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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 23 — Nov. 5, 2012
  • pp: 25572–25583
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Bistable regimes in an optically injected mode-locked laser

Tatiana Habruseva, Stephen P. Hegarty, Andrei G. Vladimirov, Alexander Pimenov, Dmitrii Rachinskii, Natalia Rebrova, Evgeny A. Viktorov, and Guillaume Huyet  »View Author Affiliations


Optics Express, Vol. 20, Issue 23, pp. 25572-25583 (2012)
http://dx.doi.org/10.1364/OE.20.025572


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Abstract

We study experimentally the dynamics of quantum-dot (QD) passively mode-locked semiconductor lasers under external optical injection. The lasers demonstrated multiple dynamical states, with bifurcation boundaries that depended upon the sign of detuning variation. The area of the hysteresis loops grew monotonically at small powers of optical injection and saturated at moderate powers. At high injection levels the hysteresis decreased and eventually disappeared.

© 2012 OSA

1. Introduction

Optical frequency combs are important for a number of applications including time and frequency metrology [1

1. J. Ye and S. Cundiff, Femtosecond Optical Frequency Comb: Principle, Operation, and Applications (Springer Berlin, 2004).

], arbitrary waveform generation, coherent communications and signal processing [2

2. P. J. Delfyett, S. Gee, M.-T. Choi, H. Izadpanah, W. Lee, S. Ozharar, F. Quinlan, and T. Yilmaz, “Optical frequency combs from semiconductor lasers and applications in ultrawideband signal processing and communications,” J. Lightwave Technol. 24, 2701–2719 (2006). [CrossRef]

]. These combs are commonly generated by mode-locked lasers (MLLs) that periodically emit short pulses with an optical spectrum composed of a set of equally spaced narrow linewidth frequencies. Mode-locked lasers based on quantum dot (QD) semiconductor materials are of particular interest due to their broadband gain and fast carrier dynamics [3

3. E. U. Rafailov, M. A. Cataluna, and W. Sibbett, “Mode-locked quantum-dot lasers,” Nat. Photonics 1, 395–401 (2007). [CrossRef]

]. These lasers possess a rich diversity of dynamical regimes [4

4. E. A. Viktorov, P. Mandel, M. Kuntz, G. Fiol, D. Bimberg, A. G. Vladimirov, and M. Wolfrum, “Stability of the mode-locked regime in quantum dot lasers,” Appl. Phys. Lett. 91, 231116 (2007). [CrossRef]

] including lasing wavelength bistability and hysteresis under variation of the reverse bias voltage [5

5. M. Feng, S. T. Cundiff, R. P. Mirin, and K. L. Silverman, “Wavelength bistability and switching in two-section quantum-dot diode lasers,” IEEE J. Quantum Electron. 46, 951–958 (2010). [CrossRef]

, 6

6. K. Silverman, M. Feng, R. Mirin, and S. Cundiff, “Exotic behavior in quantum dot mode-locked lasers: dark pulses and bistability,” in Quantum Dot Devices, Lecture Notes in Nanoscale Science and Technology13 (Springer-Verlag, NY, 2012) pp. 23–48.

]. These regimes can potentially be exploited for high speed switching or data storage in optical networks. Recent experiments on optical injection locking of QD-MLLs have shown an improved control of the pulse train, chirp reduction, wavelength tuning, and pulse stabilization [7

7. T. Habruseva, S. O’Donoghue, N. Rebrova, D. A. Reid, L. Barry, D. Rachinskii, G. Huyet, and S. P. Hegarty, “Quantum-dot mode-locked lasers with dual-mode optical injection,” IEEE Photon. Technol. Lett. 22(6), 359–361 (2010). [CrossRef]

,8

8. N. Rebrova, T. Habruseva, G. Huyet, and S. P. Hegarty, “Stabilization of a passively mode-locked laser by continuous wave optical injection,” Appl. Phys. Lett. 97, 101105 (2010). [CrossRef]

]. A number of theoretical studies revealed the bifurcation mechanisms responsible for phase locking of a MLL to an external master frequency and pulse repetition frequency locking of a hybrid MLL to external RF modulation [8

8. N. Rebrova, T. Habruseva, G. Huyet, and S. P. Hegarty, “Stabilization of a passively mode-locked laser by continuous wave optical injection,” Appl. Phys. Lett. 97, 101105 (2010). [CrossRef]

10

10. N. Rebrova, G. Huyet, D. Rachinskii, and A. G. Vladimirov, “Optically injected mode-locked laser,” Phys. Rev. E 83, 066202 (2011). [CrossRef]

].

