## Timing jitter reduction of passively mode-locked semiconductor lasers by self- and external-injection: Numerical description and experiments |

Optics Express, Vol. 21, Issue 13, pp. 16142-16161 (2013)

http://dx.doi.org/10.1364/OE.21.016142

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### Abstract

In this paper the influence of different feedback (FB) and synchronization schemes on the timing phase noise (TPN) power spectral density (PSD) of a quantum-dot based passively mode-locked laser (MLL) is studied numerically and by experiments. The range of investigated schemes cover hybrid mode-locking, an opto-electrical feedback configuration, an all-optical feedback configuration and optical pulse train injection configuration by means of a master MLL. The mechanism responsible for TPN PSD reduction in the case of FB is identified for the first time for monolithic passively MLL and relies on the effective interaction of the timing of the intra-cavity pulse and the time-delayed FB pulse or FB modulation together with an statistical averaging of the independent timing deviations of both. This mechanism is quantified by means of simulation results obtained by introducing an universal and versatile simple time-domain model.

© 2013 OSA

## 1. Introduction

1. 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. Express **19**, 14518 (2011) [CrossRef] [PubMed] .

2. A. Nejadmalayeri, M. Grein, S. J. Spector, A. Khilo, M. Y. Peng, M. Sander, J. Wang, A. J. Benedick, C. M. Sorace, M. W. Geis, M. M. Willis, D. M. Lennon, J. U. Yoon, T. M. Lyszczarz, E. Ippen, and F. Kartner, “Attosecond photonics for optical communications,” in *Optical Fiber Communication Conference*, (Optical Society of America, 2012), p. OM2C.1 [CrossRef] .

3. K. A. Williams, M. G. Thompson, and I. H. White, “Long-wavelength monolithic mode-locked diode lasers,” New J. Phys. **6**, 179–179 (2004) [CrossRef] .

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

5. H. Haus and A. Mecozzi, “Noise of mode-locked lasers,” IEEE J. Quantum Electron. **29**, 983–996 (1993) [CrossRef] .

7. R. Paschotta, “Noise of mode-locked lasers (Part II): Timing jitter and other fluctuations,” Appl. Phys. B **79**, 163–173 (2004) [CrossRef] .

8. M. J. Heck, E. J. Salumbides, A. Renault, E. A. Bente, Y.-S. Oei, M. K. Smit, R. van Veldhoven, R. Nötzel, K. S. Eikema, and W. Ubachs, “Analysis of hybrid mode-locking of two-section quantum dot lasers operating at 1.5 *μ*m,” Opt. Express **17**, 18063 (2009) [CrossRef] [PubMed] .

9. E. Avrutin, J. Marsh, and E. Portnoi, “Monolithic and multi-gigahertz mode-locked semiconductor lasers: Constructions, experiments, models and applications,” IEE Proceedings - Optoelectronics **147**, 251 (2000) [CrossRef] .

10. R. J. Helkey, D. J. Derickson, A. Mar, J. G. Wasserbauer, J. E. Bowers, and R. L. Thornton, “Repetition frequency stabilisation of passively mode-locked semiconductor lasers,” Electron. Lett **28**, 1920–1922 (1992) [CrossRef] .

11. S. Breuer, W. Elsäßer, J. G. McInerney, K. Yvind, J. Pozo, E. A. J. M. Bente, M. Yousefi, A. Villafranca, N. Vogiatzis, and J. Rorison, “Investigations of repetition rate stability of a mode-locked quantum dot semiconductor laser in an auxiliary optical fiber cavity,” IEEE J. Quantum Electron. **46**, 150–157 (2010) [CrossRef] .

13. G. Fiol, M. Kleinert, D. Arsenijevic, and D. Bimberg, “1.3 um range 40 GHz quantum-dot mode-locked laser under external continuous wave light injection or optical feedback,” Semicond. Sci. Technol. **26**, 014006 (2011) [CrossRef] .

14. C. Otto, K. Lüdge, A. G. Vladimirov, M. Wolfrum, and E. Schöll, “Delay-induced dynamics and jitter reduction of passively mode-locked semiconductor lasers subject to optical feedback,” New J. Phys. **14**, 113033 (2012) [CrossRef] .

15. E. A. Avrutin and B. M. Russell, “Dynamics and spectra of monolithic mode-locked laser diodes under external optical feedback,” IEEE J. Quantum Electron. **45**, 1456–1464 (2009) [CrossRef] .

16. L. Drzewietzki, S. Breuer, and W. Elsäßer, “Timing phase noise reduction of modelocked quantum-dot lasers by time-delayed optoelectronic feedback,” Electronics Letters **49**, 557–559 (2013) [CrossRef] .

## 2. Devices and experimental setups

17. R. Paschotta, A. Schlatter, S. Zeller, H. Telle, and U. Keller, “Optical phase noise and carrier-envelope offset noise of mode-locked lasers,” Appl. Phys. B **82**, 265–273 (2005) [CrossRef] .

18. H. A. Haus, “Mode-locking of lasers,” IEEE J. Sel. Top. Quantum Electron. **6**, 1173–1185 (2000) [CrossRef] .

19. D. Linde, “Characterization of the noise in continuously operating mode-locked lasers,” Appl. Phys. B **39**, 201–217 (1986) [CrossRef] .

*P*(

*f*) of the optical output power of the MLL is measured by means of an optical high-frequency detector and a high-frequency electrical spectrum analyzer (ESA) and evaluated properly. This method is well applicable to MLL exhibiting a significant amount of TJ. However, ultra-low noise MLL require a different method, which is not limited by the noise of the electrical components [20

20. 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**, 3522 (2010) [CrossRef] [PubMed] .

19. D. Linde, “Characterization of the noise in continuously operating mode-locked lasers,” Appl. Phys. B **39**, 201–217 (1986) [CrossRef] .

*L*(

*f*) is then given by with

*ν*

_{0}being the frequency of the RR line,

*P*the total integrated power of the RR line and

_{tot}*RBW*the resolution bandwidth used. It is evident, that

*L*(

*f*) is a normalized power spectrum

*P*(

*f*). For estimation of

*P*the peak power obtained using a RBW much wider than the RR line-width could also be used. This integrated

_{tot}*P*corresponds to the so called carrier power of an actively driven oscillating system. In the measurements, the total TPN PSD is composed of multiple aligned PSD each covering one order of frequency range. The final PSD is obtained by linearly averaging 10 measured PSD with the detection mode of the ESA set to sample-mode. The common integrated TJ (

_{tot}*σ*) can be obtained from the TPN PSD

_{int}*L*(

*f*) by with

*f*

_{1}and

*f*

_{2}being the desired integration bandwidth limits.

