Abstract

We investigate the operational principle of mode-locking in monolithic semiconductor lasers incorporating coupled-resonator optical waveguides. The size of mode-locked lasers operating at tens of GHz repetition frequencies can be drastically reduced owing to the significantly decreased group velocity of light. The dynamics of such devices are analyzed numerically based on a coupled-oscillator model with the gain, loss, spontaneous emission, nearest-neighbor coupling and amplitude phase coupling (as described by the linewidth enhancement factor α) taken into account. It is demonstrated that active mode-locking can be achieved for moderate α parameter values. Simulations also indicate that large α parameters may destabilize the mode-locking behavior and result in irregular pulsations, which nevertheless can be effectively suppressed by incorporating detuning of individual cavity resonant frequencies in the device design.

© 2005 Optical Society of America

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References

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  26. L. A. Coldren and S.W. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley-Interscience, New York, 1995).
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  29. J. Vuckovic, O. Painter, Y. Xu, A. Yariv, and A. Scherer, �??Finite-difference time-domain calculation of the spontaneous emission coupling factor in optical microcavities,�?? IEEE J. Quantum Electron. 35, 1168�??1175 (1999).
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Appl. Phys. Lett. (5)

H. Altug and J. Vuckovic, �??Two-dimensional coupled photonic crystal resonator arrays,�?? Appl. Phys. Lett. 84, 161�??163 (2004).
[CrossRef]

S. Mookherjea, �??Semiconductor coupled-resonator optical waveguide laser,�?? Appl. Phys. Lett. 84, 3265�??7 (2004).
[CrossRef]

S. S. Wang and H. G. Winful, �??Dynamics of phase-locked semiconductor laser arrays,�?? Appl. Phys. Lett. 52, 1774�??6 (1988).
[CrossRef]

H. G. Winful and S. S. Wang, �??Stability of phase locking in coupled semiconductor laser arrays,�?? Appl. Phys. Lett. 53, 1894-6 (1988).
[CrossRef]

Y. Liu, K. D. Choquette, and K. Hess, �??The electrical turn-on characteristics of vertical-cavity surface-emitting lasers,�?? Appl. Phys. Lett. 83, 4104�??6 (2003).
[CrossRef]

Coherence, Amplification, and Quantum (1)

C. H. Henry, �??Line Broadening of Semiconductor Lasers,�?? in Coherence, Amplification, and Quantum Effects in Semiconductor Lasers, Y. Yamamoto, ed., pp. 5�??76 (Wiley, New York, 1991).

Diode Laser Arrays (2)

H. G. Winful and R. K. Defreez, �??Dynamics of coherent semiconductor laser arrays,�?? in Diode Laser Arrays, D. Botez and D. R. Scifres, ed., pp. 226�??253 (Cambridge University Press, New York, 1994).
[CrossRef]

D. Botez, �??Monolithic phase-locked semiconductor laser arrays,�?? in Diode Laser Arrays, D. Botez and D. R. Scifres, ed., pp. 1�??67 (Cambridge University Press, New York, 1994).
[CrossRef]

IEE Proc.-Optoelectron. (1)

E. A. Avrutin, J. H. Marsh, and E. L. Portnoi, �??Monolithic and multi-GigaHertz mode-locked semiconductor lasers: constructions, experiments, models and applications,�?? IEE Proc.-Optoelectron. 147, 251�??278 (2000).
[CrossRef]

IEEE J. Quantum Electron. (4)

G. A. Wilson, R. K. DeFreez, and H. G. Winful, �??Modulation of phased-array semiconductor lasers at K-band frequencies,�?? IEEE J. Quantum Electron. 27, 1696-1704, 1991.
[CrossRef]

J. Vuckovic, O. Painter, Y. Xu, A. Yariv, and A. Scherer, �??Finite-difference time-domain calculation of the spontaneous emission coupling factor in optical microcavities,�?? IEEE J. Quantum Electron. 35, 1168�??1175 (1999).
[CrossRef]

