We report the behavior of two Yb3+ doped ceramics (i.e. 10% at. and 20% at.) under quasi-continuous wave laser pumping. Two different behaviors are found depending on the density of Yb3+ in the excited level. Experimental results show that at low population inversion density, the maximum output power and the efficiency are almost independent on the doping concentration. In particular, an output power as high as 8.9 W with a corresponding slope efficiency of 52% with respect to the injected pump power was reached with the 20% at. sample. Conversely, at high population inversion densities, the 20% doped sample shows a sudden decrease of the laser output for increasing pump power, due to the onset of a nonlinear loss mechanism. Finally, we report a comparison of the experimental results with numerical simulations for the evaluation of the inversion density and of the temperature distribution.
© 2010 OSA
Among the rare earth used as lasing materials ytterbium is still a buoyant field of investigation as testified by the excellent and exciting results achieved with ytterbium-doped crystals and glasses for both CW [1–4] and pulsed applications [5–10]. Recent developments have been triggered by the availability of new host materials as transparent polycrystalline YAG ceramics, because of the possibility to achieve a higher uniformity in the distribution and higher concentrations of dopants, with optical properties comparable to their crystalline counterpart and better mechanical properties . As a consequence, ceramics can withstand higher thermo-mechanical stresses making them more suitable for high intensity laser pumping. It has been demonstrated that lasers based on polycrystalline ceramics such as Y2O3 are able to reach either laser output power up to 9 W [12,13], whereas Lu2O3 ceramics can generate very short pulses with a duration of 65 fs .
Concerning the overall potentiality of YAG ceramics , power levels of 520 W in quasi-continuous wave (QCW) operation and 414 W in continuous wave (CW) operation at fixed wavelength were achieved by a composite microchip laser , whereas a CW laser output of 6.5 kW was recently obtained in the thin disk architecture . Interesting results with a 20% doped ceramic sample were reported by Dong et al.  which obtained a CW output of 2.67 W with a slope efficiency of 52%, with a longitudinally pumped miniature laser. The shortest pulse duration so far achieved is 286 fs at 1033.5 nm .
The laser performance is influenced by an interplay of different aspects as, among others, the concentration of dopants, the presence of impurities which can allow non-radiative recombination channels, the thermal properties of the host matrix which determines the medium cooling capability, as well as the appearance of the thermal gradients due to the pumping process. In particular, in the case of Yb:YAG there are evidences that with a high doping level and with a high excitation density a nonlinear decay mechanism can occur, which reduces or even quenches the laser gain . Besides of that, it is well known that a high concentration of dopants can distort the lattice itself leading to the decrease of the thermal conductivity for increasing doping levels . Moreover, the absorption cross section at the pump wavelength and the emission cross section at the laser wavelength generally reduces for increasing temperature . Temperature gradients induce stress and strain inside the gain medium, which in turn determine a modification of the refractive index. In consequence, several problems can arise resulting in a degradation of the laser performance, e.g. a depolarization of the laser emerging beam, a change of the resonator stability condition, a degradation of the laser beam quality and more in general increased losses.
This paper is devoted to explore the laser performance which can be reached by a laser based on heavily-doped Yb:YAG ceramic (20% at.) in comparison with a material with half doping level (10% at.). The characterization and comparison of the two activated ceramics were done by measuring the output power in the same experimental conditions and with several output coupler mirrors having different transmissions (from 1.5% to 97%). The use of such a set of output couplers has two important reasons: first, to find the best lasing condition, and second, to test the effects of high/low excitation density on the laser performance, as mentioned above.
In particular, we found that with low population inversion densities (as in lasing conditions with low cavity losses, even with high pump power densities) the maximum output power, the efficiency and the threshold of the two samples are substantially comparable. The observed small differences can be addressed to the higher thermal load experienced by the heavily doped ceramic, due to the higher power dissipation per unit volume. Conversely, a marked difference was observed in lasing conditions requiring a high population inversion densities (i.e. at high pump intensity and high output coupling losses), where the highly doped ceramic exhibits a sudden decrease in the laser efficiency for increasing pump power. All the experiments were carried out using a QCW pumping regime, in order to limit the temperature increase of the samples when using high instantaneous pump power levels. This approach resulted useful in particular for the characterization of the effects related to the high population density, where the occurrence of strong thermal effects could contribute by itself to the reduction of the laser efficiency and it would complicate the interpretation of the results.
