Abstract

We present a novel laser mode locking scheme and discuss its unusual properties and feasibility using a theoretical model. A large set of single-frequency continuous-wave lasers oscillate by amplification in spatially separated gain media. They are mutually phase-locked by nonlinear feedback from a common saturable absorber. As a result, ultra-short pulses are generated. The new scheme offers three significant benefits: the light that is amplified in each medium is continuous-wave, thereby avoiding issues related to group-velocity dispersion and nonlinear effects that can perturb the pulse shape. The set of frequencies on which the laser oscillates, and therefore the pulse repetition rate, is controlled by the geometry of resonator-internal optical elements, not by the cavity length. Finally, the bandwidth of the laser can be controlled by switching gain modules on and off. This scheme offers a route to mode-locked lasers with high average output power, repetition rates that can be scaled into the THz range, and a bandwidth that can be dynamically controlled. The approach is particularly suited for implementation using semiconductor diode laser arrays.

© 2010 Optical Society of America

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  1. J. Klein and J. D. Kafka, “The Ti:Sapphire laser: the flexible research tool,” Nat. Photonics 4, 289 (2010).
    [CrossRef]
  2. U. Keller, “Recent developments in compact ultrafast lasers,” Nature 424, 831–838 (2003).
    [CrossRef] [PubMed]
  3. T. Pfeiffer and G. Veith, “40 GHz pulse generation using a widely tunable all-polarization preserving erbium fiber ring laser,” Electron. Lett. 29, 1849–1850 (1993).
    [CrossRef]
  4. U. Keller and A. Tropper, “Passively modelocked surface-emitting semiconductor lasers,” Phys. Rep. 429, 67–210 (2006).
    [CrossRef]
  5. A. Robertson, M. Klein, M. Tremont, K.-J. Boller, and R. Wallenstein, “2.5-GHz repetition-rate singly resonant optical parametric oscillator synchronously pumped by a mode-locked diode oscillator amplifier system,” Opt. Lett. 25, 657–659 (2000).
    [CrossRef]
  6. F. Hansteen, A. Kimel, A. Kirilyuk, and T. Rasing, “Femtosecond photomagnetic switching of spins in ferrimagnetic garnet films,” Phys. Rev. Lett. 95, 047402 (2005).
    [CrossRef] [PubMed]
  7. A. Aschwanden, D. Lorenser, H. Unold, and R. Paschotta, “10 GHz passively mode-locked external-cavity semiconductor laser with 1.4 W average output power,” Appl. Phys. Lett. 86, 131102 (2005).
    [CrossRef]
  8. P. Harding, T. Euser, Y. Nowicki-Bringuier, J. Gérard, and W. Vos, “Dynamical ultrafast all-optical switching of planar GaAs/AlAs photonic microcavities,” Appl. Phys. Lett. 91, 111103 (2007).
    [CrossRef]
  9. U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. A. 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, 435–453 (1996).
    [CrossRef]
  10. R. Rooth, F. van Goor, and W. Witteman, “An independently adjustable multiline AM mode-locked TEA CO2 laser,” IEEE J. Quantum Electron. QE-19, 1610–1612 (1983).
    [CrossRef]
  11. V. Daneu, A. Sanchez, T. Y. Fan, H. K. Choi, G. W. Turner, and C. C. Cook, “Spectral beam combining of a broad-stripe diode laser array in an external cavity,” Opt. Lett. 25, 405–407 (2000).
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  12. M. J. R. Heck, E. A. J. M. Bente, Y. Barbarin, D. Lenstra, and M. K. Smit, “Simulation and design of integrated femtosecond passively mode-locked semiconductor ring lasers including integrated passive pulse shaping components,” IEEE J. Sel. Top. Quantum Electron. 12, 265–276 (2006).
    [CrossRef]
  13. T. Hänsch, “A proposed sub-femtosecond pulse synthesizer using separate phase-locked laser oscillators,” Opt. Commun. 80, 71–75 (1990).
    [CrossRef]
  14. R. Grange, M. Haiml, R. Paschotta, G. Spühler, L. Krainer, O. Ostinelli, M. Golling, and U. Keller, “New regime of inverse saturable absorption for selfstabilizing passively modelocked lasers,” Appl. Phys. B 80, 151–158 (2005).
    [CrossRef]
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    [CrossRef]

