[CrossRef]

Li, D.

Lours, M.

Ludlow, A.

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics5(7), 425–429 (2011).
[CrossRef]

Ludwig, F.

Luiten, A. N.

Matos, L.

Matuschek, N.

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Honninger, N. Matuschek, and J. Aus der Au, “Semiconductor saturable absorber mirrors (SESAM's) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Top. Quantum Electron.2(3), 435–453 (1996).
[CrossRef]

McFerran, J. J.

E. N. Ivanov, J. J. McFerran, S. A. Diddams, and L. Hollberg, “Noise properties of microwave signals synthesized with femtosecond lasers,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control54(4), 736–745 (2007).
[CrossRef] [PubMed]

Mecozzi, A.

H. A. Haus and A. Mecozzi, “Noise of Mode-Locked Lasers,” IEEE J. Quantum Electron.29(3), 983–996 (1993).
[CrossRef]

Millo, J.

Mücke, O. D.

Nam, C. H.

Nejadmalayeri, A. H.

Oates, C. W.

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics5(7), 425–429 (2011).
[CrossRef]

Park, M. J.

Paschotta, R.

R. Paschotta, “Timing jitter and phase noiseof mode-locked fiber lasers,” Opt. Express18(5), 5041–5054 (2010).
[CrossRef] [PubMed]

R. Paschotta, “Noise of mode-locked lasers (Part I): numerical model,” Appl. Phys. B79(2), 153–162 (2004).
[CrossRef]

R. Paschotta, “Noise of mode-locked lasers (Part II): timing jitter and other fluctuations,” Appl. Phys. B79(2), 163–173 (2004).
[CrossRef]

Perrott, M. H.

Petrich, G. S.

U. Demirbas, G. S. Petrich, D. Li, A. Sennaroglu, L. A. Kolodziejski, F. X. Kärtner, and J. G. Fujimoto, “Femtosecond tuning of Cr:colquiriite lasers with AlGaAs-based saturable Bragg reflectors,” J. Opt. Soc. Am. B28(5), 986–993 (2011).
[CrossRef]

U. Demirbas, M. Schmalz, B. Sumpf, G. Erbert, G. S. Petrich, L. A. Kolodziejski, J. G. Fujimoto, F. X. Kärtner, and A. Leitenstorfer, “Femtosecond Cr:LiSAF and Cr:LiCAF lasers pumped by tapered diode lasers,” Opt. Express19(21), 20444–20461 (2011).
[CrossRef] [PubMed]

D. Li, U. Demirbas, J. R. Birge, G. S. Petrich, L. A. Kolodziejski, A. Sennaroglu, F. X. Kärtner, and J. G. Fujimoto, “Diode-pumped passively mode-locked GHz femtosecond Cr:LiSAF laser with kW peak power,” Opt. Lett.35(9), 1446–1448 (2010).
[CrossRef] [PubMed]

U. Demirbas, D. Li, J. R. Birge, A. Sennaroglu, G. S. Petrich, L. A. Kolodziejski, F. X. Kaertner, and J. G. Fujimoto, “Low-cost, single-mode diode-pumped Cr:Colquiriite lasers,” Opt. Express17(16), 14374–14388 (2009).
[CrossRef] [PubMed]

T. R. Schibli, J. Kim, O. Kuzucu, J. T. Gopinath, S. N. Tandon, G. S. Petrich, L. A. Kolodziejski, J. G. Fujimoto, E. P. Ippen, and F. X. Kaertner, “Attosecond active synchronization of passively mode-locked lasers by balanced cross correlation,” Opt. Lett.28(11), 947–949 (2003).
[CrossRef] [PubMed]

T. R. Schibli, J. Kim, O. Kuzucu, J. T. Gopinath, S. N. Tandon, G. S. Petrich, L. A. Kolodziejski, J. G. Fujimoto, E. P. Ippen, and F. X. Kaertner, “Attosecond active synchronization of passively mode-locked lasers by balanced cross correlation,” Opt. Lett.28(11), 947–949 (2003).
[CrossRef] [PubMed]

Quinlan, F.

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics5(7), 425–429 (2011).
[CrossRef]

Rosenband, T.

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics5(7), 425–429 (2011).
[CrossRef]

Santarelli, G.

Schibli, T. R.

Schmalz, M.

Scott, R. P.

R. P. Scott, C. Langrock, and B. H. Kolner, “High-dynamic-range laser amplitude and phase noise measurement techniques,” IEEE J. Sel. Top. Quantum Electron.7(4), 641–655 (2001).
[CrossRef]

Sennaroglu, A.

Song, Y.

Sumpf, B.

