In this configuration, the simultaneously Q-switched and mode-locked operation of the laser can be achieved by increasing the pump power above 80 mW. Similarly, the time period of Q-switched envelope is not regular and the pulses have relative large amplitude fluctuations. The stable QML output pulses with regular time period can be seen when the pump power is above 100 mW. Fig. 3.6 shows the time traces of stable Q-switched mode-locked pulses on the oscilloscope with modulation frequency around 100 kHz and the pump power of 188 mW. In terms of Q-switched envelope trains, the repetition rate is almost regular about 100 kHz and the fluctuations are relatively small. By expanding the Q-switched envelopes in time domain, we can see that there are evident mode-locked pulse trains inside every Q-switched envelope. Fig. 3.6 (b) reveals the expanded single Q-switching envelope, in which a number of discrete and periodic mode-locked pulses with time period about 25 ns (corresponding to the repetition rate of 40 MHz) can be obviously seen. The corresponding optical spectrum shown in the inset of Fig. 3.6 (a) indicates that the center wavelength is 1025 nm and the bandwidth is about 3.68 nm. The shape of the optical
spectrum shown on the optical spectrum analyzer resembles the Gaussian function, which is also a feature of the mode-locked operation of the fiber laser.
Fig. 3.6 (a) Time traces of Q-switched pulse trains at 100 kHz (b) Expanded time trace of single Q-switched envelope. The corresponding optical spectrum is shown in the inset.
By alternating the modulation frequency of the AOM, the time traces of Q-switched envelopes will become unstable with larger amplitude fluctuations and timing jitters, but the
0 20 40 60 80
In te n s it y ( A .U .)
Time (
µµµµs) (a)
1015 1020 1025 1030 -70
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Int e ns it y ( A .U .) Int e ns it y ( A .U .)
(e) (f ) (c) (d)
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Int e ns it y ( A .U .) (a)
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Time (
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mode-locked pulses can still exist inside the envelope. As we decrease the modulation frequency, the satellite pulses near the main pulses will be seen similar to the previously behavior in the Q-switched operation. Fig. 3.7 (a)-(f) show the time traces of QML pulses on the oscilloscope at the pump power of 188 mW by lowering the AOM modulation frequency at 5 kHz, 10 kHz, 20 kHz, 30 kHz, 40 kHz, 60 kHz.
Fig. 3.7 Time traces of Q-switched pulse trains at (a) 5 kHz (b) 10 kHz (c) 20 kHz (d) 30 kHz (e) 40 kHz (f) 60 kHz.
Like the Q-switching operation, the number of satellite pulses will increase by lowering the modulation frequency of AOM. In Fig. 3.7 (a), there are about fourteen satellite pulses behind the main pulse at 5 kHz modulation frequency. The number of satellite pulses will decrease to be about 9, 5, 3, 2, 1 at 10 kHz, 20 kHz, 30 kHz, 40 kHz, 60 kHz as shown in Fig. 3.7 (b) to (d). The tendency of satellite pulse generation in Q-switched mode-locked pulse operation is the same as that in Q-switched pulse operation, which has the same formation mechanism mentioned above.
At the pump power of 188 mW, the expanded Q-switching envelopes at the AOM modulation frequencies of 10 kHz, 60 kHz and 100 kHz are shown in Fig. 3.8 (a)-(c). As we see, the width and the number of mode-locked pulses in the Q-switched will increase as the modulation frequency increase. In order to obtain the rising time t1, and the falling time t2 of the Q-switched envelopes, we fit the envelopes with the following formula
1 2 2 in which a is the scaling factor. Besides, we define the pulse widths τ and asymmetric factors F of these Q-switched envelopes by the relation of τ = (t1+t2)/2 and t1/t2.
At 10 kHz modulation frequency, the rising time t1=0.449μs and the falling time t2=0.226 μs can be obtained by the fitted red curve as shown in Fig. 3.8 (a). The width (τ) of Q-switched envelope is estimated to be about τ=0.338 μs and the asymmetry factor F is estimate to be about 2, which indicates a relatively large asymmetric shape. As the modulation frequency increase to 60 kHz, the rising and the falling time t2 increase simultaneously as shown in Fig. 3.8 (b), so that he total width τ is increased to be 0.496 µs.
If we further increase the modulation frequency to be about 100 kHz, the width τ is increased to be about 0.699μs. However, the asymmetry factor (F) becomes about 1, which reveals the Q-switched envelope now has a symmetric shape.
