Spontaneous subpicosecond pulse formation
with pulse repetition rate of 80 GHz in a
diode-pumped Nd:SrGdGa
3
O
7
disordered crystal laser
Y. F. Chen,1,* H. C. Liang,1J. C. Tung,1K. W. Su,1Y. Y. Zhang,2H. J. Zhang,2H. H. Yu,2and J. Y. Wang2 1
Department of Electrophysics, National Chiao Tung University, Hsinchu 30010, Taiwan
2State Key Laboratory of Crystal Materials and Institute of Crystal Materials, Shandong University, Jinan 250100, China
*Corresponding author: [email protected]
Received November 2, 2011; revised December 20, 2011; accepted December 20, 2011; posted December 20, 2011 (Doc. ID 157449); published February 6, 2012
We explore the operation of spontaneous mode locking in a diode-pumped Nd:SrGdGa3O7disordered crystal laser.
The first- and second-order autocorrelations are simultaneously performed to evaluate the temporal characteristics. An 80 GHz pulse train with a pulse duration as short as 616 fs is observed. The maximum output power is 415 mW at
a pump power of 6.1 W. © 2012 Optical Society of America
OCIS Codes: 140.3380, 140.4050, 140.6810.
Since disordered laser crystals have the properties of broad absorption and emission spectra and high thermal conductivity, they have recently attracted a great deal of attention for achieving powerful ultrashort pulse lasers.
The Nd:ABC3O7 crystals are a class of disordered laser
gain media [1–3], where A Ca, Sr, Ba; B La, Gd;
and C Ga, Al. In addition to the Nd:SrLaGa3O7 and
Nd:BaLaGa3O7 crystals, the Nd:SrGdGa3O7 (Nd:SGGM)
is another kind of Nd:ABC3O7 crystal [4–6]. In the Nd:
SGGM crystal, Nd3 ions substitute for Sr2 and Gd3
ions that are distributed randomly in a 1∶1 ratio [7–9],
producing a disordered structure and large inhomoge-neous spectral broadening. This feature is not only ben-eficial to diode pumping but also for the production of ultrashort pulses.
For ideal mode locking, all modes of the whole spec-trum of a multimode laser have equally separated frequency differences and time-independent constant amplitudes to lead to a train of bandwidth-limited short
pulses [10]. The occurrence of spontaneous mode
lock-ing is an intrigulock-ing phenomenon observed in a laser sys-tem without any saturable absorber. This phenomenon has been observed on different types of lasers, including He–Ne [11], ruby [12], Nd-doped crystal [13], argon ion [14], fiber [15], and semiconductor [16–18] laser systems. Realistically, the spontaneous mode locking belongs to a nonideally mode-locked operation. The time dependence of a multimode laser at a point in the cavity can be given by Et Re e−iωc−NΩ∕2tX N n1 ante−inΩtφnt ; (1)
whereωcis the central frequency,Ω is the frequency
spa-cing of adjacent longitudinal modes, N is the total
num-ber of lasing modes, and ant and φnt are the real
amplitude and phase of the nth mode. Weber and
Dändli-ker [19] explored the time-dependent output intensity of
a nonideally mode-locked laser by considering the influ-ence of statistical phase variations in the modes of a mul-timode laser. They found that, as long as the phase variations is not completely random, the output intensity
of a multimode laser can maintain a train with the pulse duration the same as that of ideally mode-locked pulses.
Figure1shows three numerical examples of the
instan-taneous intensity for 10 modes with equal amplitude and
with the phases randomly distributed in the interval (−φ,
φ), where the results include φ 0, φ π∕6, and φ π∕3. It can be seen that the influence of the phase variations in a multimode laser is only to introduce a fluc-tuating background to the ideally mode-locked inten-sity. The phase variations in diode-pumped lasers are expected to be considerably less than those in lamp pumped counterparts because the thermal effect is signif-icantly reduced.