5. H. Haus and A. Mecozzi, “Noise of mode-locked lasers,” IEEE J. Quantum Electron. **29**, 983–996 (1993) [CrossRef] .

6. D. Eliyahu, R. A. Salvatore, and A. Yariv, “Effect of noise on the power spectrum of passively mode-locked lasers,” J. Opt. Soc. Am. B **14**, 167 (1997) [CrossRef] .

6. D. Eliyahu, R. A. Salvatore, and A. Yariv, “Effect of noise on the power spectrum of passively mode-locked lasers,” J. Opt. Soc. Am. B **14**, 167 (1997) [CrossRef] .

*σ*for a frequency offset from zero to half of the RR yields a constant value which is independent of the RR line-width thus indicating the limitation of Eq. (1) for passively MLL. Therefore a tailored TPN PSD and pulse-to-pulse TJ (

_{int}*σ*) estimation method was proposed specifically addressing free-running passively MLL [21

_{ptp}21. F. Kefelian, S. O’Donoghue, M. T. Todaro, J. G. McInerney, and G. Huyet, “RF linewidth in monolithic passively mode-locked semiconductor laser,” IEEE Photonics Technol. Lett. **20**, 1405–1407 (2008) [CrossRef] .

*L*(

*f*) and the pulse to pulse TJ

*σ*is obtained by with Δ

_{ptp}*ν*being the RR line-width. Based on this relation it is emphasized, that for passively MLL the

*σ*and RR line-width are equivalent and a fully sufficient measure for TJ if no additional instabilities are existent. In other words,

_{ptp}*σ*is, besides the RR, the only necessary universal parameter to describe the TJ of a stably running and undisturbed passively MLL. Both specifications

_{ptp}*σ*as well as

_{ptp}*σ*are root-mean-square (RMS) based. It should be noted that a stably running passively MLL exhibits a Lorentzian shaped RR line. Figure 2 shows calculated TPN PSD for various RR line-widths. Plots (a) are obtained using Eq. (1) and a Lorentzian shaped RR line and plots (b) using (3). As plots (b) represent the correct TPN PSD for a passively MLL it can be seen that the evaluation based on Eq. (1) is only valid for frequency offsets well above the RR line-width. It is essential to be aware of this limitation when performing TPN PSD measurements of passively MLL, as calculating

_{int}*σ*for a frequency integration range starting below the RR-line width would lead to a significant underestimation of the TJ.

_{int}## 3. Model description

22. M. Rossetti, P. Bardella, and I. Montrosset, “Modeling passive mode-locking in quantum dot lasers: A comparison between a finite-difference traveling-wave model and a delayed differential equation approach,” IEEE J. Quantum Electron. **47**, 569–576 (2011) [CrossRef] .

24. R. Paschotta, “Noise of mode-locked lasers (Part I): Numerical model,” Appl. Phys. B **79**, 153–162 (2004) [CrossRef] .

14. C. Otto, K. Lüdge, A. G. Vladimirov, M. Wolfrum, and E. Schöll, “Delay-induced dynamics and jitter reduction of passively mode-locked semiconductor lasers subject to optical feedback,” New J. Phys. **14**, 113033 (2012) [CrossRef] .

15. E. A. Avrutin and B. M. Russell, “Dynamics and spectra of monolithic mode-locked laser diodes under external optical feedback,” IEEE J. Quantum Electron. **45**, 1456–1464 (2009) [CrossRef] .

25. H. Simos, C. Simos, C. Mesaritakis, and D. Syvridis, “Two-section quantum-dot mode-locked lasers under optical feedback: Pulse broadening and harmonic operation,” IEEE J. Quantum Electron. **48**, 872–877 (2012) [CrossRef] .

26. Y. Takushima, H. Sotobayashi, M. E. Grein, E. P. Ippen, and H. A. Haus, “Linewidth of mode combs of passively and actively mode-locked semiconductor laser diodes,” in *Active and Passive Optical Components for WDM Communications IV*, A. K. Dutta, A. A. S. Awwal, N. K. Dutta, and Y. Ohishi, eds., Proc. SPIE 5595, 213–227 (2004) [CrossRef] .

28. W. Lee and P. Delfyett, “Dual-mode injection locking of two independent modelocked semiconductor lasers,” Electron. Lett **40**, 1182 (2004) [CrossRef] .

11. S. Breuer, W. Elsäßer, J. G. McInerney, K. Yvind, J. Pozo, E. A. J. M. Bente, M. Yousefi, A. Villafranca, N. Vogiatzis, and J. Rorison, “Investigations of repetition rate stability of a mode-locked quantum dot semiconductor laser in an auxiliary optical fiber cavity,” IEEE J. Quantum Electron. **46**, 150–157 (2010) [CrossRef] .

29. F. Rana, H. L. T. Lee, R. J. Ram, M. E. Grein, L. A. Jiang, E. P. Ippen, and H. A. Haus, “Characterization of the noise and correlations in harmonically mode-locked lasers,” J. Opt. Soc. Am. B **19**, 2609–2621 (2002) [CrossRef] .

30. F. R. Ahmad and F. Rana, “Fundamental and subharmonic hybrid mode-locking of a high-power (220 mW) monolithic semiconductor laser,” IEEE Photonics Technol. Lett. **20**, 1308–1310 (2008) [CrossRef] .

*T*(

*n*) of the optical pulses with respect to the inverse RR. HML is described by Eq. (5), EO and AO FB by Eq. (6) and OPTI by Eq. (7).

*σ*denotes directly the pulse-to-pulse TJ value and is also the direct representation of the noise source strength, Γ is a normally distributed normalized noise term,

_{ptp}*γ*denotes the timing interaction strength,

*n*denotes the discretized time delay of the FB in terms of number of pulses,

_{d}*T*

_{2}(

*n*) denote the absolute timing deviation of an independent master MLL and

*W*(Δ

*T*) is a weighting function. The weighting function is a Gaussian function with a FWHM of Δ

*τ*for the AO FB to account for the assumption that pulses cannot interact if their timing deviation Δ

*T*is larger then their pulse width. For OE FB

*W*(Δ

*T*) is set to 1 due to the large period of the electrical modulation frequency corresponding to the inverse RR. The denominator is obligatory for the timing averaging effect. As a consequence of the finite-difference approach, integer matching of RR and inverse external-delay time is always fulfilled leading to a constant and unchanged RR. Therefore the RR-snapping effect [11

11. S. Breuer, W. Elsäßer, J. G. McInerney, K. Yvind, J. Pozo, E. A. J. M. Bente, M. Yousefi, A. Villafranca, N. Vogiatzis, and J. Rorison, “Investigations of repetition rate stability of a mode-locked quantum dot semiconductor laser in an auxiliary optical fiber cavity,” IEEE J. Quantum Electron. **46**, 150–157 (2010) [CrossRef] .

