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We report the laser performance of resonantly diode-pumped Er:YAG from liquid nitrogen temperature to above room temperature. Relative to incident pump power, the best performance was observed at approximately 160 K. Spectroscopy and modeling show that this is due primarily to the changing efficiency of diode pump absorption as the absorption lines broaden with temperature. However, the physics of the Er:YAG system indicates that even with arbitrarily narrow pump linewidth the most efficient laser performance should occur at a temperature somewhat above 77 K. The causes of the temperature dependence are at least qualitatively understood.
©2009 Optical Society of America
1. Introduction
For solid-state lasers, and particularly for their high power operation, it is very desirable to keep the quantum defect as low as possible, so that heat deposition in the gain medium is minimized. Although cross-relaxation can reduce thermal loading by other means in some systems [1,2], quantum defect reduction usually requires pumping the laser ion into the same excited state manifold as the upper laser level. This pumping approach, often called “resonant pumping,” has become feasible in recent years, largely due to diode pumping and the development of diode lasers at an increasing range of wavelengths. Such small-quantum-defect pumping has been pursued to good effect for the Yb3+ laser ion for several years [3,4], and more recently it has been possible to apply the same ideas to the Er3+ ion, in some cases pumped by an Er-doped fiber laser [5–7], and still more recently pumped by diode lasers [6,8,9]. Er3+ is an attractive laser ion, since its laser wavelengths are in spectral regions where the eye is far less susceptible to laser-induced damage than is true of Yb3+ [10].
Where thermal management is important, crystalline hosts for the laser ion are preferred over glass due to their generally superior thermal conductivity. Yttrium aluminum garnet (YAG) is a particularly interesting crystalline host. Its success in many laser applications over nearly the full history of the laser is due to its attractive combination of spectroscopic and thermomechanical properties, and the resulting extensive development of YAG crystal growth makes it a relatively mature laser host. Thus, it is not surprising that much of the work on resonantly pumped Er lasers has focused on Er:YAG [5–9], and this material continues to be of great interest.
In recent years, there has been increasing interest in cryogenic solid-state lasers. Of course, early lasers were often operated at cryogenic temperatures to counteract the deleterious effects of thermal quenching and ground state absorption in systems with relatively low crystal quality and inefficient pumping mechanisms [11]. By contrast, the recent resurgence of interest in cryogenic solid-state lasers has been driven by the same concerns for thermal management that drive much of the interest in resonant pumping. Crystalline materials have higher thermal conductivity at low temperatures than at room temperature, and many materials also exhibit smaller values of the thermal expansion and thermo-optic coefficients [12–14]. Impressive results have been obtained, particularly for cryogenic Yb lasers [15,16].
We have recently undertaken investigations of cryogenic operation of Er lasers, including Er:YAG [17–19]. In this paper, we report in more detail the results of our study of Er:YAG laser operation from liquid nitrogen temperature to above room temperature. This includes presentation and interpretation of the temperature dependence of the laser output power and wavelength in terms of the spectroscopy of Er3+ in YAG.
2. Experimental details
The Er:YAG samples investigated in this study are from two sources. Ceramic YAG with 0.5 atomic % Er was obtained from Konoshima Chemical Company. A sample of this material 0.283 cm thick was used for absorption spectra, and another piece of this material was powdered to minimize reabsorption for fluorescence spectra and lifetime data. A 2 atomic % Er:YAG single-crystal sample from Scientific Materials was fabricated to be 1.0 cm long with both lateral dimensions 0.5 cm, and the 0.5×0.5 cm2 ends were antireflection coated for both the pump and laser wavelength ranges. Due to the nearly-equal ionic radii of Y3+ and Er3+, we take the segregation coefficient of Er in YAG to be sufficiently close to 1.0 that we use these nominal concentrations as correct [20]. We treat spectra taken on the 0.5% Er:YAG ceramic material as valid for single-crystal Er:YAG, based on the nearly-identical spectroscopy of Er reported for ceramic and single-crystalline YAG [21,22].
