Abstract

Analytical theory of the high-power passively mode-locked laser with a slow absorber is developed. In distinguishing from previous treatment, our model is valid at pulse energies well exceeding the saturation energy of absorber. This is achieved by solving the mode-locking master equation in the pulse energy-domain representation. The performances of monolithic sub-picosecond blue-violet GaN mode-locked diode laser in the high-power operation regime are analyzed using the developed approach.

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  1. S. Nakamura, M. Senoh, S.- Nagahama, N. Iwasa, T. Matsushita, and T. Mukai, “Blue InGaN-based laser diodes with an emission wavelength of 450 nm,” Appl. Phys. Lett. 76(1), 22–24 (2000).
    [CrossRef]
  2. K. Saito, H. Watanabe, T. Miyajima, M. Ikeda, and H. Yokoyama, “Mode locking of an external-cavity bisection GaInN blue-violet laser diode producing 3 ps duration optical pulses,” Appl. Phys. Lett. 96(3), 031112 (2010).
    [CrossRef]
  3. P. P. Vasil'ev, Ultrafast diode lasers: fundamentals and applications (Artech House, Boston, 1995).
  4. G. H. C. New, “Pulse evolution in mode-locked quasi-continuous lasers,” IEEE J. Quantum Electron. 10(2), 115–124 (1974).
    [CrossRef]
  5. H. A. Haus, “Theory of mode-locking with a slow saturable absorber,” IEEE J. Quantum Electron. 11, 736-746 (1975); “Mode-locking of lasers,” IEEE J. Sel,” Topics in QE 6(6), 1173–1185 (2000).
    [CrossRef]
  6. R. G. M. P. Koumans and R. van Roijen, “Theory for passive Mode-Locking in Semiconductor Laser Structures Including the Effects of Self-phase Modulation, Dispersion, and Pulse Collisions,” IEEE J. QE. 32(3), 478–492 (1996).
    [CrossRef]
  7. J. Leegwater, “Theory of Mode-Locked Semiconductor Lasers,” IEEE J. Quantum Electron. 32(10), 1782–1790 (1996).
    [CrossRef]
  8. J. L. A. Dubbeldam, J. A. Leegwater, and D. Lenstra, “Theory of mode-locked semiconductor lasers with finite absorber relaxation times,” Appl. Phys. Lett. 70(15), 1938 (1997).
    [CrossRef]
  9. J. Piprek, Semiconductor optoelectronic devices (Academic, 2002)
  10. W. G. Scheibenzuber, U. T. Schwarz, L. Sulmoni, J. Dorsaz, J.-F. Carlin, and N. Grandjean, “Recombination coefficients of GaN-based laser diodes,” J. Appl. Phys. 109(9), 093106 (2011).
    [CrossRef]
  11. A. G. Vladimirov and D. Turaev, “Model for passive mode locking in semiconductor lasers,” Phys. Rev. A 72(3), 033808 (2005).
    [CrossRef]
  12. J. Dorsaz, D. L. Boïko, L. Sulmoni, J.-F. Carlin, W. G. Scheibenzuber, U. T. Schwarz, and N. Grandjean, “Optical bistability in InGaN-based multi-section laser diodes,” Appl. Phys. Lett. 98(19), 191115 (2011).
    [CrossRef]

2011 (2)

W. G. Scheibenzuber, U. T. Schwarz, L. Sulmoni, J. Dorsaz, J.-F. Carlin, and N. Grandjean, “Recombination coefficients of GaN-based laser diodes,” J. Appl. Phys. 109(9), 093106 (2011).
[CrossRef]

J. Dorsaz, D. L. Boïko, L. Sulmoni, J.-F. Carlin, W. G. Scheibenzuber, U. T. Schwarz, and N. Grandjean, “Optical bistability in InGaN-based multi-section laser diodes,” Appl. Phys. Lett. 98(19), 191115 (2011).
[CrossRef]

