## Modeling of mode locking in a laser with spatially separate gain media |

Optics Express, Vol. 18, Issue 22, pp. 22996-23008 (2010)

http://dx.doi.org/10.1364/OE.18.022996

Acrobat PDF (1365 KB)

### Abstract

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

© 2010 Optical Society of America

## 1. Introduction

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

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

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

*μ*m, such as can be realized in semiconductor lasers. Indeed, very high repetition rates of hundreds of GHz can be obtained [4

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

5. A. Robertson, M. Klein, M. Tremont, K.-J. Boller, and R. Wallenstein, “2.5-GHz repetition-rate singly resonant optical parametric oscillator synchronously pumped by a mode-locked diode oscillator amplifier system,” Opt. Lett. **25**, 657–659 (2000). [CrossRef]

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

^{2}(over 100 fs) to initiate a switching operation. A 1 THz pulse repetition rate laser, focused to a diffraction limited spot, therefore, requires an average power of approximately 10 W, which is well beyond the range of the capabilities of current mode-locked diode lasers [7

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

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

### 1.1. Concept

9. U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. A. der Au, “Semiconductor saturable absorber mirrors (SESAM’s) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Top. Quantum Electron. **2**, 435–453 (1996). [CrossRef]

10. R. Rooth, F. van Goor, and W. Witteman, “An independently adjustable multiline AM mode-locked TEA CO_{2} laser,” IEEE J. Quantum Electron. **QE-19**, 1610–1612 (1983). [CrossRef]

11. V. Daneu, A. Sanchez, T. Y. Fan, H. K. Choi, G. W. Turner, and C. C. Cook, “Spectral beam combining of a broad-stripe diode laser array in an external cavity,” Opt. Lett. **25**, 405–407 (2000). [CrossRef]

*et al.*[14

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

*τ*, modulation depth, Δ

*R*, and the saturation fluence Φ

*. The effect of two-photon absorption at high pulse fluences is described with another parameter, Φ*

_{sat}*.*

_{TPA}## 2. Model

*μ*m, each with a front aperture of 4

*μ*m along the slow axis. The gain material is InGaAs with a spectral gain bandwidth of 30 nm around a center wavelength of 975 nm and a maximum output of 1 W CW per element, thus providing a substantial output power of 49 W. The cavity, with a total length of 1 m as illustrated in Fig. 1, contains a spherical lens (

*f*

_{(b)}=300 mm, diameter is 50.8 mm), a 1800-lines/mm diffraction grating, and a semiconductor saturable absorber mirror (SESAM). The focal length of the second lens (

*d*) is not specified. Instead we vary the fluence on the SESAM to represent different focusing conditions and account for losses between the emitters and the SESAM.

*n*th and

*m*th gain element, is given by: with

*n*= 0 denoting the gain element located in the center of the array (total number of element equals 2

*n*+1),

*c*is the speed of light, Λ

*is the grating period,*

_{g}*α*=

*sin*(

*θ*) where

_{i}*θ*is the angle of diffraction of the -1st order compared to the normal of the grating,

_{i}*β*=

*sin*(

*θ*

_{0}) where

*θ*

_{0}is the angle of the incident light at the grating originating from the central gain element,

*γ*=

*cos*(

*θ*

_{0}),

*d*is the physical distance between two adjacent gain elements at the diode array and

*f*is the distance between the grating and the collimating lens. Note that Eq. 1 is independent of cavity length but is weakly dependent on the incident light frequency, since

*θ*

_{0}indirectly depends on frequency. This means that an equal spacing between the emitters does not yield an equal spacing between adjacent frequencies, as can also be seen in Fig. 2, where the spacing varies by a few percent. For mode-locked operation, which imposes a precisely equidistant comb of light frequencies, this deviation is accommodated for within the angular and spatial acceptance of the gain elements as long as the mark / space ratio is equal to or exceeds the deviation. In our case the mark / space ratio is 2% (4

*μ*m / 200

*μ*m) and the nonlinearity in Fig. 2 is 2% over a limited range. This means that an equally spaced frequency comb can be achieved over a range of 19 emitters, as indicated by the red lines in Fig. 2. However, taking the numerical aperture of the collimation lens into account, the diffraction limited spotsize of the light fed back to the diodes has a (1/

