Spectroscopic features of Er:YAG at cryogenic temperatures are studied in detail. We report that the major absorption line at ~1532.3 nm is much narrower and much stronger than previously measured. Spectroscopic analysis suggests that its impact on the laser performance is limited because of the strong pump saturation effect. It is shown that the high efficiency of the laser is, in fact, achieved due to absorption in the wing of this line, which is comprised of a few other transitions. It is also shown that pumping into the relatively weak 1534 nm absorption line provides practically the same laser efficiency (~75%) as pumping into the major 1532 nm absorption line. This is explained by a numerical laser model which takes into account saturation effects of pump and laser intensities. The model is validated by experimental data.
©2011 Optical Society of America
Recent developments in resonantly-pumped, cryo-cooled, eye-safe Er:YAG lasers have demonstrated great progress in reducing the thermal load and improving the laser efficiency [1–3]. In spite of the perceived complexity from the engineering point of view, cryogenic cooling offers numerous benefits. Along with improved thermal and thermo-optical properties of the host materials , most transitions in Er:YAG become narrower and stronger. The reduction of the thermal population of terminal laser energy levels enables the lowest quantum defect (QD) operating schemes that are either inefficient or impossible at room temperature.
The 4I15/2 →4I13/2 absorption spectrum of the Er in YAG consists of two distinct groups of transitions in the wavelength ranges of 1450–1490 nm and 1520–1550 nm. This clear distinction arises from the large split in the energy levels of the 4I13/2 manifold, see Fig. 1 .
Both groups originate from the four lowest Stark sublevels of the 4I15/2 manifold. The transitions of the first group terminate at four upper Stark sublevels of the 4I13/2 manifold and, they remain broad (around 1nm), even at cryogenic temperatures. Recently, a record ~400W laser output at 1645 nm from a cryogenically cooled Er:YAG laser was reported with pumping into the 1452.85 nm absorption line using spectrally-narrowed diode lasers with a bandwidth of approximately 1.2 nm full width at half maximum (FWHM) . However, pumping into any of the 14XX nm lines does not offer the lowest QD, defined as . Meanwhile, QD defines the theoretical limit of laser optical-to-optical efficiency – the smaller the QD, the higher the laser efficiency, and the lower the thermal load which can be potentially achieved. The second group of lines, which terminate at the four lowest Stark sublevels of the 4I13/2 manifold, enables laser schemes with much lower QD. Unfortunately, at cryogenic temperatures these absorption lines become extremely narrow and require even more advanced pump sources targeting the 15XX nm wavelength range. With continuing technological advances, it has become possible to develop and implement diode pump lasers with the output bandwidth as narrow as 0.2 nm  around 1532 nm, but moving in this direction is very costly and may not be very practical.
Previous attempts to operate Er:YAG lasers in the lowest-QD mode relied heavily on pumping into the 1532 nm absorption band. It has generally been assumed that the strongest Z2→Y1 absorption line centered at ~1532.3 nm was the one mostly responsible for the efficient resonant excitation of Er3+ ions into 4I13/2 manifold, while the impact of all other adjacent transitions was minimal. While this assumption is satisfactory for lasers operating at room temperature, experimental evidence suggests that cryogenic operation requires a more detailed analysis of Er:YAG fine spectral features. For example, we recently found that the widths and strengths of absorption lines in the 1520–1550 nm range measured by standard spectrophotometry were not adequately defined due to their extremely narrow bandwidths . At 77 K, the absorption cross-sections of these transitions are very strong (~10−18–10−19 cm2) and have a bandwidth of only ~0.02–0.05 nm. For comparison, a typical line-narrowed pump diode spectrum has a bandwidth of 0.5–1 nm. Also, with such strong absorption, significant pump saturation should take place. Indeed, for the strongest transition at 1532 nm with an absorption coefficient of ~50 cm−1 at 1% of Er concentration, the pump saturation fluence is only 86 W/cm2.
