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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 25 — Dec. 7, 2009
  • pp: 23098–23103

Optics InfoBase > Optics Express > Volume 17 > Issue 25 > Page 23098

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Compact picosecond mode-locked and cavity-dumped Nd:YVO4 laser

U. Wegner, J. Meier, and M. J. Lederer  »View Author Affiliations


Optics Express, Vol. 17, Issue 25, pp. 23098-23103 (2009)
http://dx.doi.org/10.1364/OE.17.023098


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Abstract

We report on a diode pumped, semiconductor saturable absorber mirror mode-locked picosecond Nd:YVO4 oscillator with cavity-dumping. In pure cw-mode-locking this laser produced up to 17W of average power at a pulse repetition rate of 9.7MHz, corresponding to a pulse energy of 1.7µJ. Using an electro-optic cavity dumper, we achieved average powers up to 7.8W at 500kHz and 10W at 1MHz dumping rate. With corresponding pulse energies of 15.6µJ and 10µJ respectively and pulsewidths around 10ps, this laser could become a compact source for materials processing applications, alternative to more complex schemes such as regenerative amplifiers or ultra-long resonator oscillators.

© 2009 OSA

1. Introduction

Many applications in fields like materials processing and harmonic generation benefit from picosecond laser pulses with energies in the µJ-regime and at MHz repetition rates. Typical means of achieving these kinds of specifications include the master-oscillator-power-amplifier (MOPA) principle using fiber e.g [1

J. Limpert, N. Deguil-Robin, I. Manek-Hönninger, F. Salin, T. Schreiber, A. Liem, E. Röser, H. Zellmer, A. Tünnermann, A. Courjaud, C. Hönninger, and E. Mottay, “High-power picosecond fiber amplifier based on nonlinear spectral compression,” Opt. Lett. 30(7), 714–716 ( 2005). [CrossRef] [PubMed]

] or bulk-crystal e.g [2

B. Luther-Davies, V. Z. Kolev, M. J. Lederer, N. R. Madsen, A. V. Rode, J. Giesekus, K.-M. Du, and M. Duering, “Table-top 50-W laser system for ultra-fast laser ablation,” Appl. Phys., A Mater. Sci. Process. 79(4-6), 1051–1055 ( 2004). [CrossRef]

–4

C. Gerhard, F. Druon, P. Blandin, M. Hanna, F. Balembois, P. Georges, and F. Falcoz, “Efficient versatile-repetition-rate picosecond source for material processing applications,” Appl. Opt. 47(7), 967–974 ( 2008). [CrossRef] [PubMed]

] based oscillators and amplifiers, the mode-locked ultra-long resonator [5

V. Z. Kolev, M. J. Lederer, B. Luther-Davies, and A. V. Rode, “Passive mode locking of a Nd:YVO4 laser with an extra-long optical resonator,” Opt. Lett. 28(14), 1275–1277 ( 2003). [CrossRef] [PubMed]

–8

T. Südmeyer, S. V. Marchese, C. R. Baer, S. Hashimoto, A. G. Engqvist, M. Golling, D. J. H. C. Maas, and U. Keller, Femtosecond Thin Disk Lasers with >10 μJ Pulse Energy,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, 2008 Technical Digest (Optical Society of America, Washington, DC, 2008), CFP1.

] and the regenerative amplifier e.g [9

F. Dausinger, et al ., Femtosecond Technology for Technical and Medical Applications, (Springer, 2004), pp. 17–33.

,10

D. A. Clubley, A. S. Bell, and G. Friel, “High average power Nd:YVO4 based pico-second regenerative amplifier,” Proc. SPIE 6871, 68711D ( 2008). [CrossRef]

]. Another approach, which could be considered suitable for the generation of the above mentioned parameters, is cavity-dumping of a mode-locked oscillator. Regarding system complexity the cavity-dumped oscillator has certain advantages over the aforementioned schemes. Firstly, the required resonator length is only moderate compared to that of high energy oscillators with a few MHz repetition rate. Secondly, there is only one resonator with the dumping element inside, instead of the seeder and amplifier combination required by both the MOPA and the regenerative amplifier. In the past, both femtosecond and picosecond diode-pumped, passively mode-locked oscillators with cavity-dumping were reported e.g [11