R. J. Lang and A. Yariv, �??An exact formulation of coupled-mode theory for coupled-cavity lasers,�?? IEEE J. Quantum Electron. QE-24, 66�??72, 1988.
[CrossRef]

D. Marcuse, �??Computer simulation of laser photon fluctuations: theory of single-cavity laser,�?? IEEE J. Quantum Electron. QE-20, 1139�??1148 (1984).
[CrossRef]

IEEE Journal of Selected Topics in Quan. (1)

H. A. Haus, �??Mode-locking of lasers,�?? IEEE Journal of Selected Topics in Quantum Electronics 6, 1173�??1185 (2000).
[CrossRef]

IEEE Photonic Technology Letters (1)

Y. Yu, G. Giuliani, and S. Donati, �??Measurement of the linewidth enhancement factor of semiconductor lasers based on the optical feedback self-mixing effect,�?? IEEE Photonic Technology Letters 16, 990-992 (2004).
[CrossRef]

IEEE Photonics Technology Letters (1)

G. A. Keeler, B. E. Nelson, D. Agarwal, and D. A. B. Miller, �??Skew and jitter removal using short optical pulses for optical interconnection,�?? IEEE Photonics Technology Letters 12, 714�??716 (2000).
[CrossRef]

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

Opt. Express (2)

Opt. Lett. (4)

Phys. Rev. A (1)

R. .J. Lang and A. Yariv, �??Local-field rate equations for coupled optical resonators,�?? Phys. Rev. A 34, 2038-2043, 1986.
[CrossRef] [PubMed]

Phys. Rev. B (1)

N. Stefanou and A. Modinos, �??Impurity bands in photonic insulators,�?? Phys. Rev. B 57, 12,127�??12,133 (1998).
[CrossRef]

Phys. Rev. Lett. (1)

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, �??Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,�?? Phys. Rev. Lett. 87, 253,902 (2001).
[CrossRef]

Other (3)

A. E. Siegman, Lasers (University Science Books, Sausalito, CA, 1986).

N. W. Ashcroft and N. D. Mermin, Solid State Physics, Ch. 10 (Saunders College Publishing, 1976).

L. A. Coldren and S.W. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley-Interscience, New York, 1995).

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Figures (9)

Fig. 1.
Fig. 1.

Schematic plot of a typical CROW structure that is tailored for mode-locked lasing operations. The air holes in general need not to penetrate into the active region. The propagation direction is along the z-axis.

Fig. 2.
Fig. 2.

Calculated defect-band dispersion relation of the proposed CROW laser diode. Calculations based on both the plane-wave expansion method [20] and the coupled-oscillator model show good agreement. The inset is the calculated field pattern of an uncoupled single resonant cavity from the plane-wave expansion method.

Fig. 3.
Fig. 3.

Device configuration of the proposed monolithic CROW laser to achieve the mode-locking. The circles represent the resonant cavities in the CROWarray as depicted in Fig. 1. The CROW array is grouped into three segments: gain, loss and modulated loss.

Fig. 4.
Fig. 4.

Simulated transient behavior of the photon number distribution in the resonant cavities of the CROW array at three stages: (a) initial stage; (b) intermediate stage; (c) cw mode-locking. The propagation of an optical pulse is evident in (c), indicating the action of mode locking. The inter-cavity distance is R=1.5µm. The linewidth enhancement factor α=2.

Fig. 5.
Fig. 5.

(a) Simulated time-dependent optical output power from the output coupling of the first cavity; (b) a close-up view. The linewidth enhancement factor is α=2.

Fig. 6.
Fig. 6.

A Gaussian fit of a simulated optical pulse at the cw condition in Fig. 5 (note the log scale in the output power). The FWHM of the pulse is found to be 6.2 ps.

Fig. 7.
Fig. 7.

