An efficient, acousto-optically Q-switched, and compact Yb:Gd3Ga5O12 laser oscillating around 1026 nm is demonstrated, producing an output power of 5.15 W at a pulse repetition rate of 2 kHz, with optical-to-optical and slope efficiencies being 35.8% and 52%, respectively. The generated laser pulses are 6.4 ns in duration (FWHM), with pulse energy and peak power amounting, respectively, to 2.58 mJ and 403 kW.
© 2013 Optical Society of America
For laser transitions in the 1-μm region, ytterbium (Yb) ion crystals are known to have longer upper-level lifetimes and smaller emission cross sections when compared with neodymium (Nd) ion crystals. For example, Yb:YAG possesses an upper level (2F5/2) lifetime of 0.95 ms, and a maximum emission cross section of 2.1 × 10−20 cm2; whereas the corresponding numbers for Nd:YAG (4F3/2→4I11/2) are 0.23 ms and 2.8 × 10−19 cm2, respectively . Consequently, Yb-ion crystals are in general of greater energy storage capability and hence more advantageous in generating high-energy laser pulses through Q-switching techniques. During the past decade, passively Q-switched laser action has been demonstrated with many Yb-ion crystals, in either microchip or compact resonator configurations, showing very promising performance [2–5]. In contrast to the situation of passive Q-switching, studies on active Q-switching of Yb crystal lasers with acousto-optic (AO) modulators have not attracted much attention of researchers. As a matter of fact, even for Yb:YAG, the most extensively studied and widely used Yb laser crystal, the relevant work on compact acousto-optically Q-switched lasers still remains very limited [6–8], despite the fact that some special big high-power or high-energy devices have already been developed in the early days of Yb lasers [9–14]. Besides Yb:YAG, actively Q-switched laser operation with AO modulator reported so far involves only Yb:YAB and Yb:KGdW, with emphasis placed on self-frequency doubling or two-polarization oscillation [15, 16].
In this work we demonstrated, for the first time to our knowledge, a very compact acousto-optically Q-switched Yb:Gd3Ga5O12 (Yb:GGG) laser, which could be operated at various repetition rates ranging from 2 to 50 kHz. Laser pulses of mJ level energy and several ns duration were generated at repetition rates ≤ 5 kHz.
2. Description of experiment
As illustrated schematically in Fig. 1, the actively Q-switched Yb:GGG laser was built with a compact resonator that was formed by a plane reflector, M1, which was coated for high reflectance at 1030 nm and for high transmittance at 935 nm; and a concave coupler, M2, having a radius-of-curvature of 25 mm, whose transmission (output coupling) was T = 60% at 1030 nm. Inside the resonator the laser crystal (LC) was positioned close to the reflector, while the acousto-optic (AO) modulator was placed between the laser crystal and the output coupler. The uncoated, 4 mm long Yb:GGG crystal with a square aperture of 3 mm × 3 mm, which was utilized for the laser, was cut along its  crystallographic direction, the Yb concentration in the crystal was 8.55 at. %. For efficient laser action the Yb:GGG crystal was fixed in a copper holder which was cooled by cycling water at temperature of 10 °C. The AO modulator (33080-16-.7-I-TB, Gooch & Housego), having an interaction length of 20 mm, with its end faces coated for antireflection (AR) at 1.06 μm, was driven at 80 MHz with 16 W of rf power. The Yb:GGG laser was pumped by a fiber-coupled diode laser emitting around 935 nm (fiber core diameter of 200 μm and NA of 0.22), whose output radiation was focused first by a focusing unit and then delivered into the laser crystal with a beam spot radius of approximately 100 μm. To generate efficient laser oscillation the resonator was adjusted in a near hemispherical configuration, with the physical cavity length being about 30 mm. With the help of a beam splitter, one could measure the output power of the laser beam while recording the lasing spectrum or the pulse profile. To monitor and measure the laser pulses a digital oscilloscope (Infiniium DSO80304B, Agilent Co. Ltd.), with a bandwidth of 3 GHz and sampling rate up to 40 GS/s, was employed. The laser emission spectrum was measured by use of a spectrometer (AvaSpec-3648, Avantes B.V.) with a resolution of 0.3 nm.
3. Results and discussion
Efficient actively Q-switched operation was achieved with the compact Yb:GGG laser, with its pulse repetition frequency (PRF) being changed in a wide range from 2 to 50 kHz. To prevent the internal elements from optical damage caused by the extremely high circulating peak intensity, the output coupling for the laser was chosen to be T = 60%, although the optimum output coupling for the most efficient operation was much lower than this.
