We report on the generation of highly stable active continuous mode-locked pulses in diode pumped Nd:YVO4 with an adjustable pulse duration between 34 ps and 1 ns. With this laser an average output power of up to 7.3 W with an excellent stability and beam quality with a M2-value of < 1.1 is obtained. For all pulse durations the pulses were within a factor of 1.15 above the Fourier limit. Due to these characteristics the presented system is an attractive oscillator for OPCPA concepts.
© 2009 Optical Society of America
Today the generation of mode-locked pulses with pulse durations of a few 10 picoseconds down to a few femtoseconds is well developed [1, 2] and widely used in science and technology. Similarly Q-switched lasers, which provide pulses with durations typically longer than 5 ns, are well established. However a source which provide pulses with durations of some hundred ps is hardly found today. On one hand Q-switching is too slow to provide pulse durations well below 1 ns and on the other hand it is difficult to maintain stable mode-locking with pulse durations significantly longer than 100 ps.
Nevertheless pulses with durations between 100 ps and 1 ns are interesting for numerous applications, since they allow for a moderate peak power and simultaneously a high pulse energy. Hence nonlinear effects such as self phase modulation (SPM) or a destruction of the components in the setup can be avoided even for a high average output power . This is in particular interesting for chirped pulse amplification (CPA) of fs-pulses in an optical parametric amplifier (OPA), for instance [4, 5]. OPAs are attractive amplifiers for CPA, due to the extreme broad amplification bandwidth, the high gain as well as the excellent output-beam quality and intensity contrast ratio [6, 7]. In order to achieve an optimal overlap between the pump pulse and the stretched fs-pulse the pulse durations of both pulses have to be very similar. The shortest possible pulse duration of the stretched pulses is often limited by the damage threshold of the used components, because of nonlinear effects, such as small-scale self-focusing which leads to beam filamentation , and is typically in the order of some hundred picoseconds. Moreover pump and signal pulses have to be stable and precisely synchronized. Otherwise the result is a poor conversion efficiency due to a deficient temporal overlap and a fluctuation in the OPA gain and bandwidth. Further requirements for this application are a high pump pulse energy and an excellent beam quality of the pump light to ensure an efficient amplification in the OPA.
Ultrashort pulse lasers with pulse durations from some 100 ps up to 1 ns were demonstrated using different principles. Among others regenerative amplifiers with frequency selective elements  or stacked pulses [10, 11] were used. Furthermore different lamp-pumped oscillators were reported which utilized frequency selective elements for long pulse durations [12–16]. These oscillators utilized nearly exclusively Q-switch mode-locking to reach directly high pulse energies, but the used flash lamps limited the repetition rate to a few Q-switched pulse trains per second. A continuous diode pumped solid state laser in contrast is able to produce a infinite pulse train with constant pulse amplitude and therefore makes a much higher repetition rate possible. Furthermore a diode pumped solid state laser is more efficient, compact and reliable compared to lamp pumped oscillators. An attractive concept for this purpose is a frequency doubled diode pumped and mode-locked solid-state laser based on Nd:YVO4. This laser concept is proven to provide stable pulses with pulse durations around 10 ps and an excellent beam quality [17–19]. To obtain the required pulse energy, regenerative amplifier systems are commonly used. However the pulse durations obtained from conventional Nd:YVO4 oscillators are to short for high power CPA. A suitable way to increase the pulse duration is gain narrowing by a resonator internal etalon, for instance. But this may result in perturbations of the mode-locking process which lead to severe instabilities. The major task which has to be solved in order to develop a suitable pump source for CPA is to develop an oscillator which provides simultaneously stable mode-locking and long pulse durations up to the ns range.
During the last years it has turned out that passive mode-locking using a saturable absorber provides very stable and reliable mode-locking of Nd:YVO4 oscillators. But the stability of this method strongly depends on the fluence on the saturable absorber and hence on the pulse energy, duration and beam diameter. Thus a changed pulse duration always require a new resonator design with other beam diameters or a different saturable absorber with adjusted properties for stable mode-locking. With a saturable absorber setup we achieved from 14 ps up to 120 ps with one type of resonator and absorber but a continuous tuning or a broader tuning range was not possible. Neither the achieved pulse duration nor the achieved tuning range of the pulse duration is sufficient for the planed application. Furthermore it is difficult to synchronize the stretched fs-pulse and the pump pulse generated by passive mode-locking, which is required for efficient CPA.
