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Abstract
The precise characterisation of the ground state absorption cross section around 800 nm for Nd:YAG from room temperature to liquid nitrogen temperature is presented. These results enabled the measurement of the energy transfer upconversion macroparameter over the same temperature range for 0.3at.%- and 0.6at.%-doped samples via a simple automated z-scan technique. The main absorption cross section peak at 808 nm is found to increase from (6.90 ± 0.30) pm2 at the highest, to (42.30 ± 2.10) pm2 at the lowest temperatures. Over the same range, the energy transfer upconversion parameter increases from (21.5 ± 2.3) 10−18 cm3/s to (52.6 ± 2.5) 10−18 cm3/s and from (36.0 ± 2.8) 10−18 cm3/s to (65.7 ± 1.9) 10−18 cm3/s, for the 0.3at.%- and 0.6at.%-doped crystals, respectively. Although energy transfer upconversion is known to limit room temperature operation on the 946 nm transition for this laser, we demonstrate that when the crystal is cooled to liquid nitrogen temperature, despite a twofold increase in the macroparameter, it has a negligible effect on performance.
Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
1. Introduction
Nd:YAG is one of the best known, and widely used, crystals for diode-pumped solid-state lasers [1]; however, some key parameters defining laser performance are still to be investigated. Mainly employed for its strong $1.06\ \mu m$-transition, Nd:YAG’s energy level structure also encompasses the transition $^4F_{3/2}\ \rightarrow ^4I_{9/2}$, with the dominant emission wavelength of $946\ nm$. Particularly when in-band pumped, this transition resembles Yb:YAG’s system, which has been successfully demonstrated at both Room Temperature (RT) and in the cryogenically-cooled regime, with multi-hundred-W CW output power for the latter in bulk-systems [2,3]. However, Nd:YAG’s $946\ nm$- is hampered by relatively low gain at RT [4] and gain competition with the stronger $1.06\ \mu m$-transition, aggravated by detrimental effects like Energy Transfer Upconversion (ETU) and Cross Relaxation (CR) [5] that add to the thermal load and induced losses. These dynamics have strongly limited laser performance for this transition, with the best results confined to less than $40\ W$ of output power in bulk configurations [6–9], and a maximum of $105\ W$ demonstrated with the planar waveguide architecture [10].
Following the successful power- and energy-scaling of the Yb:YAG system via the enhancement of thermo-optical and spectroscopic properties provided by cryogenic-cooling [11], the equivalent Nd:YAG $946\ nm$ has started to be explored as well [12,13]. In this regime, however, the spectroscopic properties, and in particular the factors that limit RT laser performance of this transition, e.g. ETU and CR, have not been extensively characterised. In this paper, following on from our previous works reported in [14–16], we present a detailed investigation of the ground absorption cross section into the $^2H_{9/2}+^4F_{5/2}$ energy levels, for temperatures spanning from RT to Liquid Nitrogen Temperature (LNT), performed via small-signal absorption measurements. Over the same range of temperatures, we report the measurement of the ETU macroparameter, enabled by the previous spectroscopic characterisation, and performed via an automated z-scan technique [16].
By employing existing laser-performance models including the effects of ETU [5], and accounting for the presented temperature-dependent results, we calculate that despite an increase in the ETU macroparameter with decreasing temperature, the net effect of cryogenic-cooling is overwhelmingly positive.
2. Methodology
2.1 Absorption cross section measurement
The characterisation of the ground $^4I_{9/2}$ to $^2H_{9/2}+^4F_{5/2}$ energy level’s absorption cross section, for temperatures in the RT to LNT range, was executed via small-signal absorption measurements as defined by the Beer-Lambert law (1):
Employing (1) with an accepted value for $\sigma _{abs}(\lambda )$ [17], we measured the doping-ion concentration $C_\%$ of the tested crystals at RT, as in [16], by averaging the concentration values $c_{\%,i}$ obtained over multiple absorption peaks at wavelengths $\lambda _i$ within the explored band:
Once the concentration was fixed, we could, again employing (1), characterise the absorption cross section $\sigma _{abs}(\lambda )$ dependence on temperature.