Figure 2 shows the output power versus the absorbed pump power (Pabs) for two PRFs of 2 and 10 kHz. For clarity the results for PRF > 10 kHz are not presented. The amount of Pabs is related to the incident pump power (Pin) by Pabs = ηpPin, with ηp being the pumping efficiency, which was measured under nonlasing conditions to be ηp = 0.76−0.65, decreasing with Pin and thus indicating the existence of absorption saturation. The determination of ηp in this way might be appropriate for the Q-switched operation, as the pumping action and hence the accumulation of population inversion is accomplished actually under nonlasing conditions during the period between two consecutive laser pulses. Indeed, such a measurement may lead to some extent of underestimation of ηp for continuous-wave (cw) operation, particularly in situations where a very low output coupling is used for the laser oscillator, due to the increasing “population recycling” effect arising from the presence of stimulated emission from the upper laser level, which tends to diminish the saturation of pump absorption. To give a direct comparison, the results for cw operation, measured with the inactive AO modulator leaving in its place, are also plotted in the figure. One sees first that the Q-switched output power, produced at PRF of 10 kHz, was only slightly lower than the cw output at a given pump power; and the output power obtained under conditions of PRF > 10 kHz was actually in between the two output levels. The absorbed pump power required for reaching oscillation threshold, in either cw or Q-switching mode, was measured to be 2.8 W. In excess of the threshold pumping level, the output power scaled with pump power, exhibiting very similar output characteristics when the laser was operated at different PRFs. In the case of PRF = 2 kHz, the average output power reached 5.15 W at Pabs = 14.4 W with an optical-to-optical efficiency of 35.8%; whereas the slope efficiency, determined for Pabs > 5.5 W, was 52%, which was close to that for cw operation (57%). The single pulse energy amounted to 2.58 mJ at this highest output level. To avoid possible damage to the internal elements, the maximum pump power applied was limited to Pabs = 14.4 W. With PRF lowered further to < 2 kHz, the pulse amplitude fluctuations would become enhanced substantially (> ~50%). This means the lowest PRF at which the Yb:GGG laser could be repetitively Q-switched properly, under the current resonator conditions, was limited to 2 kHz.
The inset presented in Fig. 2 shows a typical laser beam profile, recorded at an intermediate output power level of 2.0 W. The corresponding beam quality factors (M2), which were determined for the horizontal and vertical directions, are 3.04 and 2.85, respectively. Due to the much smaller fundamental mode size than the pump spot radius for the current resonator that was adjusted in a near hemispherical configuration, higher-order transverse modes oscillation would occur inevitably, giving rise to a laser beam that was roughly three times diffraction limited.
For a repetitively Q-switched four-level laser, the pulse energy, duration and peak power can be expressed analytically in terms of Ni and Nf, the initial inversion density accumulated before the pulse building up and the residual inversion density left when the pulse is over, under the simple space-independent rate-equation approximation . These expressions prove to be equally valid for a quasi-three-level laser, provided the two parameters, Ab (effective mode area) and Rp (pump rate) which are involved in the expressions, are replaced by Ab* and Rp*: Ab* = (σe/(σe + σa))Ab; Rp* = Rp(1 + f) − fNtτ−1, here σe and σa are the stimulated emission and absorption cross sections at the lasing wavelength, τ is the fluorescence lifetime, Nt is the concentration of the active ions in the laser medium, and f = σa/σe.
With the help of this analytical model, we carried out a theoretical calculation of the average output power as a function of Pabs, for the case of PRF = 10 kHz. The parameters involved in the calculation, which are denoted by using the same symbols as in , are as follows: Nt = 9.4 × 1020 cm−3 (8.55 at. %), σe = 2.0 × 10−20 cm2, σa = 1.5 × 10−21 cm2, τ = 0.80 ms [18, 19], wp (pump spot radius) = 100 μm, wl (laser mode radius) = 80 μm, λp = 935 nm, λl = 1026 nm, Le = 45 mm, γ2 = 0.916 (T = 60%), and γi = 0.04. The theoretical curve obtained from this calculation is also plotted in Fig. 2 (solid line), showing a very good agreement with the experimental measurement.