2010 (1)

K. Saito, H. Watanabe, T. Miyajima, M. Ikeda, and H. Yokoyama, “Mode locking of an external-cavity bisection GaInN blue-violet laser diode producing 3 ps duration optical pulses,” Appl. Phys. Lett. 96(3), 031112 (2010).
[CrossRef]

2005 (1)

A. G. Vladimirov and D. Turaev, “Model for passive mode locking in semiconductor lasers,” Phys. Rev. A 72(3), 033808 (2005).
[CrossRef]

2000 (1)

S. Nakamura, M. Senoh, S.- Nagahama, N. Iwasa, T. Matsushita, and T. Mukai, “Blue InGaN-based laser diodes with an emission wavelength of 450 nm,” Appl. Phys. Lett. 76(1), 22–24 (2000).
[CrossRef]

1997 (1)

J. L. A. Dubbeldam, J. A. Leegwater, and D. Lenstra, “Theory of mode-locked semiconductor lasers with finite absorber relaxation times,” Appl. Phys. Lett. 70(15), 1938 (1997).
[CrossRef]

1996 (2)

R. G. M. P. Koumans and R. van Roijen, “Theory for passive Mode-Locking in Semiconductor Laser Structures Including the Effects of Self-phase Modulation, Dispersion, and Pulse Collisions,” IEEE J. QE. 32(3), 478–492 (1996).
[CrossRef]

J. Leegwater, “Theory of Mode-Locked Semiconductor Lasers,” IEEE J. Quantum Electron. 32(10), 1782–1790 (1996).
[CrossRef]

1975 (1)

H. A. Haus, “Theory of mode-locking with a slow saturable absorber,” IEEE J. Quantum Electron. 11, 736-746 (1975); “Mode-locking of lasers,” IEEE J. Sel,” Topics in QE 6(6), 1173–1185 (2000).
[CrossRef]

1974 (1)

G. H. C. New, “Pulse evolution in mode-locked quasi-continuous lasers,” IEEE J. Quantum Electron. 10(2), 115–124 (1974).
[CrossRef]

Boïko, D. L.

J. Dorsaz, D. L. Boïko, L. Sulmoni, J.-F. Carlin, W. G. Scheibenzuber, U. T. Schwarz, and N. Grandjean, “Optical bistability in InGaN-based multi-section laser diodes,” Appl. Phys. Lett. 98(19), 191115 (2011).
[CrossRef]

Carlin, J.-F.

W. G. Scheibenzuber, U. T. Schwarz, L. Sulmoni, J. Dorsaz, J.-F. Carlin, and N. Grandjean, “Recombination coefficients of GaN-based laser diodes,” J. Appl. Phys. 109(9), 093106 (2011).
[CrossRef]

J. Dorsaz, D. L. Boïko, L. Sulmoni, J.-F. Carlin, W. G. Scheibenzuber, U. T. Schwarz, and N. Grandjean, “Optical bistability in InGaN-based multi-section laser diodes,” Appl. Phys. Lett. 98(19), 191115 (2011).
[CrossRef]

Dorsaz, J.

J. Dorsaz, D. L. Boïko, L. Sulmoni, J.-F. Carlin, W. G. Scheibenzuber, U. T. Schwarz, and N. Grandjean, “Optical bistability in InGaN-based multi-section laser diodes,” Appl. Phys. Lett. 98(19), 191115 (2011).
[CrossRef]

W. G. Scheibenzuber, U. T. Schwarz, L. Sulmoni, J. Dorsaz, J.-F. Carlin, and N. Grandjean, “Recombination coefficients of GaN-based laser diodes,” J. Appl. Phys. 109(9), 093106 (2011).
[CrossRef]

Dubbeldam, J. L. A.

J. L. A. Dubbeldam, J. A. Leegwater, and D. Lenstra, “Theory of mode-locked semiconductor lasers with finite absorber relaxation times,” Appl. Phys. Lett. 70(15), 1938 (1997).
[CrossRef]

Grandjean, N.