*t*= 0

*s*evaluation is performed after a sufficient waiting time to guarantee a relaxation of the system. The resulting TJ time-series is Fourier transformed by a fast Fourier transform algorithm (FFT) using a Hanning window and squared to obtain the timing-noise power spectrum

*L*

_{Δt}(

*f*). In general, the term power spectrum denotes the squared Fourier-transform of a quantity which is also the case for the experimentally measured ESA (power) spectrum

*P*(

*f*). The TPN PSD

*L*(

*f*) can then be obtained from the timing-noise power spectrum by

*L*(

*f*) = (2

*πν*

_{0})2

*L*

_{Δt}(

*f*) [24

24. R. Paschotta, “Noise of mode-locked lasers (Part I): Numerical model,” Appl. Phys. B **79**, 153–162 (2004) [CrossRef] .

*N*/(

*ν*

_{0}

*π*) with

*N*being the number of the pulses in the time-series. The presented calculated spectra are obtained by averaging the spectra of 10 simulation runs each containing a series of 6.4 · 10

^{5}pulses. A noise floor was added to the calculated spectra to account for the noise floor of the whole experimental setup.

## 4. Results and discussion

*σ*of 152 fs. On the one hand these biasing conditions are intentionally chosen to ensure a local minimum of the TJ but on the other hand still to provide a relatively high TPN to be not limited by the setup noise floor. In particular it is essential to ensure that the MLL does not exhibit non-regular mode-locking operation or any sort of instabilities.

_{ptp}8. M. J. Heck, E. J. Salumbides, A. Renault, E. A. Bente, Y.-S. Oei, M. K. Smit, R. van Veldhoven, R. Nötzel, K. S. Eikema, and W. Ubachs, “Analysis of hybrid mode-locking of two-section quantum dot lasers operating at 1.5 *μ*m,” Opt. Express **17**, 18063 (2009) [CrossRef] [PubMed] .

*P*and corresponding timing interaction strengths

_{mod}*γ*, respectively. In experiment, already for the weakest applied modulation power of 12.2 dBm a RR locking is achieved together with a broad-band TPN PSD reduction up to a frequency of around 100 kHz. With increasing modulation power the TPN PSD plateau decreases thus also extending to higher frequencies of up to around 1 MHz for a modulation power of 31.2 dBm. Above this frequency the free-running TPN PSD is unchanged. Therefore HML significantly reduces timing fluctuations on slow time-scales but due to the wide electric gating window which generally amounts to multiples of the optical pulse-width the high-frequency TPN PSD is not affected. In accordance with [31

31. G. Carpintero, M. Thompson, R. Penty, and I. White, “Low noise performance of passively mode-locked 10 Ghz quantum-dot laser diode,” IEEE Photonics Technol. Lett. **21**, 389–391 (2009) [CrossRef] .

10. R. J. Helkey, D. J. Derickson, A. Mar, J. G. Wasserbauer, J. E. Bowers, and R. L. Thornton, “Repetition frequency stabilisation of passively mode-locked semiconductor lasers,” Electron. Lett **28**, 1920–1922 (1992) [CrossRef] .

*γ*in the simulations based on Eq. (5) the numerically obtained TPN PSD results accord with the experimental results in the whole frequency range. A comparison of modulation power

*P*in experiment and corresponding timing interaction strength

_{mod}*γ*in the simulations is shown in Fig. 4 and yields a square-root dependence of timing interaction strength

*γ*on modulation power. The exponent of 0.5 is expected to be valid for HML in general while the scaling factor of 9.6 · 10

^{−4}results from the realized electrical setup. This estimated dependence is necessary in the following to obtain the correct timing interaction strength

*γ*for an applied modulation power

*P*in the OE FB configuration simulation.

_{mod}28. W. Lee and P. Delfyett, “Dual-mode injection locking of two independent modelocked semiconductor lasers,” Electron. Lett **40**, 1182 (2004) [CrossRef] .

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

*W*(Δ

*T*) = 1 and using the estimated parameters from the HML simulation [Fig. 4] coincide with the experimental results very well except for the significantly lower noise resonance peaks. A time-domain representation of these noise peaks will be given later. Due to the good accordance between experiment and simulation the assumption of a timing interaction of intra-cavity pulse and time-delayed absorption gating is validated. Reduction of TPN PSD or TJ can be attributed to an statistical averaging of the independent timing deviations of the intra-cavity pulse and the time-delayed absorption gating leading to a reduced TJ. [11

**46**, 150–157 (2010) [CrossRef] .

*W*(Δ

*T*). However, another possible explanation for the timing interaction could base on interference effects.

**46**, 150–157 (2010) [CrossRef] .

12. C.-Y. Lin, F. Grillot, Y. Li, R. Raghunathan, and L. F. Lester, “Microwave characterization and stabilization of timing jitter in a quantum-dot passively mode-locked laser via external optical feedback,” IEEE J. Sel. Top. Quantum Electron. **17**, 1311–1317 (2011) [CrossRef] .

33. L. A. Jiang, K. S. Abedin, M. E. Grein, and E. P. Ippen, “Timing jitter reduction in modelocked semiconductor lasers with photon seeding,” Appl. Phys. Lett. **80**, 1707 (2002) [CrossRef] .

*γ*, respectively. In the experiment a broadband TPN reduction of 15 dB is achieved up to a frequency of around 3 MHz for the maximum applied FB ratio of 1.6 · 10

^{−3}. At 8.7 MHz and its harmonics distinct noise resonance peaks are evident which originate from the AO FB delay with a frequency of 9.4 MHz. For a high FB ratio of 1.6 · 10

^{−3}the frequency of these observed narrow resonance peaks corresponds quite well to the delay length whereas for a weak FB ratio of 4 · 10

^{−4}these peaks are located at a lower frequency of 8.4 MHz and are strongly broadened. In addition it was found that the dependence of the spectral amplitude of the resonance peaks on harmonic number of the RR lines shows a square-law thus proving that these peaks are pure timing fluctuations [19

19. D. Linde, “Characterization of the noise in continuously operating mode-locked lasers,” Appl. Phys. B **39**, 201–217 (1986) [CrossRef] .