*e*

^{2}) diameter of 7.4

*μ*m, which is larger than the emitter aperture. This causes an overall loss but also an insensitivity to misalignment and allows equidistant comb elements over a larger number of emitters. For instance, if we consider that only 33% of the maximum modal overlap with the laser aperture is required to ensure lasing at the correct frequency, then an equidistant frequency comb extending over a range of 37 emitters is possible (effective mark/space of 8%). Since diode lasers only need a limited amount of feedback for frequency locking, an even larger range of emitters might be frequency locked in an equally spaced frequency comb. For optimum performance, however, a chirped emitter spacing or suitable correction optics should be employed. In the following calculations, we assume that an ideal equidistant frequency comb is possible. Eq. 1 can thus be seen as an expression to design the repetition rate. For instance, a more dispersive diffractive grating generates a larger frequency spacing and, therefore, a higher repetition rate.

*δν*, and the Fourier-limited pulse duration is determined by the total bandwidth, Δ

*ν*= (2

*n*)

*δν*. Therefore, the ratio of the pulse duration and the pulse spacing (duty cycle) is fixed and amounts approximately to the inverse number of spaces between the gain elements, i.e., (1/(2

*n*)). If a lens system with an adjustable magnification is inserted between the grating and the gain elements, the repetition rate and pulse duration are simultaneously changed. To increase the pulse duration independently of the repetition rate, a number of the outer elements could be switched off.

^{14}+ 1 = 16385 elements. The frequency spacing between each frequency-array element is chosen as 6.7 GHz, providing a bandwidth of 110 THz over the total array length. This bandwidth provides sufficient resolution (9.1 fs) in the time domain to describe the dynamics of the SESAM and resolve the pulse shape. The time array spans 150 ps. The center frequencies of the gain elements are placed 67 GHz (10 array elements) apart, so that the total bandwidth covered by the gain elements is 3.3 THz, which corresponds to 10.5 nm at a center wavelength of 975 nm. Mode locking will result in 10 pulses within the time array, all of which are processed in one computational loop. This choice for the frequency spacing of the gain elements corresponds to the proposed setup as discussed earlier in this paper. However, the computational frequency resolution is many times less than the cold-cavity mode spacing, which is ∼150 MHz (for a 1 m total cavity length) so that more than 400 pulses occupy the cavity simultaneously, rather than 10.

### 2.1. Gain model

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

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

*n*th to the

*n*th center modes, i.e., for the total bandwidth of the modeled laser, we assume a flat profile. This indicates that this bandwidth is substantially smaller than that of the InGaAs gain [18

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

*I*= 1/(

_{sat}*g*

_{0}– 1), which normalizes the extractable power [19] and fixes the relationship between the small signal gain and the saturation intensity. The remaining degree of freedom is the value of the small-signal gain,

*g*

_{0}, which we choose to be a typical value of 100 over the full length of the gain. Roundtrip losses are set to a typical value of 90% and are taken to include all losses as described before. These losses are applied to all the light that is fed back into the individual gain elements before calculating the gain. For the gain of each individual element we assume homogeneous broadening which implies that, upon amplification, the center mode and the side modes compete for gain. This is approximated as [19]: where

*I*is the sum of intensities of the center and side modes. The gain in each iteration is calculated using Eq. 2 rather than using an integration over the full volume of the gain element. In the initial iterations this approximation does not strictly conserve energy per roundtrip. But, in the steady state, the saturation reduces the roundtrip gain to a value of 1 for a per-emitter power of 1 W, conserving power over multiple round trips and therefore the energy. The amplified spectrum is transformed to the time domain using a fast Fourier transform.