W. G. Scheibenzuber, U. T. Schwarz, L. Sulmoni, J. Dorsaz, J.-F. Carlin, and N. Grandjean, “Recombination coefficients of GaN-based laser diodes,” J. Appl. Phys. 109(9), 093106 (2011).
[CrossRef]

J. Dorsaz, D. L. Boïko, L. Sulmoni, J.-F. Carlin, W. G. Scheibenzuber, U. T. Schwarz, and N. Grandjean, “Optical bistability in InGaN-based multi-section laser diodes,” Appl. Phys. Lett. 98(19), 191115 (2011).
[CrossRef]

Haus, H. A.

H. A. Haus, “Theory of mode-locking with a slow saturable absorber,” IEEE J. Quantum Electron. 11, 736-746 (1975); “Mode-locking of lasers,” IEEE J. Sel,” Topics in QE 6(6), 1173–1185 (2000).
[CrossRef]

Ikeda, M.

K. Saito, H. Watanabe, T. Miyajima, M. Ikeda, and H. Yokoyama, “Mode locking of an external-cavity bisection GaInN blue-violet laser diode producing 3 ps duration optical pulses,” Appl. Phys. Lett. 96(3), 031112 (2010).
[CrossRef]

Iwasa, N.

S. Nakamura, M. Senoh, S.- Nagahama, N. Iwasa, T. Matsushita, and T. Mukai, “Blue InGaN-based laser diodes with an emission wavelength of 450 nm,” Appl. Phys. Lett. 76(1), 22–24 (2000).
[CrossRef]

Koumans, R. G. M. P.

R. G. M. P. Koumans and R. van Roijen, “Theory for passive Mode-Locking in Semiconductor Laser Structures Including the Effects of Self-phase Modulation, Dispersion, and Pulse Collisions,” IEEE J. QE. 32(3), 478–492 (1996).
[CrossRef]

Leegwater, J.

J. Leegwater, “Theory of Mode-Locked Semiconductor Lasers,” IEEE J. Quantum Electron. 32(10), 1782–1790 (1996).
[CrossRef]

Leegwater, J. A.

J. L. A. Dubbeldam, J. A. Leegwater, and D. Lenstra, “Theory of mode-locked semiconductor lasers with finite absorber relaxation times,” Appl. Phys. Lett. 70(15), 1938 (1997).
[CrossRef]

Lenstra, D.

J. L. A. Dubbeldam, J. A. Leegwater, and D. Lenstra, “Theory of mode-locked semiconductor lasers with finite absorber relaxation times,” Appl. Phys. Lett. 70(15), 1938 (1997).
[CrossRef]

Matsushita, T.

S. Nakamura, M. Senoh, S.- Nagahama, N. Iwasa, T. Matsushita, and T. Mukai, “Blue InGaN-based laser diodes with an emission wavelength of 450 nm,” Appl. Phys. Lett. 76(1), 22–24 (2000).
[CrossRef]

Miyajima, T.

K. Saito, H. Watanabe, T. Miyajima, M. Ikeda, and H. Yokoyama, “Mode locking of an external-cavity bisection GaInN blue-violet laser diode producing 3 ps duration optical pulses,” Appl. Phys. Lett. 96(3), 031112 (2010).
[CrossRef]

Mukai, T.

S. Nakamura, M. Senoh, S.- Nagahama, N. Iwasa, T. Matsushita, and T. Mukai, “Blue InGaN-based laser diodes with an emission wavelength of 450 nm,” Appl. Phys. Lett. 76(1), 22–24 (2000).
[CrossRef]

Nagahama, S.-

S. Nakamura, M. Senoh, S.- Nagahama, N. Iwasa, T. Matsushita, and T. Mukai, “Blue InGaN-based laser diodes with an emission wavelength of 450 nm,” Appl. Phys. Lett. 76(1), 22–24 (2000).
[CrossRef]

Nakamura, S.