34. F. Grillot, C.-Y. Lin, N. A. Naderi, M. Pochet, and L. F. Lester, “Optical feedback instabilities in a monolithic InAs/GaAs quantum dot passively mode-locked laser,” Appl. Phys. Lett. **94**, 153503 (2009) [CrossRef] .

*γ*for this AO FB configuration this parameter is varied to obtain a matching of the TPN PSD in the low frequency regime up to 1 MHz while keeping the full-width at half maximum Δ

*τ*of the Gaussian shaped timing weighting function

*W*(Δ

*τ*) in Eq. (6) at 4 ps corresponding to the measured Gaussian shaped optical pulse-width of 4 ps. This variation is performed for FB ratios higher than 1 · 10

^{−4}. As can be seen in Fig. 6 the simulation results coincide with the experimental results very well except for the significantly lower noise resonance peaks which is more clearly shown in Fig. 7. In addition, it is found that the dependence of

*γ*on FB ratio yields a simple power-law with an exponent of around

*a*= +0.45. This found relation represents the connection of model and experiment.

^{−3}in experiment and two corresponding simulated TPN PSD is shown in Fig. 7. In the presented simulation results two combinations of timing interaction strengths

*γ*and interaction widths Δ

*τ*are chosen which both match the TPN PSD reduction up to 3 MHz. The parameter combination

*γ*= 3.0 · 10

^{−2}and Δ

*τ*= 4 ps match the measured noise resonance peak frequency of 8.7 MHz exactly and the amplitude much better than the parameter combination

*γ*= 4.8 · 10

^{−3}and Δ

*τ*=

**∞**. This better accordance implies that a timing interaction width is indeed necessary to reproduce well the experimentally obtained results and substantiates the chosen timing-interaction approach. The deviation of measured and simulated noise resonance frequency of 8.7 MHz from the realized delay-frequency of 9.4 MHz is a direct consequence of the timing-mechanism because with increasing timing interaction strength

*γ*in simulation or increasing FB ratio in experiment the resonance-peak frequency converges towards the realized delay-frequency. Also like the OE FB scheme this AO FB scheme shows a dependence of TPN PSD on frequency following a

*f*

^{−2}law at frequencies below the resonance peak frequency which indicates that this configuration is still subject to a random walk. From the overall accordance of TPN PSD and resonance-peak frequency in experiment and simulation it can be deduced that the assumption of an optical timing interaction between intra-cavity pulse and returning time-delayed FB pulse is valid similar to the OE FB case. In is emphasized, that the FB pulses still carry the timing noise generated inside the cavity and are still able to reduce the TJ of the intra-cavity pulses. To depict the efficiency of the AO FB it is pointed out that the returning delayed pulse with a power of much less (due to unknown coupling losses) then 1.6 · 10

^{−3}times the intra-cavity pulse power influences the timing of the intra-cavity pulse by significant 3% per round-trip which is more than one order of magnitude higher than the FB ratio of 1.6 · 10

^{−3}itself.

^{−4}the TPN PSD should be sufficiently spaced from the free running TPN PSD to allow for meaningful evaluation. Hereby a power-law-fit describing the dependence of TPN PSD on optical FB ratio yields an exponent of

*a*= −0.90 which also corresponds to reported experimental results covering AO FB in [35

35. M. Haji, L. Hou, A. E. Kelly, J. Akbar, J. H. Marsh, J. M. Arnold, and C. N. Ironside, “High frequency optoelectronic oscillators based on the optical feedback of semiconductor mode-locked laser diodes,” Opt. Express **20**, 3268 (2012) [CrossRef] [PubMed] .

*γ*on FB ratio:

*γ*which yields a power-law with an exponent of

*a*= −2.1 which matches quite well the expected exponent of

*a*= 2 which directly arises from theory. With the found relations and assuming a

*γ*of 1 which corresponds to an interaction strength of 100%, a corresponding FB ratio of 4.3 is found by means of Eq. (8). An interaction strength

*γ*of 1 should correspond to a FB ratio of 100%. As coupling losses are not included in the given FB ratio the inverse of 4.3 amounting to 23% should reflect these coupling losses. This value of 23% lies in an experimentally reasonable range when laser to fiber coupling or the other way round is regarded which is the case for the realized setup.

36. T. Habruseva, G. Huyet, and S. Hegarty, “Dynamics of quantum-dot mode-locked lasers with optical injection,” IEEE J. Sel. Top. Quantum Electron. **17**, 1272–1279 (2011) [CrossRef] .

37. J. Kim, A. Ardey, and P. J. Delfyett, “Coherent spectral bandwidth combining by optical pulse injection locking in quantum dot modelocked semiconductor diode lasers,” Electron. Lett **48**, 720–721 (2012) [CrossRef] .

*σ*of the free running master MLL amounts to 46 fs corresponding to a RR line-width of 1.7 kHz. In Fig. 9 the measured and corresponding calculated TPN PSD of the slave MLL in OPTI configuration are shown for different injection ratios and corresponding timing interaction strengths

_{ptp}*γ*, respectively. Injection ratio is defined as the ratio of master MLL input power to slave MLL output power. In the experiment, at a low injection ratio of 1.5 · 10

^{−3}a broad band reduction of TPN PSD in the low frequency region is observed with a reduction of 5 dB up to a frequency of 1 MHz. At an increased injection ratio of 3.0 · 10

^{−3}the TPN PSD reduction is significantly higher with a reduction in the range of 20 dB up to a frequency of around 200 kHz and at higher frequencies with a reduction in the range of 5 dB. Finally at an injection ratios above 3.0 · 10

^{−3}the TPN PSD of the slave MLL completely matches the TPN PSD of the master MLL thus successfully demonstrating optical locking of the timing jitter. In addition, OPTI represents an experimentally convenient way to optically transfer and distribute the TJ characteristics from one MLL with low TJ to multiple slave MLL.

*σ*of 46 fs and a

_{ptp}*γ*of 3 · 10

^{−4}for HML operation. The timing interaction width Δ

*τ*is kept at 4 ps. The parameter

*γ*was varied to obtain best possible matching of TPN PSD in simulation and experiment. In general the accordance of experimental and simulated TPN PSD is good and the TJ locking effect can be well reproduced. However, clear differences are evident in the frequency range above 300 kHz which may originate in the difference of performance of the two MLL. First the master and slave MLL have a different spectral width of 0.5 nm and 3.4 nm respectively and second the pulse width of the master MLL could not be estimated due to non-sufficient output power for nonlinear auto-correlation. Nevertheless simulations reproduce the discontinuous transition from TPN PSD reduction to complete TJ locking above an interaction strength of

*γ*= 3.55 · 10

^{−2}thus extending the validity of the timing-interaction approach.