_{tot}### 2.2. Temporal dynamics

*et al.*[14

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

*is the pulse fluence (for a pulse much shorter than the recovery time*

_{P}*τ*), Δ

*R*is the modulation depth of the reflectivity, and

*R*incorporates the non-saturable losses. Two-photon absorption is described using a two-photon fluence Φ

_{ns}*, where*

_{TPA}14. R. Grange, M. Haiml, R. Paschotta, G. Spühler, L. Krainer, O. Ostinelli, M. Golling, and U. Keller, “New regime of inverse saturable absorption for selfstabilizing passively modelocked lasers,” Appl. Phys. B **80**, 151–158 (2005). [CrossRef]

*S*

_{0}= 10, for a typical commercially available SESAM [20

20. BATOP-GmbH, “BATOP website, a SESAM manufacturer,” http://www.batop.com (2010).

*S*

_{0}). As the temporal and spectrally independent cavity losses are combined into a single loss term, which is taken into account in the gain section of the model, we set

*R*= 1.

_{ns}*S*as the ratio of the pulse fluence for a Fourier-limited pulse over the saturation fluence of the SESAM:

*S*= Φ

*/Φ*

_{opt}*. This ratio defines the effective size of the beam on the SESAM and allows for a pulse energy to be converted to a pulse fluence.*

_{sat}*τ*. To derive this “short-pulse fluence” Φ

*from the temporal intensity we use Eq. 4, in which the integration of the intensity is weighted by the exponential decay of the SESAM, i.e., the recovery time. Please note that this pulse fluence can only be applied when used in combination with the SESAM’s recovery time and does not describe the pulse energy directly. In this expression,*

_{P}*τ*, represents the recovery time of the SESAM. The integration is performed as a running sum and the resulting value for Φ

*is inserted into Eq. 3 to obtain the time-dependent intensity reflectivity,*

_{P}*R*(Φ

*). The time-domain field amplitude is multiplied by the square root of*

_{P}*R*(Φ

*). This concludes the time-domain portion of the calculation iteration and the time-domain field amplitude is transformed by discrete fast Fourier transform to the frequency domain to begin a new iteration.*

_{P}### 2.3. Initial conditions and evaluation

*S*,

*τ*, and Δ

*R*. To evaluate the numerous time traces, we defined a criterion for successful mode locking by comparing each calculated time trace with that of a Fourier-limited pulse train that possesses the maximum possible peak power. Successful mode locking was defined as the occurrence of any peak power that exceeds half of this maximum possible peak power. With this criterion we obtain the probability of mode locking by determining how many times, out of a given number of simulations with identical parameters, successful mode locking was observed. The results showed that ten runs are sufficient to identify a parameter range where mode locking occurs, which we call the mode-locking regime, with a distinguishable boundary to parameters with which no mode locking occurs. So we have now defined the probability of mode locking as the number of times mode locking was observed, divided by the number of simulations per parameter set (which we chose to be ten).

## 3. Results

*S*above

*S*= 1, where the pulse fluence equals the SESAM’s saturation fluence. At

*S*= 10 we expect mode locking over the largest range of SESAM parameters, Δ

*R*and

*τ*. For higher values of

*S*, however, two-photon absorption is expected to decrease the mode-locking regime. We show results for

*S*: 0.1, 1, 3, 5, 10, 20, and 50. The values for the SESAM’s recovery time and modulation depth are chosen similar to what current, commercially available SESAMs provide [20

20. BATOP-GmbH, “BATOP website, a SESAM manufacturer,” http://www.batop.com (2010).

*R*is chosen to be between 5% and 40%, in steps of 5%, and

*τ*is chosen between 0.5 ps and 10 ps.

*R*= 40 %,

*τ*= 3

*ps*and

*S*= 3), to have a clear evolution of the pulses over a large range of the 500 iterations. Fig. 4

*(a)*and

*(b)*show the spectral power and corresponding time trace, after one iteration,

*(c)*and

*(d)*after 100 iterations, and

*(e)*and

*(f)*after 500 iterations. The insets in

*(a)*,

*(c)*and

*(e)*show the spectrum including all side modes over the range of the gain.

*(a)*,

*(c)*and

*(e)*show a zoom-in of the spectrum to ten array numbers (array numbers 8079–8089, the distance between two neighboring center modes). The dots (and vertical lines) show the calculated power of the light at these frequencies. The insets in

*(b)*,

*(d)*and

*(f)*show the full time trace of our calculations.

*(b)*and

*(d)*show a zoom-in over 2000 array numbers.

*(f)*shows a zoom-in over only 400 array numbers to resolve the pulse shape at the end of the calculation.