S. Nakamura, M. Senoh, S.- Nagahama, N. Iwasa, T. Matsushita, and T. Mukai, “Blue InGaN-based laser diodes with an emission wavelength of 450 nm,” Appl. Phys. Lett. 76(1), 22–24 (2000).
[CrossRef]

New, G. H. C.

G. H. C. New, “Pulse evolution in mode-locked quasi-continuous lasers,” IEEE J. Quantum Electron. 10(2), 115–124 (1974).
[CrossRef]

Saito, K.

K. Saito, H. Watanabe, T. Miyajima, M. Ikeda, and H. Yokoyama, “Mode locking of an external-cavity bisection GaInN blue-violet laser diode producing 3 ps duration optical pulses,” Appl. Phys. Lett. 96(3), 031112 (2010).
[CrossRef]

Scheibenzuber, W. G.

W. G. Scheibenzuber, U. T. Schwarz, L. Sulmoni, J. Dorsaz, J.-F. Carlin, and N. Grandjean, “Recombination coefficients of GaN-based laser diodes,” J. Appl. Phys. 109(9), 093106 (2011).
[CrossRef]

J. Dorsaz, D. L. Boïko, L. Sulmoni, J.-F. Carlin, W. G. Scheibenzuber, U. T. Schwarz, and N. Grandjean, “Optical bistability in InGaN-based multi-section laser diodes,” Appl. Phys. Lett. 98(19), 191115 (2011).
[CrossRef]

Schwarz, U. T.

J. Dorsaz, D. L. Boïko, L. Sulmoni, J.-F. Carlin, W. G. Scheibenzuber, U. T. Schwarz, and N. Grandjean, “Optical bistability in InGaN-based multi-section laser diodes,” Appl. Phys. Lett. 98(19), 191115 (2011).
[CrossRef]

W. G. Scheibenzuber, U. T. Schwarz, L. Sulmoni, J. Dorsaz, J.-F. Carlin, and N. Grandjean, “Recombination coefficients of GaN-based laser diodes,” J. Appl. Phys. 109(9), 093106 (2011).
[CrossRef]

Senoh, M.

S. Nakamura, M. Senoh, S.- Nagahama, N. Iwasa, T. Matsushita, and T. Mukai, “Blue InGaN-based laser diodes with an emission wavelength of 450 nm,” Appl. Phys. Lett. 76(1), 22–24 (2000).
[CrossRef]

Sulmoni, L.

W. G. Scheibenzuber, U. T. Schwarz, L. Sulmoni, J. Dorsaz, J.-F. Carlin, and N. Grandjean, “Recombination coefficients of GaN-based laser diodes,” J. Appl. Phys. 109(9), 093106 (2011).
[CrossRef]

J. Dorsaz, D. L. Boïko, L. Sulmoni, J.-F. Carlin, W. G. Scheibenzuber, U. T. Schwarz, and N. Grandjean, “Optical bistability in InGaN-based multi-section laser diodes,” Appl. Phys. Lett. 98(19), 191115 (2011).
[CrossRef]

Turaev, D.

A. G. Vladimirov and D. Turaev, “Model for passive mode locking in semiconductor lasers,” Phys. Rev. A 72(3), 033808 (2005).
[CrossRef]

van Roijen, R.

R. G. M. P. Koumans and R. van Roijen, “Theory for passive Mode-Locking in Semiconductor Laser Structures Including the Effects of Self-phase Modulation, Dispersion, and Pulse Collisions,” IEEE J. QE. 32(3), 478–492 (1996).
[CrossRef]

Vladimirov, A. G.

A. G. Vladimirov and D. Turaev, “Model for passive mode locking in semiconductor lasers,” Phys. Rev. A 72(3), 033808 (2005).
[CrossRef]

Watanabe, H.