Spectroscopic data were taken using several apparati. Absorption spectra were taken on a Varian Cary 6000i spectrophotometer, with care taken to narrow the slits to get sufficient resolution at the lowest temperatures. Emission spectra were taken on an Acton SpectraPro 2500i 0.5-m monochromator equipped with a Sciencetech thermoelectrically cooled InGaAs detector. Excitation for these emission spectra was accomplished by using a temperature stabilized 975-nm fiber coupled laser diode.
For fluorescence decay (lifetime) data, the excitation source was a 975-nm fiber coupled laser diode in pulsed mode (~1-1.5 msec). The decay waveforms were captured using a Tektronix TDS 7104 digitizing oscilloscope.
For spectroscopic measurements, the temperature was controlled using a Janis CCS-350 cryogenic refrigerator.
3. Laser data
Laser experiments were performed using the apparatus diagrammed in Fig. 1. The Er:YAG laser crystal was mounted on a copper cold plate inside a boil-off liquid nitrogen cryostat. It was quasi-CW pumped with a 10-bar microchannel-cooled laser diode array (Princeton Lightwave) with corrected fast and slow axis divergences. This InGaAsP/InP diode bar stack was designed specifically for resonant pumping of Er3+. It had a spectral full width at half maximum of approximately 9 nm, was centered at 1530 nm and temperature tuned to achieve maximum laser output. The pump was delivered through a dichroic mirror (which also served as the high reflector of the laser cavity) with a combination of cylindrical lenses yielding an oblong 80×400 micrometer focal spot. The Rayleigh range of the pump beam was observed to be approximately 0.25 cm in air, significantly shorter than the laser crystal, so that the average pump beam area was considerably larger than its value at focus. The cavity length was 10 cm, defined by the high reflector and by an output coupler with 25 cm radius of curvature. Due to the cavity mirrors being outside the liquid nitrogen cryostat, the sample sat at approximately the center of the cavity, where the lowest-order mode would have a radius at e-2 intensity of about 250 μm. We have observed the output beam to have a shape similar to the pump beam, and thus to be multimode.
Fig. 1. Apparatus for low-temperature laser experiments. A: Pump laser diode array. B: Pump beam focusing optics. C: dichroic mirror. D: Output coupler. E: Er:YAG laser gain medium. F: Liquid nitrogen optical cryostat.
The pump pulses were 5 ms in duration, and the pulse repetition frequency was set to 2 Hz. As will be discussed later, only a modest fraction of the pump light was absorbed, and for this reason the data are presented in terms of absorbed pump power. The fraction absorbed can be increased by optimization of the sample length and by double-passing the pump.
Fig. 2. Laser performance of 2% Er:YAG at approximately 78 K, with output coupler reflectivity = 0.9. The error bars represent the estimated uncertainty of ±10% for the absorbed pump and ±5% for the output.
The typical quasi-CW performance of a 2% Er:YAG laser operated at about liquid nitrogen temperature is shown in Fig. 2. The performance of this laser was rather satisfactory, in view of the non-ideal pump beam shape. With an approximately optimal output coupler reflectivity of 90%, the laser threshold was 66 mJ absorbed and the optical-to-optical slope efficiency was 0.66, referred to absorbed pump energy.
We have investigated the temperature dependence of this laser by fixing the incident pump energy at 2.1 J per pulse and monitoring the laser output as the temperature was varied. The results are shown in Fig. 3. There was a striking increase in output from liquid nitrogen temperature up to about 160 K, followed by a decrease as the temperature was further increased to room temperature and beyond. The reasons for this behavior will be discussed in Section 5. We observed that the laser wavelength was 1618 nm below about 90 K, 1645 nm above 110 K, and that both lines could be observed between those temperatures. This behavior, too, will be discussed in Section 5. Before these discussions can be given, we must note some details of the spectroscopy of Er:YAG.
Fig. 3. Laser output of 2% Er:YAG vs temperature for fixed incident pump power. Solid curve: experimental data. Open circles: fit with pump area = 0.050 cm2 and mode fill efficiency = 0.5. The dotted curve is a guide to the eye. Filled triangles: fit with pump area = 0.35 cm2 and mode fill efficiency = 0.6. The error bar represents the ±5% uncertainty in output energy.