The setup employed, shown in Fig. 1(a), comprised a symmetric telescope, a sub-threshold fibre-coupled diode laser (LIMO60-F200-DL808), coupling optics and an Optical Spectrum Analyser (OSA, model ANDO AQ6317). The Amplified Spontaneous Emission (ASE) from the pump diode covered a wavelength span of $(770-840)\ nm$ and was measured to have an excellent power- and spectral-stability over multiple measurements executed through an extended time-window. This source produced an output of around $6\ mW$, which was used to probe each sample. The crystals were mounted in a closed-loop cryostat (Q-Drive 2s132K) used to set their temperature.
Lenses L$_1$ ($f=30\ mm$) and L$_2$ ($f=150\ mm$) provided a $\sim 500\ \mu m$ beam radius in the crystal, while lenses L$_3$ ($f=150\ mm$) and L$_4$ ($f=30\ mm$) coupled the transmitted light into the fibre-coupled OSA, which recorded the transmitted spectra with a resolution of $0.01\ nm$. The reference spectra $I_{in}(\lambda )$ measured without the crystal in place. Figure 1(b) shows sample signals $I_{in}(\lambda )$ and $I_{out}(\lambda )$ before being converted to absorption cross section $\sigma _{abs}(\lambda )$ by applying Eq. (1).
Fig. 1. (a) Absorption cross section measurement setup. (b) Raw data for the probe’s incident spectrum (black) and transmitted spectra (red and blue) for RT and LNT, respectively.
2.2 ETU measurement
The measurement of the ETU macroparameter via the z-scan technique is a well known and accepted method [14–16,18,19]. The z-scan technique relies upon varying the incident irradiance on the investigated crystal by scanning it through the focus of a probe beam, enabling the scaling of the irradiance from very low (large pump beam diameter, small-signal absorption regime) to levels higher, or comparable to, the saturation irradiance (small pump beam diameter, high irradiance regime).
A two-level rate-equation model, Eqs. (4)–(6) , described in detail in [14], was employed to predict the transmission of the pump beam through the crystal. We compared this prediction to the measured transmission, and use the $W_{ETU}$ coefficient as the only fitting parameter.
With all the other parameters fixed, Eqs. (4)–(6) were numerically solved in the steady state regime $\partial N_i/ \partial t = 0\ \ (i=1,2)$, as experimentally provided by the $\sim 1\ ms$ long pump pulses, a long enough time for populations to reach steady state, and short enough for heat to diffuse away from the pumped region. For each step (irradiance level) of the z-scan, the transmitted power was measured, and a fitting procedure based on the minimisation of the variance employed to determine the $W_{ETU}$ value for several different temperatures in the range (RT-LNT). Further details about the computation can be found in [16]. Figure 2(b) shows sample z-scan curves for RT and LNT, and their relative fitting curves derived from model Eqs. (4)–(6).
Fig. 2. (a) Automated ETU measurement setup. Tested crystal enclosed in the cryo-chamber and held at fixed temperatures between (RT-LNT). Lenses: L$_1$ ($f=50\ mm$), L$_2$ ($f=300\ mm$, or $f=100\ mm$), L$_3$ ($f=200\ mm$), L$_4$ ($f=175\ mm$); high reflectivity mirrors at $808\ nm$: M$_1$ and M$_2$; glass wedges: W$_1$ and W$_2$; Si photodiodes: Reference PD, Transmission PD. (b) Sample z-scan experimental (circles and triangles) and theoretical (red and green) transmission curves for 0.3at.%-doped Nd:YAG at RT and LNT, respectively.