In this work we study the complex dynamical regimes and bifurcation phenomena of QD-MLLs injected by a master laser. Using two-section QD-MLLs subject to a narrow linewidth optical injection, we experimentally identify the different dynamical states of operation, their locking boundaries and the multiple bistabilities of the system.

2. Experimental setup

In the experiments, the slave laser was an uncoated two-section monolithic InAs/GaAs QD-MLL, similar to that described in [11

11. M. Todaro, J. Tourrenc, S. P. Hegarty, C. Kelleher, B. Corbett, G. Huyet, and J. G. McInerney, “Simultaneous achievement of narrow pulse width and low pulse-to-pulse timing jitter in 1.3 μm passively mode-locked quantum-dot lasers,” Opt. Lett. 31, 3107–3109 (2006). [CrossRef] [PubMed]

], emitting at 1.3 μm with a repetition rate of 10.3 GHz. The device (20% absorber section) was mounted on a temperature controlled stage at room temperature, an enclosure was used to exclude draughts and reduce temperature fluctuations to the order of 10 mK. The absorber bias was −2.0 V for the experiments described here, with a laser threshold of 157 mA at −2.0 V. The master laser was a commercial external cavity tunable laser source (TLS, Agilent 81672 B) with a linewidth of ∼ 200 kHz. The master light was injected through a polarization maintaining (PM) fibre circulator and coupled to the slave gain section via a PM lens fibre. The experimental setup is shown in Fig. 1. The slave laser output was measured using optical and electrical spectrum analyzers, a power meter, an autocorrelator (Fig. 1(a)), and a linear pulse recovery instrument (frequency-resolved Mach-Zehnder gating, Southern Photonics EG130, Fig. 1(b)) [7

7. T. Habruseva, S. O’Donoghue, N. Rebrova, D. A. Reid, L. Barry, D. Rachinskii, G. Huyet, and S. P. Hegarty, “Quantum-dot mode-locked lasers with dual-mode optical injection,” IEEE Photon. Technol. Lett. 22(6), 359–361 (2010). [CrossRef]

]. The optical linewidth of slave individual modes was measured through heterodyne beating of the slave modes with a tunable laser source TLS 2 having a narrow linewidth of ∼ 200 kHz as shown in Fig. 1(c).

Fig. 1 Schematic of the experimental setup for characterization of the QD-MLL under external optical injection. TLS: tunable laser source; PC: polarization controller; AC: autocorrelator; OSA: optical spectrum analyzer; ESA: electronic spectrum analyzer; FRMZG: frequency-resolved Mach-Zehnder gating.

For characterization of optically injected QD-MLL dynamics we varied the detuning Δ between master and slave, Δ = ωmωs, and measured the average power and the optical and electronic spectra of the slave for each value of the detuning. Tuning steps of our TLS were only possible in a non-monotonic “overshoot-return” manner, unusable for characterization of hysteresis phenomena. To ensure continuous scanning of Δ, the master frequency ωm was fixed and monotonic steps in the slave laser current were made, with the current step starting from 0.01 mA, which corresponded to a frequency shift of ∼ 10 MHz. The effect of this tuning technique can be seen in the locking cones of adjacent modes, the apparent variation in bifurcation position is due in fact to variation of the master/slave power ratio.

3. Free running QD-MLL

Without injection, the slave laser emitted pulses of ∼ 1.6 ps duration at the fundamental mode-locking frequency of 10.3 GHz with an optical spectral width of ∼5 nm at −10 dB and average power of ∼ 600 μW at 172 mA. Figure 2 shows the measured pulse shape and phase of the free-running laser (i.e. without optical injection) at −2.0 V absorber bias and 172 mA gain current. At gain currents below 200 mA the pulses emitted by the slave laser had a slightly asymmetrical shape with faster leading edge, and nearly-parabolic phase. Figure 2 shows the root-mean square fit (blue dashes) to the measured phase (red circles) assuming quadratic time dependence of the phase during the pulse, i.e. ϕ = at2 + ϕ0. The data can be fitted well with the parabola showing the linear pulse chirp with instantaneous frequency of ν=dϕdt=2at, with a=0.62(rads2). The laser exhibited a double pulse shape above a gain current of 200 mA and no pulse shape recovery was possible for the free-running laser at higher currents, similar to [8

8. N. Rebrova, T. Habruseva, G. Huyet, and S. P. Hegarty, “Stabilization of a passively mode-locked laser by continuous wave optical injection,” Appl. Phys. Lett. 97, 101105 (2010). [CrossRef]

].