*γ*as a function of the corresponding FB ratio or input ratio of the AO FB or OPTI configuration, respectively. Both optical configurations yield almost identical dependency of

*γ*and input ratio thus validating the proposed TJ interaction also in the OPTI case.

38. H. Tsuchida, “Time-domain measurement of pulse-timing fluctuations in a mode-locked laser diode,” IEEE Photonics Technol. Lett. **14**, 513–515 (2002) [CrossRef] .

*σ*of 152 fs, for the AO FB configuration with a FB ratio of 3 · 10

_{ptp}^{−2}(

*γ*= 3.0·10

^{−2}), for the OE FB configuration with a modulation power of 31.2 dBm (

*γ*= 1.10·10

^{−3}) and HML with a modulation power of 31.2 dBm (

*γ*= 1.10 · 10

^{−3}). It can be seen that for of the free-running MLL the timing deviation performs a random walk which may lead to an unlimited accumulation of timing deviation. This is a direct consequence of the accumulation of Gaussian distributed pulse-to-pulse timing deviations driven by direct emission of spontaneous emission onto the optical pulse per round-trip. In the AO FB configuration the walk is significantly reduced on this selected time-scale and in addition a particular periodicity is evident with a period of

*n*= 538 pulses. This periodicity corresponds to the resonance peaks shown in the TPN PSD in Fig. 6 and represents a recurring noise-pattern which is partially preserved and even enhanced by the external delay. This external delay therefore represents an effective timing noise memory of the system. Hints of this periodicity can also be observed in the OE FB case. For the HML operation the timing deviation is also reduced and tends to be located around zero. Calculating the mean of the timing difference of consecutive pulses yields the expected

_{d}*σ*for the passively MLL with a value of around 152 fs. But also for all the other presented schemes the

_{ptp}*σ*amounts to a value around 152 fs. This is clear because from the presented model the noise source (

_{ptp}*σ*), namely the spontaneous emission, is hardly influenced by the timing interaction strength

_{ptp}*γ*which for example for the HML operation is three orders of magnitude smaller (

*γ*= 1.10·10

^{−3}) than the noise source (

*σ*) itself. As a consequence of the unchanged noise source the TPN PSD is unchanged with respect to the free-running case at very high frequencies above 1 MHz which is most clearly seen for HML in Fig. 3. Even for AO FB the TPN PSD is not reduced at very high frequencies above 10 MHz as seen in Fig. 6. To conclude, the

_{ptp}*σ*represents solely the unchanged noise-source-strength of the MLL and the TPN PSD represents in addition the important statistical and spectral distribution of TJ. It should be noted that significant TPN PSD reduction and the occurrence of TPN PSD resonances can only be achieved for ratios of FB length to MLL cavity length higher than 1 · 10

_{ptp}^{2}due to the required long timing memory of the delay line. Therefore too small ratios used in literature to study FB effects may not reveal statistical timing interaction effects.

*σ*on pulse number

*n*follows a square-root law with

*β*describing the RMS timing deviation per pulse of a random walk system. The standard deviation

*σ*obtained from 100 simulation runs is visualized in Fig. 12 for the free running MLL, for the AO FB configuration, for the OE FB configuration and for HML. For the free running MLL the law is fulfilled yielding a

*β*of 144 fs close to the expected value of 152 fs which corresponds to

*σ*. For the AO FB and OE FB configuration the standard deviation

_{ptp}*σ*also follows the square-root law therefore both FB schemes still represent a random walk. Hereby a reduced

*β*of 37 fs and 102 fs is obtained for the AO FB and OE FB configuration, respectively which correspond well to the values of 36 fs and 94 fs obtained by utilizing Eq. (4), which is only valid for free running MLL, and the RR line-width while excluding the resonance peaks. For both FB schemes

*β*or the RR line-width reflect a measure of the low-frequency fluctuations but disregard the high-frequency timing noise contributions. Finally, the HML operation exhibits a bounded timing deviation as expected thus not representing a random walk process.

*σ*, representing the timing noise source strength, is unchanged in all investigated configurations a different strategy has to be pursued to target this timing noise source directly. In [39

_{ptp}39. M. Rossetti, T. Xu, P. Bardella, and I. Montrosset, “Impact of gain saturation on passive mode locking regimes in quantum dot lasers with straight and tapered waveguides,” IEEE J. Quantum Electron. **47**, 1404–1413 (2011) [CrossRef] .

40. P. Beaud, J. Bi, W. Hodel, and H. Weber, “Experimental observation of the self-stabilization of a synchronously pumped dye laser,” Opt. Commun. **80**, 31–36 (1990) [CrossRef] .

15. E. A. Avrutin and B. M. Russell, “Dynamics and spectra of monolithic mode-locked laser diodes under external optical feedback,” IEEE J. Quantum Electron. **45**, 1456–1464 (2009) [CrossRef] .

*σ*, would be clearly identifiable by a reduced high frequency TPN, which is not observed in the AO FB experimental results presented here. In addition in the OPTI configuration which has shown TPN PSD reduction the required detuning is not possible in principle because the slave MLL pulse-train is locked to the timing-phase and RR of the master MLL pulse-train. Therefore, it can be deduced that this mechanism of noise source strength reduction can be excluded for the investigated MLL and the chosen biasing conditions.

_{ptp}35. M. Haji, L. Hou, A. E. Kelly, J. Akbar, J. H. Marsh, J. M. Arnold, and C. N. Ironside, “High frequency optoelectronic oscillators based on the optical feedback of semiconductor mode-locked laser diodes,” Opt. Express **20**, 3268 (2012) [CrossRef] [PubMed] .

*σ*of 56 fs and a FB pulse width of 2.1 ps. Output power is 1.26 mW, pulse Energy is 64 fJ and FB power is 5 uW (without coupling losses) resulting in a total FB ratio of 4 · 10

_{ptp}^{−3}corresponding to a

*γ*of 4.5 · 10

^{−2}obtained by Eq. (8) whereby an identical coupling efficiency as compared to the measurements presented here has been assumed. For dual AO FB a

*γ*of 4.05 · 10

^{−2}and a

*γ*of 0.45 · 10

^{−2}are assumed for the long and short FB cavity, respectively. In our simulations a timing interaction width of 2.1 ps corresponding to the FB pulse width was used. Hereby, the experimental TPN PSD reduction [35

35. M. Haji, L. Hou, A. E. Kelly, J. Akbar, J. H. Marsh, J. M. Arnold, and C. N. Ironside, “High frequency optoelectronic oscillators based on the optical feedback of semiconductor mode-locked laser diodes,” Opt. Express **20**, 3268 (2012) [CrossRef] [PubMed] .