The automated setup employed is depicted in Fig. 2(a). As in [16], the CW Ti:Sapphire pump-laser (Spectra-Physics, 3900S), tuned to Nd:YAG’s $808\ nm$ absorption peak, was conditioned via the beam expander comprising lenses L$_1$ and L$_2$ and the focussing lens L$_3$ ($f=200\ mm$), providing a suitable spot size in the samples. One of the assumptions of Eqs. (4)–(6) is that the pump’s Rayleigh range is greater than the crystal length, so that the pump radius doesn’t change significantly across the sample. The two investigated crystals, of doping-concentrations 0.30at.% and 0.57at.%, were respectively $(5.10 \pm 0.01)\ mm$ and $(1.08 \pm 0.01)\ mm$ long. To achieve an appropriate Rayleigh range for the respective crystals we employed a 2x beam-expander ($f_{L_1} = 50\ mm$ and $f_{L_2} = 100\ mm$) in the first case, and a 6x beam-expander ($f_{L_1} = 50\ mm$ and $f_{L_2} = 300\ mm$) in the second case, providing measured radii of $\omega _x=(36.9 \pm 0.3)\ \mu m$ and $\omega _y=(36.3 \pm 0.3)\ \mu m$, and $\omega _x=(19.7 \pm 0.2)\ \mu m$ and $\omega _y=(19.9 \pm 0.2)\ \mu m$, respectively.
Lenses L$_3$ ($f=200\ mm$) and L$_4$ ($f=175\ mm$) were positioned on an automated translation stage (Stackshot), while the crystal was mounted in a fixed vacuum chamber and held at a chosen temperature, controlled by the same closed-loop cryostat employed in the absorption measurements. The translation of lenses L$_3$ and L$_4$ provided the change of the spot size in the crystal as required for the z-scan technique. The glass wedges W1 and W2 reflected a small percentage of the pump power to Si-photodiodes, Reference-PD and Transmission-PD, respectively, so that, once the quantitative relations $V_{1,2}(P_{1,2})$ were characterised, the incident and transmitted powers could be monitored simultaneously via voltage measurements. The pump was mechanically modulated by a chopper. The data collection was automated via a LabView-driven interface, controlling the translation stage motion (z-scan steps), recording the oscilloscope readings (input and output powers), and only keeping the data corresponding to input powers within a selected range in order to minimise noise associated with the power instability of the Ti:sapphire laser. Further details can be found in [16].
3. Experimental results and discussion
3.1 Absorption cross section
We tested two Nd:YAG samples (Castech), of lengths $(5.10 \pm 0.01)\ mm$ and $(1.08 \pm 0.01)\ mm$. By averaging the 6 strongest absorption peaks distinguishable in Fig. 3, the Nd-concentration of these crystals was determined to be $(0.30 \pm 0.02)\ at.\%$ and $(0.57 \pm 0.03)\ at.\%$, respectively.
Only the 1.08-$mm$ long crystal was employed to execute absorption cross section measurements over the temperature range (RT-LNT). The temperature-dependent spectra are shown in Fig. 3: the absorption peaks’ intensity increase while their bandwidths reduce with decreasing temperature. The strongest absorption peak, at $\sim 808\ nm$, exploited in the ETU parameter measurements, increases from $(6.9 \pm 0.3)\ pm^2$ at RT to $(42.30 \pm 2.10)\ pm^2$ at LNT, it blueshifts by $(0.21 \pm 0.02)\ nm$ while its bandwidth decreases from $(0.93 \pm 0.02)\ nm$ to $(0.21 \pm 0.02)\ nm$ over the same temperature range, as shown in Fig. 4 and 5. These results at cryogenic temperatures have a better resolution than previously published values [17,20].
The temperature dependence of both the amplitude of the 808-$nm$ peak and its bandwidth are well described by a second degree polynomial. The data and the fitting curves are displayed in Fig. 5; the fitting coefficients are displayed in Table 1.
Fig. 5. Measured $808\ nm$ peak amplitude and bandwidth vs low-temperatures, and their respective quadratic fits.
Table 1. Coefficients for the second degree polynominal fitting curves in Fig. 5.
3.2 ETU macroparameter
We performed z-scan measurements on the two, 0.30at.%- and 0.57at.%-doped, Nd:YAG samples in the same temperature range (RT-LNT). In the cases where the strong absorption at low temperatures meant a transmitted power too low to be confidently measured, the pump was tuned off-peak to increase the signal-to-noise ratio. Off-peak tuning of the pump has already been employed in [18] for equivalent measurements on Er:YAG samples, and in our reported measurements on Nd-doped vanadates [16].