2010 (1)

J. Klein and J. D. Kafka, “The Ti:Sapphire laser: the flexible research tool,” Nat. Photonics 4, 289 (2010).
[CrossRef]

2009 (1)

D. Byrne, W. Guo, Q. Lu, and J. Donegan, “Broadband reflection method to measure waveguide loss,” Electron. Lett. 45, 322–323 (2009).
[CrossRef]

2007 (1)

P. Harding, T. Euser, Y. Nowicki-Bringuier, J. Gérard, and W. Vos, “Dynamical ultrafast all-optical switching of planar GaAs/AlAs photonic microcavities,” Appl. Phys. Lett. 91, 111103 (2007).
[CrossRef]

2006 (2)

M. J. R. Heck, E. A. J. M. Bente, Y. Barbarin, D. Lenstra, and M. K. Smit, “Simulation and design of integrated femtosecond passively mode-locked semiconductor ring lasers including integrated passive pulse shaping components,” IEEE J. Sel. Top. Quantum Electron. 12, 265–276 (2006).
[CrossRef]

U. Keller and A. Tropper, “Passively modelocked surface-emitting semiconductor lasers,” Phys. Rep. 429, 67–210 (2006).
[CrossRef]

2005 (3)

F. Hansteen, A. Kimel, A. Kirilyuk, and T. Rasing, “Femtosecond photomagnetic switching of spins in ferrimagnetic garnet films,” Phys. Rev. Lett. 95, 047402 (2005).
[CrossRef] [PubMed]

A. Aschwanden, D. Lorenser, H. Unold, and R. Paschotta, “10 GHz passively mode-locked external-cavity semiconductor laser with 1.4 W average output power,” Appl. Phys. Lett. 86, 131102 (2005).
[CrossRef]

R. Grange, M. Haiml, R. Paschotta, G. Spühler, L. Krainer, O. Ostinelli, M. Golling, and U. Keller, “New regime of inverse saturable absorption for selfstabilizing passively modelocked lasers,” Appl. Phys. B 80, 151–158 (2005).
[CrossRef]

2003 (1)

U. Keller, “Recent developments in compact ultrafast lasers,” Nature 424, 831–838 (2003).
[CrossRef] [PubMed]

2000 (2)

1996 (1)

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. A. 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, 435–453 (1996).
[CrossRef]

1993 (1)

T. Pfeiffer and G. Veith, “40 GHz pulse generation using a widely tunable all-polarization preserving erbium fiber ring laser,” Electron. Lett. 29, 1849–1850 (1993).
[CrossRef]

1992 (1)

K. Garner and G. Massey, “Laser mode locking by active external modulation,” IEEE J. Quantum Electron. 28, 297–301 (1992).
[CrossRef]

1990 (2)

L. Eng, D. Mehuys, M. Mittelstein, and A. Yariv, “Broadband tuning (170 nm) of InGaAs quantum well lasers,” Electron. Lett. 26, 1675–1677 (1990).
[CrossRef]

T. Hänsch, “A proposed sub-femtosecond pulse synthesizer using separate phase-locked laser oscillators,” Opt. Commun. 80, 71–75 (1990).
[CrossRef]

1983 (1)

R. Rooth, F. van Goor, and W. Witteman, “An independently adjustable multiline AM mode-locked TEA CO2 laser,” IEEE J. Quantum Electron. QE-19, 1610–1612 (1983).
[CrossRef]

1981 (1)

S. Kobayashi and T. Kimura, “Injection locking in AlGaAs semiconductor lasers,” IEEE J. Quantum Electron. QE-17, 681–689 (1981).
[CrossRef]

Aschwanden, A.

A. Aschwanden, D. Lorenser, H. Unold, and R. Paschotta, “10 GHz passively mode-locked external-cavity semiconductor laser with 1.4 W average output power,” Appl. Phys. Lett. 86, 131102 (2005).
[CrossRef]

Barbarin, Y.