Thus we turned back to active mode-locking, which solves many of these problems. In general an active mode-locking technique provides longer pulses compared to passive mode-locking, which is an advantage in this case. Moreover the active mode-lock process is independent of the fluence on nonlinear components. Therefore stable mode-locking is achieved on a wide range of intracavity losses. This allows for a wide variation of the pulse durations by changing the intracavity etalons. Furthermore the possibility of a external variation of the modulation permits a continuous tuning of pulse durations. Finally the typical drawback of instability in actively mode-locked lasers can be avoided with long pulse durations.
Thus we report on our experimental results on an actively mode-locked Nd:YVO4 oscillator, which provides stable mode-locked pulses with pulse durations adjustable between 34 ps and well above 1 ns.
2. Experimental setup
Figure 1 shows the experimental setup of the laser oscillator, which consists of a six mirror cavity in double z configuration, the Nd:YVO4 crystal and an acousto-optic modulator (AOM). The cavity is formed by 3 plane mirrors (the output coupler M1, M4 and M6) and three curved mirrors M2 (R=500 mm), M3 and M5 (R=400 mm). In this setup, the curvature and the distances between mirrors have been optimized with respect to stability and mode matching of the laser and pump beam. The Nd:YVO4 crystal is pumped through mirror M4 by a fiber coupled pump diode, which provides 15 W at 808 nm from a fiber with a diameter of 800 μm. In continuous-wave (cw) operation the laser delivers an output power of 7.6 W into a diffraction limited beam (M2 < 1.1) for an output coupler with a transmission of 9.5 %. Active mode-locking of this system has been obtained by amplitude modulation (AM) with an AOM. The laser repetition rate was 108 MHz, corresponding to the AOM frequency of 54 MHz.
Active mode-locked systems are typically very sensitive to detuning of the mode-lock frequency and the cavity round trip time. Therefore these parameter are mostly actively synchronized in order to stabilize the systems. The stability of externally driven mode-locking with respect to detuning depends on the phase dispersion ∂Φ/∂ν between phase shift and round trip frequency. In the past mostly the shortest possible pulse duration was interesting, which is in the order of some 10 ps for AOM mode-locked lasers. In our case the desired pulse duration is significant longer. Due to 
a 10 times longer pulse durations result into a reduction of the sensibility to detuning by a factor of 100. Therefore it was not necessary to actively stabilize the system during our experiments.
This setup without a resonator internal etalon provided stable active mode-locking with an average output power of 6.4 W and good beam quality with an M2 factor of less than 1.15. The pulses emitted in active mode-locked operation were characterized by an autocorrelator and a scanning Fabry-Perot interferometer (SFPI). The measured autocorrelation and spectrum were well fitted by a Gaussian function, as assumed in the theory of active mode-locking. From this fit a pulse duration of 33.7 ps and a spectral full width at half maximum (FWHM) of 15.0 GHz were obtained. This results into a time-bandwidth product of 0.506, which is 1.15 times above the Fourier limit of 0.441.
In order to extend the pulse duration of these pulses obtained from the oscillator, the overall gain bandwidth in the cavity has to be artificially reduced. The pulse duration, which can be expected from an active frequency modulation (FM) mode-locked oscillator with additional frequency selective elements within the cavity, can be calculated for pulse durations much shorter than the modulation period tm . A very similar relation can be obtained for AM mode-locking. Compared to the result for FM mode-locking the pulse duration is shorter by a factor of √2:
with δ the losses caused by the AOM for a cw-beam.
For a systematic reduction of the bandwidth we used different etalons between the curved mirror M5 and the AOM. The thickness t, the reflectivity R per side, the FWHM in double pass of the etalon transmission ∆νFWHM,2  and free spectral range (FSR) ∆νFSR are summarized in Table 1 for the different etalons, respectively. Of particular interest is ∆νFWHM,2, since this parameter determines the effective gain bandwidth within the cavity and thus the shortest possible pulse duration. However the FSR has to be sufficiently large, to ensure that only in one transmission maximum of the etalon the laser reaches the threshold. Otherwise severe instabilities in the laser process are expected. From a conservative estimation we expect that the FSR of the etalon has to be at least as wide as amplification bandwidth of the laser. In our experiment we found that an etalon FSR of 35 GHz is sufficient to suppress radiation in adjacent etalon transmission maxima for a laser based on Nd:YVO4 with a gain bandwidth of 210 GHz .