2. Experimental set-up
The two ceramic samples used in the experiment are high quality commercial samples provided by Konoshima Chemical Corp., Ltd, Japan, having a doping level of 20% at. with a thickness of 1 mm and 10% at. doping with a thickness of 2 mm, in order to provide the same absorption of the pump power. The samples are anti-reflection (AR) coated at the pump and the lasing wavelengths (<0.5% residual reflection). The values of the upper level lifetime in the two samples have been measured by means of the pinhole method described in . No significant differences in the decay time with different doping levels were observed. We measured a decay time of 1.01±0.02 ms and 0.99±0.02 ms for the 10% and 20% doped samples respectively. For comparison, we also measured the decay time of a 8.9% at. doped single crystal sample, which gave a value of 0.95±0.02 ms, in agreement with the commonly accepted value of about 950 μs .
A scheme of the laser experimental set-up is shown in Fig. 1 . The pump source is a laser diode with emission wavelength around 940 nm. It is coupled into a fiber with 200 μm core diameter and a numerical aperture of 0.22. The pump beam is focused into the sample through the cavity end mirror (EM) by a pair of achromatic doublets with a magnification of 1:1. The pump intensity distribution in the region of the focal plane was thoroughly characterized with a CCD camera (Pulnix LM765) and a beam analysis software (Spiricon LBA). In the focal plane the pump intensity distribution is almost Gaussian with a spot radius around 150 μm at 1/e2. In the proximity of the focal plane, thepump beam is rapidly divergent (we measured a M2 factor of about 92), but its intensity distribution still keeps a quasi-gaussian shape. EM is a flat mirror with a dichroic coating with high transmission around 940 nm and high reflectivity for wavelengths longer than 1000 nm. The samples (having a square shape, 5×5 mm2) are soldered with indium on a copper heat sink (see inset in Fig. 1) which is cooled at 18 °C with a Peltier device. The fundamental cavity mode radius at the plane of EM was calculated as w0=50 μm. Flat output couplers (OC) were employed with transmissions ranging from 1.5% to 97%. All experimental data were obtained by using a QCW pumping configuration, obtained by modulating the pump laser with rectangular pulses at 10 Hz and with a pulse length of 20 ms.
3. Experimental results
At low pump power level, the 10% doped sample absorbed 69.3±0.5% of the incident pump power, and the 20% doped sample absorbed 70.4±0.5%. For increasing pump power and in no lasing conditions, a progressive reduction of the absorption was observed, down to 59.7±0.5% (for the 10% doped sample) and to 59.1±0.5% for the 20% doped sample for an incident power of 21 W. This decrease is due to the absorption saturation and to the reduction of the absorption cross section induced by the local heating . The absorption measurements were carried out in the same QCW pumping regime used in the rest of the experiments, in order to provide approximately the same thermal load to the samples. Nonetheless, in lasing conditions the pump absorption is expected to remain closer to the unsaturated value, because the fast de-excitation of the upper level due to the laser action counteracts the saturation of the pump absorption, as shown in [3,15].
Figure 2 (a)-(b) report the laser output power of both samples at 1030 nm as a function of the pump power Pin. In the graphs of Fig. 2 and 3 , the pump power Pin and the laser output power are reported as the averages over the time interval when the pump is on. Three output couplers were used, with transmission TOC=6.0%, TOC=12.0% and TOC=18.7%. It can be seen that the output power, the slope efficiency as well as the corresponding thresholds are substantially independent from the dopant concentration. In particular, with the heavily-doped sample we found a maximum output power of 8.9 W with a slope efficiency of 54% with TOC=6.0%, a maximum power of 8.7 W (slope efficiency 52%) with TOC=12%, and a maximum power of 8.8 W (slope efficiency 53%) with TOC=18.7%. With the 10% doped sample, the maximum power was 8.7 W with TOC=6.0%, 8.7 W with TOC=12%, and 8.6 W with TOC=18.7%; the slope efficiency resulted around 54% with all the OC. With these OC transmissions, the threshold values set around 1 W for both samples (the lowest value is 0.96 W with TOC=6.0% for the 20% doped sample).
In Fig. 2 (c) are reported the results obtained by using a OC-mirror with a lower transmission, TOC=1.5%, which determines the oscillation at 1050 nm. Due to the lower fraction of population needed to achieve the lasing threshold, the peak of the effective gain spectrum shifts toward longer wavelengths , determining the shift of the oscillation wavelength from 1030 nm to 1050 nm. The maximum output powers are 8.2 W for the 20% at. sample and 8.9 W for the 10% at. sample; the slope efficiencies are 46% and 52% respectively. In Fig. 2 (d) we report the optical-to-optical efficiency, which saturates to a value of about 38.5% for the 20% doped sample, whereas it reaches a value of 42.4% for the 10% doped sample.