In this paper, we present the investigative results of a cryogenic Er:YAG laser utilizing different pumping transitions which can be used for the optimization of the lowest QD operation. In the first step, we carried out a detailed spectroscopic study of an Er:YAG absorption spectrum in the 1520–1550 nm wavelength range, including an investigation of the fine structure of the strongest 1532 nm absorption band. In the second step, we numerically simulated the laser operation. In order to anchor the modeling results, we also carried out laser experiments with a cryogenically-cooled Er:YAG resonantly in-band pumped at 1532-, 1534- and 1546 nm and achieved a laser operation with very high efficiency (~75%).
The necessity of detailed spectroscopic studies of the Er3+ in YAG at cryogenic temperatures was caused by insufficient knowledge of its fine spectral features. We focused our attention on the 1520–1550 nm wavelength range which is the most suitable for pumping aimed at achieving the lowest QD operation.
High resolution absorption spectra were derived from spectral scanning through a thin Er:YAG sample with the collimated output of a tunable narrow-band (~800KHz) diode laser (Santec model TSL-210). The transmitted power was measured with a Germanium detector (New Focus model 2033). The AR-coated samples were mounted on a temperature controlled “cold finger” inside a standard liquid nitrogen cryostat. In order to properly address the dynamic range issue, we used Er:YAG samples with different Er3+ concentrations and with different thicknesses depending on the absorption strength of a particular absorption transition. For the strongest absorption line, around 1532 nm, we used 1-mm thick Er:YAG samples with the lowest Er-concentrations of 0.15 and 0.2%. Weaker absorption lines were studied with 2.5 mm thick Er(1%):YAG crystals. All samples were acquired from Scientific Materials, Inc.
The resulting absorption spectrum of Er:YAG at 77 K is shown in Fig. 2a . It can be seen that along with the 1532 nm absorption band, which is commonly used for pumping, there are also two absorption transitions centered at ~1534- and ~1546 nm. Their utilization for effective pumping at cryogenic temperatures has not been investigated previously, though pumping into the 1549 nm absorption line at room temperature (the same as 1546 nm line at 77 K) was successfully demonstrated in .
A detailed spectroscopic investigation of the 1532 nm absorption band revealed that, in fact, it has a complex structure. We found that this band consists of an extremely strong and narrow peak with at least five relatively weak satellites, three of which form a long-wavelength shoulder. Only one of these satellite transitions was identified with the primary energy level scheme. Lorentzian fitting of the observed absorption spectrum with the six transitions is shown in Fig. 2b. Cross sections, FWHM and their relative strengths of each transition with respect to the total integral under the envelope are summarized in the Table 1 .
The two most intense and well-defined transitions, 1532.3 nm (Z2→Y1 major peak) and ~1532.5 nm (Z4→Y3 satellite), are displayed in the table in bold. The origin of the other transitions is not clear; they may be associated with minority sites, clusters or vibronics, but their precise identification is beyond the scope of this paper.
Figure 3 shows the temperature evolution of the 1532 nm absorption band. The most striking behavior was observed for the major 1532.3 nm ultra-narrow absorption peak. It remains quite narrow (~20–40 pm) in the entire 77–100 K temperature range and its maximum cross-section (~7.6∙10−19 cm2), measured with adequate resolution, is much higher than reported earlier . Its temperature dependence is consistent with thermal broadening due to phonon scattering, with a residual (temperature independent) contribution less than 0.02 nm. It is best fit by a Debye temperature of approximately 450 K, reasonably consistent with that reported for another transition in this material by Beghi et al .