Fig. 2 Recovered pulse shape (black solid line) and phase (red circles) of the slave QD-MLL. The blue dashed line is the least squares parabolic fit of the phase. Absorber bias: −2.0 V, gain current: 172 mA.

For experimental investigations the mode-locked regime with single asymmetric pulses was chosen (i.e. for the gain current below 200 mA, −2.0 V absorber bias). Optical and electronic spectra were measured for different current values at −2.0 V absorber bias. Laser threshold was at 157 mA; in the region between 165 mA and 190 mA the laser exhibited stable mode-locking operation with clear RF signal at the fundamental mode-locking frequency and single pulses. Laser output was similar for all the currents in the range, therefore this region was chosen for the experimental study of injected laser dynamics. Optical and power spectra of the free-running mode-locked laser for this regime are shown in Fig. 3(a) and 3(b), respectively. The gain current change leading to a slave mode shift by a free spectral range (giving 10 GHz detuning between master and slave frequencies) was 10 mA; it corresponded to ∼ 6% of the threshold current value, which meant to be remained in the same mode-locked regime despite the current tuning technique. Small changes in the gain and refractive index due to the current change can be neglected at least for a qualitative understanding of the bistability/hysteresis phenomenon.

Fig. 3 Optical (a) and RF (b) spectra of the free running QD-MLL. Optical (c) and RF (d) spectra of the slave QD-MLL when it phase-locked to the injection seed. The injection seed indicated with an arrow is close to one of the slave modes. Optical (e) and RF (f) spectra of the injected QD-MLL when it operated in a single-mode regime. Optical (g) and RF (h) spectra of the slave QD-MLL in the bounded phase regime.

4. Optical injection

Fig. 4 Measured heterodyne beating signals of the slave mode with (red) and without (black) injection-locking. The slave mode was mixed with the TLS; the frequency of the TLS was adjusted so that the beating signal was in the area of 12 – 15 GHz, in the region of the flat frequency response from detector and amplifier. Gain current: 172 mA; absorbr bias: −2.0 V; injection power: 35μW.

5. Locking boundaries

The locking boundaries in an optically injected single mode laser model are formed by saddle-node and Andronov-Hopf bifurcations, both bifurcations well reproduce the observed experimental stability features [15

15. T. B. Simpson, “Mapping the nonlinear dynamics of a distributed feedback semiconductor laser subject to external optical injection,” Opt. Commun. 215, 135–151 (2003). [CrossRef]

]. The locking boundaries in our experiment are somewhat different, as might be expected with the multiple nonlinearly coupled oscillators being subject to injection.

According to [18

18. A. Pikovsky, M. Rosenblum, and J. Kurths, “Synchronization. A universal concept in nonlinear sciences” (Cambridge University Press2001).

], the appearance of the additional frequency in a single mode laser with external injection does not necessarily mean desynchronization. When the synchronized CW regime is destabilized via an Andronov-Hopf bifurcation, a regime with small periodic amplitude modulation is born. As long as the oscillating phase of the optical field is bounded, the average frequency coincides with the frequency ωm of the external injection and, hence, the regime can be considered as synchronized to the frequency ωm. When the modulation amplitude becomes sufficiently large, the phase starts to grow in time and the periodic regime becomes desynchronized. In this scenario the transition from the synchronized to desyncronized state is continuous and is not associated with any bifurcation. This single mode laser behavior is similar to that described experimentally above for the desynchronization of a periodic mode-locked regime, i.e. a bifurcation to a regime with a quasiperiodic laser intensity.

6. Bifurcation diagram

We constructed a bifurcation diagram of the optically injected MLL in a two-parameter space: the master laser power, Pinj, and the detuning between master and slave frequency, Δ =ωmωs. As discussed above, small variations in the slave drive current were made to ensure continuous sweeping of Δ. When the current was increased, the slave frequency ωs decreased, and thus the detuning increased.