In this Letter we explore the performance of the spon-taneous mode locking in a diode-pumped Nd:SGGM dis-ordered crystal laser. We control the separation between the gain medium and the end mirror to reach the tenth-order harmonic mode-locked operation with repetition rate up to 80 GHz. Under the absorbed pump power of 6.1 W, an average output power of 415 mW was obtained, corresponding to optical efficiency of 6.8% and slope ef-ficiency of 8.1%. The pulse width was measured to be 616 fs at the output power of 400 mW. This pulse duration
I (t ) I (t ) I (t ) 0.0 0.5 1.0 0.0 0.5 1.0 t / T -4 -3 -2 -1 0 1 2 3 4 0.0 0.5 1.0 (a) (b) (c) id e a l M L n o n -id e a l M L w ith n o n -id e a l M L w ith
Fig. 1. (Color online) Numerical examples with Eq. (1) for 10 modes with equal amplitude and with the phases randomly dis-tributed in the interval (−φ, φ), where (a) φ 0, (b) φ π∕6, and (c)φ π∕3.
February 15, 2012 / Vol. 37, No. 4 / OPTICS LETTERS 461
is the shortest ever obtained in spontaneous mode-locked Nd-doped crystal lasers so far as we know.
Figure2(a)depicts the cavity configuration, which is a
linear concave–plano resonator. The gain medium is
c-cut 1.3 at. % Nd:SGGM crystal with dimensions of 3 mm × 3 mm × 6 mm. The level lifetime of the excited
state was measured to be approximately 284μs [9]. Both
end surfaces of the laser crystal were polished with no
coating. Figure 2(b) shows the fluorescence spectrum
for the 4F3∕2→4I11∕2 at room temperature.
Lumines-cence bandwidth can be seen to be nearly 24 nm. The laser crystal was wrapped with indium foil and mounted in a water-cooled copper holder. The water temperature was maintained at around 20 °C to ensure stable laser output. The input mirror was a 50 mm radius-of-curva-ture concave mirror with antireflection coating at 808 nm on the entrance face and with high-reflectance coating at 1060 nm (>99.8%) and high-transmittance coating at 808 nm on the second surface. A flat wedged output coupler with a reflection coefficient of 97.5% at 1060 nm was used in the experiment. The pump source was a 7 W 808 nm fiber-coupled laser diode with core
diameter of 200μm and NA of 0.20. A focusing lens with
25 mm focal length and 87% coupling efficiency was used to reimage the pump beam into the laser crystal. The
average pump diameter was approximately 200 μm.
The optical cavity length was set to be approximately L 19 mm, corresponding to a free spectral range of
8 GHz. Becker et al. [20] found that the etalon effect
formed by the separation between the laser crystal and the input mirror, d, could play an important role in modulating the optical spectrum of a mode-locked la-ser. In the present experiment, we found that varying the separable d in the range of 1–5 mm could lead to harmo-nic mode locking with different orders and the frequency was usually between 80 and 180 GHz. With the etalon effect, the separation d was experimentally found to be related to the expression L∕N, where the integer N corresponded to the Nth harmonic mode locking. We also observed that the separation d 1.9 mm favored
the tenth-order harmonic mode locking. Figure2(c)
de-picts the experimental result for the average output power versus incident pump power. The average output power was 415 mW at an incident pump power of 6.1 W.
The temporal output was systematically analyzed by taking first- and second-order autocorrelations. Note that no peaks were observed in the real-time trace and rf spectrum up to 10 GHz bandwidth limit of the instrument. Perhaps this is why the phenomenon of self-mode-locking in several tens of gigahertz has not been discov-ered earlier. No signs of Q-switched mode locking were observed in either autocorrelation or the rf spectrum. The lack of peaks in the rf spectrum and the peak spacing in the optical spectrum provide excellent evidence for harmonic mode locking. The first-order autocorrelation trace was measured using a Michelson interferometer (Advantest, Q8347). The autocorrelation interferometer is also capable of performing optical spectral analysis by Fourier transforming the first-order field autocorrela-tion. In comparison with the conventional second-order autocorrelation measurement, the high sensitivity and
dynamic range of the Michelson interferometer [21]
en-able us to assess the optimal cavity adjustment for
spon-taneous mode-locked operation. Figure 3(a)shows the
experimental first-order autocorrelation trace under the tuning condition of obtaining maximum power output. The pulse separation can be seen to be approximately 12.5 ps. It corresponds to a repetition rate of 80 GHz, i.e., the tenth-order harmonic mode locking. The tempor-al amplitude tempor-also displays a modulation frequency equtempor-al to second-order harmonic frequency. This modulation amplitude is mainly due to the supermode competition activated by the longitudinal spatial hole burning effects
[20,22]. Two sets of interleaved longitudinal modes can
be clearly observed from the optical spectrum shown
in Fig. 3(b). We experimentally found that the
tenth-order harmonic mode locking could be considerably im-proved by finely tuning the crystal/mirror separation d.