The 1534- and the 1546 nm absorption transitions both originate at the Z4 Stark sublevel (79 cm−1) of the 4I15/2 manifold and terminate at the Y2 (6598 cm−1) and the Y1 (6548 cm−1) Stark sublevels of the 4I13/2 manifold, respectively (see Fig. 1a). Their intensities and bandwidths are very similar to those of the wide satellite transition at ~1532.5 nm (Z4→Y3). Therefore, one can expect that the performance of the cryogenically-cooled Er:YAG laser resonantly pumped into the 1532-, 1534- or 1546 nm lines will be very similar. Thetemperature behavior of the 1534 nm absorption line is shown in the inset of Fig. 3. Its cross-section remains nearly constant within the 77–150K temperature range (~2.1∙10−20 cm2), while its bandwidth (~180 pm FWHM at 77 K) changes consistently with the theory of thermal broadening of a homogeneously broadened line. The 1546 nm absorption behaves similarly, but has a much lower cross-section (~7∙10−21 cm2) and a much wider bandwidth (~700 pm).
In order to analyze the impact of the weak, long-wavelength shoulder of the 1532 nm absorption band on the performance of a cryogenically cooled Er:YAG laser, a theoretical model has been developed. This model also explains why the relatively weak 1534- and 1546 nm absorption transitions can be used for pumping with efficiency not lower than that of the major 1532 nm absorption band. The model is based on well-known, general quasi-four-level laser equations and takes into account saturation effects of the pump and laser intensities on the laser absorption coefficient, as was shown in . For cryogenic Er:YAG lasers, the pump saturation effect is important due to the strong absorption and long fluorescence lifetime. The model also takes into account the pump-absorption spectral overlap which noticeably varies with the pumping wavelength. The influence of up-conversion was treated as a reduction in the effective lifetime of the 4I13/2 manifold. Below we will briefly describe the basic features of this model.
Let N2(λp,z) be the local population density of the upper energy manifold 4I13/2 and λp be the pumping wavelength corresponding to the Zi→Yj transition between Stark levels of 4I13/2 and 4I15/2 manifold, see Fig. 1a. When only 4I13/2 and 4I15/2 manifolds are involved and the laser transition occurs between the Y2 and the Z5 Stark levels (λlas = 1618 nm), the local population density in the steady state can be derived as:
For simplicity, we assume that the laser operates at a single wavelength and the transverse distributions of the pump and the laser beams have top hat profiles. A small dependence of Plas on z inside the laser medium was neglected. Following , the pump saturated absorption coefficient can be expressed as:
Pump intensity Ip(λ, z) decreases with pump propagation along axis z in accordance with the saturated absorption coefficient (Eq. (4)), and in the absence of lasing (Ilas = 0), i.e. before the laser threshold is reached, it can be defined at any point z from the numerical solution of the transcendental equation:
If is the incident pump intensity, then by using Eq. (6) one can calculate the pump intensity at every point z along the laser axis. According to Eq. (2), the difference between the calculated values of the pump intensities defines the absorbed pump power in every elementary volume. By integrating ΔIp(λ,z) over the length of the active medium and then over the wavelengths under the absorption contour and converting pump intensity into absorbed power, one can finally calculate the averaged population density N2(Pp) and the total absorbed pump power Pabs(Pp):
It should be emphasized that, according to definition (2), both Pabs and N2 in Eqs. (7) and (8) are implicit functions of the incident pump power Pp. Then, the laser gain coefficient, αg(Pp), which also varies with Pp, can be expressed by:(9) equals the total laser cavity losses, αloss:
Further calculations are carried out in two approximation steps. At first, we assumed that the absorption is independent of the intensity of the laser emission Ilas even after the pump exceeds the laser threshold. In this approximation the absorption saturation is caused only by the pump interaction with the laser medium and the intracavity laser emission does not affect the absorption. Then, the laser output power Pout,1 can be expressed by:
In the second step, we take into account the influence of the laser emission on the absorption coefficient which, according to Eq. (4), causes partial or full “restoration” of the saturated absorption. With Ilas > 0, the saturated absorption coefficient (4) can be expressed as:Eq. (12) reduces to αabs.las = αabs. Using Eq. (12) with Ilas ≠ 0, the laser output power can be finally determined by:
For Er:YAG with Er3+ concentration less than 1%, up-conversion losses are low and can be neglected . For higher Er3+ concentrations, the influence of the up-conversion becomes more noticeable. These losses can be described by introducing an additional term in Eq. (1) - wupN22, where wup is the up-conversion coefficient. For a continuous wave (CW) Er:YAG laser, the population of the upper 4I13/2 manifold - N2 is relatively low (N2 << N0) and it remains constant after the laser threshold is reached. Thus, wupN2 can be interpreted as a modification of the decay time the same way as τ enters the term N2/τ in Eq. (1). Let us introduce the effective lifetime of the upper laser level, τeff:
Expression (17) shows that the up-conversion essentially shortens the upper level lifetime; hence, it mainly impacts the laser threshold. The up-conversion coefficient wup for cryogenically-cooled Er:YAG is unknown. By using a smaller value of τ than its fluorescence value of τ ~10 ms , it is possible to estimate the up-conversion parameter. A good fit between experimental and calculated data can serve as a criterion for the accuracy of this approach. In our case all spectroscopic and laser parameters employed in the laser modeling (except τeff) were independently measured. Then, by varying the value of τeff only, one can find the best fit between the experimental and the calculated laser outputs described by Eq. (16). The results of the above approach and modeling were validated by the experimental data and will be presented below.
4. Laser experiments
Laser experiments were carried out with the 5-mm and 10-mm long Er(2%):YAG crystals cooled to ~80 K. Crystals were mounted on the copper cold finger inside a boil-off liquid nitrogen cryostat, see Fig. 4 . They were end-pumped by a narrowband (0.25–0.3 nm FWHM) Er-fiber laser, which could deliver up to 60 W of CW power tuned to a specific absorption peak. To reduce the thermal load of the gain medium for CW pump powers exceeding 20 W, we used the same pump laser in a quasi-CW regime (chopped) with a duty cycle of 25% (tpulse = 25 ms, f = 10 Hz), which is, in all aspects, equivalent to the CW mode. During the experiments, only the pumping wavelength was allowed to change between 1532-, 1534- or 1546 nm absorption transitions, while the laser resonator and pumping geometry remained unchanged. The collimated pump beam was focused into the crystal by a spherical lens with a focal length of 100 mm. The pumped region inside the crystal had a cylindrical shape with the diameter of ~470 μm (at e −2) along the entire crystal length. A plano-concave laser cavity (lcav = 65 mm, Rout = 0.85) provided nearly perfect matching between the TEM00-mode of the cavity and the pumped volume. The laser output wavelength was 1618 nm.
5. Results and discussion
Figure 5 shows the CW performance of the cryo-cooled Er(2%):YAG laser pumped in the 1532-, 1534- and 1546 nm absorption bands with a 20W pump source. Figures (a) and (b) correspond to the 5-mm long laser crystal; (c) and (d) - for the 10 mm.
As was expected, the laser outputs corresponding to pumping into each of these three absorption transitions were almost identical with respect to the absorbed pump power (see Figs. 5b and 5d). Pumping into the 1534- and 1532 nm absorption lines provided nearly identical laser outputs even with respect to the incident pump power (see Figs. 5a and 5c), whereas pumping into the 1546 nm absorption lines resulted in lower laser output and efficiency. Similar results were obtained with the quasi-CW (QCW) pumping up to ~53 W of incident power into the same three absorption lines, see Fig. 6 . As in the previous case, pumping into the 1532- and 1534 nm absorption bands yielded approximately the same laser output and pumping into the 1546 nm transition resulted in lower output with respect to the incident pump power. But with respect to the absorbed power, pumping in these three transitions yielded identical results. The obtained laser efficiency was ~75% with respect to the absorbed and ~53% with respect to the incident pump power.