A schematic diagram of the regimes observed when the frequency ωs was swept across an interval approximately two times larger than the cavity free spectral range is shown in Fig. 5 for Δ decrease (a), Δ increase (b) and both together (c). The upper boundaries of the regimes, denoted in the figure, were similar for both sweep directions, while the lower boundaries were significantly different for Δ increase and decrease, which resulted in regions with hysteresis as denoted in Fig. 5(c) by the cross-hatching. The measured diagrams overlain for both directions of the Δ sweep are shown in Fig. 6.

Fig. 5 Schematic representation of experimental data presented in Fig. 6. (a) corresponds to a decrease and (b) corresponds to an increase of Δ. Both maps are overlain in (c). The numbers and capital letters indicate the following regions: U: unlocked, L: Locked, SM: single-mode, MSM: modulated single-mode, 1: Unlocked, 2: Locked, 3: Single-mode, 4: Single-mode with modulation, 5: Unlocked or Locked bistable regime, 6: Unlocked or Single-mode bistable regime, 7: Single-mode 1 with modulation or Single-mode 2 bistable regime, 8: Single-mode 1 or Single-mode 2 bistable regime. The bistable regions are indicated with cross-hatching.
Fig. 6 Measured bifurcation diagram in two-parameter plane: master-slave detuning (ordinate) and master power (abscissa). Absorber bias: −2.0 V; gain current: 165 – 190 mA. (a) The numbers indicate the following regions: 1: Unlocked, 2: Locked, 3: Single-mode, 4: Single-mode with modulation, 5: Unlocked or Locked bistable regime, 6: Unlocked or Single-mode bistable regime, 7: Single-mode 1 with modulation or Single-mode 2 bistable regime, 8: Single-mode 1 or Single-mode 2 bistable regime. The capital blue letters with stars indicate the boundaries. (b) The dashed vertical lines and small letters indicate the points of transitions between different regimes for three different injection powers: 54 μW (black), 745 μW (blue) and 6.2 mW (red).

The bifurcation phenomena leading to locked/unlocked operation strongly depend on the injection power.

a) Low injection powers, Pinj < Ps (Pinj = 54 μW, Ps = 600 μW, black vertical line in Fig. 6(b))

Fig. 7 (a) Slave power vs detuning for Δ decrease (blue) and increase (red). Low frequency spectrum vs detuning for decrease (b) and for increase (c) of Δ. Absorber bias: −2.0 V; gain current: 165 – 185 mA.

b) Moderate injection powers, Pinj ∼ Ps (Pinj = 745 μW, Ps = 600 μW, blue vertical line in Fig. 6(b))

At moderate optical injection powers, regions with single-mode laser operation started to appear. Figure 8(a) shows the slave power vs detuning for Δ decrease (blue) and increase (red). Corresponding diagrams of low frequency spectra are presented in Fig. 8(b) and (d).

Fig. 8 (a) Slave power vs detuning for Δ decrease (blue) and increase (red). Low frequency spectrum vs detuning for decrease (b) and for increase (d) of Δ. Fundamental harmonic RF spectrum vs detuning for Δ decrease, (c). Absorber bias: −2.0 V; gain current: 165 – 185 mA.

When Δ was decreased, between points e(h) and g(j) the slave laser was locked to the master, with no instabilities observed, as shown in Fig. 8(b). The gradual decrease of the output power and narrowing of the optical spectrum in this locked regime (Fig. 8(a)) eventually resulted in a single-mode operation regime between points f(i) and g(j) in Fig. 8(c). The single-mode regime was not detected for Δ increase at these injection powers. The locking ranges between points k(l) and h(e) were much smaller compared to the case of Δ decrease.

The locking boundaries are shown in Fig. 6. For Δ decrease the slave mode was locked from the blue side at the boundary AH (which includes points c and h in Fig. 6 and unlocked at the boundary ABC (which includes points d and j in Fig. 6). For Δ increase the laser was locked only at boundary DE and unlocked again at boundary DH.

The upper locking boundaries, AH and DH, were practically the same for both directions of the master-slave detuning (see Fig. 6). The lower locking boundary was shifted from ABC for Δ decrease to DE for Δ increase resulting in the areas of bistability (regions 5 and 6 in Fig. 6).

