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We present measurements of the concentration dependence of the energy transfer upconversion (ETU) macro-parameter in Nd:YAG obtained via the Z-scan technique. The ETU coefficient is found to increase from 27 × 10−18 cm3∕s to 75 × 10−18 cm3∕s when the concentration increases from 0.31 at.% to 1.07 at.%.
© 2015 Optical Society of America
1. Introduction
Since the inception of solid-state lasers, neodymium doped crystals have been widely used to generate lasers in near-infrared region. Due to its excellent spectroscopic and thermo-optic properties, Nd:YAG is one of the primary active crystals for many industrial, medical and scientific laser systems. Mostly it is employed in lasers operating on the dominant emission line around 1064 νm, however, the lower gain 946 νm transition could be more efficient due to a lower quantum defect between pump and output wavelengths. Unfortunately this latter transition is weak and susceptible to detrimental thermal effects associated with waste heat produced during the excitation process [1–3]. Several techniques have been employed to dissipate the heat-load efficiently and mitigate the ensuing thermal effects via the laser architecture, essentially the geometry of the gain medium, with the output powers at 946 nm now exceeding 100 W [4]. Despite the maturity of this gain material further improvement in its laser performance may be possible if key fundamental contributors to the thermal input are well characterized. For this purpose we have configured a simple experimental setup to characterize one such parameter, namely energy transfer upconversion (ETU) and its dependence upon the neodymium concentration.
In the ETU process, two neighboring ions in their meta-stable (4F3/2) energy state interact, one of which relaxes to a lower level while the other is excited to a higher energy level. Therefore ETU depopulates the upper laser level, generating additional heat via the non-radiative relaxation paths taken by both ions, the first arriving in its ground state, while for the vast majority of these pairs the second returns back to the meta-stable manifold that both were in originally. The influence of ETU can be quite significant for the laser design and its optimization, especially for low gain lasers that typically require high-irradiance pumping, such as the quasi-four-level Nd3+ system. It is relatively well known that the magnitude of the ETU coefficient is dependent on the concentration of the rare earth ion, and is an important parameter that is currently not well covered in the literature for Nd:YAG.
In this work, we investigate the concentration dependence of the ETU coefficient in Nd:YAG with a sensitive Z-scan technique [5], comparing measured transmission as a function of incident pump irradiance. The data is compared with simulation based upon a two-level spatially (and temporally) dependent rate equation system, with the only variable being the ETU coefficient (once a Cross Relaxation (CR) parameter, WCR, is fixed for the concentration in question). The ETU coefficient was found to increase from 27 ± 7 × 10−18 cm3/s to 75 ± 10 × 10−18 cm3/s when the doping concentration increased from 0.31 at.% to 1.07 at.%.
2. Numerical model
For Nd:YAG the terminal energy levels for the pump (~808 nm) and dominant 1064 nm emission, are de-excited via rapid multi-phonon decay channels. Consequently, the population density of the trivalent neodymium ions can be modelled by simple rate equations such that their ground-state or meta-stable excited levels are represented by N1(r,z) - 4I9/2 and N2(r,z) - 4F3/2, respectively. For a suitabily short crystal with no external feed back of the fluorescence it is realistic to assume that CR, ETU and fluorescence are the only dexcitation channels for the upper level, N2. Therefore the spatially dependent rate equations can be expressed as:
where τ0 is the intrinsic lifetime for Nd:YAG, σabs is the effective absorption cross section for the ground state population density N1(r, z), at the pump photon energy of hνP, while WETU is the ETU coefficient and WCR is the CR coefficient. The CR coefficient can be simply calculated by measuring the fluorescence lifetime at very weak excitation densities, i.e. where the ground state population density is essentially equal to the total density of active neodymium ions, and noting that in this regime after the end of the pump pulse, Eq. (1) simplifies to:Where Ntotal is the total Nd ion density. This leads to the simple expression for WCR,IP(r,z) is the pump irradiance distribution along the sample’s length, described by:An effective beam area (Aeff), obtained from the average beam radius over the crystal length, is calculated using Gaussian beam propagation theory, where it is assumed that the pump irradiance incident on the crystal is defined with a Gaussian distribution,Further details of our theoretical model were reported in [6].
