By examining beam patterns, temporal pulse forms, and radio-frequency spectra as functions of resonator configuration and pump power, we found that a passively mode-locked Nd:GdVO4 laser exhibited four main regimes of operation that were single-transverse-mode Q-switched mode locking (QSML), single-transverse-mode continuous-wave mode locking (CWML), multiple-transverse-modes QSML, and multiple-transverse-modes CWML. The effect of multiple transverse modes on CWML was giving rise to amplitude instability in the pulse train. In the regime of multiple-transverse-modes QSML, we observed the phenomenon of spatiotemporal dynamics that spatial patterns vary with the time.
© 2007 Optical Society of America
Short optical pulses can be conveniently generated by the technique of passive mode-locking and are very useful for many applications such as time-resolved spectroscopy, optical clocking and telecommunications. Recently, the semiconductor saturable absorber mirror (SESAM) has been successfully demonstrated as an effective optical element for achieving passive mode-locking in a variety of solid-state lasers [1–5]. The use of a saturable absorber as a passive mode locker in a solid-state laser, however, can introduce a tendency for Q-switched mode-locked operation. While a systematic investigation of the Q-switching stability limits in the passively mode-locked solid-state laser was carried out , the effect of multiple transverse modes (MTMs) on the laser received minor attention. In this paper, we experimentally studied passive mode locking of a diode-pumped Nd:GdVO4 laser with a SESAM in presence of MTMs. We find that the onset of MTMs can lead to instability and a rich variety of spatiotemporal dynamics in the mode-locked laser. For continuous wave (CW) mode locking, MTMs result in amplitude modulation of the pulse train. For MTMs Q-switched mode locking, we find that the Q-switched pulse forms measured from different parts of the laser pattern are dissimilar except off-axis beams  that consist of the axi-symmetric pair of spots. We also observe interpulse period doubling of mode-locked pulses  that have a temporal shift of one cavity round trip time between different spots of the off-axis beam.
2. Experimental setup
The schematic experimental setup is sketched in Fig. 1, where a diode-pumped Nd:GdVO4 laser with a five element (two plane mirrors, an output coupler, and two lenses) cavity is used. The pump source was a 30 W fiber-coupled diode laser system (Coherent, FAP-30W system) with a fiber core diameter of 800 μm and a numerical aperture of 0.22. The pump beam was focused into a gain medium with a spot diameter of 450 μm by an optical imager module which was attached to the fiber and had a magnification of 0.58. The optical imager module was mounted on a translation stage to allow an adjustment of pump beam waist at different position of the gain medium. An a-cut Nd:GdVO4 laser crystal with 0.5 at. % doping concentration and 8-mm length was employed as the gain medium. The Nd:GdVO4 was high transmission coated at 808 nm and high reflection coated at 1064-nm at the surface facing the pumping beam. This surface was also used as an end mirror (M1) of the cavity. The second surface of the crystal was antireflection coated at 1064-nm and was wedged at a 2° angle to avoid an intracavity etalon effect. The laser crystal was wrapped with indium foil and mounted in a water-cooled copper block. The water temperature was maintained at 20°C. A piece of SESAM (BATOP Optoelectronics, Germany) was used simultaneously as a saturable absorber and an end mirror (M2). The SESAM used in our experiment had a center wavelength of 1064 nm, a saturation fluence of ~ 7 mJ/mm2, a relaxation time of 20 ps, and a saturable absorptance of 2.0%, while the nonsaturable loss was less than 0.3%. Two lenses L1 and L2 were both antireflection coated and were separated by d3 ≈ 1100 mm. L1 was a planoconvex lens and the focal length was 125 mm, which had a distance of d1 from M1. L2 was also a plano-convex lens and the focal length was 25 mm, which had a distance of d2 from M2. The overall cavity length is about 1250 mm. Both L1 and L2 were placed on the translation stage to allow the adjustment of d1 and d2, which resulted in the change of the beam spot size on the laser crystal and on the SESAM. For example, if d2 = 26.04 mm and d1 = 160 mm, the beam diameter of the fundamental transverse mode on the SESAM w2 and on the laser crystal w1 are calculated to be 0.021 mm and 0.149 mm, respectively. For the same d2, a change of d1 will lead to a smaller w1 (0.06 mm at d1 = 142 mm and 0.084 mm at d1 = 177 mm) but a larger w2 (0.075 mm) at shorter d1 (142 mm) and smaller w2 (0.008 mm) at longer d1 (177 mm). Small fundamental mode spot sizes on the laser crystal and on the SESAM in our arrangement can facilitate the excitation of MTMs and result in a low threshold for CW mode locked operation. This allows us to examine the MTM effect on a passively mode-locked laser with a relatively low pump power and to prevent the damage of the SESAM in presence of the Q-switched mode locking. The output coupler (OC) was a plane mirror with 2 % transmission, which was placed between two lenses and was near L2. A digital oscilloscope, a radio-frequency (RF) spectrum analyzer, and a CCD camera were employed to observe the pulse waveforms, spectra, and beam patterns.