The appearance of locked single mode operation at moderate injection powers thus gives another form of bistability, i.e. between the unlocked ML operation and locked single mode regime.

c) High injection powers, Pinj > Ps (Pinj = 6200 μW, Ps = 600 μW, red vertical line in Fig. 6(b))

At high injection powers, the regions of single-mode operation became significantly larger. The slave laser operated in a single-mode regime within the black-dashed boundary CBHF for Δ decrease and within the blue boundary GEHL for Δ increase (see Fig. 6(a)).

The evolution of the RF spectra with detuning for Δ decrease is shown in Fig. 9(b). The slave laser operated in a single-mode regime between points m and n, and became single mode again below point o. For Δ increase the regions of single-mode operation were much smaller (between points r and o, and between points s and m), as shown in Fig. 9(c). The laser was unlocked between the intervals of single-mode behavior.

Fig. 9 (a) Slave power vs detuning for Δ decrease (blue) and increase (red). Fundamental harmonic RF spectrum vs detuning for decrease (b) and increase (c) of Δ. Low frequency spectrum vs detuning for Δ increase (d). Absorber bias: −2.0 V; gain current: 165 – 185 mA.

As the intervals of single-mode operation became larger, for certain parameters a weak modulation was seen as shown in Fig. 9(d). The regions of modulated single mode operation did not show any obvious bistability, as shown in Fig. 6, yellow areas. The modulation in the RF spectrum was gradually weakened with the increase of the injection power and could no longer be resolved for Pinj > 9.6 mW.

When the laser operated continuously single-mode, a transition between adjacent slave modes locked to the master was accompanied by an abrupt change in the laser power, see transition pq in Fig. 9(a). These changes occurred at different detuning values for Δ decrease (FK boundary, see Fig. 6) and increase (LN boundary), indicating a new bistability between two single mode regimes (regions 7 and 8) with different powers, see Fig. 10(a–c). The effect of the detuning-induced switching between adjacent modes has previously been investigated for a single section semiconductor laser [20

20. J. K. White, J. V. Moloney, A. Gavrielides, V. Kovanis, A. Hohl, and R. Kalmus, “Multilongitudinal-mode dynamics in a semiconductor laser subject to optical injection,” IEEE J. Quantum. Elecron. 34, 1469–1473 (1998). [CrossRef]

].

Fig. 10 Slave power vs master-slave detuning for Δ decrease (blue) and increase (red) at injection powers of 14 mW (a), 22.4 mW (b), 33 mW (c), and 120 mW (d). Absorber bias: −2.0 V; gain current: 165 – 190 mA.

7. Hysteresis

The observed bistability led to a hysteresis in the laser output characteristics shown in Fig. 7(a) and Fig. 8(a) for low and moderate injection powers, respectively. The blue (red) line shows the slave laser power vs master-slave detuning for Δ decrease (increase). The area of the hysteresis loop increased with Pinj and saturated at moderate power injection. For higher injection power, the hysteresis area started to decrease and disappeared at ultra-high powers of 120 mW. Some examples of the hysteresis loop for a range of injection powers are shown in Fig. 10 for injection powers of 14 mW (a), 22.4 mW (b), 33 mW (c), and 120 mW (d).

8. Conclusion

For the first time we have constructed a two-parameter experimental bifurcation diagram of a QD-MLL under external CW optical injection. Four main laser operation regimes were identified in experiments and described: unlocked, locked, single mode, and single mode with modulation. We have determined the essential conditions for the optical comb being locked to the injection and revealed the bifurcation phenomena at the locking boundaries. Multiple hysteresis regions have been identified, which can potentially be utilized for wavelength switching and on-off power switching. The hysteresis regions initially grew with injection power and disappeared at the highest powers used in the experiment.

Acknowledgments

This work was funded by the EU FP7 Marie Curie Action FP7-PEOPLE-2010-ITN through the PROPHET project, Grant No. 264687, by the INSPIRE programme, funded by the Irish Government’s Programme for Research in Third Level Institutions, Cycle 4, National Development Plan 2007–2013 and by Science Foundation Ireland under Contract No. 07/IN.1/I929. A.G.V. and A.P. acknowledge the support from SFB Project 787 of the DFG. A.G.V. was also supported by the Walton Visitor Award of the Science Foundation of Ireland and the program “Research and Pedagogical Cadre for Innovative Russia” (Grant No. 2011-1.5-503-002-038).

References and links

1.