Figure 2(a) shows the calculated transmission of etalon no. 8 and Fig. 2(b) those of etalon no. 5. Number 8 provides a ∆νFWHM,2 of 5.86 GHz which allows for sufficient narrowing of the gain bandwidth. However due to the small FSR of 16.3 GHz a lot of close adjacent transmission maxima are located within the gain bandwidth of Nd:YVO4. In contrast to etalon no. 8 only one transmission maxima of etalon no. 5 is within the gain bandwidth, but ∆νFWHM,2 is comparable to the gain bandwidth of Nd:YVO4. Hence no significant reduction in gain bandwidth and therefore pulse elongation can be achieved. So neither etalon no. 5 nor no. 8 are sufficient for the experiments. To assume ideal etalons a narrow transmission bandwidth comparable with etalon no. 8 together with a large FSR like etalon no. 5 and a transmittance of 1 can be obtained with one single etalon. But a real etalon lacks perfect plane-parallel surfaces which cause a lower limit for the transmission bandwidth and reduce the transmittance significantly for reflectivities near unity. Therefore often etalons with different properties are combined .
In order to better understand the interaction of the transmission of both etalons and the gain of Nd:YVO4 the combined transmission of the two etalons in the cavity and the transmission of both etalons together with the gain of the laser medium are illustrated in Figs. 2(c) and 2(d), respectively. The dashed curve in (d) represents the gain bandwidth of Nd:YVO4, which is supposed to be a Lorentzian function and normalized to one. The solid curve gives the effective gain with etalon no. 5 and no. 8 in the cavity for the case where the maxima of the etalon transmission and the maxima of the gain bandwidth are at the same frequency. The coincidence between all these maxima promises the lowest losses in the laser and therefore the highest output power.
To adjust the position of the etalon transmission to the center of the gain bandwidth the optical path length in the etalon can be adjusted by tilting the etalons. Furthermore the tilting of the etalon avoids the operation in a coupled multi-resonator configuration and hence instabilities in the mode-locking process. But tilting the etalons results in walk off losses, which increases with the tilt angle, etalon thickness and reflectivity . For this reason the tilt angle should be as small as possible. For relatively slim etalons with a FSR larger or in the order of the gain bandwidth the optimal tilt angle is given by the coincidence of etalon transmission and maximum laser gain. For thick etalons with a FSR much narrower than the gain bandwidth, the losses, because of a little off-center laser wavelength operation, can be neglected. In this case the tilt angle has to be chosen in order to to avoid coupled multi-resonator configurations and to minimize walk off losses.
3. Experimental results
3.1. Temporal and spectral behavior
The etalon transmission bandwidth was systematically varied between 3.70 GHz and 508 GHz by etalon exchange. Due to our results for a sufficient suppression of radiation in adjacent etalon transmission maxima only etalon no. 8 and no. 9, which have a ∆νFSR < 35 GHz, were used in combination with an other etalon (no. 5). The ∆νFWHM,2 of those etalon combinations differ of less than 1% compared to the ∆νFWHM,2 without etalon no. 5. For this reason the influence of etalon no. 5 to ∆νFWHM,2 can be neglected.
For each transmission bandwidth the pulse duration has been measured with a fast photo-diode and a sampling oscilloscope. The measured response time of this setup was 19.3 ps. The spectrum has been measured with different SFPI with an adequate FSR between 2 GHz and 75 GHz for the particular pulse duration. The results of these measurements of the temporal and spectral intensity distributions are shown exemplary for etalon no. 5 together with no. 8 in Figs. 3(a) and 3(b), respectively. As expected the temporal intensity distribution and the envelope of the spectral distribution are well fitted by a Gaussian function. The spectrum shows equidistant peaks with a separation determined by the repetition rate 108 MHz. For an infinite undisturbed pulse train the width of these peaks is theoretically infinitesimally small. However in the measurement the width is limited by the resolution of the SFPI. Assuming a constant repetition rate the position of the maxima is given by the carrier envelope offset frequency of the pulse train .
Figure 4 shows the pulse duration 4(a) and the time-bandwidth product 4(b) as function of ∆νFWHM,2 for a high and a low value of δ respectively. From Fig. 4(a) it is seen that a larger modulation result in shorter pulses due to the higher losses in the AOM. The experimental data corresponds very well with the solid curves calculated from Eq. 2 for δ = 39% and δ = 11%, respectively. This behavior provides an easy method for a fine tuning of the pulse duration in the order of 10–30%, but with the drawback of a slightly lower stability at low modulations. However large tuning of the pulse duration has to be done by changing the etalons. Finally it is obvious from Fig. 4(a) that it is possible to tune the laser with different etalons and changing of the modulation from pulse durations of 33.7 ps to well above 1 ns.