A. Killi, J. Dörring, U. Morgner, M. J. Lederer, J. Frei, and D. Kopf, “High speed electro-optical cavity dumping of mode-locked laser oscillators,” Opt. Express 13(6), 1916–1922 ( 2005). [CrossRef] [PubMed]

,12

G. Palmer, M. Emons, M. Siegel, A. Steinmann, M. Schultze, M. J. Lederer, and U. Morgner, “Passively mode-locked and cavity-dumped Yb:KY(WO(4))(2) oscillator with positive dispersion,” Opt. Express 15(24), 16017–16021 ( 2007). [CrossRef] [PubMed]

]. However, so far, the achieved pulse energy was limited to a few µJ. Here, we present a picosecond passively mode-locked and electro-optically cavity-dumped oscillator with pulse energy up to 15µJ, average power up to 10W, and MHz dumping rates. To the best of our knowledge this constitutes the highest pulse energy from such a laser to date whilst power, dumping frequency and energy could still be scaled up further.

2. Nd:YVO4 laser head with two crystals, mode-locked operation

The laser head used for the experiments is an adaption of the previously presented dual-crystal cavity employing Yb:KYW [13

A.-L. Calendron, K. S. Wentsch, and M. J. Lederer, “High power cw and mode-locked oscillators based on Yb:KYW multi-crystal resonators,” Opt. Express 16(23), 18838–18843 ( 2008). [CrossRef] [PubMed]

] for operation with Nd:YVO4 as gain material. This design concept allows us to spread the thermal load and the associated negative effects on beam quality over two crystals. At the same time, due to the optimized overlap between pump and mode when using multiple shorter crystals compared to a single longer one, the small signal gain and the extraction efficiency of the resonator for standard doping levels and diode brightness is higher. We modified the design presented in [13

A.-L. Calendron, K. S. Wentsch, and M. J. Lederer, “High power cw and mode-locked oscillators based on Yb:KYW multi-crystal resonators,” Opt. Express 16(23), 18838–18843 ( 2008). [CrossRef] [PubMed]

] to employ two Nd:YVO4-crystals. The use of Nd:YVO4 with its relatively short upper level lifetime and very large gain cross section [14

W. Köchner, Solid-State Laser Engineering (Springer, 2006), pp. 69–73.

] allows for high values of output coupling during mode-locking operation and a large mode size inside the crystal, minimizing the detrimental effects from nonlinear phase shifts during the high energy pulse build-up phase of cavity dumping. Also, due to the large small signal gain, extraction of high pulse energies is possible with a minimal number of resonator round trips.

Figure 1 shows the schematic of the laser setup. The symmetric short cavity is terminated by M6 as well as an output coupler (OC) of 30% in position of M3 for characterization. It includes the two 3mm long, a-cut, 0.27% doped Nd:YVO4 crystals out of focus. The crystals are end pumped through dichroic mirrors with two fibre coupled laser diodes (400µm core, NA = 0.22) with up to 20W per laser diode at 880nm. The end faces of the 400µm core diameter fibers are imaged to an 800µm wide pump spot inside the laser crystals. With a total pump power of 40W a maximum cw laser output of 19.5W at 1064nm can be extracted from the short cavity through the 30% output coupler (M3). The laser emission is characterized by an M2 factor of < 1.15 (measured with Coherent ModeMaster) and is linearly polarized along the c-axis of the crystal.

Fig. 1 Schematic of the laser cavity: M3 is an output coupler of 30% (cw) or 0.8% (mode-locking or cavity-dumping), M1 and M4 are dichroic mirrors, M2 and M5 are curved mirrors with R = 500mm. L represents the collimating and focusing optics of the fiber coupled pump diodes LD1 and LD2, XTAL1 and 2 are 0.27% doped Nd:YVO4-crystals, M6 is an optional end mirror of the short cavity, M9 and M10 are the in and out coupling mirrors of the Herriott cell M11 (R = 1600mm), M12 and M13 (both flat); M8 is a curved mirror with R = 1600mm; M7 and M14 are both flat HR-mirrors; TFP is a thin-film polarizer; PDG is a pulse delay generator.