J. Ye and S. Cundiff, Femtosecond Optical Frequency Comb: Principle, Operation, and Applications (Springer Berlin, 2004).

2.

P. J. Delfyett, S. Gee, M.-T. Choi, H. Izadpanah, W. Lee, S. Ozharar, F. Quinlan, and T. Yilmaz, “Optical frequency combs from semiconductor lasers and applications in ultrawideband signal processing and communications,” J. Lightwave Technol. 24, 2701–2719 (2006). [CrossRef]

3.

E. U. Rafailov, M. A. Cataluna, and W. Sibbett, “Mode-locked quantum-dot lasers,” Nat. Photonics 1, 395–401 (2007). [CrossRef]

4.

E. A. Viktorov, P. Mandel, M. Kuntz, G. Fiol, D. Bimberg, A. G. Vladimirov, and M. Wolfrum, “Stability of the mode-locked regime in quantum dot lasers,” Appl. Phys. Lett. 91, 231116 (2007). [CrossRef]

5.

M. Feng, S. T. Cundiff, R. P. Mirin, and K. L. Silverman, “Wavelength bistability and switching in two-section quantum-dot diode lasers,” IEEE J. Quantum Electron. 46, 951–958 (2010). [CrossRef]

6.

K. Silverman, M. Feng, R. Mirin, and S. Cundiff, “Exotic behavior in quantum dot mode-locked lasers: dark pulses and bistability,” in Quantum Dot Devices, Lecture Notes in Nanoscale Science and Technology13 (Springer-Verlag, NY, 2012) pp. 23–48.

7.

T. Habruseva, S. O’Donoghue, N. Rebrova, D. A. Reid, L. Barry, D. Rachinskii, G. Huyet, and S. P. Hegarty, “Quantum-dot mode-locked lasers with dual-mode optical injection,” IEEE Photon. Technol. Lett. 22(6), 359–361 (2010). [CrossRef]

8.

N. Rebrova, T. Habruseva, G. Huyet, and S. P. Hegarty, “Stabilization of a passively mode-locked laser by continuous wave optical injection,” Appl. Phys. Lett. 97, 101105 (2010). [CrossRef]

9.

G. Fiol, D. Arsenijevic, D. Bimberg, A. G. Vladimirov, M. Wolfrum, E. A. Viktorov, and P. Mandel, “Hybrid mode-locking in a 40 GHz monolithic quantum dot laser,” Appl. Phys. Lett. 96, 011104 (2010). [CrossRef]

10.

N. Rebrova, G. Huyet, D. Rachinskii, and A. G. Vladimirov, “Optically injected mode-locked laser,” Phys. Rev. E 83, 066202 (2011). [CrossRef]

11.

M. Todaro, J. Tourrenc, S. P. Hegarty, C. Kelleher, B. Corbett, G. Huyet, and J. G. McInerney, “Simultaneous achievement of narrow pulse width and low pulse-to-pulse timing jitter in 1.3 μm passively mode-locked quantum-dot lasers,” Opt. Lett. 31, 3107–3109 (2006). [CrossRef] [PubMed]

12.

T. Habruseva, S. O’Donoghue, N. Rebrova, S. P. Hegarty, and G. Huyet, “Quantum-dot mode-locked lasers with optical injection,” SPIE Proceedings 7608, 760803 (2010). [CrossRef]

13.

T. Habruseva, N. Rebrova, S. P. Hegarty, and G. Huyet, “Mode-locked semiconductor lasers with optical injection,” in Quantum Dot Devices, Lecture Notes in Nanoscale Science and Technology, 13Springer-Verlag, NY, 2012) pp. 65–91.

14.

P. M. Varangis, A. Gavrielides, T. Erneux, V. Kovanis, and L. F. Lester, “Frequency entrainment in optically injected semiconductor lasers,” Phys. Rev. Lett. 78, 2353–2356 (1997). [CrossRef]

15.

T. B. Simpson, “Mapping the nonlinear dynamics of a distributed feedback semiconductor laser subject to external optical injection,” Opt. Commun. 215, 135–151 (2003). [CrossRef]

16.

P. A. Braza and T. Erneux, “Constant phase, phase drift, and phase entrainment in lasers with an injected signal,” Phys. Rev. A 41, 6470–6479 (1990). [CrossRef] [PubMed]

17.

