Characterising energy transfer upconversion in Nd-doped vanadates at elevated temperatures

The Energy Transfer Upconversion (ETU) macroparameter is measured for Nd-doped GdVO4 and YVO4 samples at temperatures ranging from Room Temperature (RT) to 450K , by means of a simple and automated z-scan technique. Furthermore, the ground state absorption cross section into the H9/2 +4 F5/2 energy levels is characterised for both crystals over the same range of temperatures. The 808 nm π-polarisation absorption cross section is found to decrease from (58.6 ± 0.2) pm2 to (30.9 ± 0.6) pm2 for Nd:YVO4 and (54.0 ± 0.3) pm2 to (25.7 ± 0.5) pm2 for Nd:GdVO4, from RT to 450K . Over the same range the ETU coefficient decreases from (3.2±0.7) 10−16 cm3/s to (1.8±0.4) 10−16 cm3/s and (5.0±0.5) 10−16 cm3/s to (3.4±0.2) 10−16 cm3/s for 0.6at.% and 1at.% Nd:YVO4 respectively, and (3.3±0.5) 10−16 cm3/s to (0.8 ± 0.2) 10−16 cm3/s and (5.5 ± 0.5) 10−16 cm3/s to (3.1 ± 0.3) 10−16 cm3/s for 0.5at.% and 1.1at.% Nd:GdVO4. © 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement OCIS codes: (190.7220) Upconversion, (140.3530) Lasers, neodymium, (300.1030) Absorption. References and links 1. T. Y. Fan and R. L. Byer, “Modeling and CW Operation of a Quasi-Three-Level 946 nm Nd:YAG Laser,” IEEE J. Quantum Electron. 23(5), 605–612 (1987). 2. W. P. Risk, “Modeling of longitudinally pumped solid-state lasers exhibiting reabsorption losses,” J. Opt. Soc. Am. B 5(7), 1412–1423(1988). 3. S. Bjurshagen and R. Koch, “Modeling of Energy-Transfer Upconversion and Thermal Effects in End-Pumped Quasi-Three-Level Lasers,” Appl. Opt. 43(24), 4753–4767 (2004). 4. V. Ostroumov, T. Jensen, J.-P. Meyn, G. Huber, and M. A. Noginov, "Study of luminescence concentration quenching and energy transfer upconversion in Nd-doped LaSc3(BO3)4 and GdVO4 laser crystals," J. Opt. Soc. Am. B 15(3), 1025–1060 (1998). 5. Y.F. Chen, C.C. Liao, Y.P. Lan, and S.C. Wang, "Determination of the Auger upconversion rate in fiber-coupled diode end-pumped Nd:YAG and Nd:YVO4 crystals," Appl. Phys. B 70(4), 487–490 (2000). 6. R. Yan, S. J. Yoon, S. J. Beecher, and J. I. Mackenzie, “Measuring the elevated temperature dependence of upconversion in Nd:YAG,” IEEE J. Sel. Top. Quantum Electron. 21(1), 1–7 (2015). 7. Y. Sato and T. Taira, “Temperature dependencies of stimulated emission cross section for Nd-doped solid-state laser materials,” Opt. Mater. Express 2(8), 1076–1087 (2012). 8. J. O. White and C. E. Mungan, “Measurement of up-conversion in Er:YAG via z-scan,” J. Opt. Soc. Am. B 28(10), 2358–2361 (2011). 9. S. J. Yoon, R. P. Yan, S. J. Beecher, and J. I. Mackenzie, “Concentration dependence of energy transfer upconversion in Nd:YAG,” Opt. Mater. Express 5(5), 926–931 (2015). 10. W. J. Lima, V. M. Martins, A. F. G. Monte, D. N. Messias, N. O. Dantas, M. J. V. Bell, and T. Catunda, “Energy transfer upconversion on neodymium doped phosphate glasses investigated by Z-scan technique,” Opt. Mater. Express 35(9), 1724–1727 (2013). 11. S. Goldring, R. Lavi, V. Lupei, “Decay dynamics of excited Nd3+ ions in YVO4 following weak excitation,” IEEE J. Quantum Electron. 46(2), 169–181 (2010). 12. S. Guy, C. L. Bonner, D. P. Shepherd, D. C. Hanna, A. C. Tropper, and B. Ferrand, “High-inversion densities in Nd:YAG: up-conversion and bleaching,” IEEE J. Quantum Electron. 34(5), 900–909 (1998). 13. C. Czeranowsky, “Resonatorinterne Frequenzverdopplung von diodengepumpten Neodym-Lasern mit hohen Ausgangsleistungen im blauen Spektralbereich,” Dissertation, Universitat Hamburg (2002). 14. J. W. Kim, J. I. Mackenzie, and W. a. Clarkson, “Influence of energy-transfer-upconversion on threshold pump power in quasi-three-level solid-state lasers,” Opt. Express 17(14), 11935–11943 (2009). 15. D. C. Brown, R. Nelson, and L. Billings, “End-cooled Nd:YVO4 Diode-pumped Laser,” Appl. Opt. 36(33), 2–4 (1991).