*(a)*, after one iteration, it can be seen that all side modes are still present at the spectrum, however their power relative to the center frequency is lower due to gain competition and a lower relative gain. After 100 iterations (Fig. 4

*(c)*), no significant power is observed for the side modes anymore and the available power is present in the center frequencies. Furthermore, one sees that the power at the different gain elements is not precisely equal anymore (the envelope over the full laser spectrum is not entirely smooth; the largest difference in height between the adjacent frequencies is 1.6% the average it is 0.3%). This can be addressed to the phase dependent exchange of energy between the modes caused by sideband generation in the SESAM. After 500 iterations (Fig. 4

*(e)*), the envelope is smooth again, which is an indication for mode locking [21

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

*(e)*is significantly smoother than the spectrum in Fig. 4

*(c)*). The spectrum has an almost square-shaped envelope, which is expected because the spatial separation of the gain for the 49 light frequencies acts as an inhomogeneous broadening of the gain. In the time trace after one iteration (Fig. 4

*(b)*), only a randomly fluctuating power is observed, indicating that all the frequencies have a random phase. After 100 iterations (Fig. 4

*(d)*), the initial stages of a pulse train can be observed, with irregularly shaped pulses, but at a regular interval. Since not all phases in the spectrum are locked, the peak power is still rather low. After 500 iterations (Fig. 4

*(f)*), short, almost Fourier-limited, pulses are observed, with a FWHM pulse duration of 273 fs (i.e., 30 array numbers).

^{2}-shaped pulses, with side pulses.

*S*< 50, 5% < Δ

*R*< 40% and 0.2 ps <

*τ*< 10 ps. Fig 5 shows the observed mode-locking probability in graphs with pair-wise variation of

*τ*and Δ

*R*for various values of

*S*. Black indicates a mode-locking probability of unity and mode locking was observed less often for lighter shades of gray. The small crosses in the figure represent the calculations in which mode locking was not observed. We found generally that for low values of

*S*(corresponding to weaker focusing on the SESAM or a lower saturation fluence), mode locking is only observed for fast absorbers (small

*τ*) and absorbers with a high modulation depth (large Δ

*R*). This is expected, because, in Eq. 3 for small values of

*S*, the SESAM’s reflectivity shows a modulation of less than Δ

*R*, making the loss differential too small to induce mode locking.

*S*increases with sharper focusing on the SESAM, so does the parameter range for which mode locking successfully occurs. This is the case because, for larger

*S*, the modulation due to saturation increases, which relaxes the requirements for the modulation depth and response time. However, it can be seen in Fig. 5

*(f)*and

*(g)*that a further increased fluence in the SESAM (

*S*= 20 and

*S*= 50, respectively) narrows the mode locking regime for Δ

*R*and

*τ*again. This can be understood, because in Eq. 3 for values of

*S*> 10, two-photon absorption becomes significant enough to reduce the modulation of the reflectivity. In general, selecting a larger Δ

*R*means that the same reflectivity change, and thus the same effect on the laser dynamics, is reached for a lower fluence, thereby broadening the operating regime for which mode locking is observed. Similarly, a short

*τ*ensures a stronger differential gain for the pulsed state which improves the mode locking.

20. BATOP-GmbH, “BATOP website, a SESAM manufacturer,” http://www.batop.com (2010).

*τ*> 0.5 ps and with modulation depths, Δ

*R*, between 15 and 30%. The calculations show that such values should suffice for mode locking if a sufficiently high fluence of the incident pulses, about

*S*= 10, can be realized in spite of the high repetition rate. If we assume a mode area at the SESAM of 50

*μ*m

^{2}and a typical SESAM value for Φ

*of 60*

_{sat}*μ*J/cm

^{2}, it would be possible to achieve

*S*= 10 with a total power of 20 W in the common arm. This power is a value which is well below the specifications of the diode arrays that we consider here. This estimate, thus, indicates that our novel mode-locking scheme is just feasible with currently available components.