M. J. R. Heck, E. A. J. M. Bente, Y. Barbarin, D. Lenstra, and M. K. Smit, “Simulation and design of integrated femtosecond passively mode-locked semiconductor ring lasers including integrated passive pulse shaping components,” IEEE J. Sel. Top. Quantum Electron. 12, 265–276 (2006).
[CrossRef]

Bente, E. A. J. M.

M. J. R. Heck, E. A. J. M. Bente, Y. Barbarin, D. Lenstra, and M. K. Smit, “Simulation and design of integrated femtosecond passively mode-locked semiconductor ring lasers including integrated passive pulse shaping components,” IEEE J. Sel. Top. Quantum Electron. 12, 265–276 (2006).
[CrossRef]

Boller, K.-J.

Braun, B.

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. A. 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, 435–453 (1996).
[CrossRef]

Byrne, D.

D. Byrne, W. Guo, Q. Lu, and J. Donegan, “Broadband reflection method to measure waveguide loss,” Electron. Lett. 45, 322–323 (2009).
[CrossRef]

Choi, H. K.

Cook, C. C.

Daneu, V.

der Au, J. A.

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. A. 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, 435–453 (1996).
[CrossRef]

Donegan, J.

D. Byrne, W. Guo, Q. Lu, and J. Donegan, “Broadband reflection method to measure waveguide loss,” Electron. Lett. 45, 322–323 (2009).
[CrossRef]

Eng, L.

L. Eng, D. Mehuys, M. Mittelstein, and A. Yariv, “Broadband tuning (170 nm) of InGaAs quantum well lasers,” Electron. Lett. 26, 1675–1677 (1990).
[CrossRef]

Euser, T.

P. Harding, T. Euser, Y. Nowicki-Bringuier, J. Gérard, and W. Vos, “Dynamical ultrafast all-optical switching of planar GaAs/AlAs photonic microcavities,” Appl. Phys. Lett. 91, 111103 (2007).
[CrossRef]

Fan, T. Y.

Fluck, R.

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. A. 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, 435–453 (1996).
[CrossRef]

Garner, K.

K. Garner and G. Massey, “Laser mode locking by active external modulation,” IEEE J. Quantum Electron. 28, 297–301 (1992).
[CrossRef]

Gérard, J.

P. Harding, T. Euser, Y. Nowicki-Bringuier, J. Gérard, and W. Vos, “Dynamical ultrafast all-optical switching of planar GaAs/AlAs photonic microcavities,” Appl. Phys. Lett. 91, 111103 (2007).
[CrossRef]

Golling, M.

R. Grange, M. Haiml, R. Paschotta, G. Spühler, L. Krainer, O. Ostinelli, M. Golling, and U. Keller, “New regime of inverse saturable absorption for selfstabilizing passively modelocked lasers,” Appl. Phys. B 80, 151–158 (2005).
[CrossRef]

Grange, R.

R. Grange, M. Haiml, R. Paschotta, G. Spühler, L. Krainer, O. Ostinelli, M. Golling, and U. Keller, “New regime of inverse saturable absorption for selfstabilizing passively modelocked lasers,” Appl. Phys. B 80, 151–158 (2005).
[CrossRef]

Guo, W.

D. Byrne, W. Guo, Q. Lu, and J. Donegan, “Broadband reflection method to measure waveguide loss,” Electron. Lett. 45, 322–323 (2009).
[CrossRef]

Haiml, M.

R. Grange, M. Haiml, R. Paschotta, G. Spühler, L. Krainer, O. Ostinelli, M. Golling, and U. Keller, “New regime of inverse saturable absorption for selfstabilizing passively modelocked lasers,” Appl. Phys. B 80, 151–158 (2005).
[CrossRef]

Hänsch, T.

T. Hänsch, “A proposed sub-femtosecond pulse synthesizer using separate phase-locked laser oscillators,” Opt. Commun. 80, 71–75 (1990).
[CrossRef]

Hansteen, F.