B. Sumpf, P. Adamiec, M. Zorn, H. Wenzel, and G. Erbert, “Nearly diffraction-limited tapered lasers at 675 nm with 1-W output power and conversion efficiencies above 30%,” IEEE Photon. Technol. Lett.23(4), 266–268 (2011).
[CrossRef]

U. Demirbas, M. Schmalz, B. Sumpf, G. Erbert, G. S. Petrich, L. A. Kolodziejski, J. G. Fujimoto, F. X. Kärtner, and A. Leitenstorfer, “Femtosecond Cr:LiSAF and Cr:LiCAF lasers pumped by tapered diode lasers,” Opt. Express19(21), 20444–20461 (2011).
[CrossRef] [PubMed]

Tandon, S. N.

Taylor, J.

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics5(7), 425–429 (2011).
[CrossRef]

Townes, C. H.

F. DeMartini, C. H. Townes, T. K. Gustafson, and P. L. Kelley, “Self-Steepening of Light Pulses,” Phys. Rev.164(2), 312–323 (1967).
[CrossRef]

Tsuda, S.

S. Tsuda, W. H. Knox, S. T. Cundiff, W. Y. Jan, and J. E. Cunningham, “Mode-locking ultrafast solid-state lasers with saturable Bragg reflectors,” IEEE J. Sel. Top. Quantum Electron.2(3), 454–464 (1996).
[CrossRef]

Weingarten, K. J.

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Honninger, N. Matuschek, and J. Aus der Au, “Semiconductor saturable absorber mirrors (SESAM's) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Top. Quantum Electron.2(3), 435–453 (1996).
[CrossRef]

Wenzel, H.

B. Sumpf, P. Adamiec, M. Zorn, H. Wenzel, and G. Erbert, “Nearly diffraction-limited tapered lasers at 675 nm with 1-W output power and conversion efficiencies above 30%,” IEEE Photon. Technol. Lett.23(4), 266–268 (2011).
[CrossRef]

Zorn, M.

B. Sumpf, P. Adamiec, M. Zorn, H. Wenzel, and G. Erbert, “Nearly diffraction-limited tapered lasers at 675 nm with 1-W output power and conversion efficiencies above 30%,” IEEE Photon. Technol. Lett.23(4), 266–268 (2011).
[CrossRef]

Appl. Opt.

Appl. Phys. B

R. Paschotta, “Noise of mode-locked lasers (Part I): numerical model,” Appl. Phys. B79(2), 153–162 (2004).
[CrossRef]

R. Paschotta, “Noise of mode-locked lasers (Part II): timing jitter and other fluctuations,” Appl. Phys. B79(2), 163–173 (2004).
[CrossRef]

IEEE J. Quantum Electron.

H. A. Haus and A. Mecozzi, “Noise of Mode-Locked Lasers,” IEEE J. Quantum Electron.29(3), 983–996 (1993).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

S. Tsuda, W. H. Knox, S. T. Cundiff, W. Y. Jan, and J. E. Cunningham, “Mode-locking ultrafast solid-state lasers with saturable Bragg reflectors,” IEEE J. Sel. Top. Quantum Electron.2(3), 454–464 (1996).
[CrossRef]

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Honninger, N. Matuschek, and J. Aus der Au, “Semiconductor saturable absorber mirrors (SESAM's) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Top. Quantum Electron.2(3), 435–453 (1996).
[CrossRef]

F. X. Kärtner, I. D. Jung, and U. Keller, “Soliton mode-locking with saturable absorbers,” IEEE J. Sel. Top. Quantum Electron.2(3), 540–556 (1996).
[CrossRef]

R. P. Scott, C. Langrock, and B. H. Kolner, “High-dynamic-range laser amplitude and phase noise measurement techniques,” IEEE J. Sel. Top. Quantum Electron.7(4), 641–655 (2001).
[CrossRef]

IEEE Photon. Technol. Lett.

B. Sumpf, P. Adamiec, M. Zorn, H. Wenzel, and G. Erbert, “Nearly diffraction-limited tapered lasers at 675 nm with 1-W output power and conversion efficiencies above 30%,” IEEE Photon. Technol. Lett.23(4), 266–268 (2011).
[CrossRef]

IEEE Trans. Ultrason. Ferroelectr. Freq. Control

E. N. Ivanov, J. J. McFerran, S. A. Diddams, and L. Hollberg, “Noise properties of microwave signals synthesized with femtosecond lasers,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control54(4), 736–745 (2007).
[CrossRef] [PubMed]

J. Opt. Soc. Am. B

Laser Photon. Rev.

J. Kim and F. X. Kärtner, “Attosecond-precision ultrafast photonics,” Laser Photon. Rev.4(3), 432–456 (2010).
[CrossRef]

Nat. Photonics

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics5(7), 425–429 (2011).
[CrossRef]

A. J. Benedick, J. G. Fujimoto, and F. X. Kärtner, “Optical flywheels with attosecond jitter,” Nat. Photonics6(2), 97–100 (2012).
[CrossRef]

Opt. Express

Opt. Lett.