## 4. Conclusion and outlook

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

## References and links

1. | J. Klein and J. D. Kafka, “The Ti:Sapphire laser: the flexible research tool,” Nat. Photonics |

2. | U. Keller, “Recent developments in compact ultrafast lasers,” Nature |

3. | T. Pfeiffer and G. Veith, “40 GHz pulse generation using a widely tunable all-polarization preserving erbium fiber ring laser,” Electron. Lett. |

4. | U. Keller and A. Tropper, “Passively modelocked surface-emitting semiconductor lasers,” Phys. Rep. |

5. | A. Robertson, M. Klein, M. Tremont, K.-J. Boller, and R. Wallenstein, “2.5-GHz repetition-rate singly resonant optical parametric oscillator synchronously pumped by a mode-locked diode oscillator amplifier system,” Opt. Lett. |

6. | F. Hansteen, A. Kimel, A. Kirilyuk, and T. Rasing, “Femtosecond photomagnetic switching of spins in ferrimagnetic garnet films,” Phys. Rev. Lett. |

7. | A. Aschwanden, D. Lorenser, H. Unold, and R. Paschotta, “10 GHz passively mode-locked external-cavity semiconductor laser with 1.4 W average output power,” Appl. Phys. Lett. |

8. | P. Harding, T. Euser, Y. Nowicki-Bringuier, J. Gèrard, and W. Vos, “Dynamical ultrafast all-optical switching of planar GaAs/AlAs photonic microcavities,” Appl. Phys. Lett. |

9. | U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. A. der Au, “Semiconductor saturable absorber mirrors (SESAM’s) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Top. Quantum Electron. |

10. | R. Rooth, F. van Goor, and W. Witteman, “An independently adjustable multiline AM mode-locked TEA CO |

11. | V. Daneu, A. Sanchez, T. Y. Fan, H. K. Choi, G. W. Turner, and C. C. Cook, “Spectral beam combining of a broad-stripe diode laser array in an external cavity,” Opt. Lett. |

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

13. | T. Hänsch, “A proposed sub-femtosecond pulse synthesizer using separate phase-locked laser oscillators,” Opt. Commun. |

14. | R. Grange, M. Haiml, R. Paschotta, G. Spühler, L. Krainer, O. Ostinelli, M. Golling, and U. Keller, “New regime of inverse saturable absorption for selfstabilizing passively modelocked lasers,” Appl. Phys. B |

15. | S. Kobayashi and T. Kimura, “Injection locking in AlGaAs semiconductor lasers,” IEEE J. Quantum Electron. |

16. | D. Byrne, W. Guo, Q. Lu, and J. Donegan, “Broadband reflection method to measure waveguide loss,” Electron. Lett. |

17. | N. Trela, H. Baker, R. McBride, and D. Hall, “Low-loss wavelength locking of a 49-element single mode diode laser bar with phase-plate beam correction,” Conference Proceedings CLEO Europe - EQEC 2009 (2009). |

18. | L. Eng, D. Mehuys, M. Mittelstein, and A. Yariv, “Broadband tuning (170 nm) of InGaAs quantum well lasers,” Electron. Lett. |

19. | A.E. Siegman, |

20. | BATOP-GmbH, “BATOP website, a SESAM manufacturer,” http://www.batop.com (2010). |

21. | K. Garner and G. Massey, “Laser mode locking by active external modulation,” IEEE J. Quantum Electron. |

**OCIS Codes**

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

(320.7090) Ultrafast optics : Ultrafast lasers

(140.3298) Lasers and laser optics : Laser beam combining

**ToC Category:**

Lasers and Laser Optics

**History**

Original Manuscript: August 16, 2010

Revised Manuscript: October 1, 2010

Manuscript Accepted: October 6, 2010

Published: October 15, 2010

**Citation**

R. M. Oldenbeuving, C. J. Lee, P. D. Van Voorst, H. L. Offerhaus, and K. -. Boller, "Modeling of mode locking in a laser with spatially separate gain media," Opt. Express **18**, 22996-23008 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-22-22996