For mode-locking we extended the cavity length using a Herriott type multi-pass cell [15

D. Herriott, H. Kogelnik, and R. Kompfner, “Off-Axis Paths in Spherical Mirror Interferometers,” Appl. Opt. 3(4), 523 ( 1964). [CrossRef]

] (HMPC, mirrors M9 −13) in order to achieve a repetition rate of around 10MHz. The four-pass HMPC is used in a double passage geometry, i.e. the beam exiting the HMPC after the first passage is sent through the HMPC in opposing direction again. Using this approach we achieve a total cavity length of about 15m with the HMPC having a period length (M11-13) of 800mm, therefore still maintain a very compact setup. Separation of the double passage beams is achieved in the vertical dimension with the incoming beam passing above the SESAM and the outgoing beam passing below M9 and M10 to hit the semiconductor saturable absorber mirror (SESAM) via a second bounce off M8. We use a SESAM with a response time of 10ps, a saturation fluence of Fsat = 20µJ/cm2 and a modulation depth of around 1.5% as a turning mirror inside the laser resonator. The SESAM was mounted on a water cooled copper block to avoid damage and thermal detuning. Finally, to facilitate cavity dumping we added a quarter-wave (λ/4) plate, a thin-film polarizer (TFP) and a Pockels-cell.

In pure mode-locking operation the OC is set to 0.8% and the laser radiation is coupled out from the thin film polarizer (TFP), following polarization rotation by the quarter-waveplate. At a total pump power of 40W (35W absorbed) and with the Pockels-cell still not in place, a maximum output power of 17W can be extracted from the mode-locked resonator without suffering instability from q-switched mode-locking [16

F. X. Kärtner, L. R. Brovelli, D. Kopf, M. Kamp, I. Calasso, and U. Keller, “Control of solid state laser dynamics by semiconductor devices,” Opt. Eng. 34(7), 2024 ( 1995). [CrossRef]

]. Figure 2 depicts an oscilloscope trace of the mode-locked pulse train with a frequency of 9.7MHz.

Fig. 2 Pulse train of mode-locked laser with 9.7 MHz repetition rate.

As is typical for purely saturable absorber mode-locked lasers, varying the output coupling, here via rotation of the λ/4-plate, allows to change the pulsewidth. Table 1 shows the dependence of both output power and pulsewidth upon output coupling. Additionally, there are calculated values, gathered from a numerical simulation of the master equation of the laser [17

H. A. Haus, “Theory of modelocking with a fast saturable absorber,” J. Appl. Phys. 46(7), 3049–3058 ( 1975). [CrossRef]

] which are in close agreement with the experiment. For reference, Table 2 contains the parameters used in the simulation.

Table 1  Overview over calculated and measured output power and pulse duration
ROC [%]P [W]τ [ps]
measuredcalculatedmeasuredcalculated
901312.91312.2
851515.419.517
651717.62625
Table 2  Simulation parameters
gain cross-section σYVO4 15·10−19 cm2
vanadate fluorescence lifetime τYVO4 100 μs
beam radius in the crystal ωxtal 400 μm
beam radius on the SESAM ωSESAM 420 μm
modulation depth of the SESAM ΔR 1.5%
response time of the SESAM τSESAM 10 ps
saturation fluence of the SESAM FSat 20 μJ/cm2
parasitic losses of the resonator lpara 0.1
absorbed power Pabs 35 W

3. Cavity-dumped operation

In order to achieve cavity-dumping, the laser is fitted with a BBO-Pockels-cell (λ/4 @3.6kV) and associated driver for switching frequencies up to 1MHz. Using suitable attenuation, the output from mirror M3 (0.8% OC) is placed onto a photodiode, whose signal is used to synchronize a pulse-delay generator (PDG). The latter is used to trigger the Pockels-cell driver. Cavity-dumping of a single pulse is then achieved with appropriate settings of the fine delay on the PDG, whilst the degree of dumping is conveniently adjusted via the high voltage. Figure 3(a) shows the intra-cavity pulse train during dumping operation with 1MHz repetition rate. Due to loss of synchronization of the PDG, the degree of dumping was found to be limited to 70%, which could be improved using appropriate electronic circuitry. At this dumping rate we achieve an output power of 10W and a corresponding pulse energy of 10µJ. Switching the oscillator at a rate of 500kHz we get an average power of 7.8W and an energy of 15.6µJ. Higher dumping frequencies are possible in principle but are not supported by the high voltage (HV) driver. At significantly lower dumping frequencies the laser acquired an instability, also observed in earlier work [11

A. Killi, J. Dörring, U. Morgner, M. J. Lederer, J. Frei, and D. Kopf, “High speed electro-optical cavity dumping of mode-locked laser oscillators,” Opt. Express 13(6), 1916–1922 ( 2005). [CrossRef] [PubMed]

]. Figure 3(b) depicts the result of a simulation, using the approach and parameters of section 2 for comparison.