0 . 0 0 . 5 1 . 0 1 . 5
Fig. 3.8 Expanded temporal shape of a single Q-switched & mode-locked pulse trains with 188 mW pumping at (a) 10 kHz, (b) 60 kHz and (c) 100 kHz.
The rising time and falling time can be obtained by fitting the Q-switched envelope using equation 3.1 from 5 kHz to 110 kHz. Therefore, the width τ and the asymmetry factor can be obtained and are listed in table 3.1. Table 3.1 shows the rising time t1, the falling time t2, the pulse widths τ and the peak power of Q-switch envelopes. Fig. 3.9 shows the estimated widths (red circles) and measured peak power voltage (square triangles) for different AOM frequencies at the pump power of 188 mW. The width of the Q-switched envelopes show the increase tendency as the modulation frequency is increasing from 5 kHz to 110 kHz. In addition, the peak powers decrease rapidly as the modulation frequency is increasing.
Table 3.1 The rising time t1, the falling time t2, the pulse widths τ and the peak
Fig. 3.9 Measured widths and peak power voltage of Q-switched envelopes versus different AOM frequencies at the pump power of 188 mW.
Fig. 3.10 Comparison of pulse width and peak power of Q-switched envelopes at (a) low and (b) high AOM frequencies.
As shown in Fig. 3.10, at lower modulation frequencies, the switch-off time duration for
Q-switch turns on. The falling time of population inversion is faster because the population inversion is larger. This results in narrower pulse width and higher peak power of Q-switch envelope. We also substitute experimental parameters into the pulse width equation 2.21 from the Q-switch laser dynamics theory as shown in Eq. (3.2)
Np is the photon number at the peak of the pulse. The initial population inversion is larger at lower modulation frequencies, so we set the initial population inversion ni to be 5,
4, 3 and 2 times larger than the threshold population inversion
n
th as the AO modulation frequency increases. We can obtain that the pulse width decreases as the modulation frequency increases as shown in Table 3.2, which is similar to our observation in experimental results.Now, we will investigate the characteristics of Q-switched mode-locked operation by increasing the pump power from 25 mW to 300 mW and fixing the modulation frequency at 100 kHz. The QML operation can be achieved by increasing the pump power above 80 mW but the output pulse trains are relative unstable at this pump power. Figure 3.11 (a)-(c) shows the time traces of Q-switched pulse trains at 100 kHz modulation frequencies for the
pump power of 100 mW, 130 mW and 180 mW. The Q-switched pulse trains will become more stable as the pump power is above 100 mW but some sequential pulses will disappear as shown in Fig. 3.11 (a). At higher pump powers as shown in Fig. 3.11 (b), the pulses will become more regular but the period is still not matching the modulation frequency. At 180 mW pump power as shown in Fig. 3.11 (c), the relatively regular Q-switched envelope in time sequence matching the modulation frequency with smaller amplitude fluctuations can be seen.
Fig. 3.11 Time traces of Q-switched pulse trains at 100 kHz for (a) 100 mW (b) 130 mW (c) 180 mW pump power.
When the pump power is increasing above 180 mW, the QML pulses begin to be unstable again with large amplitudes fluctuations. In addition, the satellite pulses appear again after the main pulse at higher pump power as shown in figure 3.12(a). However, unlike many satellite pulses generation at lower modulation frequency, only one satellite pulse can be observed at higher pumping power. Figure 3.12(b) shows the expanded time trace of
single Q-switched envelope, in which the extended pulse is still connected to the main pulse that is unlike the satellite pulses generation at lower modulation frequency, which is due to higher pump power resulting in fast population inversion increase.
Fig. 3.12 (a) Time traces of Q-switched and mode-locked pulse trains at 100 kHz for 300 mW (b) Expanded time trace of single Q-switched envelope.
In order to demonstrate that AOM play the dominant role that results in the mode-locked pulse generation in our experiment, we change the focal length of the convergence lens to vary the focus beam size on the AOM. Here, the lens with 12 cm focal length outside the collimator is used instead of the 7.5 cm focal length, so as to produce a larger focus spot size on the AOM. The end mirror is 16 cm away from the focal lens, and the AOM is placed in front of mirror as close as possible. We observe that the Q-switched operation with the use of 12 cm focal length is less stable than the previous case of 7.5 cm focal lens.
At pump power of 188 mW, relatively stable Q-switched pulse operation can be shown in
0 2 5 5 0 7 5
(b )
In te n s it y ( A .U .)