Figure 3 depicts the laser emission spectra measured at Pabs = 8.1 W for cw as well as Q-switched operation. The laser emission spectrum depended strongly on the output coupling, but varied only slightly with PRF or pumping level. One sees from Fig. 3 that the oscillation wavelengths, for either cw or Q-switched operation, fall in a range of roughly 1024.5−1027.0 nm, coinciding with the main emission band that is peaked at 1025 nm [18, 19]. It is also worth pointing out that the AR coating on the end faces of the AO modulator, which was designed for 1.06 μm, proved to work satisfactorily at the actual oscillation wavelengths of the present laser.
As in the situation of a typical actively Q-switched laser, the pulse duration was dependent not only on the PRF at which the Yb:GGG laser was operated, but on the pump power as well, in particular for cases of high PRFs. Figure 4 illustrates the variation of pulse width with pump power for PRF = 50, 10, and 2 kHz, respectively. The pulse duration was determined as the FWHM (full width at half maximum) of the laser pulse profile. It can be seen that with the PRF decreased, the resulting pulse width could be reduced substantially. In the case of PRF = 50 kHz, the pulse duration dropped from 107 to 16 ns, with the pump power raised from above threshold to Pabs = 14.4 W. When operated at a lower PRF of 10 kHz, the laser produced pulses that were shortened from 25 to 6.9 ns with pump power rising in the operational range. As the PRF was lowered sufficiently, the pulse duration tended to remain roughly fixed, independent of the pump power, except that the laser was operated near its threshold. In the case of PRF = 2 kHz, the pulse width, measured for Pabs > 9 W, was 6.4 ns.
Illustrated in Fig. 5 are a typical pulse train (a) and a laser pulse profile (b), which were recorded at Pabs = 11.2 W in the case of PRF = 5 kHz. By monitoring a pulse train consisting of about 10 laser pulses at different time instant, the amplitude fluctuations were estimated to be less than 15%, while no timing jitter was observed, since the laser repetition rate was set precisely by the external driver of the AO modulator. Such relatively large fluctuations might result partly from the impact of insufficient sampling in the measurement of signals with low repetition rates, but other unknown reasons cannot be ruled out. It seems to be a common feature for actively Q-switched operation of Yb lasers that pulse amplitude fluctuations tend to become increasingly strengthened, when the laser operates at sufficiently low PRFs.
Having measured the pulse energy (Ep) and duration (tp), one can estimate the peak power by Pp = Ep/tp, assuming a rectangular pulse shape, which is usually taken as a convention [1, 17]. Obviously, the highest peak power was achieved when the laser was operated at 2 kHz, the lowest PRF, amounting to 403 kW. In terms of pulse energy, duration, and peak power, the performance of the Yb:GGG laser, demonstrated in the current experiment, turns out to be much superior to that reported previously for an acousto-optically Q-switched Yb:YAG laser that was built with a similar resonator, which produced laser pulses of 0.32 mJ in energy, 37.4 ns in duration, and 6.8 kW in peak power . The results presented here also prove to be a significant improvement compared to other compact Yb:YAG lasers [7, 8].
Using the same analytical model and taking the same parameters as listed above, we also calculated the average output power (Pavr,cal), pulse energy (Ep,cal) and duration (tp,cal) for the Yb:GGG laser operating at PRFs in the range 2−50 kHz, for Pabs = 14.4 W which was the highest pump power applied. The calculated results, along with the corresponding measured ones, are listed in Table 1.
From Table 1 one can see that the calculated pulse energies or output powers show a fairly good agreement with the experimental results measured at various PRFs in the range of 2−50 kHz. On the other hand, significant discrepancies are found to exist between the calculated and measured results for the pulse duration. This is believed to arise from the theoretical model itself, in which the space dependence of both the inversion density and the photon number is ignored. Such an approximation will introduce considerable errors to the calculation of pulse width .
In summary, we have demonstrated an efficient, very compact, acousto-optically Q-switched Yb:Gd3Ga5O12 crystal laser, producing an output power of 5.15 W at a pulse repetition rate of 2 kHz with an optical-to-optical efficiency of 35.8% and slope efficiency of 52%, the resulting pulse energy, duration and peak power being respectively 2.58 mJ, 6.4 ns and 403 kW. The results presented here reveal the great potential of this Yb-ion garnet crystal in making high-energy, high-peak-power compact pulsed lasers by using the acousto-optic Q-switching technique.
This work was supported by the National Natural Science Foundation of China (Grant 60978023).
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