4. Spectroscopic data
The spectroscopy of Er3+ in both single-crystal and ceramic YAG has been studied rather extensively, both at room temperature [22–24] and at cryogenic temperatures [21,23,25–27]. Thus, we need only investigate the temperature dependence of the absorption and stimulated emission cross section spectra in the region covering the observed laser lines, and the absorption spectra in the pump wavelength region.
The spectra of 0.5% Er:YAG over the emission wavelength range relevant to this study are given for three representative temperatures in Fig. 4. The stimulated emission spectra were obtained by the Fuchtbauer-Ladenburg method as outlined by Aull and Jenssen [28], using fluorescence spectra taken with the equipment described in Section 2 and fluorescence lifetimes discussed later in this section.
At sufficiently low temperatures laser action was observed at 1618 nm, as would be anticipated based on the 77-K spectra. This peak is somewhat stronger than the 1645-nm peak, and at this low temperature neither line contends with significant ground state absorption (GSA.) However, by 150 K GSA at the 1618-nm peak is already perceptible, and is (of course) larger than that at the 1645-nm peak. Since the difference in GSA is small, it is not obvious by eye that this difference will force laser operation to prefer the 1645-nm line. Modeling results, to be presented in the next section, are required to see that the small GSA at 1618 nm is indeed enough to switch the laser wavelength. By 300 K, it is clear that the stimulated emission cross sections are reduced due to line broadening and that the GSA cross sections are substantially higher. Thus, it is to be expected that the laser threshold will be higher at room temperature than at lower temperatures.
Fig. 4. Ground state absorption (dashed curves) and stimulated emission (solid curves) spectra of 0.5% Er:YAG at 77, 150 and 300 K.
To convert the fluorescence spectra into stimulated emission data, the radiative lifetime is needed. We observed the fluorescence decay kinetics of 0.5% Er:YAG at both 1618 and 1645 nm, following excitation by 1.5-msec pulses at 975 nm, which pumps the Er3+ 4I11/2 manifold. Decay from that manifold to the 4I13/2 metastable state is sufficiently fast not to obscure the 4I13/2 relaxation relevant to this study. We observed the decay to be essentially purely single-exponential. Not surprisingly, the decay rates for the two emission lines are practically identical. The results are summarized in Table 1. We believe these lifetimes to be good approximations to the radiative lifetimes, for a combination of reasons: the exponential decay waveforms, our use of powder to minimize radiative reabsorption, and the low Er concentration, which reduces the probability of upconversion and other ion-ion quenching processes. Note that there are thermally activated emission bands of significant size compared to the low-temperature emission bands, as exemplified in the 1560–1600-nm region of Fig. 4. The transitions in that spectral range appear to be strong enough that their growth with increasing temperature increases the total emission rate. Thus the reduction in lifetime with increasing temperature is consistent with the assumption of radiative decay. These fluorescence lifetimes were used in the Fuchtbauer-Ladenburg calculations that yield the stimulated emission spectra of Fig. 4.
Table 1. Temperature dependence of the fluorescence lifetime of 0.5% Er:YAG, averaged over the two emission wavelengths.
Fig. 5. Single-pass transmission of the diode laser array pump by 2% Er:YAG laser sample at two temperatures. Dashed curve: incident pump spectrum. Solid curve: calculated transmitted pump spectrum.
The temperature dependence of the absorption spectra can also affect the efficiency with which pump light is absorbed. To obtain a useful approximation to this absorption efficiency, we have used the emission spectrum of the laser diode pump array and the absorption spectra in the same wavelength range to calculate the fraction of pump light absorbed for several temperatures. The calculated transmitted diode pump spectra are given for 77 and 300 K in Fig. 5, along with the incident pump spectrum, for the 1.0-cm thick laser sample with 2% Er concentration. Clearly, these calculations indicate that much more of the pump light is absorbed at room temperature than at liquid nitrogen temperature. At the wavelengths of some peaks, there is actually less absorption at room temperature due to the reduced peak cross sections, but temperature broadening of the absorption lines more than compensates for this. The resulting fraction of pump light absorbed is given for several temperatures in Table 2. Interpolated values are given for temperatures at which emission data were taken. These calculations are approximations, in that they assume the absorption spectra observed at low light levels apply to all pumping levels. In laser operation, some bleaching must take place to overcome the non-zero absorption at the laser wavelengths. However, this absorption is small compared to the stimulated emission, so that the amount of bleaching required is also small and thus the approximation involved in Fig. 5 and Table 2 is a reasonable one.