K. Saito, H. Watanabe, T. Miyajima, M. Ikeda, and H. Yokoyama, “Mode locking of an external-cavity bisection GaInN blue-violet laser diode producing 3 ps duration optical pulses,” Appl. Phys. Lett. 96(3), 031112 (2010).
[CrossRef]

Yokoyama, H.

K. Saito, H. Watanabe, T. Miyajima, M. Ikeda, and H. Yokoyama, “Mode locking of an external-cavity bisection GaInN blue-violet laser diode producing 3 ps duration optical pulses,” Appl. Phys. Lett. 96(3), 031112 (2010).
[CrossRef]

Appl. Phys. Lett. (4)

S. Nakamura, M. Senoh, S.- Nagahama, N. Iwasa, T. Matsushita, and T. Mukai, “Blue InGaN-based laser diodes with an emission wavelength of 450 nm,” Appl. Phys. Lett. 76(1), 22–24 (2000).
[CrossRef]

K. Saito, H. Watanabe, T. Miyajima, M. Ikeda, and H. Yokoyama, “Mode locking of an external-cavity bisection GaInN blue-violet laser diode producing 3 ps duration optical pulses,” Appl. Phys. Lett. 96(3), 031112 (2010).
[CrossRef]

J. L. A. Dubbeldam, J. A. Leegwater, and D. Lenstra, “Theory of mode-locked semiconductor lasers with finite absorber relaxation times,” Appl. Phys. Lett. 70(15), 1938 (1997).
[CrossRef]

J. Dorsaz, D. L. Boïko, L. Sulmoni, J.-F. Carlin, W. G. Scheibenzuber, U. T. Schwarz, and N. Grandjean, “Optical bistability in InGaN-based multi-section laser diodes,” Appl. Phys. Lett. 98(19), 191115 (2011).
[CrossRef]

IEEE J. QE. (1)

R. G. M. P. Koumans and R. van Roijen, “Theory for passive Mode-Locking in Semiconductor Laser Structures Including the Effects of Self-phase Modulation, Dispersion, and Pulse Collisions,” IEEE J. QE. 32(3), 478–492 (1996).
[CrossRef]

IEEE J. Quantum Electron. (3)

J. Leegwater, “Theory of Mode-Locked Semiconductor Lasers,” IEEE J. Quantum Electron. 32(10), 1782–1790 (1996).
[CrossRef]

G. H. C. New, “Pulse evolution in mode-locked quasi-continuous lasers,” IEEE J. Quantum Electron. 10(2), 115–124 (1974).
[CrossRef]

H. A. Haus, “Theory of mode-locking with a slow saturable absorber,” IEEE J. Quantum Electron. 11, 736-746 (1975); “Mode-locking of lasers,” IEEE J. Sel,” Topics in QE 6(6), 1173–1185 (2000).
[CrossRef]

J. Appl. Phys. (1)

W. G. Scheibenzuber, U. T. Schwarz, L. Sulmoni, J. Dorsaz, J.-F. Carlin, and N. Grandjean, “Recombination coefficients of GaN-based laser diodes,” J. Appl. Phys. 109(9), 093106 (2011).
[CrossRef]

Phys. Rev. A (1)

A. G. Vladimirov and D. Turaev, “Model for passive mode locking in semiconductor lasers,” Phys. Rev. A 72(3), 033808 (2005).
[CrossRef]

Other (2)

P. P. Vasil'ev, Ultrafast diode lasers: fundamentals and applications (Artech House, Boston, 1995).

J. Piprek, Semiconductor optoelectronic devices (Academic, 2002)

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Figures (2)

Fig. 1
Fig. 1

Schematic of illustration of InGaN/GaN ridge-waveguide multi-section laser diode (a). Sellmeier model predictions for the group velocity dispersion D * = ω L 2 2 k / ω 2 (b) and group velocity (c).