Employing the model described above, we simulated the performance of the cryogenically cooled Er(2%):YAG laser resonantly pumped in several absorption transitions. In the modeling, we used independently measured spectroscopic parameters of the crystal: σp, σg, Δλabs, g(λ), τ, N0, fZi, fYj, fZ5, fY2, parameters of the pump source - Gp(λ), Δλpump and parameters of the laser - la, Rout, RHR, L, dp, dlas.
For example, for the 1534 nm pumping, these parameters were taken as: σp = 2.2∙10−20 cm2, σg = 1.1∙10−20 cm2, Δλabs = 180 pm (FWHM), g(λ) – Lorentzian shape, τ = 10 ms, N0 = 2.76∙1020 cm−3, fZi = fZ4 = 0.103, fZ5 = 0.00018, fY2 = 0.222, fYj = fY2 = 0.222, Δλpump = 300 pm, Gp(λ) – Gaussian shape, la = 5- and 10 mm, Rout = 0.85, L = 0.05, dp = dlas = 0.47 mm. By varying τ, we determined that the best fit between the experimental data and modeling occurs when τeff = 3.7 ms for 5 mm long and τeff = 5.5 ms for 10 mm long laser crystals, respectively. This effective lifetime is much shorter than the fluorescence time τ ~10 ms measured at 77K directly . Using Eq. (17) with the averaged population of the upper laser manifold N2 ~8.5∙1019 cm−3 for the 5 mm long laser crystal and N2 ~4.4∙1019 cm−3 for the 10 mm long one, we estimated wup~2∙10−18 cm3/s. This value is close to the indirect estimation of the wup at 77K made in  and nearly twice lower than the up-conversion parameter estimated for room temperature (3.5∙10−18 cm3/s for 1% of Er in YAG ).
The results of the numerical modeling are shown in Fig. 5 by solid lines. One can see a good fit between the experimental and the calculated data. All calculated curves correspond to the same up-conversion parameter. Thus, in the case of the 1532 nm resonant pumping, the modeling shows that the major contribution to the laser operation comes not from the strongest and extremely narrow peak corresponding to Z1→Y2 line (1532.3 nm), but from the much weaker and broader satellite transition Z4→Y3 centered at 1532.5 nm (see Fig. 2b, olive bell-curve) forming a long-wavelength shoulder of the 1532 nm absorption band. The predominance of the satellite contribution to the absorbed pump power remains even when bandwidth-narrowed diodes (0.2–0.4 nm) are used. In the case of pumping in the weaker 1534 nm and 1546 nm absorption lines, modeling explains why such pumping is as effective as pumping into the 1532 nm band and provides nearly the same laser efficiency: this is simply because spectroscopic features of 1534- and 1546 nm lines are very similar to those of the satellite transition Z4 →Y3 at 1532.5 nm
Presented here are the results of a thorough spectroscopic and laser characterization of the cryogenically cooled, resonantly-pumped Er3+-doped YAG. We found that the strongest absorption line at ~1532.3 nm, which is normally used for achieving the lowest QD laser operation, is much narrower and stronger than it was previously reported. The actual spectral width of this line, measured with a spectral resolution of about 1 pm, was found to be only ~20 pm with a peak absorption cross section of ~7.6∙10−19 cm2. Our spectroscopic analysis suggests that, due to the extreme narrowness of this absorption line, its impact on the laser performance is limited because of the strong pump saturation effect. The nearby satellite absorption line, forming the tail of the 1532 nm absorption band, is mainly responsible for the high efficiency of the cryo-cooled Er:YAG laser. Experiments with a tunable spectrally-narrowed pump source and the results of the numeric simulation confirm this point. More than 25 W of the QCW output was achieved with the 75% slope efficiency (versus the absorbed pump). The results of our modeling and experiments demonstrated that because of the moderate pump saturation, the significantly weaker and broader 1534- or 1546 nm absorption lines can be used for efficient laser pumping and obtaining practically the same slope efficiency. The shapes of these transitions indicate that both of them are dominated by homogeneous broadening.
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