Figures4(a)and(b)show, respectively, the experimental
first-order autocorrelation trace and optical spectrum un-der the optimum tenth-orun-der harmonic mode locking at
Wavelength (nm) Fl u o rescence spectrum (arb. unit) 0 30 60 90 120 150 180 Pump power (W)
1000 1030 1060 1090 1120 1150 Average output power (mW) 00 1 2 3 4 5 6 7
100 200 300 400 500 (b) (c) (a) Focusing lens Laser diode Nd:SGGM Output coupler d
Fig. 2. (Color online) (a) Experimental setup of a spontaneous mode-locking laser system. (b) Fluorescence spectrum for the
4F
3∕2→4I11∕2at room temperature. (c) Experimental result for
the average output power versus the incident pump power.
Delay time (ps) | g (1 )( ) | (arb. unit ) 0 30 60 90 120 150 Wavelength (nm) -150 -100 -50 0 50 100 150 1060 1061 1062 1063 1064 1065 1066 Intensity (arb. unit) 0 50 100 150 200 250 300 (a) T (b) r=125 ps tr=12.5 ps
Fig. 3. (Color online) (a) Experimental first-order autocorre-lation trace under the tuning condition of obtaining maximum power output. (b) Optical spectrum centered near 1063 nm.
Delay time (ps) | g (1 )( ) | (arb . unit) 0 30 60 90 120 Wavelength (nm) -120 -80 -40 0 40 80 120 1060 1061 1062 1063 1064 1065 1066 In tensity (arb. un it) 0 50 100 150 200 250 300 (a) Tr=125 ps (b) tr=12.5 ps =0.32 nm
Fig. 4. (Color online) (a) Experimental first-order autocorre-lation trace and optical spectrum under the tuning condition of obtaining optimum harmonic mode locking at the output power of 400 mW. (b) Optical spectrum centered near 1062.5 nm. 462 OPTICS LETTERS / Vol. 37, No. 4 / February 15, 2012
the output power of 400 mW. The major mode spacing can be seen to be approximately 0.32 nm. This value is consistent with the pulse repetition rate of 80 GHz. There are many minor lasing longitudinal modes appearing in the optical spectrum. We did not further improve the mode-locked performance. The unwanted lasing modes
can be effectively suppressed by using a Fabry–Perot
etalon [22].
The second-order autocorrelation traces were also performed with a commercial autocorrelator (APE pulse check, Angewandte Physic & Elektronik GmbH).
Figure5(a)shows the second-order autocorrelation trace
corresponding to the experimental result shown in
Fig. 4(a). On the whole, both the pulse separation and
the temporal structure can be seen to be almost the same
as the results shown in Fig.4(a)for the first-order
auto-correlation trace. This remarkable resemblance indicates that the overall optical spectrum has a nearly constant
phase [23]. As shown in Fig. 5(b), the FWHM width of
the central peak in the second-order autocorrelation trace is approximately 950 fs. If the temporal intensity
is assumed to be a sech2 profile, the pulse duration can
be deduced to be as short as 616 fs. From Fig.4(b), the
optical spectral width can be seen to be approximately 2.1 nm with the central wavelength at 1062.5 nm. As a
result, the time–bandwidth product of the mode-locked
pulse can be found to be 0.33, which is quite close to the Fourier-limited value. The subpicosecond pulse train with very high repetition rate is attractive especially for communications via time multiplexing.
In conclusion, we have demonstrated what we believe to be the the first experimental observation of sponta-neous mode locking in a diode-pumped Nd:SGGM disor-dered crystal laser. The separation between the gain medium and the end mirror was delicately tuned to reach the tenth-order harmonic mode locking with repetition rate up to 80 GHz. The pulse width was measured to be as short as 616 fs at the output power of 400 mW.