3. Methodology
The Z-scan technique is a simple method, in which the change in the transmission of a pump laser through the sample, and potentially an aperture, is measured as the sample is moved through the focus of the beam. In our case, at high irradiances close to the focus, depletion of ions occupying the ground state increases the pump transmission. ETU weakens the ground state bleaching, counteracting the increasing pump transmission with the higher pump irradiance achieved by moving toward the beam focus. Provided the spectroscopic properties of the ion are accurately characterized the Z-scan technique can provide a sensitive measure of the magnitude of the ETU coefficient. In fact this Z-scan technique was previously employed to measure the upconversion parameters for Er-doped YAG [5] and Nd-doped glasses [7].
A schematic diagram of the Z-scan experimental setup is shown in Fig. 1. The output beam of a continuous wave Ti:Sapphire laser was expanded 4 times with a telescope system (L1, f = 75 and L2, f = 300) and modulated by a mechanical-chopper. The pulse duration of ~2.5 ms is sufficient to reach steady state without inducing a significant temperature rise during the pulse, while the duty cycle of 10% is small enough to ensure the heat generated, considering our few hundred mW average power, diffuses away from the region of interest before the next pulse arrives. A focusing lens (L3) of f = 200 mm was mounted to an electronically-controlled translation stage to change the beam size in the laser crystal, which provides precise control of the irradiance in the sample. The transmitted beam was collected and collimated by a second lens (L4), mounted on the same translation stage, then split with an uncoated glass wedge, with ~92% passing directly to a power meter and one surface reflection (~4%) directed to a silicon photodiode (PD1). Spontaneous emission was collected with a concave mirror (L5, f = 50) and a focusing lens (L6, f = 75), was monitored by an InGaAs photodiode (PD2). A digital oscilloscope was used to record the amplitude of transmitted signal and measure the fluorescence lifetime.
Fig. 1 Experimental setup for Z-scan measurements with simultaneous capturing of the fluorescence waveforms.
Using a beam profiler placed at the position of the sample, the laser beam size at many positions along the z-axis relative to the beam waist was measured by scanning the focusing lens position as was done with the actual sample. The beam quality of the pump laser beam was calculated to be M2~1.17 in both directions, and had waist radii of wx = 20.7 ± 0.2 µm and wy = 19.7 ± 0.2 µm after the focusing lens, L3. At focus the “on axis” available pump irradiance reached 50 kW·cm−2, nearly four times higher than the saturation irradiance, when the wavelength was tuned to the absorption peak of Nd:YAG around 808.5 nm.
4. Results and discussion
Four Nd:YAG samples were tested, their parameters shown in Table 1, to determine the variation of the ETU coefficient as a function of neodymium concentration. The fluorescence lifetime of the 0.95 at.% Nd:YAG crystal was measured, in the small signal regime with the major component found to be 235 +/− 5 µs as is typical for this concentration [8,9]. With the pump beam waist in the middle of the sample, i.e. Iinc = 50 kWcm-2, this value reduced to 220 +/− 5 µs, the trend of a reducing lifetime at higher irradiances was observed for all the samples, consistent with an irradiance dependent de-excitation process, such as ETU.
Table 1. The parameters of Nd:YAG sample
We determined the respective WCR coeffcients for each sample from their fluorescence lifetime measured under weak excitation, as per Eq. (4), assuming that the intrinsic lifetime of Nd3+ in YAG is 260 µs [10] and that CR is the only decay mechanism apart from spontaneous emission under these conditions. The resulting values are given in Table 1.
Figure 2 shows the numerically predicted transmission of the pump beam by solving Eq. (1)-(6), with the pump power fixed to 400 mW and the beam radii varied, similar to that achieved experimentally by scanning the sample to the focus. The expected transmitted power without ETU is then compared to that with ETU, using coefficient values ranging from 5 x 10 −18 cm3/s to 500 x 10 −18 cm3/s, to illustrate the sensitivity of this measurement technique. Note at our maximum available pump power we would expect an approximately 40% higher transmission of the pump beam for an ETU parameter of 180 x 10-18 cm3/s [11], compared with the value of 50 x 10-18 cm3/s reported by Guy et al [12].