**20**, 3268 (2012) [CrossRef] [PubMed] .

## 5. Conclusion

**20**, 3268 (2012) [CrossRef] [PubMed] .

## Acknowledgment

## References and links

1. | 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. Express |

2. | A. Nejadmalayeri, M. Grein, S. J. Spector, A. Khilo, M. Y. Peng, M. Sander, J. Wang, A. J. Benedick, C. M. Sorace, M. W. Geis, M. M. Willis, D. M. Lennon, J. U. Yoon, T. M. Lyszczarz, E. Ippen, and F. Kartner, “Attosecond photonics for optical communications,” in |

3. | K. A. Williams, M. G. Thompson, and I. H. White, “Long-wavelength monolithic mode-locked diode lasers,” New J. Phys. |

4. | E. U. Rafailov, M. A. Cataluna, and W. Sibbett, “Mode-locked quantum-dot lasers,” Nat. Photonics |

5. | H. Haus and A. Mecozzi, “Noise of mode-locked lasers,” IEEE J. Quantum Electron. |

6. | D. Eliyahu, R. A. Salvatore, and A. Yariv, “Effect of noise on the power spectrum of passively mode-locked lasers,” J. Opt. Soc. Am. B |

7. | R. Paschotta, “Noise of mode-locked lasers (Part II): Timing jitter and other fluctuations,” Appl. Phys. B |

8. | M. J. Heck, E. J. Salumbides, A. Renault, E. A. Bente, Y.-S. Oei, M. K. Smit, R. van Veldhoven, R. Nötzel, K. S. Eikema, and W. Ubachs, “Analysis of hybrid mode-locking of two-section quantum dot lasers operating at 1.5 |

9. | E. Avrutin, J. Marsh, and E. Portnoi, “Monolithic and multi-gigahertz mode-locked semiconductor lasers: Constructions, experiments, models and applications,” IEE Proceedings - Optoelectronics |

10. | R. J. Helkey, D. J. Derickson, A. Mar, J. G. Wasserbauer, J. E. Bowers, and R. L. Thornton, “Repetition frequency stabilisation of passively mode-locked semiconductor lasers,” Electron. Lett |

11. | S. Breuer, W. Elsäßer, J. G. McInerney, K. Yvind, J. Pozo, E. A. J. M. Bente, M. Yousefi, A. Villafranca, N. Vogiatzis, and J. Rorison, “Investigations of repetition rate stability of a mode-locked quantum dot semiconductor laser in an auxiliary optical fiber cavity,” IEEE J. Quantum Electron. |

12. | C.-Y. Lin, F. Grillot, Y. Li, R. Raghunathan, and L. F. Lester, “Microwave characterization and stabilization of timing jitter in a quantum-dot passively mode-locked laser via external optical feedback,” IEEE J. Sel. Top. Quantum Electron. |

13. | G. Fiol, M. Kleinert, D. Arsenijevic, and D. Bimberg, “1.3 um range 40 GHz quantum-dot mode-locked laser under external continuous wave light injection or optical feedback,” Semicond. Sci. Technol. |

14. | C. Otto, K. Lüdge, A. G. Vladimirov, M. Wolfrum, and E. Schöll, “Delay-induced dynamics and jitter reduction of passively mode-locked semiconductor lasers subject to optical feedback,” New J. Phys. |

15. | E. A. Avrutin and B. M. Russell, “Dynamics and spectra of monolithic mode-locked laser diodes under external optical feedback,” IEEE J. Quantum Electron. |

16. | L. Drzewietzki, S. Breuer, and W. Elsäßer, “Timing phase noise reduction of modelocked quantum-dot lasers by time-delayed optoelectronic feedback,” Electronics Letters |

17. | R. Paschotta, A. Schlatter, S. Zeller, H. Telle, and U. Keller, “Optical phase noise and carrier-envelope offset noise of mode-locked lasers,” Appl. Phys. B |

18. | H. A. Haus, “Mode-locking of lasers,” IEEE J. Sel. Top. Quantum Electron. |

19. | D. Linde, “Characterization of the noise in continuously operating mode-locked lasers,” Appl. Phys. B |

20. | 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. |

21. | F. Kefelian, S. O’Donoghue, M. T. Todaro, J. G. McInerney, and G. Huyet, “RF linewidth in monolithic passively mode-locked semiconductor laser,” IEEE Photonics Technol. Lett. |

22. | M. Rossetti, P. Bardella, and I. Montrosset, “Modeling passive mode-locking in quantum dot lasers: A comparison between a finite-difference traveling-wave model and a delayed differential equation approach,” IEEE J. Quantum Electron. |

23. | M. Radziunas, A. G. Vladimirov, E. A. Viktorov, G. Fiol, H. Schmeckebier, and D. Bimberg, “Pulse broadening in quantum-dot mode-locked semiconductor lasers: Simulation, analysis, and experiments,” IEEE J. Quantum Electron. |

24. | R. Paschotta, “Noise of mode-locked lasers (Part I): Numerical model,” Appl. Phys. B |

25. | H. Simos, C. Simos, C. Mesaritakis, and D. Syvridis, “Two-section quantum-dot mode-locked lasers under optical feedback: Pulse broadening and harmonic operation,” IEEE J. Quantum Electron. |

26. | Y. Takushima, H. Sotobayashi, M. E. Grein, E. P. Ippen, and H. A. Haus, “Linewidth of mode combs of passively and actively mode-locked semiconductor laser diodes,” in |

27. | J. Mulet and J. Mork, “Analysis of timing jitter in external-cavity mode-locked semiconductor lasers,” IEEE J. Quantum Electron. |

28. | W. Lee and P. Delfyett, “Dual-mode injection locking of two independent modelocked semiconductor lasers,” Electron. Lett |

29. | F. Rana, H. L. T. Lee, R. J. Ram, M. E. Grein, L. A. Jiang, E. P. Ippen, and H. A. Haus, “Characterization of the noise and correlations in harmonically mode-locked lasers,” J. Opt. Soc. Am. B |

30. | F. R. Ahmad and F. Rana, “Fundamental and subharmonic hybrid mode-locking of a high-power (220 mW) monolithic semiconductor laser,” IEEE Photonics Technol. Lett. |