Fig. 2
Fig. 2

Solution Eq. (9) of the mode-locking master Eq. (1): (a) FWHM pulse width 1.76τp, ± (left axis) and output peak power per facet P ± (righ axis) v.s. pumping current for high-energy (black curves) and low energy (red curves) solution branches; (b) Bias voltage at which the self-starting modelocking regime is stable (left axis) and the relative pulse energy µ ± = W p, ± /EsA (righ axis)

Tables (1)

Tables Icon

Table 1 Dynamic model parameters for monolithic mode-locked InGaN/GaN laser diodes [10,12].

Equations (13)

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{ 1 + ( 1 i α A ) q i exp ( E ( t ) / E s A ) ( 1 i α L ) g i exp ( E ( t ) / E s L ) + ξ 2 + i ( ψ + ξ ) + + ( 1 + δ 2 i ξ ) 1 ω L d d t ( 1 + i D ) 1 ω L 2 d 2 d t 2 } a ( t ) = 0.
q i = q 0 1 exp ( T r e p / T A ) 1 exp ( W p / E s A T r e p / T A ) , g i = g 0 1 exp ( T r e p / T L ) 1 exp ( W p / E s L T r e p / T L )
q 0 = l A Γ s v g α C l C ( g n ) n t ( 1 V a ) , g 0 = l L Γ v g α C l C ( g n ) [ J T L e h n t ] ,
a = [ A G 1 / 2 ( x ) ] 1 + i β ,
2 ( 1 β D ) B 2 G G ' ' + ( 1 β 2 2 β D ) B 2 ( G ' ) 2 ( 1 + δ + 2 ξ β ) B G ' ξ 2 = = 1 + q i exp ( μ x ) g i exp ( μ x / s ) , 2 ( β + D ) B 2 G G ' ' + ( 2 β + D β 2 D ) B 2 ( G ' ) 2 ( β + δ β 2 ξ ) B G ' = = ψ + ξ α A q i exp ( μ x ) + α L g i exp ( μ x / s )
β = 2 3 γ + D 1 + D 2 Y .
γ = [ α L s α A ] 1 / ( s 1 ) , Y = 3 2 ( 1 + D 2 ) ( γ + D 2 ) { 2 + 9 4 ( 1 γ D ) 2 ( γ + D ) 2 3 2 ( 1 γ D ) ( γ + D ) } .
T 1 = Y 1 + 4 Y ( β + γ 1 + β 2 ) 2 + 2 3 4 ( γ + D ) 3 ( γ D 1 ) 1 + D 2 ,     T 2 = 4 b 1 + 8 Y ( β + γ 1 + β 2 ) 2 β b 1 + γ b 2 β + γ T 3 = 16 ( s 1 Δ 1 ) 8 b 1 2 16 Y ( ( β + γ ) ( β b 1 + γ b 2 ) ( 1 + β 2 ) ( β + γ ) ) 2 , , Δ 1 = s 1 s [ ( g i / s ) s q i ] 1 / ( s 1 ) , b 1 = s s 1 ln [ s q i g i ] , b 2 = s s 1 ln [ α A α L s q i g i ]
μ ± = T 2 T 1 ± T 2 2 T 1 2 + T 3 T 1 , τ p , ± = 4 ω L Y 1 / 2 μ ± Δ 1 1 / 2 ,
ξ = 1 2 β + γ 1 + β 2 Y 1 / 2 Δ 1 1 / 2 [ μ ± 2 β b 1 + γ b 2 β + γ ] , 1 + δ = 1 2 1 β γ 1 + β 2 Y 1 / 2 Δ 1 1 / 2 [ μ ± 2 b 1 b 2 β γ 1 β γ ] .
1 + q i g i > 0 ( x = 0 ) , 1 + q i exp ( μ ± ) g i exp ( μ ± / s ) > 0 ( x = 1 ) .
g i s q i 1 / s / ( s 1 ) ( s 1 ) / s
1 + q 0 < g 0 ,

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