Fig. 3 Internal pulse train with a cavity-dumping frequency of fdump = 1MHz. The dumped output power is 10W and the corresponding pulse energy is 10µJ(a), numerical simulation of same situation (b)

Figure 4 depicts the autocorrelation of the dumped pulses measured at 500kHz. The calculated FWHM using a sech2-fit results in 12.2ps, which translates to a τFWHM of the pulse of 7.9ps.

Fig. 4 Intensity autocorrelation of the pulses, cavity dumped at 500kHz. The pulse width is calculated from the sech2-fit also displayed.

At 1MHz dumping rate we measure slightly longer pulses with an autocorrelation of 13.8ps and a corresponding τFWHM of 8.9ps. The short pulsewidth observed when the oscillator is cavity-dumped is in line with the observations made when the laser is mode-locked with reduced output coupling.

4. Conclusion

In conclusion we have demonstrated a diode-pumped SESAM mode-locked Nd:YVO4 oscillator with cavity dumping. Mode-locked at 9.7MHz and without dumping, the oscillator produced a maximum of 17W with pulsewidths varying between of 26ps and 13ps, depending on the degree of output coupling. In cavity-dumped mode we obtain pulse energies of 10µJ and 15.6µJ at repetition rates of 1MHz and 500kHz respectively with sub-10ps pulsewidths rendering this laser a very useful and compact tool for ultrashort pulse materials processing. To the best of our knowledge, this is the highest power achieved from a diode-pumped SESAM mode-locked Nd:YVO4 oscillator with cavity dumping. Given the appropriate scaling of pump power, mode size and number of laser crystals, substantially higher output power and energy could be generated using this scheme. Similarly, higher dumping rates will soon become feasible with the development of suitable Pockels cell drivers.

Acknowledgements

This work was supported by the Austrian Forschungsförderungsgesellschaft (Basisprogramme project number 822977). We acknowledge fruitful discussions with Anne-Laure Calendron and Oswald Kleber.

References and links

1.

J. Limpert, N. Deguil-Robin, I. Manek-Hönninger, F. Salin, T. Schreiber, A. Liem, E. Röser, H. Zellmer, A. Tünnermann, A. Courjaud, C. Hönninger, and E. Mottay, “High-power picosecond fiber amplifier based on nonlinear spectral compression,” Opt. Lett. 30(7), 714–716 ( 2005). [CrossRef] [PubMed]

2.

B. Luther-Davies, V. Z. Kolev, M. J. Lederer, N. R. Madsen, A. V. Rode, J. Giesekus, K.-M. Du, and M. Duering, “Table-top 50-W laser system for ultra-fast laser ablation,” Appl. Phys., A Mater. Sci. Process. 79(4-6), 1051–1055 ( 2004). [CrossRef]

3.

L. McDonagh, R. Wallenstein, and A. Nebel, “111 W, 110 MHz repetition-rate, passively mode-locked TEM00Nd:YVO4 master oscillator power amplifier pumped at 888 nm,” Opt. Lett. 32(10), 1259–1261 ( 2007). [CrossRef] [PubMed]

4.

C. Gerhard, F. Druon, P. Blandin, M. Hanna, F. Balembois, P. Georges, and F. Falcoz, “Efficient versatile-repetition-rate picosecond source for material processing applications,” Appl. Opt. 47(7), 967–974 ( 2008). [CrossRef] [PubMed]

5.

V. Z. Kolev, M. J. Lederer, B. Luther-Davies, and A. V. Rode, “Passive mode locking of a Nd:YVO4 laser with an extra-long optical resonator,” Opt. Lett. 28(14), 1275–1277 ( 2003). [CrossRef] [PubMed]

6.