Figure 4(b) confirms the high temporal quality of the pulses. It is seen that the time-bandwidth product is less than 11 % above the Fourier-limit for all pulses. These values are even lower compared to the case without etalons. The lowest values are obtained for an etalon transmission bandwidth between 5 and 100 GHz and hence pulse durations between 150 ps and 700 ps.
3.2. Output power
Figure 4(c) shows the obtained output power as function of the effective etalon transmission bandwidth ∆νFWHM,2. For narrow bandwidths the output power strongly decreases, due to high walk-off losses in the thick etalons. Some of the other etalons can be applied with nearly no output power reduction compared to the laser output power of 6.4 W without etalons. As expected the output power for a low modulation depth is higher, due to smaller overall losses in the AOM compared to the high modulation depth. Even with the highest pulse durations of 1040 ps the output power achieved nearly half of the output power without pulse elongation. The M2 factor for all measurements was lower 1.1 comparable with the mode-locked laser without etalons.
Already the visibility of the narrow equidistant maxima Fig. 3(b) is a hint for a stable mode-locked operation during the sweep time of the SFPI of about 100 ms. In addition the radio frequency (RF) spectrum in Fig. 5 shows a suppression of side bands exceeding 60 dB which also supports the assumption of stable mode-locked operation.
In order to confirm the long-term stability a measurement with a GaAsP photo diode, which is only sensitive to 2-photon processes at 1064 nm has been performed. The measurement with a pulse duration of 350 ps, for instance, in a time interval of three hours showed a standard deviation of 0.8 % and a peak-to-valley less than 7 %. These values illustrate a high long term stability in output power and pulse duration comparable with typical semiconductor saturable absorber mirror passively mode-locked lasers.
Thus it is instructive to compare the stability of the actively mode-locked system with a pulse duration elongated to several hundred picoseconds and without pulse elongation (Fig. 6). Again the measurement was done with a GaAsP photo diode. The cavity detuning was achieved by mounting M6 on a piezo and apply a delta voltage to the piezo. In the measurement for 34 ps the mode-locking is only stable in a window of 6 μm below the top on the rising edge of the signal. Outside this window the measured values are fluctuating, indicated by the light gray envelope, and the mode-locking is instable. Whereas the system with 215 ps and 340 ps shows over the hole detuning a stable mode-locking. The declension in the signal for 215 ps results from a loss of output power and a slightly increasing of pulse duration, which is not observed for a pulse duration of 340 ps.
To characterize further the stability against cavity length variations for long pulse durations, mirror M6 has been moved with a linear stage. For each position the pulse duration as well as the output power was measured. Figure 7 shows the experimental results for a cavity length detuning with an initial pulse duration of 350 ps. The experiments showed stable mode-locked operation over the whole detuning range. The pulse duration is nearly constant for a cavity length detuning over 1 mm in the vicinity of the optimum cavity length in respect to the output power. In this detuning range the output power drops less then 20 % compared to the optimum cavity length.
Compared to a stability range of 6 μm in the case of ps pulses without pulse elongation this is an improvement by more than two orders of magnitude, as expected from Eq. 1.
In conclusion we have demonstrated an actively mode-locked picosecond Nd:YVO4 oscillator, with adjustable pulse durations between 34 ps and 1 ns. This is to the best of our knowledge the first diode pumped oscillator, which simultaneously provides stable continuously mode-locked pulses and adjustable pulse durations of some hundred picoseconds. The beam quality as well as temporal and spectral quality are very good.
Due to the demonstrated properties this system is an excellent base for an oscillator-amplifier-system designed for optical parametric chirped pulse amplification of fs-pulses. The development of a suitable amplifier is currently in progress.
We grateful acknowledge support by the German ministry of education and research (BMBF) under contract number 13N9030.