B. Kelleher, D. Goulding, B. B. Pascual, S. P. Hegarty, and G. Huyet, “Bounded phase phenomena in the optically injected laser,” Phys. Rev. E 85, 046212 (2012). [CrossRef]

18.

A. Pikovsky, M. Rosenblum, and J. Kurths, “Synchronization. A universal concept in nonlinear sciences” (Cambridge University Press2001).

19.

T. Erneux, E. A. Viktorov, B. Kelleher, D. Goulding, S. P. Hegarty, and G. Huyet, “Optically injected quantum dot lasers,” Opt. Lett. 35, 937–939 (2010). [CrossRef] [PubMed]

20.

J. K. White, J. V. Moloney, A. Gavrielides, V. Kovanis, A. Hohl, and R. Kalmus, “Multilongitudinal-mode dynamics in a semiconductor laser subject to optical injection,” IEEE J. Quantum. Elecron. 34, 1469–1473 (1998). [CrossRef]

OCIS Codes
(140.0140) Lasers and laser optics : Lasers and laser optics
(140.4050) Lasers and laser optics : Mode-locked lasers
(190.1450) Nonlinear optics : Bistability
(250.5590) Optoelectronics : Quantum-well, -wire and -dot devices

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: August 2, 2012
Revised Manuscript: September 28, 2012
Manuscript Accepted: October 3, 2012
Published: October 25, 2012

Citation
Tatiana Habruseva, Stephen P. Hegarty, Andrei G. Vladimirov, Alexander Pimenov, Dmitrii Rachinskii, Natalia Rebrova, Evgeny A. Viktorov, and Guillaume Huyet, "Bistable regimes in an optically injected mode-locked laser," Opt. Express 20, 25572-25583 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-23-25572


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References

  1. J. Ye and S. Cundiff, Femtosecond Optical Frequency Comb: Principle, Operation, and Applications (Springer Berlin, 2004).
  2. P. J. Delfyett, S. Gee, M.-T. Choi, H. Izadpanah, W. Lee, S. Ozharar, F. Quinlan, and T. Yilmaz, “Optical frequency combs from semiconductor lasers and applications in ultrawideband signal processing and communications,” J. Lightwave Technol.24, 2701–2719 (2006). [CrossRef]
  3. E. U. Rafailov, M. A. Cataluna, and W. Sibbett, “Mode-locked quantum-dot lasers,” Nat. Photonics1, 395–401 (2007). [CrossRef]
  4. E. A. Viktorov, P. Mandel, M. Kuntz, G. Fiol, D. Bimberg, A. G. Vladimirov, and M. Wolfrum, “Stability of the mode-locked regime in quantum dot lasers,” Appl. Phys. Lett.91, 231116 (2007). [CrossRef]
  5. M. Feng, S. T. Cundiff, R. P. Mirin, and K. L. Silverman, “Wavelength bistability and switching in two-section quantum-dot diode lasers,” IEEE J. Quantum Electron.46, 951–958 (2010). [CrossRef]
  6. K. Silverman, M. Feng, R. Mirin, and S. Cundiff, “Exotic behavior in quantum dot mode-locked lasers: dark pulses and bistability,” in Quantum Dot Devices, Lecture Notes in Nanoscale Science and Technology13 (Springer-Verlag, NY, 2012) pp. 23–48.
  7. T. Habruseva, S. O’Donoghue, N. Rebrova, D. A. Reid, L. Barry, D. Rachinskii, G. Huyet, and S. P. Hegarty, “Quantum-dot mode-locked lasers with dual-mode optical injection,” IEEE Photon. Technol. Lett.22(6), 359–361 (2010). [CrossRef]
  8. N. Rebrova, T. Habruseva, G. Huyet, and S. P. Hegarty, “Stabilization of a passively mode-locked laser by continuous wave optical injection,” Appl. Phys. Lett.97, 101105 (2010). [CrossRef]
  9. G. Fiol, D. Arsenijevic, D. Bimberg, A. G. Vladimirov, M. Wolfrum, E. A. Viktorov, and P. Mandel, “Hybrid mode-locking in a 40 GHz monolithic quantum dot laser,” Appl. Phys. Lett.96, 011104 (2010). [CrossRef]
  10. N. Rebrova, G. Huyet, D. Rachinskii, and A. G. Vladimirov, “Optically injected mode-locked laser,” Phys. Rev. E83, 066202 (2011). [CrossRef]
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