Table 2. Temperature dependence of the fraction of diode pump power absorbed, based on spectroscopically determined absorption.
5. Interpretation
The principal features of the laser data to be explained are the temperature dependence of the laser output for constant incident pump power and the change in laser wavelength with temperature. The spectroscopic features noted above suggest the likely causes for these behaviors. The switch in laser wavelength is expected to be due to the growth in GSA with temperature. The rise in laser output with temperature up to about 160 K can be attributed, at least primarily, to the increased efficiency of pump absorption with temperature, whereas the fall in output for higher temperatures is expected to be attributable to the increase in GSA and decrease in stimulated emission cross sections at the laser wavelength. In this section we will apply simple models to see if these expectations are borne out by our data.
To determine which emission line should lase at a given temperature, we can apply the familiar threshold condition, as follows.
Here, gnet is the net gain parameter for the laser cavity, σtrue is the true cross section of the transition between the upper and lower laser levels, obtained from the observed GSA or stimulated emission cross section by correcting for the fractional thermal occupation of the initial state. n Er is the Er3+ concentration, Lgain is the length of the gain medium (the laser crystal,) fexc is the fraction of Er ions excited, f UL and f LL are the fractional thermal populations of the upper and lower laser levels, respectively, which become simply the ratio of the Boltzmann factors to the corresponding partition functions since the degeneracy factors for all levels equal two for Er in YAG. R OC is the reflectance of the output coupler, and (1 - R OC) is taken to approximate the total passive loss. The Boltzmann factors and partition functions require the energy level spacings, obtained from Kaminskii as corrected by Setzler et al [6,29].
Sufficient cross section data were taken at five temperatures, and the relevant parameters for those temperatures are given in Table 3. The temperature-independent parameters are: n Er = 2.78×1020 cm-3 and R OC = 0.9. For each temperature and each transition, (1618 and 1645 nm,) g net was calculated for a range of fexc values using Eq. (1). For all temperatures gnet was larger at 1645 nm than at 1618 nm for very small fractions excited, due to the larger GSA at 1618 nm, but the gain grew faster for 1618 nm due to that line’s larger stimulated emission cross section. For 77 K, the calculation gives a positive gnet for the 1618-nm line at a lower excited fraction than for the 1645-nm line. For temperatures of 125 K and higher, gnet becomes positive first for the 1645-nm line, due to the increased GSA at 1618 nm. These results are consistent with the observed behavior, which gives 1618-nm laser operation below 90 K, 1645-nm operation above 110 K, and both wavelengths for temperatures between 90 and 110 K. Thus, although one would not expect such a simple model (with no passive loss other than the output coupling and with the spatial variation of the excited fraction neglected) to work perfectly, it appears that the basic physics of the wavelength change with temperature is understood.
Table 3. Temperature-dependent parameters used in laser wavelength and power models. The meanings of the symbols are given in the text.
To determine whether the temperature dependence of the output power is also adequately understood, a model is needed that can predict laser threshold and slope efficiency, and thus output power for a given pump power. We have chosen to apply the quasi-three level CW laser model of Beach [30]. Although this model was developed for Yb3+ lasers, it is readily adaptable to Er3+ by substitution of the appropriate energy levels, with one proviso. Due to the sparse energy level structure of Yb3+, upconversion is not a significant issue for that ion and is not taken into account in the Beach model. Since upconversion is an issue for Er3+, the model will work well only for sufficiently low concentrations.
Since our diode laser array pump is sufficiently broad-band to pump several transitions at once, we have modified the Beach model. We have replaced its explicit dependence on the cross section and upper and lower level populations of a presumed single pump transition with the fraction of pump light absorbed, resulting in the following expressions.
Here ηslope is the slope efficiency with respect to incident pump power, Fpump is the fraction of pump power absorbed, ηM is the efficiency of laser mode filling of the pumped volume, v L and v p are the laser and pump photon frequencies, σtrue is the true cross section at the laser wavelength, T is the single-pass transmittance of the cavity taking into account only passive losses other than output coupling, h is Planck’s constant, A is the cross-sectional area of the pumped region, and τ is the upper laser level storage time (lifetime.) N 2 and N 2l are given as follows.