Introduction
Nd-doped vanadate crystals are widely used in diode-pumped solid-state lasers.Compared to Nd:YAG, both Nd:YVO 4 and Nd:GdVO 4 have a higher absorption cross section at 808 nm (π-pol), coupled with a larger emission cross section, making it possible to achieve much higher gains per unit length.Most of their key spectroscopic properties have been largely investigated and characterised in order to model and optimise laser performance.However, some parameters have not yet been determined with sufficient precision or reported at all, with consequent difficulties in making a reliable choice of design parameters, e.g. the Energy Transfer Upconversion (ETU) parameter and the temperature dependence of the absorption cross section.
Vanadate crystals are typically employed in lasers operating on the strongest 1.06 µm emission line; however, the lower gain quasi-four-level system operating on the 0.9 µm transition could potentially be quite efficient, thanks to a lower quantum defect between pump and output wavelengths.As the latter transition suffers reabsorption losses and it has lower emission cross section, it is susceptible to the detrimental thermal effects associated with the waste heat deposited during the excitation processes [1][2][3].As such, its laser performance could be improved if key contributors to these effects are well characterised.
Parasitic effects like ETU are also deleterious for transitions that require high-irradiance pumping, such as the 0.9 µm quasi-four-level ( 4 F 3/2 → 4 I 9.2 ) Nd 3+ system, as they compromise the already relatively-low gain [3].The ETU process (Fig. 1), in most Nd-doped hosts, leads to the excited ion relaxing back to the 4 F 3/2 level, thus reducing the upper laser level population by one.Waste heat is produced via the non-radiative decay channels of the excited ions, adding to the other sources of heat.Depending on its strength, ETU can potentially be catastrophic for laser operation on the 0.9 µm transition, as will be shown later.
Although some values are reported in literature for the ETU parameter of Nd-doped vanadates [4,5], the temperature dependence of such parameters has not been investigated so far: in previous work we demonstrated a strong temperature-dependence of the ETU macroparameter in Nd:YAG [6] and here we use the same z-scan technique to probe the analogous dependence in Nd:YVO 4 and Nd:GdVO 4 .In addition in this work, we present a comprehensive study of the absorption cross section into the 2 H 9/2 + 4 F 5/2 energy levels, over the range of temperatures from RT to 450K.These results, which show a decrease in peak cross section with increasing temperature, were key to the characterisation of the macroscopic ETU parameter over the same range of temperatures.
In the z-scan technique the incident pump irradiance is controlled by scanning a sample through the focus of a laser beam, and the change in transmission is then related back to the input irradiance (position).We compared the measured transmission curve to the prediction of a spatially dependent two-level rate-equation model, using the ETU coefficient as the only fitting parameter.
This information, coupled with elevated temperature emission cross section data [7], provide a new level of detail for the design parameters needed for these materials, which may have direct impact on further optimisation of vanadate lasers operating at elevated temperatures or under intense pumping conditions.