3. Results and discussion
Prior to investigating the passively mode-locked Nd:GdVO4 laser, the laser resonator was aligned such that the translation stages were moving along the cavity axis. The laser output waveforms and their spectra were then examined in the digital oscilloscope and RF spectrum analyzer as d1 and d2 were changed. By adjusting d1 and d2, we were able to observe CW mode locking when the pump power exceeded 1.1 W. The repetition rate of mode-locked pulses was found to be about 120 MHz, which consisted with the cavity round trip frequency. The pulse width measured by an autocorrelator was around 12 ps. We have measured the laser output power as a function of the pump power. This is shown in Fig. 2. From Fig. 2, we can see that as the pump power increases above threshold the laser begins operating at Q-switched mode-locked state. A typical waveform and RF spectrum are shown in Fig. 3. Where the waveform is high frequency mode-locked pulses with a low frequency Q-switched pulse envelop and the spectrum shows the mode-locked frequency comb with a Q-switched pulse related side band. When the pump power exceeded 1.1 W, the laser turned to CW mode locking as shown in Fig. 4. Now we can see the pulse train without amplitude modulation and the frequency comb without side band. When the pump power is further increased, the laser output becomes unstable and exhibits amplitude modulation in the pulse train. The waveform and RF spectrum are shown in Fig. 5. Other than Q-switched mode locking, we can see additional frequency components in relative to transverse modes for MTMs CW mode locking. An examination of the waveform and the RF spectrum show that the instability of mode-locked pulses is always accompanied with MTMs and can be eliminated by inserting an appropriate aperture into the cavity.
We have also examined the laser output as a function of d1. This is shown in Fig. 6. There are four regimes in which the laser exhibits different behaviors. These are single transverse mode (STM) Q-switched mode locking (i, vi), STM CW mode locking (ii), MTM CW mode locking (iii, v), and MTM Q-switched mode locking (iv, vii). The STM Q-switched mode locking and CW mode locking behaved in a manner like that theoretically described in reference . However, the MTM Q-switched mode locking (typical waveform and RF spectrum are shown in Fig. 7) and CW mode locking (described above) exhibited fairly different phenomena and were worth further investigation. By using a CCD camera to observe the laser output patterns in different regions (Fig. 8), we found that in region iv the laser beam was splitting into multiple spots. A study of laser waveforms at different spots showed that these spots had different Q-switched pulse forms (as shown in Fig. 9) except those off-axis spots that were symmetrical with respect to optical axis. This result revealed that the laser was operating at the MTMs rather than at higher-order transverse mode and had time-varying spatial patterns. We also found that mode-locked pulses in this region had a period of about 16.67 ns corresponding to the double of the cavity round trip time. Moreover, the observation of mode-locked pulses within the same Q-switched pulse envelop illustrated that the pulse train had a temporal shift of one cavity round trip time and alternately emerged at different spots of the off-axis beam (Fig. 10). This can be explained by interpulse period doubling of the off-axis beam [7, 8] or in terms of total mode locking [9, 10], i.e., simultaneous transverse mode locking and longitudinal mode locking. It is worth mentioning that by observing the center spot of multiple spots pattern, we found its mode-locked pulse train and RF spectrum also exhibiting period doubling. The period doubled (half cavity round trip frequency) spectral power increases when a half beam spot to be detected is blocked. This result reveals that the center spot is also comprised of off-axis beams and exhibits interpulse period doubling.
In conclusion, we have experimentally investigated effects of MTMs in a passively mode locked Nd:GdVO4 laser with the SESAM. We found that for CW mode locking, MTMs would lead to amplitude instability of mode-locked pulses. For Q-switched mode locking, spatiotemporal dynamics and period doubling were observed along with the occurrence of MTMs. Our investigation shows that the MTM Q-switched mode-locked Nd:GdVO4 laser is a suitable system for studying spatiotemporal dynamic phenomena, whereas, to obtain a stable train of mode-locked pulses, the MTM operation should be avoided. The latter situation can be achieved by selecting a resonator configuration such that its fundamental mode has a well overlap with the pump beam in the laser crystal or inserting an appropriate aperture into cavity to suppress higher order transverse modes.
The authors thank the National Science Council of the Republic of China for financially supporting this research under Contract No. NSC-93-2112-M-029-002.
References and links
1. U. Keller, D. A. B. Miller, G. D. Boyd, T. H. Chiu, J. F. Ferguson, and M. T. Asom, “Solid-state low-loss intracavity saturable absorber for Nd:YLF lasers : an antiresonant semiconductor Fabry-Perot saturable absorber,” Opt. Lett. 17, 505–507 (1992). [CrossRef] [PubMed]
2. K. J. Weingarten, U. Keller, T. H. Chiu, and J. F. Ferguson, “Passively mode-locked diode-pumped solid-state laser using an antiresonant Fabry-Perot saturable absorber,” Opt. Lett. 18, 640–642 (1993). [CrossRef] [PubMed]
3. R. Fluck, G. Zhang, U. Keller, K. J. Weingarten, and M. Moser, “Diode-pumped passively mode-locked 1.3μm Nd: YVO4 and Nd:YLF lasers using semiconductor saturable absorbers,” Opt. Lett. 21, 1378–1380 (1996). [CrossRef] [PubMed]
5. B. Zhang, G. Li, M. Chen, Z. Zhang, and Y. Wang, “Passive mode locking of a diode-end-pumped Nd:GdVO4 laser with a semiconductor saturable absorber mirror,” Opt. Lett. 28, 1829–1831 (2003). [CrossRef] [PubMed]
6. C. Hönninger, R. Paschotta, F. Morier-Genoud, M. Moser, and U. Keller, “Q-switching stability limits of continuous-wave passive mode locking,” J. Opt. Soc. Am. B 16, 46–56 (1999) [CrossRef]
7. H.-H. Wu, “Formation of off-axis beams in an axially pumped solid-state laser,” Opt. Express 12, 3459–3464 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-15-3459. [CrossRef] [PubMed]
8. H.-H. Wu, “Interpulse period doubling in a self-mode-locked Ti:sapphire laser,” J. Opt. Soc. Am. B 18, 1597–11600 (2001) [CrossRef]
9. D. H. Auston, “Transverse mode locking,” IEEE J. Quantum Electron. 4, 420–422 (1968). [CrossRef]
10. P. L. Smith, “Mode-locking of lasers,” Proc. IEEE 58, 1342–1357 (1968). [CrossRef]