The results are summarised in Fig. 6: the ETU macroparameter increases from $(21.5 \pm 2.3)\ 10^{-18}\ cm^3/s$ to $(52.6 \pm 2.5)\ 10^{-18}\ cm^3/s$ and from $(36.0 \pm 2.8)\ 10^{-18}\ cm^3/s$ to $(65.7 \pm 1.9)\ 10^{-18}\ cm^3/s$ from RT to LNT for the two concentrations investigated, respectively.
Fig. 6. ETU parameter vs sub-ambient temperatures and quadratic fits for 0.30at.% and 0.57at.% doped Nd:YAG.
The values measured at RT are compatible within uncertainties to reported values in [15], and provide better precision enabled by the automation developed in [16] and exploited in this work, particularly with respect to previous reports [14,15]. Furthermore, the trend of an increasing ETU macroparameter with decreasing temperature is consistent with the equivalent measurements executed in [14] for the elevated-temperature regime.
Assuming that $W_{ETU}$ has a linear dependence upon Nd$^{3+}$ concentration [15], $m(C_\%)$, and the temperature dependence is a function proportional to the spectral overlap integral, $O(T)$, this can be described by
where the overlap integral $O(T) = \int \sigma _e(\lambda , T) \sigma _{ESA}(\lambda , T)\ \mathrm {d} \lambda$ is calculated between the emission $\sigma _e(\lambda , T)$ and $\sigma _{ESA}(\lambda , T)$ Excited State Absorption (ESA) cross sections of the ions involved in the energy transfer process, as described in [21].In Nd:YAG, ETU involves transitions from the metastable state $^4F_{3/2}$ to the manifolds $^4I_{15/2}$, $^4I_{13/2}$, or $^4I_{11/2}$, and respective transitions from the same metastable level to $^4G_{5/2}$, $^4G_{7/2}$, or $^4G_{9/2}$. A detailed study on the evolution of the overlap integral $O(T)$ requires an extensive characterisation not only of emission cross section, which can be found in [17], but also of the temperature-dependence of the ESA cross section. The latter measurements are not straightforward to execute, and although some data for the RT case can be found in the literature [22], no temperature-dependence studies have been presented for this parameter, to the best of our knowledge. An example of the spectral overlap that determines the value of $O(T)$ around $1\ \mu m$ is presented in Fig. 7: it is appreciable that the lack of data for the low temperatures of the ESA cross section doesn’t allow the calculation of $O(T)$, and comparison with the experimental results.
Fig. 7. Spectral overlap between the emission transition $^4F_{3/2} \rightarrow ^4I_{11/2}$ (solid coloured lines, from [17]) and the 10x-magnified ESA transition $^4F_{3/2} \rightarrow ^4G_{9/2}$ (red dashed line, from [22]).
In light of this discussion, we provide in Table 2 the best fitting parameters for a second degree polynomial, the simplest function that fits our experimental data, for the respective concentrations. The two curves only differ from a rigid shift in the y-axis.
Table 2. Coefficients for the second degree polynominal fitting curves in Fig. 6.
3.3 Implications of ETU on laser threshold
The combined results of [14,15] and this work demonstrate that in order to minimise the detrimental effects of ETU on laser performance, employing low-concentration samples is essential, as it is also observed in other crystals [16,18]. Despite the trend of increasing ETU with decreasing temperatures, using the model reported in [5], which includes the effects of ETU, we determine that the laser performance is dominated by the improved spectroscopic properties at cryogenic temperatures.
To illustrate, we have calculated the threshold pump power for a $170\ mm$-long plano-concave linear cavity comprising a flat high-reflectance mirror and a T=10%, 200mm radius of curvature output coupler, as in [23]. The Nd:YAG crystal, coated for $946\ nm$ operation, and positioned $50\ mm$ from the input mirror, was in-band pumped by a $869\ nm$ diode-laser bar providing a $350\ \mu m$ beam radius. For the calculations we studied 0.30at.%- and 0.60at.%-doped Nd:YAG samples, of lengths $15\ mm$ and $7.5\ mm$ respectively, in order to keep the pump absorption over the two crystal lengths consistent.
As shown in Fig. 8, without considering the effects of ETU ($W_{ETU} = 0$), the temperature-dependent threshold pump-power reduces due to enhanced gain and lower reabsorption losses, and is the same for both doping concentrations – as one would expect from the fact that the product $C_{\%}l_R$ is a constant. When ETU is accounted however, the temperature-dependent threshold pump-power exhibits two separate curves for the two doping concentrations.