31. | G. Carpintero, M. Thompson, R. Penty, and I. White, “Low noise performance of passively mode-locked 10 Ghz quantum-dot laser diode,” IEEE Photonics Technol. Lett. |

32. | T. Habruseva, S. O’Donoghue, N. Rebrova, D. A. Reid, L. P. Barry, D. Rachinskii, G. Huyet, and S. P. Hegarty, “Quantum-dot mode-locked lasers with dual-mode optical injection,” IEEE Photonics Technol. Lett. |

33. | L. A. Jiang, K. S. Abedin, M. E. Grein, and E. P. Ippen, “Timing jitter reduction in modelocked semiconductor lasers with photon seeding,” Appl. Phys. Lett. |

34. | F. Grillot, C.-Y. Lin, N. A. Naderi, M. Pochet, and L. F. Lester, “Optical feedback instabilities in a monolithic InAs/GaAs quantum dot passively mode-locked laser,” Appl. Phys. Lett. |

35. | M. Haji, L. Hou, A. E. Kelly, J. Akbar, J. H. Marsh, J. M. Arnold, and C. N. Ironside, “High frequency optoelectronic oscillators based on the optical feedback of semiconductor mode-locked laser diodes,” Opt. Express |

36. | T. Habruseva, G. Huyet, and S. Hegarty, “Dynamics of quantum-dot mode-locked lasers with optical injection,” IEEE J. Sel. Top. Quantum Electron. |

37. | J. Kim, A. Ardey, and P. J. Delfyett, “Coherent spectral bandwidth combining by optical pulse injection locking in quantum dot modelocked semiconductor diode lasers,” Electron. Lett |

38. | H. Tsuchida, “Time-domain measurement of pulse-timing fluctuations in a mode-locked laser diode,” IEEE Photonics Technol. Lett. |

39. | M. Rossetti, T. Xu, P. Bardella, and I. Montrosset, “Impact of gain saturation on passive mode locking regimes in quantum dot lasers with straight and tapered waveguides,” IEEE J. Quantum Electron. |

40. | P. Beaud, J. Bi, W. Hodel, and H. Weber, “Experimental observation of the self-stabilization of a synchronously pumped dye laser,” Opt. Commun. |

**OCIS Codes**

(140.4050) Lasers and laser optics : Mode-locked lasers

(140.5960) Lasers and laser optics : Semiconductor lasers

(140.7090) Lasers and laser optics : Ultrafast lasers

(230.5590) Optical devices : Quantum-well, -wire and -dot devices

(270.2500) Quantum optics : Fluctuations, relaxations, and noise

(140.3425) Lasers and laser optics : Laser stabilization

**ToC Category:**

Lasers and Laser Optics

**History**

Original Manuscript: May 6, 2013

Revised Manuscript: June 14, 2013

Manuscript Accepted: June 17, 2013

Published: June 28, 2013

**Citation**

Lukas Drzewietzki, Stefan Breuer, and Wolfgang Elsäßer, "Timing jitter reduction of passively mode-locked semiconductor lasers by self- and external-injection: Numerical description and experiments," Opt. Express **21**, 16142-16161 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-13-16142