Absorption cross section
Small signal absorption measurements, well described by the Beer-Lambert law, can provide an accurate measure of the absorption cross section or the doping ion concentration, once the other parameters are known.
Beer-Lambert law describes how light is absorbed as it propagates inside a material: where I out is the transmitted irradiance, I in is the pump-laser incident irradiance, α abs (λ) is the absorption coefficient per unit length, σ abs (λ) is the absorption cross section, L is the length of the crystal, C % the doping-ion percentage, with N 0 the density of doping-ions at 1at.%.Inverting eqn.
(1) we have We recorded the input and the transmission spectra of the broadband amplified spontaneous emission (ASE) of a LIMO fibre-coupled diode-laser.Enabling the calculation of I in /I out , once the corrections due to Fresnel reflections at the uncoated facets of the crystal for the appropriate polarisation state, were made.
To determine C % , the usual practice is to measure α abs (λ) for a fixed wavelength λ * , usually one corresponding to the strongest absorption line, and applying Eqn.(2), with σ abs (λ * ) known from trusted sources.In order to minimise the error on the doping ion concentration determination, or rather, increase the confidence in its value, we employed eqn.(3).
Using several different values of λ i , corresponding to different absorption peaks of known σ abs (λ i ), and averaged, the (ideally identical, but in reality not) results: where N is the total number of absorption lines used and Eqn.(4.2) is the standard deviation from the average, the uncertainty associated to our concentration measurement.
Once we established the doping ion concentration for our 4 samples, we thoroughly characterised the 2 H 9/2 + 4 F 5/2 absorption cross section and its dependence upon temperature by applying eqn.
(2) and retrieving the absorption cross section spectra σ abs (λ) in the range RT to 450K.

ETU model and data interpretation
The z-scan technique has been previously used to determine the magnitude of the ETU parameter for various rare-earth ions in different host media [6,[8][9][10].It consists in scanning the sample through the waist of a converging/diverging pump beam, thus enabling the scaling of the input irradiance from values significantly lower than (small-signal transmission regime) to ones comparable to, or higher than, the saturation irradiance.The transmission through the sample with respect to each z-scan position (irradiance) is compared to the predictions of the spatially dependent two-level rate-equation model ( 5), described in detail in [6].
where for the neodymium-doped host N 1 (r, z) is the population density of the ground state 4 I 9/2 , N 2 (r, z) is the population density of the excited state 4 F 3/2 , σ abs is the measured absorption cross section at the pump photon energy hν p , and W ETU is the macroscopic ETU coefficient to be determined.The parameter τ f is the measured fluorescence lifetime in the small signal transmission regime (i.e.weak excitation densities) and it accounts for both the intrinsic lifetime of the sample in question and the cross relaxation rate [11].I p is the spatial pump irradiance distribution that changes according to (5.3), which was characterised through a preliminary automated beam quality measurement and confirmed to be Gaussian within the experimental errors.
The pump transmission through the sample at each step of the z-scan, corresponding to different beam sizes, was calculated by numerically solving the system of Eqs.(5) for a fixed power P in , measured beam dimensions, and by iteratively calculating the variation of I p (r, z), accounting for the Gaussian spatial distribution and its dependence upon N 1 (r, z).In order to facilitate the computation and increase the density of the grid used for the iterative calculation (300 radial and 1000 longitudinal steps), system (5) was solved for the steady state conditions ∂N i /∂t = 0 (i = 1, 2).Using these conditions and (6.1), N 1 was obtained from the analytical solution of (5.1), (6.2).
At the end of the iteration steps the transmitted irradiance I t (r, z) is integrated over the effective beam area in order to obtain the transmitted pump power P t , to compare the simulated transmittance, T th = P t /P in , with the measured one.The automated data collection focussed on the minimisation of the uncertainty associated with the fixed parameters of model ( 5).The automated setup shown in Fig. 2 was employed to first perform M 2 measurements of the Ti:sapphire pump-laser, and, successively, z-scan measurements.x,y = (1.06 ± 0.01), w x = (19.7 ± 0.2) µm and w y = (19.9± 0.2) µm.The z-scan setup was calibrated in order to retrieve quantitative relations between the voltages produced by the reference and transmission photodiodes PD 1 and PD 2 and the power after the 200 mm moving lens (L 3 ), i.e. incident power P in , and before the 175 mm moving collection lens (L 4 ), i.e. transmitted power P t , respectively.Once determined, the analytical forms of the relations were obtained by fitting polynomial curves to the calibration data, P in = f (V PD 1 ) and P t = g(V PD 2 ), which could always precisely quantify P in and P t from PD 1 and PD 2 's voltage readings.The goodness of the calibration was verified by making sure that z-scan measurements performed with no sample in the setup always returned, after the conversion of voltages into powers, a transmittance of (100 ± 1)%.
The way the errors associated to each modelling parameter affected the resultant ETU parameter was evaluated by propagating the uncertainties associated to these parameters through the numerical model (5).It was established that the power instability of the pump beam dominated.
Therefore, constant and precise monitoring of the incident and transmitted powers (voltages) through a LabView driven interface mitigated the Ti:sapphire power instabilities by fixing a suitable tolerance window for the input power: the measurements corresponding to incident powers outside the allowed band were discarded.Furthermore, the transmittance measurement was repeated multiple times, of the order of 50 samples, at each z-scan position, in order to increase the confidence in the measured value and at the same time determine an uncertainty on each data point given by the standard deviation from the mean as defined in (4.2).
Defining a band, whose limits were Tz ± ∆T z , the data was fitted to the model (5), giving outlying curves corresponding to limiting ETU values that established the error on the final result.
The fitting procedure is based on the minimisation of the sum of the squared residuals defined as where the dependence of the theoretical transmission value T th (z) (calculated numerically from model ( 5)) on the ETU parameter W ETU is emphasised, because the latter is the minimising parameter being sought.The same fitting procedure was employed for the measurement of the small-signal fluorescence lifetime: theoretical model ( 8) was fitted to the fluorescence waveform collected at each step of the z-scan (sample in Fig. 3) by using V 0 and τ f as fitting parameters.We only accounted for the data collected in the small signal transmission regime, obtaining a number of usable waveforms in the order of 100 and a typical dispersion around the average result of ∼ 1%, that gave us good confidence in the resulting value for the fluorescnce lifetime, moderated by the cross relaxation process.The fluorescence signal was monitored throughout the z-scan: the effect of ETU in shortening the lifetime in the high irradiance regime can be observed in Fig. 3. Unlike [12], this shortened lifetime could not be used to determine the ETU macroparameter due to the Gaussian distribution of the pump beam.