D. N. Papadopoulos, S. Forget, M. Delaigue, F. Druon, F. Balembois, and P. Georges, “Passively mode-locked diode-pumped Nd:YVO4 oscillator operating at an ultralow repetition rate,” Opt. Lett. 28(19), 1838–1840 ( 2003). [CrossRef] [PubMed]

7.

J. Neuhaus, D. Bauer, J. Kleinbauer, A. Killi, S. Weiler, D. Sutter, and T. Dekorsy, “Pulse Energies Exceeding 20 µJ Directly from a Subpicosecond Yb:YAG Oscillator by Use of Active Angular Multiplexing,” in Advanced Solid-State Photonics (ASSP) 2009 paper: MC1.

8.

T. Südmeyer, S. V. Marchese, C. R. Baer, S. Hashimoto, A. G. Engqvist, M. Golling, D. J. H. C. Maas, and U. Keller, Femtosecond Thin Disk Lasers with >10 μJ Pulse Energy,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, 2008 Technical Digest (Optical Society of America, Washington, DC, 2008), CFP1.

9.

F. Dausinger, et al ., Femtosecond Technology for Technical and Medical Applications, (Springer, 2004), pp. 17–33.

10.

D. A. Clubley, A. S. Bell, and G. Friel, “High average power Nd:YVO4 based pico-second regenerative amplifier,” Proc. SPIE 6871, 68711D ( 2008). [CrossRef]

11.

A. Killi, J. Dörring, U. Morgner, M. J. Lederer, J. Frei, and D. Kopf, “High speed electro-optical cavity dumping of mode-locked laser oscillators,” Opt. Express 13(6), 1916–1922 ( 2005). [CrossRef] [PubMed]

12.

G. Palmer, M. Emons, M. Siegel, A. Steinmann, M. Schultze, M. J. Lederer, and U. Morgner, “Passively mode-locked and cavity-dumped Yb:KY(WO(4))(2) oscillator with positive dispersion,” Opt. Express 15(24), 16017–16021 ( 2007). [CrossRef] [PubMed]

13.

A.-L. Calendron, K. S. Wentsch, and M. J. Lederer, “High power cw and mode-locked oscillators based on Yb:KYW multi-crystal resonators,” Opt. Express 16(23), 18838–18843 ( 2008). [CrossRef] [PubMed]

14.

W. Köchner, Solid-State Laser Engineering (Springer, 2006), pp. 69–73.

15.

D. Herriott, H. Kogelnik, and R. Kompfner, “Off-Axis Paths in Spherical Mirror Interferometers,” Appl. Opt. 3(4), 523 ( 1964). [CrossRef]

16.

F. X. Kärtner, L. R. Brovelli, D. Kopf, M. Kamp, I. Calasso, and U. Keller, “Control of solid state laser dynamics by semiconductor devices,” Opt. Eng. 34(7), 2024 ( 1995). [CrossRef]

17.

H. A. Haus, “Theory of modelocking with a fast saturable absorber,” J. Appl. Phys. 46(7), 3049–3058 ( 1975). [CrossRef]

OCIS Codes
(140.3480) Lasers and laser optics : Lasers, diode-pumped
(140.3580) Lasers and laser optics : Lasers, solid-state
(140.4050) Lasers and laser optics : Mode-locked lasers
(320.7090) Ultrafast optics : Ultrafast lasers

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: October 2, 2009
Revised Manuscript: November 27, 2009
Manuscript Accepted: November 27, 2009
Published: December 2, 2009

Citation
U. Wegner, J. Meier, and M. J. Lederer, "Compact picosecond mode-locked and cavity-dumped Nd:YVO4 laser," Opt. Express 17, 23098-23103 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-25-23098