F. Hansteen, A. Kimel, A. Kirilyuk, and T. Rasing, “Femtosecond photomagnetic switching of spins in ferrimagnetic garnet films,” Phys. Rev. Lett. 95, 047402 (2005).
[CrossRef] [PubMed]

Harding, P.

P. Harding, T. Euser, Y. Nowicki-Bringuier, J. Gérard, and W. Vos, “Dynamical ultrafast all-optical switching of planar GaAs/AlAs photonic microcavities,” Appl. Phys. Lett. 91, 111103 (2007).
[CrossRef]

Heck, M. J. R.

M. J. R. Heck, E. A. J. M. Bente, Y. Barbarin, D. Lenstra, and M. K. Smit, “Simulation and design of integrated femtosecond passively mode-locked semiconductor ring lasers including integrated passive pulse shaping components,” IEEE J. Sel. Top. Quantum Electron. 12, 265–276 (2006).
[CrossRef]

Hönninger, C.

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. A. 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, 435–453 (1996).
[CrossRef]

Jung, I. D.

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. A. 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, 435–453 (1996).
[CrossRef]

Kafka, J. D.

J. Klein and J. D. Kafka, “The Ti:Sapphire laser: the flexible research tool,” Nat. Photonics 4, 289 (2010).
[CrossRef]

Kärtner, F. X.

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. A. 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, 435–453 (1996).
[CrossRef]

Keller, U.

U. Keller and A. Tropper, “Passively modelocked surface-emitting semiconductor lasers,” Phys. Rep. 429, 67–210 (2006).
[CrossRef]

R. Grange, M. Haiml, R. Paschotta, G. Spühler, L. Krainer, O. Ostinelli, M. Golling, and U. Keller, “New regime of inverse saturable absorption for selfstabilizing passively modelocked lasers,” Appl. Phys. B 80, 151–158 (2005).
[CrossRef]

U. Keller, “Recent developments in compact ultrafast lasers,” Nature 424, 831–838 (2003).
[CrossRef] [PubMed]

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. A. 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, 435–453 (1996).
[CrossRef]

Kimel, A.

F. Hansteen, A. Kimel, A. Kirilyuk, and T. Rasing, “Femtosecond photomagnetic switching of spins in ferrimagnetic garnet films,” Phys. Rev. Lett. 95, 047402 (2005).
[CrossRef] [PubMed]

Kimura, T.

S. Kobayashi and T. Kimura, “Injection locking in AlGaAs semiconductor lasers,” IEEE J. Quantum Electron. QE-17, 681–689 (1981).
[CrossRef]

Kirilyuk, A.

F. Hansteen, A. Kimel, A. Kirilyuk, and T. Rasing, “Femtosecond photomagnetic switching of spins in ferrimagnetic garnet films,” Phys. Rev. Lett. 95, 047402 (2005).
[CrossRef] [PubMed]

Klein, J.

J. Klein and J. D. Kafka, “The Ti:Sapphire laser: the flexible research tool,” Nat. Photonics 4, 289 (2010).
[CrossRef]

Klein, M.

Kobayashi, S.

S. Kobayashi and T. Kimura, “Injection locking in AlGaAs semiconductor lasers,” IEEE J. Quantum Electron. QE-17, 681–689 (1981).
[CrossRef]

Kopf, D.

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. A. 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, 435–453 (1996).
[CrossRef]

Krainer, L.

R. Grange, M. Haiml, R. Paschotta, G. Spühler, L. Krainer, O. Ostinelli, M. Golling, and U. Keller, “New regime of inverse saturable absorption for selfstabilizing passively modelocked lasers,” Appl. Phys. B 80, 151–158 (2005).
[CrossRef]

Lenstra, D.

M. J. R. Heck, E. A. J. M. Bente, Y. Barbarin, D. Lenstra, and M. K. Smit, “Simulation and design of integrated femtosecond passively mode-locked semiconductor ring lasers including integrated passive pulse shaping components,” IEEE J. Sel. Top. Quantum Electron. 12, 265–276 (2006).
[CrossRef]

Lorenser, D.