Experimental setup
The setup employed for the small signal absorption measurements, shown in Fig. 4, comprising a simple symmetric telescope, coupling the broadband amplified spontaneous emission (ASE) of a sub-threshold fibre-coupled diode-laser (LIMO60-F200-DL808) to the sample under test.The incident 6 mW ASE, extending for ∼ 40 nm around 808 nm, was collimated by lens L 1 ( f = 30 mm) and focused by lens L 2 ( f = 150 mm) onto the analysed sample.The incident light was polarised with a polariser.The transmitted light was re-collimated by lens L 3 ( f = 150 mm) and finally re-imaged into a fibre-coupled Optical Spectrum Analyser (ANDO AQ6317B) by lens L 4 ( f = 30 mm).When probing different polarisations, the setup was kept fixed, and the crystal rotated, providing access to both π-and σ-polarisations for the anisotropic vanadate crystals.
A beam radius of 500 µm with a confocal parameter of b 36 mm was produced in the sample.The input, P in (λ), and the transmitted, P out (λ), power spectra of the diode were recorded with a resolution of 0.05 nm using the OSA.Given our experimental conditions that the beam size doesn't vary significantly over the crystal length (L b, with L 1mm), the equivalence I in (λ) I out (λ) = P in (λ) P out (λ) could be made.The crystal was positioned on a heated copper mount, whose temperature could be changed in the range from RT to 450K.We could thus characterise the absorption cross section of Nd:YVO 4 and Nd:GdVO 4 for several different elevated temperatures by applying eqn.(2).

Results and discussion
With small signal absorption measurements performed in the band 780 − 830 nm around the peak absorption at 808 nm, for both polarisations σ-pol and π-pol, there were on the order of 7 peaks available (N).We obtained the results summarised in table 1 for the doping-ion concentrations of the respective samples and associated errors, assuming reference peaks from [13].

Fig. 3 .
Fig. 3. Sample of waveforms collected at each z-scan step.Solid lines: PD 1 and PD 2 signals [V], in red and pink respectively; dashed lines: small-signal and high irradiance regimes fluorescence normalised signals [a.u.], in blue and green respectively.