References and links
1. G. P. A. Malcolm and A. I. Ferguson, “Mode-locking of diode laser-pumped solid-state lasers,” Opt. Quantum Electron. 24, 705–717 (1992). [CrossRef]
3. A. Dubietis, G. Jonušauskas, and A. Piskarskas, “Powerful femtosecond pulse generation by chirped and stretched pulse parametric amplification in BBO crystal,” Opt. Commun. 88, 437–440 (1992). [CrossRef]
4. I. N. Ross, J. L. Collier, P. Matousek, C. N. Danson, D. Neely, R. M. Allott, D. A. Pepler, C. Hernandez-Gomez, and K. Osvay, “Generation of terawatt pulses by use of optical parametric chirped pulse amplification,” Appl. Opt. 39, 2422–2427 (2000). [CrossRef]
5. X. Yang, Z. Xu, Y. Leng, H. Lu, L. Lin, Z. Zhang, R. Li, W. Zhang, D. Yin, and B. Tang, “Multiterawatt laser system based on optical parametric chirped pulse amplification,” Opt. Lett. 27, 1135–1137 (2004). [CrossRef]
6. H. Yoshida, E. Ishii, R. Kodama, H. Fujita, Y. Kitagawa, Y. Izawa, and T. Yamanaka, “High-power and high-contrast optical parametric chirped pulse amplification in β-BaB2O4 crystal,” Opt. Lett. 28, 257–259 (2003). [CrossRef] [PubMed]
7. R. Butkus, R. Danielius, A. Dubietis, A. Piskarskas, and A. Stabinis, “Progress in chirped pulse optical parametric amplifiers,” Appl. Phys. B 79, 693–700 (2004). [CrossRef]
8. G. Mourou, “The ultrahigh-peak-power laser: present and future,” Appl. Phys. B 65, 205–211 (1997). [CrossRef]
9. T. A. Hall and W. K. Hamundi, “Passive laser pulse synchronisation technique using a regenerative amplifier,” J. Phys. B 23, 599–609 (1990). [CrossRef]
11. Y. Leng, L. Lin, X. Yang, H. Lu, Z. Zhang, and Z. Xu, “Regenerative amplifier with continuously variable pulse duration used in an optical parametric chirped-pulse amplification laser system for synchronous pumping,” Opt. Eng. 42, 862–866 (2003). [CrossRef]
12. D. J. Kuizenga and A. E. Siegman, “FM and AM mode locking of the homogeneous laser-Part II: Experimental results in a Nd:YAG laser with internal FM modulation,” IEEE J. Quantum Electron. 6, 709–715 (1970). [CrossRef]
13. J. M. McMahon and J. L. Emmett, “Development of high power Nd:glass laser systems,” in Record of the 11th Symposium on Electron, Ion and Laser Beam Technology, R. F. M. Thornley, ed. (San Francisco Press, Inc., San Francisco, Calif., 1971), pp. 269–278.
14. D. J. Kuizenga, “Short-pulse oscillator development for the Nd:glass laser-fusion systems,” IEEE J. Quantum Electron. 17, 1694–1708 (1981). [CrossRef]
15. M. S. White, A. D. Damerell, E. M. Hodgson, I. N. Ross, R. W. Wyatt, and C. L. Ireland, “An ultra low jitter synchronized laser-pulse generator,” Opt. Commun. 43, 53–58 (1982). [CrossRef]
16. A. K. Sharma, R. A. Joshi, R. K. Patidar, P. A. Naik, and P. D. Gupta, “A simple highly stable and temporally synchronizable Nd:glass laser oscillator delivering laser pulses of variable pulse duration from sub-nanosecond to few nanoseconds,” Opt. Commun. 272, 455–460 (2007). [CrossRef]
17. L. Krainer, R. Paschotta, S. Lecomte, M. Moser, K. J. Weingarten, and U. Keller, “Compact Nd:YVO4 lasers with pulse repetition rates up to 160 GHz,” IEEE J. Quantum Electron. 38, 1331–1338 (2002). [CrossRef]
19. J. Kleinbauer, R. Knappe, and R. Wallenstein, “A powerful diode-pumped laser source for micro-machining with ps pulses in the infrared, the visible and the ultraviolet,” Appl. Phys. B 80, 315–320 (2005). [CrossRef]
20. L. Turi and F. Krausz, “Amplitude modulation mode locking of lasers by regenerative feedback,” Appl. Phys. Lett. 58, 810–812 (1991). [CrossRef]
21. D. J. Kuizenga and A. E. Siegman, “FM and AM mode locking of the homogeneous laser-Part I: Theory,” IEEE J. Quantum Electron. 6, 694–708 (1970). [CrossRef]
22. C. L. Fincher and R. A. Fields, “Test Report on 1% Nd:YVO4,” ITI Electro-Optics Corporation (1993).
23. D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-Envelope Phase Control of Femtosecond Mode-Locked Lasers and Direct Optical Frequency Synthesis,” Science 288, 635–639 (2000). [CrossRef] [PubMed]
24. G. Hernandez, Fabry-Perot Interferometers (Cambridge University Press, Cambridge, 1986).
25. W. R. Leeb, “Losses introduced by tilting intracavity etalons,” Appl. Phys. A 6, 267–272 (1975).