J. P. Gordon and H. A. Haus, “Random walk of coherently amplified solitons in optical fiber transmission,” Opt. Lett.11(10), 665–667 (1986).
[CrossRef] [PubMed]

J. Kim, J. Chen, J. Cox, and F. X. Kärtner, “Attosecond-resolution timing jitter characterization of free-running mode-locked lasers,” Opt. Lett.32(24), 3519–3521 (2007).
[CrossRef] [PubMed]

T. R. Schibli, J. Kim, O. Kuzucu, J. T. Gopinath, S. N. Tandon, G. S. Petrich, L. A. Kolodziejski, J. G. Fujimoto, E. P. Ippen, and F. X. Kaertner, “Attosecond active synchronization of passively mode-locked lasers by balanced cross correlation,” Opt. Lett.28(11), 947–949 (2003).
[CrossRef] [PubMed]

D. Li, U. Demirbas, J. R. Birge, G. S. Petrich, L. A. Kolodziejski, A. Sennaroglu, F. X. Kärtner, and J. G. Fujimoto, “Diode-pumped passively mode-locked GHz femtosecond Cr:LiSAF laser with kW peak power,” Opt. Lett.35(9), 1446–1448 (2010).
[CrossRef] [PubMed]

H. A. Haus and E. P. Ippen, “Group velocity of solitons,” Opt. Lett.26(21), 1654–1656 (2001).
[CrossRef] [PubMed]

J. Millo, R. Boudot, M. Lours, P. Y. Bourgeois, A. N. Luiten, Y. L. Coq, Y. Kersalé, and G. Santarelli, “Ultra-low-noise microwave extraction from fiber-based optical frequency comb,” Opt. Lett.34(23), 3707–3709 (2009).
[CrossRef] [PubMed]

T. R. Schibli, J. Kim, O. Kuzucu, J. T. Gopinath, S. N. Tandon, G. S. Petrich, L. A. Kolodziejski, J. G. Fujimoto, E. P. Ippen, and F. X. Kaertner, “Attosecond active synchronization of passively mode-locked lasers by balanced cross correlation,” Opt. Lett.28(11), 947–949 (2003).
[CrossRef] [PubMed]

J. A. Cox, A. H. Nejadmalayeri, J. Kim, and F. X. Kärtner, “Complete characterization of quantum-limited timing jitter in passively mode-locked fiber lasers,” Opt. Lett.35(20), 3522–3524 (2010).
[CrossRef] [PubMed]

T. K. Kim, Y. Song, K. Jung, C. Kim, H. Kim, C. H. Nam, and J. Kim, “Sub-100-as timing jitter optical pulse trains from mode-locked Er-fiber lasers,” Opt. Lett.36(22), 4443–4445 (2011).
[CrossRef] [PubMed]

Y. Song, K. Jung, and J. Kim, “Impact of pulse dynamics on timing jitter in mode-locked fiber lasers,” Opt. Lett.36(10), 1761–1763 (2011).
[CrossRef] [PubMed]

Phys. Rev.

F. DeMartini, C. H. Townes, T. K. Gustafson, and P. L. Kelley, “Self-Steepening of Light Pulses,” Phys. Rev.164(2), 312–323 (1967).
[CrossRef]

Other

U. Demirbas, A. Benedick, A. Sennaroglu, D. Li, J. Kim, J. G. Fujimoto, and F. X. Kärtner, “Attosecond resolution timing jitter characterization of diode pumped femtosecond Cr:LiSAF lasers,” 2010 Conference on Lasers and Electro-Optics (Cleo) and Quantum Electronics and Laser Science Conference (Qels) (2010).

J. A. Cox, J. Kim, and F. X. Kärtner, “Long-term, long-distance, all-optical synchronization of ultrafast fiber lasers at the quantum limit,” 2010 Conference on Lasers and Electro-Optics (Cleo) and Quantum Electronics and Laser Science Conference (Qels) (2010).

“IEEE standard definitions of physical quantities for fundamental frequency and time metrology-random instabilities,” IEEE STD 1139–2008, c1–35 (2009).

SNLO nonlinear optics code available from A.V.Smith, AS-Photonics, Albuquerque, NM.

K. Petermann, Laser Diode Modulation and Noise (Kluwer Academic Publishers, Norwell, MA, 1988).

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Figures (10)

Fig. 1
Fig. 1

Cavity layout of saturable absorber mode-locked Cr:LiSAF lasers. LD1, LD2: pump laser diodes. M1, M2, M3: cavity mirrors. L1, L2: input lenses. OC: output coupler. SA: saturable absorber.