Significant differences were found by employing output couplers with TOC=79% and TOC=97%, as reported in Fig. 3. These output couplers were used to test the behavior of the samples with high population inversion levels. In the case of the heavily-doped sample the output power with TOC=79% is always significantly lower that the level obtained with the 10% doped sample; moreover the output power shows a clear roll-over at a pump power level exceeding 17 W, whereas such a behavior does not appear (at least in the power range explored in our experiments) with the 10% at. sample. With TOC=97%, the 10% doped sample was still able to start the laser action with a threshold of about 13.6 W and a slope efficiency of about 19%, whereas no laser action was obtained with the 20% doped sample.
The output beam quality was measured by means of the same CCD camera and beam analyzing software mentioned above. In all cases, the beam quality factor at the maximum pump power levels was found equal to about M2=3. The multimode operation is due to the mismatch between the pump spot size radius and the fundamental cavity mode radius.
4. Thermal modeling
The two samples are expected to have a rather different behavior with respect to the thermal load. Indeed, the 20% doped sample has an absorption per unit length that is twice with respect to the 10% doped sample; the former also features a smaller thermal conductivity. Furthermore for both samples the power dissipation is higher when lasing at 1050 nm than at 1030 nm, because of the larger energy difference between the absorbed and the emitted photon.
In order to get better insight into the thermal behavior of the two samples, we carried out simulations to calculate the temperature distribution in the ceramics by Finite Element Analysis (FEA), using the MATLAB Partial Differential Equation Toolbox. We set up a time-dependent model reproducing the QCW pumping conditions. The simulation started with an uniform temperature distribution, corresponding to the heat sink temperature and was conducted typically up to the 40th pump period, in order to calculate the regime temperature distribution. We considered a geometry with cylindrical symmetry, with a sample radius of 2.5 mm and length of 1 and 2 mm. According to the measurements acquired with the beam diagnostics system (see § 2) the pump beam was modeled as to have a Gaussian intensity distribution along the whole sample length, with a radius in the focal plane of wp 150 μm and an equivalent diffraction length of 1.46 mm in the material.
The focus is set in the center of the sample. The absorbed power density is calculated assuming an exponential absorption of the pump beam in the sample, with an absorptionlength determined by the unsaturated absorption level measured on the samples (6 cm−1 for 10% doping, 12 cm−1 for 20% doping). As already discussed, this is a reasonable approximation in lasing condition, because the fast de-excitation of the upper level due to the laser beam counteracts the saturation of the absorption at the pump wavelength (see for instance [3,15]). The dependence of the absorption cross section from the local temperature was not accounted for. The multimode laser beam intensity distribution was modeled with the so-called embedded Gaussian formalism : the laser beam in the active medium was assumed to have a Gaussian intensity distribution, with radius where w0 is the calculated TEM00 radius for the cavity at the crystal position (50 μm in our case), and M2meas is the measured value of the beam quality factor reported above. This results in wL=87 μm. The laser beam diffraction along the sample length was neglected. The power dissipated at a given sample point depends on the local balance between spontaneous decay rate, which is assumed to occur at the average wavelength λF=1011 nm of the fluorescence band, and the stimulated emission at the laser wavelength λL (see for instance Chénais ). In absence of other decay processes, the dissipated power distribution is then28]). On the other surfaces, a small amount of heat is removed by free air convection and radiation(heat transfer coefficient 10 W/(m2K) ). In our simulation we used the data for the incident pump power and for the intracavity laser power derived from the measurements reported in Fig. 2. No additional decay paths were considered in this model.
Figure 4 shows the temperature distributions obtained for laser action at 1050 nm, as well as the time dependence of the peak and spatially averaged temperature over a single pump cycle. The peak temperature reached by the 20% doped sample is much higher than for the sample with 10% doping, mainly because of the higher power dissipation per unit volume.
On the other hand, laser operation at 1030 nm results in a lower temperature increase for both samples. This is shown in Fig. 5 , that reports the temperature peak value, and the value spatially averaged in a volume with radius 150 µm around the beam axis, for both samples, for laser operation at 1030 nm (TOC=6%) and at 1050 nm (TOC=1.5%).
As a first approximation, the two samples should achieve the same laser performance, because they absorb the same fraction of the pump power, as the different doping levels are compensated by the different sample thicknesses. The reasons for a different behavior between the two samples could be ascribed to the different temperature increase experienced by the two samples, as evidenced in § 4, and/or to the different density of excited Yb3+ ions.