As noted in Sec. 3, the pump beam at focus has a cross-sectional area of roughly 0.025 cm2, but averaged over the length of the gain medium A must be somewhat larger. The observed output beam is not clean enough to facilitate calculation of its cross-sectional area in the cavity, so that ηM is best treated as an adjustable parameter. Model calculations were performed using R OC = 0.9, (as used in the experiments,) Fpump from Table 2, τ from Table 1 and the parameters from Table 3. Assuming as before that the output coupling is the only passive loss, thus T = 1, we find that with A = 0.050 cm2 (a plausible value for the average pump area) and ηM = 0.5 the increase in output power at low temperatures for a pump power of 420 W (2.1 J in a pulse of 5 ms) can be fit rather well. However, with these parameters the laser threshold does not rise sufficiently to reproduce the fall-off of output at higher temperatures, as shown by the open circles in Fig. 3. To achieve a good fit to the overall temperature dependence of the output power (and thus pulse energy) we must adjust the mode fill efficiency slightly, to 0.6, but must assume a far larger pump area of 0.35 cm2. The resulting temperature dependence is shown by the solid triangles in Fig. 3.
6. Discussion and conclusions
The calculations given above indicate that the rise in output power from 77 to about 160 K is due primarily to the increased pump efficiency attributable to the large pump bandwidth. With a pump source narrower than the pumped absorption line, the increase in pump efficiency with temperature would be greatly reduced. However, some rise in laser output with temperature can be expected even with an arbitrarily narrow pump line. The upper laser level for both the 1618-nm and 1645-nm lines is approximately 58 cm-1 above the bottom of the 4I13/2 manifold, so that thermal activation increases the population of this level rapidly up to liquid nitrogen temperature, and even beyond [6,29].
Thus, it is likely that the optimum temperature for efficient laser action in Er:YAG is above liquid nitrogen temperature for any pump source, and more so for cases such as the present one, where the pump spectrum is broader than the absorption line. Published data on thermo-optic properties indicate that these are more favorable at 77 K than at any higher temperature [13,14]. Thus, a study of the trade-off between spectroscopic and thermo-optic properties would be required to find the optimum temperature for laser operation. The result will undoubtedly be application-dependent, and will also depend on the availability and performance of spectrally narrowed laser diode pumps to better fit the absorption linewidth. We are currently investigating these trade-offs.
Although straightforward models explain the temperature dependence of the laser wavelength quite satisfactorily and of the output power qualitatively, the pump area required to fit the power’s temperature dependence is unphysically large. Since the main effect of this large pump area is to dilute the gain, this result suggests either that the gain is substantially lower than expected or that there is some loss mechanism not accounted for in the model. We have attempted to achieve a comparable fit for a more realistic pump area by varying T in Eq. (2), and thus the passive loss, without success. This suggests that no temperature-independent loss mechanism is likely to explain the temperature dependence.
One possible cause for reduced gain in any laser that relies on populating the Er3+ 4I13/2 manifold is upconversion. We have recently developed a model for quasi-three level laser operation that includes upconversion [31], and are now pursuing experiments to quantify the parameters needed to apply that model.
In summary, we have investigated the temperature dependence of resonantly diode-pumped Er:YAG laser performance from liquid nitrogen temperature to above room temperature, using a broadband (not spectrally narrowed) InGaAsP/InP diode bar stack, and the spectroscopy needed to interpret that performance. We find that the output relative to incident pump power is considerably better at low temperatures than at room temperature. Interestingly, we find that optimum output occurs at temperatures above that of liquid nitrogen, quite substantially higher with pumping by the InGaAsP/InP diode bar stack. This behavior is at least qualitatively consistent with simple laser models, but more detailed studies will be required to achieve a realistic quantitative fit to the data. Our results indicate that the optimum performance can be pushed closer to nitrogen temperature by employing diode laser pumps spectrally narrowed to be better absorbed by a single Er absorption line, as this would greatly reduce the temperature dependence of pump absorption.
Acknowledgment
The authors gratefully acknowledge financial support for this work from the High Energy Lasers Joint Technology Office.
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