T im e ( µ µ µ µ s ) (a )
0 2 4 6 8 1 0
T im e ( µ µ µ µ s )
Figs. 3.13 (a)-(b) with the modulation frequency around 180 kHz. The expanded single Q-switched envelope is shown in Fig. 3.13 (b). Only small modulation waves instead of mode-locked pulses on the Q-switched envelope can be obviously seen. This is due to the fact that a larger spot size resulting in a narrower bandwidth of the AOM.
Fig. 3.13 (a) Time traces of Q-switched pulse trains at 180 kHz and 188 mW pump power by using 12 cm focal lens (b) Expanded time trace of single Q-switched envelope.
The comparison of the Q-switched pulse trains by using 12 cm focal lens and 7.5 cm focal lens at 100 kHz AOM frequency and 188 mW pump power is shown in Fig. 3.14 (a) and (b). In contrast to the stable QML pulses generation by using 7.5 cm focal length as shown in Fig. 3.14 (b), only Q-switched pulses can be seen by using 12 cm focal length as shown in Fig. 3.14 (a). Besides the main pulse, the splitting pulses with small modulation signal on the Q-switched envelope can be apparent seen. As we use a longer focal length, a larger spot size will be produced on the AOM so that the diffraction efficiency by the
0 2 0 4 0 6 0 8 0
In te n s ity (A .U .)
T i m e (
µµµµs ) ( a )
0 . 0 0 . 5 1 . 0 1 . 5 2 . 0 T i m e (
µµµµs )
( b )
spatial grating produced by the 40 MHz RF acoustic wave become smaller. Only the slow amplitude modulation will act to result in Q-switched pulse output as shown in Fig. 3.14 (a).
Fig. 3.14 The comparison of the Q-switched pulse trains at 100 kHz and 188 mW pump power between using (a) 12 cm focal lens and (b) 7.5 cm focal lens.
3.3 Analysis
Our experiment successfully demonstrates the simultaneous Q-switched and mode-locked operation in Yb-doped fiber laser by an AO modulator. Unlike the previously Q-switched pulses generation using a double cladding gain fiber at a relatively high pump power, in this work only a single cladding Yb-doped fiber is selected to operate at a lower pump power. In our studies, we recognize that the AO modulator play an important role to result in both Q-switched and mode-locked pulses generation. The periodic mode-locked pulses within the Q-switched envelope are with a time period about 25 ns. It corresponds to a repetition rate of 40 MHz, which is the same as the 40MHz radio frequency of the acoustic wave.
0 2 0 4 0 6 0 8 0
In te n s it y ( A .U .)
T i m e (
µµµµs ) ( a )
0 2 0 4 0 6 0 8 0 1 0 0
T i m e (
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( b )
According to the specification of our AO modulator, the acoustic wave is a traveling wave in the AO crystal and will produce a light deflection angle of 7.5 mrad. By adjusting appropriately the position of the AO modulator and the end reflected mirror, the first order optical wave is reflected for Q-switching. We define that ω and Ω are the frequencies of laser and radio frequencies (RF, 40MHz) of the acoustic wave. Because the beam divergence angle (0.2 rad) is much larger than deflection angle (7.5 mrad) of AO modulator, the overlap between 0th (ω) and 1st order (ω+Ω) optical beam will interfere to form a 40MHz interference signal within the switch on duration. The interference effect is equivalent to amplitude modulation which will result in repeated injection locking and thus the mode locking operation is achieved. The repetition rate of mode-locking in our experiment is 40 MHz which is the same as the 40 MHz RF acoustic wave applied to the Q-switch in our case.
In addition, the total cavity round trip length in our experiment is 14.4 m, and the mode spacing c/2nd is 13.53 MHz. The repetition rate of mode locking 40MHz is corresponding to the 3 times of the mode spacing 40.58 MHz of the cavity. We also infer that a proposed explanation for self-mode-locking in our lasers may be based on self-phase modulation (SPM).
The SPM will lead to the spectral broadening resulting in that more longitudinal modes can lase and cause axial mode beating to force self-mode-locking operation. It appears that the interaction of amplitude modulation and SPM plays a significantly generating and stabilizing role in mode-locked pulse formation.
By tuning the polarization controller in the fiber loop, the output power and the amplitude of the Q-switch envelope will decrease but the mode-lock pulse trains can still exist. This result suggests that the fiber loop is not the main source for mode-locking. From the observation of the optical spectrum in our results, the FWHM of the output beam is about 3.68 nm, which corresponds to the 400 fs pulsewidth by considering the Fourier transform limit for the sech pulse-shape. Generally, the pulses generated by active mode-locking are typically about several picosecond to several hundred picosecond. So there must be some
nonlinear effects inside the cavity to compress the pulse width. One possible cause is certainly the Kerr effect in the silica fiber and nonlinear fiber loop.