To shed light on this latter feature, we calculated the excited population densities in the different lasing conditions by means of a rate equation model  using the beam parameters resulting from the experiments. The numerical model was validated by comparing the calculated laser output at different pump power levels with the experimental data of Fig. 2 (where both samples exhibit a regular behaviour). In this pump geometry the maximum of the Yb excitation density is located on the pump beam axis on the input side of the pump beam. The excited population density increases with the pump power up to the laser threshold; for increasing pump power levels above threshold the gain is clamped to the saturated level while the population still slowly increases to counteract the temperature dependence of emission and absorption cross section. At the threshold the population is higher for increasing TOC, because of the higher gain level required to achieve oscillation. The results reported in Tab. 1 show that the excited population density needed to achieve laser action with the 20% at. sample is always almost twice than with the 10% at. ceramic, for all the values of TOC.
Since the dramatic decrease of the laser intensity evidenced in Fig. 3(c) is observed only at the highest excitation density obtained with the 79% transmission OC mirror, these calculations suggest that the loss mechanism takes place at a given threshold of the excitation density. A non-linear loss mechanism occurring at high Yb3+ excitation densities in oxide host materials was reported by S.T. Fredrich-Thornton et al.  and U. Wolters et al. . According to the model that they proposed, in presence of a sufficiently high density of Yb3+ in the excited state, an Yb2+ ion can be formed through the excitation of an hole in the host valence band (which increases the host electrical conductivity), via the collective de-excitation of a number of excited Yb3+ ions in the neighborhoods . This process has a strong nonlinear dependence on the Yb3+ excitation density, therefore it should be more evident for high values of the output coupler transmissions which requires high population inversion levels to reach the oscillation threshold. Indeed this behavior was also observed in thin disk lasers based on both Yb:YAG and Yb:Lu2O3 . Furthermore, it can be enhanced by the presence of lattice defects, so that it is also influenced by the fabrication process.
It is interesting to compare our results reported in Tab. 1 with those presented by Larionov et al. , which measured the gain quenching effect occurring in thin Yb:YAG single crystals with different doping levels (8.8%, 12.7%, 15.7%) for increasing pump power density. Small signal gain quenching was observed to occur above an absorbed pump intensity of about 2 kW/cm2 (for the 8.8% doping), 0.7 kW/cm2 (for the 12.7% doping) and 0.5 kW/cm2 (for the 15.7% doping), which resulted in an Yb3+ excitation density levels of about 4.2×1020 cm−3, 3.0×1020 cm−3, 2.2×1020 cm−3 respectively. It appears that our samples were able to safely operate at excitation density levels which, in crystalline samples, are sufficient to induce gain quenching effects.
Due to the high temperature reached by the 20% doped sample, a question can arise whether the roll-over in the output power shown by this sample with high output coupling (see Fig. 3) can be ascribed to the temperature increase alone through the temperature dependence of σe(λL), σa(λP) and σa(λL) , i.e. without the need of additional decay paths. The results of the numerical simulations for the temperature distribution can be exploited to get insight on this aspect. We have used the results of the temperature simulations shown in Fig. 4 and 5 as an input for the rate equation model previously described. If we assume that additional decay paths are not present, for a given pump power value the temperature levels shown in Fig. 5 can be considered as a worst case estimation for the temperature reached by the samples in the experimental conditions of Fig. 2, because they are calculated for higher intracavity power densities. In the rate equations model the values of σe(λL), σa(λP) and σa(λL) were calculated with the value of the spatially average temperature of Fig. 5 and approximated as spatially uniform. The rate equation model was then applied to the measurements shown in Fig. 3 and it was able to predict the laser output curves obtained with the 10% doped sample both with TOC=79% and TOC=97%. On the other hand, when applied to the 20% doped sample with TOC=79%, for increasing pump power the rate equation model provided a monotonically increasing output power, without the roll-over observed above 17 W. This behavior was confirmed also by using the peak temperature values (although in this case the model provided a lower output power in the first part of the curve) and this is due to the fact that under ordinary conditions the increase in the average temperature is about proportional to the pump power.
These results confirm that to explain the observed roll-over, an additional decay mechanism is needed, that at high excitation levels determines a sudden reduction in the quantum efficiency and/or an increase in the heat generation rate.
On the other hand, the results shown in Fig. 2(a)-(b) indicate that at sufficiently low excitation density, the laser performances of the two samples for TOC ranging from 6% to 18.7% are comparable. This clearly indicates that loss mechanisms related to the Yb3+ concentration are still not occurring.
It is interesting to note that Dong et al.  observed a slightly different behavior when testing ceramic samples at doping levels ranging from 9.8% to 20%. In his paper, 20% doped ceramic showed a lower efficiency with respect to the samples at 9.8% and 15% doping. This could be ascribed to the different pumping regime used there (CW instead of QCW) possibly resulting in a more severe temperature increase in the samples with respect to our situation.