Fig. 2 Modelled 808nm transmission through a 3.25mm 0.95at.% doped Nd:YAG crystal (AR coated) versus incident pump irradiance, pump power 400mW, 20μm beam waist
Figure 3 and Fig. 4 show the Z-scan experimental data and simulation results for the different doping concentrations tested. The doping concentration was determined by comparing the small signal absorption and calibrating with well accepted absorption cross section data [13], in addition to our own evaluation of the absorption cross section at the 808.5 nm peak which we measured to be 6.8 x 10−20 cm2 [14]. Figure 3 shows the temporal response of the transmitted pump beam at the beam waist. The rate of bleaching is slower for two of the crystals (0.31 at.% and 0.95 at.%), primarily driven by the larger effective beam area and thus lower “maximum” irradiance level due to their longer lengths. Nonetheless, the data fits very well with the simulation results supporting the assumption of using the effective area calculated from Eq. (6).
Fig. 3 Measured (symbol) and simulated (solid line) temporal waveform of the transmitted power at (a) low pump irradiance, and (b) the maximum pump irradiance for the different doping concentrations.
Fig. 4 (a) Nd:YAG crystal transmission at 808 nm versus sample position relative to the focus for the different dopant concentrations (b) Concentration dependence of ETU coefficient in Nd:YAG.
The Z-scan pump beam transmission through each of the samples is shown in Fig. 4(a). The good fit between simulation and experimental data across the whole range of irradiance levels generated through the Z-scan give confidence in the ETU coefficient values obtained.
By fitting the model to the experimentat data, with the ETU coefficient taken as the only free variable, we found that the magnitude of the ETU coefficient increased from 27 ± 7 × 10 –18 cm3/s for 0.31 at. % doped Nd:YAG to 75 ± 10 × 10 −18 cm3/s for a 1.07 at.%. doping concentration, as presented in Fig. 4(b). For the 1.07 at.% doped crystal, a longer crystal was also tested to compare it with a shorter crystal to ensure that there were no crystal length dependencies in the measurement, for both lengths of crystal we obtained the same ETU coefficient within our error range. These error margins are dominated by the sensitivity of the experimental setup. Over the concentration range investigated, and within experimental errors, the ETU coefficient is found to have a linear dependence on dopant concentration (DC). We fixed the ETU coefficient value to 0 at 0 at.% to allow for the probability of energy transfer processes tending to zero as the inter-ionic distance tends to infinity. The linear fit of the experimentally determined ETU coefficient is WETU = 65.2 * DC (cm3/s.at.%), up to the highest investigated concentration of 1.07 at.%. Guy et al reported a quadratic relation of upconversion to varying doping concentration of Nd:YAG [10], whereas Lima et al using the Z-scan technique reported linear dependency of upconversion for Nd doped glasses [15]. We claim no phenomenological significance from our experimentally measured linear dependence but to within experimental uncertainty this is the simplest function capable of fully fitting our results.
For some of the samples investigated there appeared to be a strong transverse variation in the transmission for lateral movements of the crystal at the beam waist position, assumed to be caused by a non-uniform distribution of the Nd3+. This will have an adverse effect on our measurement accuracy since the model relies on the assumption that the total Nd3+ population density is homogeneous.
5. Conclusion
In conclusion, we have determined the effect of dopant concentration on the ETU coefficient in single crystal YAG via the Z-scan technique. We also measured the shortening of the fluorescence lifetime which occurs under high excitation densities, and with increasing Nd3+ doping concentration. The Z-scan technique offers a simple and sensitive measurement of the ETU parameter by monitoring a pump beam’s transmission with varying incident irradiance levels obtained by varying the beam size in the sample, in our case moving the beam focus along the beams’ propagation direction. Using a simple two-level rate equation model, the experimental data is well matched by fitting only the ETU coefficient. We obtained values of 27 ± 7 × 10 - 18 cm3/s to 75 ± 10 × 10 - 18 cm3/s when the Nd3 + doping concentration increases from 0.31 at. % to 1.07 at. %, with a linear dependence of 65.2 × 10−18 cm3/s.at. %.
The information presented in this paper will allow laser designers to consider the effects of upconversion on their systems. These effects are expected to be especially significant for the lower gain transitions of Nd:YAG such as 946 nm and are invariably dependent upon the selected configuration of the laser.
Acknowledgments
S. J. Yoon would like to thank Charm Engineering Inc. (Korea) for financial support via a PhD scholarship, S. J. Beecher and J. I. Mackenzie acknowledge support from EPSRC grants nos. EP/H005412/1 and EP/J008052/1.
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