Fig. 2
Fig. 2

Quantum-limited SSB phase noise at 100-MHz carrier. (a) Gordon-Haus jitter with HWHM gain bandwidth of 25.5 THz (850 nm – 870 nm). (b) Phase noise only due to direct phase noise from ASE. (c) Phase noise due to shot noise. Other parameters used: θ = 1, intracavity power = 6 W, 2g = 0.03, D = −100 fs2 and pulse width = 80 fs.

Fig. 3
Fig. 3

Schematic of measurement system. (a) System block diagram. HWP: half-wave plate.
PBS: polarizing beam-splitter. (b) BOC using a type-II phase-matched BBO crystal.

Fig. 4
Fig. 4

Timing discriminator. (a) Calculated cross-correlation signals (dashed) and balanced output (solid) using Eq. (5). (b) Measured phase error discriminator, with a zero-crossing slope of 240 mV/fs.

Fig. 5
Fig. 5

CMRR of the modified balanced detector. (a) Measurement setup. FA: fixed attenuator; BS: beam splitter; M1: metallic mirror; VA: variable attenuator (b) CMRR when the two channels are balanced.

Fig. 6
Fig. 6

SSB phase noise PSD of a single laser at 100-MHz carrier. (a) Measured Cr:LiSAF phase noise (b) Quantum-limited estimation, summing up all three noise sources in Fig. 2. (c) Balanced detector’s noise floor. Inset: integrated timing jitter from 50 MHz (d) Cr:LiSAF (e) Balanced detector’s noise floor.

Fig. 7
Fig. 7

RIN of (a) pump laser diode and (b) mode-locked Cr:LiSAF laser.

Fig. 8
Fig. 8

RIN noise and timing jitter. (a) Measurement setup. (b) Pump RIN mapped to phase noise (dashed), compared with measured phase noise using BOC (solid, reproduced from curve (a) in Fig. 6).

Fig. 9
Fig. 9

Transfer functions (magnitude) from pump RIN to Cr:LiSAF laser RIN. (a) Measured transfer functions. ML: mode-locked, cw: continouse-wave (b) Modeled responses using Eqs. (11) and (12).

Fig. 10
Fig. 10

AM-to-PM conversion factors. (a) Absolute value of S*dt/dS in units of one thousandth pulse width for 1ps and >10 ps recovery time (b) Coupling factors due to self-steepening and timing shift on slow saturable absorber (SA) with recovery time longer than 10 ps and S = 8.2.

Equations (15)

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T R T Δt=2| D |Δp+ T R S t (T)
L(f)= 1 2 ( 2π f rep ) 2 1 ( 2πf ) 2 ( π 2 τ 2 6w P ASE ) = ( 2π f rep ) 2 1 12 θ f rep f 2 g τ 2 N 0
L( f )= 1 2 ( 2π f rep ) 2 4 | D | 2 T R 2 1 ( 2πf ) 2 [ ( 2πf ) 2 + τ p 2 ] ( 2 3w τ 2 P ASE ) = ( 2π f rep ) 2 3 π 2 θ( f rep 3 Ω g 4 ( 2g ) 2 f rep 2 + ( 3π ) 2 f 2 Ω g 4 τ 4 ) | D | 2 g f 2 τ 2 N o
L( f )= ( 2π f rep ) 2 0.82 1 f rep τ 2 N 0
V(τ) τ 0 G L 2 I 2 csc h 2 ( t 1 t 2 +τ τ 0 )[ ( t 1 t 2 +τ τ 0 )coth( t 1 t 2 +τ τ 0 )1 ] τ 0 G L 2 I 2 csc h 2 ( 2 t 1 2 t 2 +τ τ 0 )[ ( 2 t 1 2 t 2 +τ τ 0 )coth( 2 t 1 2 t 2 +τ τ 0 )1 ]
L( f )= 1 2 ( f rep 2 φ NL πfν ) 2 S I (f)
L( f )= 1 2 ( f rep 2 f t ˜ s ( S ) S S ) 2 S I (f)
T R dP dt =2[ glq( P ) ]P T R dg dt = g g 0 τ L / T R g P P sat,L
g 0 = τ L η L η P P P w sat,L
dΔP dt = 2 P s T R Δg 2 P s T R dq( P ) d P s ΔP dΔg dt = 1 τ stim Δg g s w sat,L ΔP+ η p η L w sat,L Δ P P
ΔP ˜ Δ P P ˜ = 2 r1 T R η p η L τ L s 2 +( 1 τ stim + 2 P s T R dq( P ) d P s )s+ 2( r1 ) T R l+ q s τ L + 2 P s T R dq( P ) d P s 1 τ stim
ΔP ˜ Δ P P ˜ = 2 r1 T R η p η L τ L s 2 + 1 τ stim s+ 2( r1 ) T R l+ q s τ L
2 P s T R dq( P ) d P s =0.6 1 τ stim
dq( S ) dS =0.6 2r P s τ L w S
q(S)= q 0 S ( 1 e S )

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