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References

  1. J. Limpert, N. Deguil-Robin, I. Manek-Hönninger, F. Salin, T. Schreiber, A. Liem, E. Röser, H. Zellmer, A. Tünnermann, A. Courjaud, C. Hönninger, and E. Mottay, “High-power picosecond fiber amplifier based on nonlinear spectral compression,” Opt. Lett. 30(7), 714–716 (2005). [CrossRef] [PubMed]
  2. B. Luther-Davies, V. Z. Kolev, M. J. Lederer, N. R. Madsen, A. V. Rode, J. Giesekus, K.-M. Du, and M. Duering, “Table-top 50-W laser system for ultra-fast laser ablation,” Appl. Phys., A Mater. Sci. Process. 79(4-6), 1051–1055 (2004). [CrossRef]
  3. L. McDonagh, R. Wallenstein, and A. Nebel, “111 W, 110 MHz repetition-rate, passively mode-locked TEM00Nd:YVO4 master oscillator power amplifier pumped at 888 nm,” Opt. Lett. 32(10), 1259–1261 (2007). [CrossRef] [PubMed]
  4. C. Gerhard, F. Druon, P. Blandin, M. Hanna, F. Balembois, P. Georges, and F. Falcoz, “Efficient versatile-repetition-rate picosecond source for material processing applications,” Appl. Opt. 47(7), 967–974 (2008). [CrossRef] [PubMed]
  5. V. Z. Kolev, M. J. Lederer, B. Luther-Davies, and A. V. Rode, “Passive mode locking of a Nd:YVO4 laser with an extra-long optical resonator,” Opt. Lett. 28(14), 1275–1277 (2003). [CrossRef] [PubMed]
  6. D. N. Papadopoulos, S. Forget, M. Delaigue, F. Druon, F. Balembois, and P. Georges, “Passively mode-locked diode-pumped Nd:YVO4 oscillator operating at an ultralow repetition rate,” Opt. Lett. 28(19), 1838–1840 (2003). [CrossRef] [PubMed]
  7. J. Neuhaus, D. Bauer, J. Kleinbauer, A. Killi, S. Weiler, D. Sutter, and T. Dekorsy, “Pulse Energies Exceeding 20 µJ Directly from a Subpicosecond Yb:YAG Oscillator by Use of Active Angular Multiplexing,” in Advanced Solid-State Photonics (ASSP) 2009 paper: MC1.
  8. T. Südmeyer, S. V. Marchese, C. R. Baer, S. Hashimoto, A. G. Engqvist, M. Golling, D. J. H. C. Maas, and U. Keller, Femtosecond Thin Disk Lasers with >10 μJ Pulse Energy,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, 2008 Technical Digest (Optical Society of America, Washington, DC, 2008), CFP1.
  9. F. Dausinger, et al., Femtosecond Technology for Technical and Medical Applications, (Springer, 2004), pp. 17–33.
  10. D. A. Clubley, A. S. Bell, and G. Friel, “High average power Nd:YVO4 based pico-second regenerative amplifier,” Proc. SPIE 6871, 68711D (2008). [CrossRef]
  11. A. Killi, J. Dörring, U. Morgner, M. J. Lederer, J. Frei, and D. Kopf, “High speed electro-optical cavity dumping of mode-locked laser oscillators,” Opt. Express 13(6), 1916–1922 (2005). [CrossRef] [PubMed]
  12. G. Palmer, M. Emons, M. Siegel, A. Steinmann, M. Schultze, M. J. Lederer, and U. Morgner, “Passively mode-locked and cavity-dumped Yb:KY(WO(4))(2) oscillator with positive dispersion,” Opt. Express 15(24), 16017–16021 (2007). [CrossRef] [PubMed]
  13. A.-L. Calendron, K. S. Wentsch, and M. J. Lederer, “High power cw and mode-locked oscillators based on Yb:KYW multi-crystal resonators,” Opt. Express 16(23), 18838–18843 (2008). [CrossRef] [PubMed]
  14. W. Köchner, Solid-State Laser Engineering (Springer, 2006), pp. 69–73.
  15. D. Herriott, H. Kogelnik, and R. Kompfner, “Off-Axis Paths in Spherical Mirror Interferometers,” Appl. Opt. 3(4), 523 (1964). [CrossRef]
  16. F. X. Kärtner, L. R. Brovelli, D. Kopf, M. Kamp, I. Calasso, and U. Keller, “Control of solid state laser dynamics by semiconductor devices,” Opt. Eng. 34(7), 2024 (1995). [CrossRef]
  17. H. A. Haus, “Theory of modelocking with a fast saturable absorber,” J. Appl. Phys. 46(7), 3049–3058 (1975). [CrossRef]

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