The authors acknowledge the National Science Coun-cil of Taiwan for their financial support of this research under contract NSC 100-2628-M-009-001-MY3.
References
1. T. T. Basiev, N. A. Es’kov, A. Ya. Karasik, V. V. Osiko, A. A. Sobol, S. N. Ushakov, and M. Helbig, Opt. Lett. 17, 201 (1992).
2. J. Petit, P. Goldner, and B. Viana, Opt. Lett.30, 1345 (2005). 3. A. García-Cortés, J. M. Cano-Torres, M. D. Serrano, C. Cascales, C. Zaldo, S. Rivier, X. Mateos, U. Griebner, and V. Petrov, IEEE J. Quantum Electron. 43, 758 (2007).
4. A. V. Terentiev, P. V. Prokoshin, K. V. Yumashev, V. P. Mikhailov, W. Ryba-Romanowski, S. Golab, and W. Pisarski, Appl. Phys. Lett.67, 2442 (1995).
5. M. A. Scott, D. L. Russell, B. Henderson, T. P. J. Han, and H. G. Gallagher, J. Cryst. Growth183, 366 (1998). 6. W. Ryba-Romanowski, S. Gołąb, G. Dominiak-Dzik, W. A.
Pisarski, M. Berkowski, and J. Fink-Finowicki, Spectro-chim. Acta A54, 2071 (1998).
7. V. Kushawaha and L. Major, Appl. Phys. B57, 447 (1993). 8. V. Kushawaha and Y. Chen, Appl. Phys. B60, 67 (1995). 9. Y. Y. Zhang, H. J. Zhang, H. H. Yu, J. Y. Wang, W. L. Gao, M.
Xu, S. Q. Sun, M. H. Jiang, and R. I. Boughton, J. Appl. Phys. 108, 063534 (2010).
10. A. E. Siegman, Lasers (University Science, 1986). 11. M. H. Crowell, IEEE J. Quantum Electron.1, 12 (1965). 12. H. Statz and C. L. Tang, J. Appl. Phys.36, 3923 (1965). 13. H. C. Liang, R. C. C. Chen, Y. J. Huang, K. W. Su, and Y. F.
Chen, Opt. Express16, 21149 (2008).
14. O. L. Gaddy and E. M. Schaefer, Appl. Phys. Lett.9, 281 (1966).
15. P. Glas, M. Naumann, A. Schirrmacher, L. Däweritz, and R. Hey, Opt. Commun.161, 345 (1999).
16. R. Paiella, F. Capasso, C. Gmachl, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, A. Y. Cho, and H. C. Liu, Science290, 1739 (2000).
17. J. Renaudier, B. Lavigne, F. Lelarge, M. Jourdran, B. Dagens, O. Legouezigou, P. Gallion, and G. H. Duan, Elec-tron. Lett.41, 1007 (2005).
18. C. Gosset, K. Merghem, A. Martinez, G. Moreau, G. Patriarche, G. Aubin, A. Ramdane, J. Landreau, and F. Lelarge, Appl. Phys. Lett.88, 241105 (2006).
19. H. P. Weber and R. Dändliker, J. Eur. Opt. Soc. Rapid Pub. 5, 10050s (2010).
20. M. F. Becker, D. J. Kuizenga, and A. E. Siegman, IEEE J. Quantum Electron.8, 687 (1972).
21. M. De Maziere, A. Bouwen, and D. Schoemaker, J. Opt. Soc. Am. B6, 2370 (1989).
22. R. Wessel, R. Ricken, K. Rochhausen, H. Suche, and W. Sohler, IEEE J. Quantum Electron.36, 394 (2000). 23. A. M. Weiner, Ultrafast Optics (Wiley, 2009).
Delay time (ps) Delay time (ps)
| g (2) ( ) | (arb . un it) 0 30 60 90 120 150 -120 -80 -40 0 40 80 120 -2 -1 0 1 2 | g (2) ( ) | (arb. unit) 0 30 60 90 120 150 950 fs Pulse duration 616 fs (a) (b)
Fig. 5. (Color online) (a) Second-order autocorrelation trace corresponding to the result shown in Fig. 4(a). (b) Higher-resolution autocorrelation of one pulse.