A. Aschwanden, D. Lorenser, H. Unold, and R. Paschotta, “10 GHz passively mode-locked external-cavity semiconductor laser with 1.4 W average output power,” Appl. Phys. Lett. 86, 131102 (2005).
[CrossRef]

Lu, Q.

D. Byrne, W. Guo, Q. Lu, and J. Donegan, “Broadband reflection method to measure waveguide loss,” Electron. Lett. 45, 322–323 (2009).
[CrossRef]

Massey, G.

K. Garner and G. Massey, “Laser mode locking by active external modulation,” IEEE J. Quantum Electron. 28, 297–301 (1992).
[CrossRef]

Matuschek, N.

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. A. 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, 435–453 (1996).
[CrossRef]

Mehuys, D.

L. Eng, D. Mehuys, M. Mittelstein, and A. Yariv, “Broadband tuning (170 nm) of InGaAs quantum well lasers,” Electron. Lett. 26, 1675–1677 (1990).
[CrossRef]

Mittelstein, M.

L. Eng, D. Mehuys, M. Mittelstein, and A. Yariv, “Broadband tuning (170 nm) of InGaAs quantum well lasers,” Electron. Lett. 26, 1675–1677 (1990).
[CrossRef]

Nowicki-Bringuier, Y.

P. Harding, T. Euser, Y. Nowicki-Bringuier, J. Gérard, and W. Vos, “Dynamical ultrafast all-optical switching of planar GaAs/AlAs photonic microcavities,” Appl. Phys. Lett. 91, 111103 (2007).
[CrossRef]

Ostinelli, O.

R. Grange, M. Haiml, R. Paschotta, G. Spühler, L. Krainer, O. Ostinelli, M. Golling, and U. Keller, “New regime of inverse saturable absorption for selfstabilizing passively modelocked lasers,” Appl. Phys. B 80, 151–158 (2005).
[CrossRef]

Paschotta, R.

R. Grange, M. Haiml, R. Paschotta, G. Spühler, L. Krainer, O. Ostinelli, M. Golling, and U. Keller, “New regime of inverse saturable absorption for selfstabilizing passively modelocked lasers,” Appl. Phys. B 80, 151–158 (2005).
[CrossRef]

A. Aschwanden, D. Lorenser, H. Unold, and R. Paschotta, “10 GHz passively mode-locked external-cavity semiconductor laser with 1.4 W average output power,” Appl. Phys. Lett. 86, 131102 (2005).
[CrossRef]

Pfeiffer, T.

T. Pfeiffer and G. Veith, “40 GHz pulse generation using a widely tunable all-polarization preserving erbium fiber ring laser,” Electron. Lett. 29, 1849–1850 (1993).
[CrossRef]

Rasing, T.

F. Hansteen, A. Kimel, A. Kirilyuk, and T. Rasing, “Femtosecond photomagnetic switching of spins in ferrimagnetic garnet films,” Phys. Rev. Lett. 95, 047402 (2005).
[CrossRef] [PubMed]

Robertson, A.

Rooth, R.

R. Rooth, F. van Goor, and W. Witteman, “An independently adjustable multiline AM mode-locked TEA CO2 laser,” IEEE J. Quantum Electron. QE-19, 1610–1612 (1983).
[CrossRef]

Sanchez, A.

Smit, M. K.

M. J. R. Heck, E. A. J. M. Bente, Y. Barbarin, D. Lenstra, and M. K. Smit, “Simulation and design of integrated femtosecond passively mode-locked semiconductor ring lasers including integrated passive pulse shaping components,” IEEE J. Sel. Top. Quantum Electron. 12, 265–276 (2006).
[CrossRef]

Spühler, G.

R. Grange, M. Haiml, R. Paschotta, G. Spühler, L. Krainer, O. Ostinelli, M. Golling, and U. Keller, “New regime of inverse saturable absorption for selfstabilizing passively modelocked lasers,” Appl. Phys. B 80, 151–158 (2005).
[CrossRef]

Tremont, M.

Tropper, A.

U. Keller and A. Tropper, “Passively modelocked surface-emitting semiconductor lasers,” Phys. Rep. 429, 67–210 (2006).
[CrossRef]

Turner, G. W.