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### References

- J. Klein and J. D. Kafka, “The Ti:Sapphire laser: the flexible research tool,” Nat. Photonics 4, 289 (2010). [CrossRef]
- U. Keller, “Recent developments in compact ultrafast lasers,” Nature 424, 831–838 (2003). [CrossRef] [PubMed]
- T. Pfeiffer and G. Veith, “40 GHz pulse generation using a widely tunable all-polarization preserving erbium fiber ring laser,” Electron. Lett. 29, 1849–1850 (1993). [CrossRef]
- U. Keller and A. Tropper, “Passively modelocked surface-emitting semiconductor lasers,” Phys. Rep. 429, 67–210 (2006). [CrossRef]
- A. Robertson, M. Klein, M. Tremont, K.-J. Boller, and R. Wallenstein, “2.5-GHz repetition-rate singly resonant optical parametric oscillator synchronously pumped by a mode-locked diode oscillator amplifier system,” Opt. Lett. 25, 657–659 (2000). [CrossRef]
- F. Hansteen, A. Kimel, A. Kirilyuk, and T. Rasing, “Femtosecond photomagnetic switching of spins in ferrimagnetic garnet films,” Phys. Rev. Lett. 95, 047402 (2005). [CrossRef] [PubMed]
- A. Aschwanden, D. Lorenser, H. Unold, and R. Paschotta, “10 GHz passively mode-locked external-cavity semiconductor laser with 1.4 W average output power,” Appl. Phys. Lett. 86, 131102 (2005). [CrossRef]
- P. Harding, T. Euser, Y. Nowicki-Bringuier, J. Gérard, and W. Vos, “Dynamical ultrafast all-optical switching of planar GaAs/AlAs photonic microcavities,” Appl. Phys. Lett. 91, 111103 (2007). [CrossRef]
- U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. A. der Au, “Semiconductor saturable absorber mirrors (SESAM’s) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Top. Quantum Electron. 2, 435–453 (1996). [CrossRef]
- R. Rooth, F. van Goor, and W. Witteman, “An independently adjustable multiline AM mode-locked TEA CO2 laser,” IEEE J. Quantum Electron. QE-19, 1610–1612 (1983). [CrossRef]
- V. Daneu, A. Sanchez, T. Y. Fan, H. K. Choi, G. W. Turner, and C. C. Cook, “Spectral beam combining of a broad-stripe diode laser array in an external cavity,” Opt. Lett. 25, 405–407 (2000). [CrossRef]
- M. J. R. Heck, E. A. J. M. Bente, Y. Barbarin, D. Lenstra, and M. K. Smit, “Simulation and design of integrated femtosecond passively mode-locked semiconductor ring lasers including integrated passive pulse shaping components,” IEEE J. Sel. Top. Quantum Electron. 12, 265–276 (2006). [CrossRef]
- T. Hänsch, “A proposed sub-femtosecond pulse synthesizer using separate phase-locked laser oscillators,” Opt. Commun. 80, 71–75 (1990). [CrossRef]
- R. Grange, M. Haiml, R. Paschotta, G. Spühler, L. Krainer, O. Ostinelli, M. Golling, and U. Keller, “New regime of inverse saturable absorption for selfstabilizing passively modelocked lasers,” Appl. Phys. B 80, 151–158 (2005). [CrossRef]
- S. Kobayashi and T. Kimura, “Injection locking in AlGaAs semiconductor lasers,” IEEE J. Quantum Electron. QE-17, 681–689 (1981). [CrossRef]
- D. Byrne, W. Guo, Q. Lu, and J. Donegan, “Broadband reflection method to measure waveguide loss,” Electron. Lett. 45, 322–323 (2009). [CrossRef]
- N. Trela, H. Baker, R. McBride, and D. Hall, “Low-loss wavelength locking of a 49-element single mode diode laser bar with phase-plate beam correction,” Conference Proceedings CLEO Europe - EQEC 2009 (2009).
- L. Eng, D. Mehuys, M. Mittelstein, and A. Yariv, “Broadband tuning (170 nm) of InGaAs quantum well lasers,” Electron. Lett. 26, 1675–1677 (1990). [CrossRef]
- . Siegman, Lasers (University Science Books, 1986). Chapt. 7 and 8.
- BATOP-GmbH, “BATOP website, a SESAM manufacturer,” http://www.batop.com (2010).
- K. Garner and G. Massey, “Laser mode locking by active external modulation,” IEEE J. Quantum Electron. 28, 297–301 (1992). [CrossRef]

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