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### References

- 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, 14518 (2011). [CrossRef] [PubMed]
- A. Nejadmalayeri, M. Grein, S. J. Spector, A. Khilo, M. Y. Peng, M. Sander, J. Wang, A. J. Benedick, C. M. Sorace, M. W. Geis, M. M. Willis, D. M. Lennon, J. U. Yoon, T. M. Lyszczarz, E. Ippen, and F. Kartner, “Attosecond photonics for optical communications,” in Optical Fiber Communication Conference, (Optical Society of America, 2012), p. OM2C.1. [CrossRef]
- K. A. Williams, M. G. Thompson, and I. H. White, “Long-wavelength monolithic mode-locked diode lasers,” New J. Phys.6, 179–179 (2004). [CrossRef]
- E. U. Rafailov, M. A. Cataluna, and W. Sibbett, “Mode-locked quantum-dot lasers,” Nat. Photonics1, 395–401 (2007). [CrossRef]
- H. Haus and A. Mecozzi, “Noise of mode-locked lasers,” IEEE J. Quantum Electron.29, 983–996 (1993). [CrossRef]
- D. Eliyahu, R. A. Salvatore, and A. Yariv, “Effect of noise on the power spectrum of passively mode-locked lasers,” J. Opt. Soc. Am. B14, 167 (1997). [CrossRef]
- R. Paschotta, “Noise of mode-locked lasers (Part II): Timing jitter and other fluctuations,” Appl. Phys. B79, 163–173 (2004). [CrossRef]
- M. J. Heck, E. J. Salumbides, A. Renault, E. A. Bente, Y.-S. Oei, M. K. Smit, R. van Veldhoven, R. Nötzel, K. S. Eikema, and W. Ubachs, “Analysis of hybrid mode-locking of two-section quantum dot lasers operating at 1.5 μm,” Opt. Express17, 18063 (2009). [CrossRef] [PubMed]
- E. Avrutin, J. Marsh, and E. Portnoi, “Monolithic and multi-gigahertz mode-locked semiconductor lasers: Constructions, experiments, models and applications,” IEE Proceedings - Optoelectronics147, 251 (2000). [CrossRef]
- R. J. Helkey, D. J. Derickson, A. Mar, J. G. Wasserbauer, J. E. Bowers, and R. L. Thornton, “Repetition frequency stabilisation of passively mode-locked semiconductor lasers,” Electron. Lett28, 1920–1922 (1992). [CrossRef]
- S. Breuer, W. Elsäßer, J. G. McInerney, K. Yvind, J. Pozo, E. A. J. M. Bente, M. Yousefi, A. Villafranca, N. Vogiatzis, and J. Rorison, “Investigations of repetition rate stability of a mode-locked quantum dot semiconductor laser in an auxiliary optical fiber cavity,” IEEE J. Quantum Electron.46, 150–157 (2010). [CrossRef]
- C.-Y. Lin, F. Grillot, Y. Li, R. Raghunathan, and L. F. Lester, “Microwave characterization and stabilization of timing jitter in a quantum-dot passively mode-locked laser via external optical feedback,” IEEE J. Sel. Top. Quantum Electron.17, 1311–1317 (2011). [CrossRef]
- G. Fiol, M. Kleinert, D. Arsenijevic, and D. Bimberg, “1.3 um range 40 GHz quantum-dot mode-locked laser under external continuous wave light injection or optical feedback,” Semicond. Sci. Technol.26, 014006 (2011). [CrossRef]
- C. Otto, K. Lüdge, A. G. Vladimirov, M. Wolfrum, and E. Schöll, “Delay-induced dynamics and jitter reduction of passively mode-locked semiconductor lasers subject to optical feedback,” New J. Phys.14, 113033 (2012). [CrossRef]
- E. A. Avrutin and B. M. Russell, “Dynamics and spectra of monolithic mode-locked laser diodes under external optical feedback,” IEEE J. Quantum Electron.45, 1456–1464 (2009). [CrossRef]
- L. Drzewietzki, S. Breuer, and W. Elsäßer, “Timing phase noise reduction of modelocked quantum-dot lasers by time-delayed optoelectronic feedback,” Electronics Letters49, 557–559 (2013). [CrossRef]
- R. Paschotta, A. Schlatter, S. Zeller, H. Telle, and U. Keller, “Optical phase noise and carrier-envelope offset noise of mode-locked lasers,” Appl. Phys. B82, 265–273 (2005). [CrossRef]
- H. A. Haus, “Mode-locking of lasers,” IEEE J. Sel. Top. Quantum Electron.6, 1173–1185 (2000). [CrossRef]
- D. Linde, “Characterization of the noise in continuously operating mode-locked lasers,” Appl. Phys. B39, 201–217 (1986). [CrossRef]
- 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, 3522 (2010). [CrossRef] [PubMed]
- F. Kefelian, S. O’Donoghue, M. T. Todaro, J. G. McInerney, and G. Huyet, “RF linewidth in monolithic passively mode-locked semiconductor laser,” IEEE Photonics Technol. Lett.20, 1405–1407 (2008). [CrossRef]
- M. Rossetti, P. Bardella, and I. Montrosset, “Modeling passive mode-locking in quantum dot lasers: A comparison between a finite-difference traveling-wave model and a delayed differential equation approach,” IEEE J. Quantum Electron.47, 569–576 (2011). [CrossRef]
- M. Radziunas, A. G. Vladimirov, E. A. Viktorov, G. Fiol, H. Schmeckebier, and D. Bimberg, “Pulse broadening in quantum-dot mode-locked semiconductor lasers: Simulation, analysis, and experiments,” IEEE J. Quantum Electron.47, 935–943 (2011). [CrossRef]
- R. Paschotta, “Noise of mode-locked lasers (Part I): Numerical model,” Appl. Phys. B79, 153–162 (2004). [CrossRef]
- H. Simos, C. Simos, C. Mesaritakis, and D. Syvridis, “Two-section quantum-dot mode-locked lasers under optical feedback: Pulse broadening and harmonic operation,” IEEE J. Quantum Electron.48, 872–877 (2012). [CrossRef]
- Y. Takushima, H. Sotobayashi, M. E. Grein, E. P. Ippen, and H. A. Haus, “Linewidth of mode combs of passively and actively mode-locked semiconductor laser diodes,” in Active and Passive Optical Components for WDM Communications IV, A. K. Dutta, A. A. S. Awwal, N. K. Dutta, and Y. Ohishi, eds., Proc. SPIE 5595, 213–227 (2004). [CrossRef]
- J. Mulet and J. Mork, “Analysis of timing jitter in external-cavity mode-locked semiconductor lasers,” IEEE J. Quantum Electron.42, 249–256 (2006). [CrossRef]
- W. Lee and P. Delfyett, “Dual-mode injection locking of two independent modelocked semiconductor lasers,” Electron. Lett40, 1182 (2004). [CrossRef]
- F. Rana, H. L. T. Lee, R. J. Ram, M. E. Grein, L. A. Jiang, E. P. Ippen, and H. A. Haus, “Characterization of the noise and correlations in harmonically mode-locked lasers,” J. Opt. Soc. Am. B19, 2609–2621 (2002). [CrossRef]
- F. R. Ahmad and F. Rana, “Fundamental and subharmonic hybrid mode-locking of a high-power (220 mW) monolithic semiconductor laser,” IEEE Photonics Technol. Lett.20, 1308–1310 (2008). [CrossRef]
- G. Carpintero, M. Thompson, R. Penty, and I. White, “Low noise performance of passively mode-locked 10 Ghz quantum-dot laser diode,” IEEE Photonics Technol. Lett.21, 389–391 (2009). [CrossRef]
- T. Habruseva, S. O’Donoghue, N. Rebrova, D. A. Reid, L. P. Barry, D. Rachinskii, G. Huyet, and S. P. Hegarty, “Quantum-dot mode-locked lasers with dual-mode optical injection,” IEEE Photonics Technol. Lett.22, 359–361 (2010). [CrossRef]
- L. A. Jiang, K. S. Abedin, M. E. Grein, and E. P. Ippen, “Timing jitter reduction in modelocked semiconductor lasers with photon seeding,” Appl. Phys. Lett.80, 1707 (2002). [CrossRef]
- F. Grillot, C.-Y. Lin, N. A. Naderi, M. Pochet, and L. F. Lester, “Optical feedback instabilities in a monolithic InAs/GaAs quantum dot passively mode-locked laser,” Appl. Phys. Lett.94, 153503 (2009). [CrossRef]
- M. Haji, L. Hou, A. E. Kelly, J. Akbar, J. H. Marsh, J. M. Arnold, and C. N. Ironside, “High frequency optoelectronic oscillators based on the optical feedback of semiconductor mode-locked laser diodes,” Opt. Express20, 3268 (2012). [CrossRef] [PubMed]
- T. Habruseva, G. Huyet, and S. Hegarty, “Dynamics of quantum-dot mode-locked lasers with optical injection,” IEEE J. Sel. Top. Quantum Electron.17, 1272–1279 (2011). [CrossRef]
- J. Kim, A. Ardey, and P. J. Delfyett, “Coherent spectral bandwidth combining by optical pulse injection locking in quantum dot modelocked semiconductor diode lasers,” Electron. Lett48, 720–721 (2012). [CrossRef]
- H. Tsuchida, “Time-domain measurement of pulse-timing fluctuations in a mode-locked laser diode,” IEEE Photonics Technol. Lett.14, 513–515 (2002). [CrossRef]
- M. Rossetti, T. Xu, P. Bardella, and I. Montrosset, “Impact of gain saturation on passive mode locking regimes in quantum dot lasers with straight and tapered waveguides,” IEEE J. Quantum Electron.47, 1404–1413 (2011). [CrossRef]
- P. Beaud, J. Bi, W. Hodel, and H. Weber, “Experimental observation of the self-stabilization of a synchronously pumped dye laser,” Opt. Commun.80, 31–36 (1990). [CrossRef]

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