Simulated time-dependent optical amplitude gain in the first cavity. The inset is a close-up view. The linewidth enhancement factor α=2.

Fig. 8.
Fig. 8.

(a) Simulated time-dependent optical output power from the output coupling of the first cavity; (b) a close-up view. The linewidth enhancement factor is α=5.

Fig. 9.
Fig. 9.

(a) Simulated time-dependent optical output power from the output coupling of the first cavity; (b) a close-up view. The linewidth enhancement factor is α=5. Frequency detunings in the first and the last four cavities are incorporated.

Tables (1)

Tables Icon

Table 1. Parameter values used in the numerical simulations. For the loss parameters, both their modal and material values are listed.

Equations (24)

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

ω ( K ) = ω 0 Δ Ω 2 κ · cos ( K R ) ,
v g ( K ) = d ω d K = 2 κ R sin ( K R ) .
E ( r , t ) = e i ω 0 t = 1 N A ( t ) E Ω ( r R e z ) ,
× ( × E ( r , t ) ) = 1 c 2 ε ( r , t ) 2 t 2 E ( r , t ) ,
× ( × E Ω ) = ε 0 ( r ) ω 0 2 c 2 E Ω ,
ε ( r , t ) = ε ̅ ( r ) + Δ ε ( r , t ) = ε ̅ ( r ) + = 1 N Δ ε ( r , t )
2 i ω 0 = 1 N [ ε ̅ ( r ) + Δ ε ( r , t ) ] E Ω ( r R e z ) d A d t = = 1 N [ ε ̅ ( r ) ε 0 ( r R e z ) ] E Ω ( r R e z ) A
+ = 1 N Δ ε ( r , t ) E Ω ( r R e z ) A
( a + d ) A t = ω 0 2 i ( c + d ˜ ) A ,
a , m = d 3 r ε ̅ ( r ) E Ω ( r R e z ) · E Ω ( r m R e z )
c , m = d 3 r [ ε ̅ ( r ) ε 0 ( r R e z ) ] E Ω ( r R e z ) · E Ω ( r m R e z )
d , m = d 3 r Δ ε ( r , t ) E Ω ( r R e z ) · E Ω ( r m R e z ) .
A ˜ t = ω 0 2 i ( I + a ' + d ) 1 ( c + d ) A ˜ ω 0 2 i ( I a ' d ) ( c + d ) A ˜ ω 0 2 i ( c + d ) A ˜
i Δ Ω ω 0 2 i c , = ω 0 2 i d 3 r [ ε ̅ ( r ) ε 0 ( r ) ] E Ω ( r ) · E Ω ( r )
κ ω 0 2 i c , ± 1 = ω 0 2 i d 3 r [ ε ̅ ( r ) ε 0 ( r ) ] E Ω ( r ) · E Ω ( r R e z )
ω 0 2 i d , = ω 0 2 i d 3 r Δ ε ( r , t ) E Ω ( r R e z ) · E Ω ( r R e z ) ,
d A ( t ) d t = κ [ A 1 ( t ) + A + 1 ( t ) ] + i ( Δ ω Δ Ω ) A + [ G ( t ) 2 δ , 1 γ ] ( 1 i α ) A ( t ) + S ( t ) ,
E K ( r ) = = 1 N sin ( R K ) E Ω ( r R e z ) .
G ( t ) = { G ( t ) gain segment l b , transparency segment , Δ m [ 1 cos ( 2 π f r t ) ] , mod ulated loss segment ,
d N c ( t ) d t = I 0 q N c ( t ) τ c G ( t ) · N ph ( t ) ,
g ( t ) = g ' · ( n ( t ) n tr ) ,
d G ( t ) d t = 1 τ c [ G 0 G ( t ) Θ · A ( t ) 2 · G ( t ) ] ,
G 0 = Γ · ( c n r ) · g ' · ( τ c · I 0 q · d · s n tr ) ,
Θ = τ c · Γ · ( c n r ) · g ' d · s .

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