The non linear loss mechanism reminded above is a less probable explanation for the reduction of the laser output observed with the 20% doped sample in Fig. 2 (c) (with TOC=1.5% and oscillation wavelength 1050 nm), because of the lower excitation density (see Tab. 1). The difference in the laser behavior obtained with this OC, can be ascribed to the different temperature increase experienced by the samples, which has a different effect on the absorption and emission cross section at different lasing wavelengths.
In order to evaluate the impact of the temperature increase on the laser performance at different wavelengths, one should know the temperature dependence of the absorption and emission cross sections at the laser wavelengths, but unfortunately to the best of our knowledge these data are not available in literature for the transition at 1050 nm. A qualitative argument can be formulated considering the reciprocity formula, that allows to calculate the ratio between σa and σe at a frequency ν as a function of the temperature:Fig. 5, it can be seen that, although the transition at 1030 nm suffers from a higher ground level absorption at room temperature, the ratio between the emission and the absorption cross sections decreases more rapidly (for increasing temperature) for the transition at 1050 nm than at 1030 nm. Therefore, the impact on the laser operation of the temperature raise is more pronounced at 1050 nm than at 1030 nm.
We investigated and compared, in uniform experimental conditions, the performance of Yb3+:YAG 20% at. and 10% at. doped ceramics, in an end-pumped laser configuration, operating at 1030 nm and 1050 nm. Experimental data show that the laser performances reached by the two samples are very similar (in terms of laser threshold, slope efficiency and output power) when operating at 1030 nm, with output coupler transmission ranging from 6% to 18.7%. With a low transmission output coupler (1.5%), that induces the oscillation at 1050 nm on both samples, the 20% doped sample exhibits a sizeable drop in the slope efficiency with respect to the 10% doped one. By means of numerical simulations we have shown that the former undergoes a much more severe temperature increase than the latter. Qualitative arguments show that this has a stronger impact on the operation at 1050 nm with respect to 1030 nm, because of the different temperature-induced variation of the absorption and emission cross sections at the two wavelengths.
We also investigated the behavior of the two samples at high population inversion levels. This was obtained by using output coupler mirrors with very high transmission. It resulted that the 10% doped sample was able to operate even with high population inversion level, whereas the 20% doped sample exhibited a decay in the performance, that can be ascribed to the occurrence of nonlinear decay mechanisms of the Yb excited state. We have verified by means of numerical simulations that the observed behavior cannot be justified entirely by the increase in temperature (with the consequent reduction of pump absorption and net gain) due to normal de-excitation paths, which would result only in a reduction of the slope efficiency.
In conclusion, we have found that, below a given threshold of the excited population density, the increase in the doping level does not hamper the laser capabilities of the 20% doped sample with respect to 10% doping level. Actually the measured decay time and laser output do not evidence the occurrence of detrimental effects directly related to the higher dopant concentration, such as concentration quenching of the fluorescence or occurrence of parasitic decay paths or losses.
On the other hand, the efficiency loss observed for the highly doped material at high density of excited ions can be very detrimental for the operation of laser systems requiring a very high excitation density (e.g. in CW oscillators with very high output coupling losses, as in this paper) or where the energy storage capabilities of the active medium are exploited. For instance this is the case of Q-switched laser system or pulsed amplifiers, where the excitation density has to reach a high level just before of the pulse generation or amplification. Furthermore, the 20% doped material results more prone to thermal effects, because of the larger power dissipation per unit volume and the slightly smaller thermal conductivity. Therefore, highly doped materials appear to be more interesting for the laser architectures which require a very short pump absorption length, (e.g. microchip lasers, or use of highly diverging pump beams), with low power dissipation or in configurations which are capable to ensure a very efficient heat removal by minimizing the heat conduction path, e.g. in the thin disk laser architecture [10,17,31,33].
The authors gratefully acknowledge the help of Mr. Andrea Nofri and Dr. Federico Tommasi in the measurements of the fluorescence decay times. This research has been partially supported by the following projects funded by Regione Toscana: “ICT-ONE: Sistema integrato su piattaforma ICT per l’alta formazione, la ricerca e l’innovazione industriale nei settori Ottica, Nanotecnologie ed Energia” (under the program P.O.R. Ob. 3 Toscana 2000/2006), and “CTOTUS - Progetto integrato per lo sviluppo della Capacità Tecnologica e Operativa della Toscana per l’Utilizzo dello Spazio” (under the program POR FESR 2007 - 2013 Attività 1.1 Linee d'intervento D). It was also supported by the project “Ricerca Spontanea a Tema Libero (RSTL) ID 959 CNR”.
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