Fig. 8. Calculated laser threshold vs cryo-temperatures, including and not including ETU effects, for 0.3at.%-, 0.6at.%-, and 1.07at.%-doped Nd:YAG, according to [5].
At RT the higher concentration sample would have an additional 24% heat load with respect to the threshold power without ETU, compared with only 5.5% at LNT. While for the lower concentration crystal the additional load is only 10% and 2.5% of the ETU-free threshold power, respectively. This highlights two key points: first, that despite the increasing ETU parameter the spectroscopic and thermo-optical enhancement dominates through the reduction in laser threshold at cryogenic temperatures; second, higher Nd-doping leads to stronger ETU contributions and a higher fractional thermal load, which is a key parameter for cryostats due to their reducing cooling-capacity with lowering temperatures.
To characterise the effect of ETU on the $946\ nm$ transition of Nd:YAG over the range (RT-LNT), we calculate the temperature-dependence of a Figure-Of-Merit (FOM) $F_q$ as defined in [24]:
where, $\sigma _{abs}$ and $\sigma _{em}$, are the effective absorption and emission cross sections at the pump ($869\ nm$ in this example) and laser wavelength, respectively, presented in [17], and $\alpha _P$ is the absorption coefficient at the pump wavelength. By its definition, this quantity, independent of the particular laser design employed, is defined by the gain material properties, and, as argued in [24], a high $F_q$ is essential for keeping a low threshold with minimal additional thermal load. Figure 9 shows that for the $946\; nm$ transition of in-band pumped (869 nm) Nd:YAG, this parameter increases with decreasing doping concentration and temperature.Fig. 9. Figure-of-merit $F_q$ as defined in [24] vs cryo-temperatures for 0.3at.%-, 0.6at.%-, and 1.07at.%-doped Nd:YAG.
In order to estimate the FOM for the commonly used 1.10at.%-doped Nd:YAG, we have estimated an ETU curve for $\sim$1.10at.%-doping by shifting the measured 0.60at.%-doping curve by the difference between $W_{ETU}(0.60at.\%, RT)$ and $W_{ETU}(1.07at.\%, RT)$, where the second data point is reported in [15], as showed in the inset of Fig. 9.
A good approximation of the laser threshold including ETU with respect to the case without is [24]:
4. Conclusions
In conclusion, we have undertaken a thorough investigation of the absorption cross section around $808\ nm$ in Nd:YAG across the temperatures from RT to LNT. It was observed that with decreasing temperature the strongest peak at $\sim 808\ nm$ shows a 6-fold intensity increase and a similar decrease in bandwidth. Exploiting these measurements, we have characterised the ETU macroparameter for 0.57at.%- and 0.30at.%-doped Nd:YAG crystals over the same temperature range. Employing an automated z-scan technique, we established that the ETU coefficient increases quadratically with decreasing temperature. Utilising temperature-dependent spectroscopic and ETU parameters, we illustrate their effects on the temperature-dependent threshold pump power for a simple Nd:YAG laser operating at $946\ nm$. The reduction in the laser threshold is dominated by an increased 4-level characteristic and enhanced absorption at cryogenic temperatures, while the additional thermal load associated with ETU is reduced in line with an increase in $F_q$, a figure of merit for the effect of ETU.
These results provide a substantial addition to the literature regarding ETU in Nd:YAG. In addition, they demonstrate that exploiting low-concentration Nd:YAG is favourable for reducing additional thermal load due to ETU. In summary, cryogenic-cooling ultimately enhances the potential laser performance for the low-gain $946\ nm$ transition of Nd:YAG, paving the way for future power- and energy-scaling this NIR laser transition.
Funding
Engineering and Physical Sciences Research Council (EP/M020932/1).
Acknowledgements
S. Cante and J. I. Mackenzie acknowledge support from EPSRC, award reference 1921236.
Disclosures
The authors declare no conflicts of interest.
Data Availability
The datasets used in this work are available from https://doi.org/10.5258/SOTON/D1447.
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