We have also changed the focal lens with a longer focal length and demonstrated that the beam spot size on the AO crystal will influence the mode-locking formation. Using a shorter focal length, the optical spot size is closer to the acoustic wave. Thus the amplitude modulation by the acoustic wave becomes more efficient because of the more effective cross section matching between the acoustic wave and optical wave. With the focal length of 7.5 cm, the focused beam spot size of the optical wave is about 6.11μm. On the contrary, with a longer focal length, the optical spot size becomes 9.8μm with the focal length of 12 cm, which is larger than the dimension of the acoustic wave so that the modulation of optical light by the acoustic wave is decreased due to larger cross section mismatch.
Besides, we have also shown that the symmetry of the Q-switched envelope can be controlled by changing the modulation frequency. Thus, the relatively symmetric shape of the Q-switched envelope can be obtained at particular modulation frequencies. Moreover, almost all the mode-locked pulse trains inside the Q-switched are with 100% modulated depth, which should be due to the unusual AO mode-locking mechanism employed in our laser.
References
[3.1] B. N. Upadhyaya, U. Chakravarty, A. Kuruvilla, K. Thyagarajan, M. R. Shenoy, and S.
M. Oak1, “Mechanisms of generation of multi-peak and mode-locked resembling pulses in Q-switched Yb-doped fiber lasers,” Opt. Express. 11576.
[3.2] J. K. Jabczyński, W. Zendzian, J. Kwiatkowski, “Q-switched mode-locking with acousto-optic modulator in a diode pumped Nd:YVO4 laser,” Opt. Express 2184, Vol. 14, No. 6 (2006)
[3.3] Y. Wang and Chang-Qing Xu, “Modeling and optimization of Q-switched double-clad fiber lasers,” Appl. Opt. 45, 2058-2071 (2006).
[3.4] P. Myslinski, J. Chrostowski, J. A. Koningstein, and J. R. Simpson, "High power Q-switched erbium doped fiber laser," IEEE J. Quantum Electron. 28, 371-377 (1992) [3.5] M. Li, S. Zhao, K. Yang, G. Li, D. Li, and J. An, “Diode-pumped actively Q-switching
and mode-locking Nd:GdVO4 laser,” Laser Phys. Lett. 5, No. 10, 722–725 (2008)
[3.6] P. Myslinski, J. Chrostowski, J. A. Koningstein, and J. R. Simpson, “Self-mode locking in a Q-switched erbium-doped fiber laser,” Appl Opt, Vol. 32, No. 3(1993)
[3.7] J. K. Jabczyński, J. Kwiatkowski, L. Gorajek, W. Zendzian, “High repetition rate, acousto-optic Q-switched, diode pumped Tm:YLF laser,” 2008 OSA / CLEO/QELS 2008.
[3.8] A. E. Siegman, “Lasers,” Mill Valley, CA: Univ. Science, 1986, ch. 26.
[3.9] S. P. Ng, D. Y. Tang, L. J. Qian, and L. J. Qin, “Satellite Pulse Generation in
Diode-Pumped Passively Q-Switched Nd:GdVO4 Lasers,” IEEE J. Quantum Electron., Vol. 42, No. 7 (2006)
Chapter 4 Conclusions
In our work, reliable Q-switched mode-locked operation with full modulation depth has been firstly demonstrated, to the best of our knowledge, in a single cladding ytterbium fiber laser at a relatively low pump power by using an acousto-optic modulator. Inside the Q-switched envelope, fully modulation depth of mode-locked pulses with 25 ns time interval, corresponding to a 40 MHz repetition rate, can be obviously seen if the reflection mirror is placed directly behind the AO modulator. From experimental observation, the stability, shape and width of the generated Q-switched envelopes will depend on the pump power and external modulation frequency of the AOM. At a moderate external modulation frequency, the relatively symmetric shape of Q-switched envelope can be experimentally obtained. Due to excess population inversion creation at lower modulation frequencies, the satellite pulses could be generated with their number dependent on the modulation frequency. We recognize that the AO modulator plays an important role to achieve not only Q-switched but also mode-locked pulses generation. The mode-locking mechanism is due to the amplitude modulation from the interference between the 0th beam (ω) and 1st beam (ω+40MHz) diffracted from the AO modulator. This is supported by the experimental observation that the mode-locked pulses will disappear if we increase the beam spot size on the AO crystal. Finally, the relatively broad optical spectrum of the mode-locked pulses should be due to the nonlinear optical effects inside the fiber cavity.
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