Unold, H.

A. Aschwanden, D. Lorenser, H. Unold, and R. Paschotta, “10 GHz passively mode-locked external-cavity semiconductor laser with 1.4 W average output power,” Appl. Phys. Lett. 86, 131102 (2005).
[CrossRef]

van Goor, F.

R. Rooth, F. van Goor, and W. Witteman, “An independently adjustable multiline AM mode-locked TEA CO2 laser,” IEEE J. Quantum Electron. QE-19, 1610–1612 (1983).
[CrossRef]

Veith, G.

T. Pfeiffer and G. Veith, “40 GHz pulse generation using a widely tunable all-polarization preserving erbium fiber ring laser,” Electron. Lett. 29, 1849–1850 (1993).
[CrossRef]

Vos, W.

P. Harding, T. Euser, Y. Nowicki-Bringuier, J. Gérard, and W. Vos, “Dynamical ultrafast all-optical switching of planar GaAs/AlAs photonic microcavities,” Appl. Phys. Lett. 91, 111103 (2007).
[CrossRef]

Wallenstein, R.

Weingarten, K. J.

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. A. 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, 435–453 (1996).
[CrossRef]

Witteman, W.

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Figures (5)

Fig. 1
Fig. 1

(right) Overview. Light originates from the AR coated diode array (a), and is collimated by a lens (b). The light is combined by a diffraction grating (c), and focused (d) on the SESAM (e). The collimation lens (b) is placed one focal length (f) from the diode array, and the diffraction grating (c) is one focal length (f) from the lens (b). (left) Magnified view of the diode array showing several of the emitters. The gain elements (h) are spaced 200 μm apart and have a width of 4 μm. The array has a high-reflection on the back facet (g) and an anti-reflection coating on the front (i).

Fig. 2
Fig. 2

The variation in the frequency spacing δνn,0 in Eq. 1 versus the emitter number n. The red dashed line indicates the number of emitters that can be corrected assuming that the mark/space ratio of the emitters is the limiting factor. The green line indicates the number of emitters that can be corrected assuming that a 33% modal overlap is required to frequency lock the emitter. These calculations assume that the ideal frequency spacing is 67 GHz.

Fig. 3
Fig. 3

Block diagram for the laser model. One iteration consists of light amplification in 49 independent gain elements (G-24,...,G24), summation of their light-field amplitudes to the full spectrum (C), Fourier transformation to the time domain (νt), saturable absorber described in time domain (SA) and monitoring the temporal shape of the output (time trace), inverse Fourier transformation to the frequency domain (νt), decomposition into separate spectral field amplitudes (D), and return to the gain elements. Random initial phases are used to model startup of mode locking from noise.

Fig. 4
Fig. 4

Calculation results after 1 (a,b), 100 (c,d) and 500 (e,f) iterations, for ΔR = 40%, τ = 3 ps and S = 3. The power spectrum is shown in the left column with the corresponding time trace on the right. All power spectra are normalized to the maximum power for 1 W per emitter. The time traces are normalized to the Fourier-limited maximum peak power. The laser starts with multiple frequencies per gain element and a random phase spectrum. After 500 iterations the laser is mode locked.

Fig. 5
Fig. 5

Probability of mode locking as a function of ΔR and τ for (a) S = 0.1, (b) S = 1, (c) S = 3, (d) S = 5, (e) S = 10, (f) S = 20 and (g) S = 50. Darker shades represent areas where mode locking was observed more often. ⊗ indicates the most suitable SESAM for our laser that is also commercially available at this time, i.e., the SESAM with the highest ΔR and the lowest τ. For comparison, the second and third best available SESAMs are indicated by the ⊕ [20].

Equations (4)

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δ ν n , m = c Λ g ( 1 α + β γ nd f 1 α + β γ md f ) ,
g ( I tot ) = g 0 1 + I tot / I sat ,
R ( Φ P ) = R ns ( 1 e Φ P / Φ sat ) Δ R Φ P / Φ sat Φ P Φ TPA .
Φ P = I ( t ) exp ( t / τ ) dt .

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