1. Introduction

Ytterbium doped materials have recently attracted much interest as amplifying medium in high power solid state lasers [1, 2]. In the latter, it is crucial to minimize thermal effects which can lead to material failure or beam quality decrease [3–5]. This can be achieved by reducing heat generation, which is usually produced by non radiative relaxations within the active ion. The amount of heat generated is proportional to the quantum defect η_laser = 1 − λ_pump/λ_laser where λ_pump and λ_laser are the pump and laser wavelengths. The quantum defect reaches the lowest values in ytterbium doped materials where η_laser can be as low as 3% in Yb:GdVO₄ [6] and even 0.8 % in Yb:CaGdAlO₄ (CALGO) [7] compared to 25% in neodymium doped crystals. Other solutions to reduce thermal effects include high surface to volume geometries like fibers [8] and thin disks [9], and/or high thermal conductivity and low thermal expansion materials. To precisely assess the efficiency of these different approaches, it is necessary to measure temperature gradients in the material volume and during laser action to take into account pump absorption saturation effects for example. This is a difficult task as the temperature inside the material normally does not exceed 200 °C which corresponds to an infrared thermal emission peaking at 5.8 μm. Many materials, including oxide crystals are not transparent at these wavelengths and only surface temperatures can be measured by thermal cameras [10, 11]. This prevents direct measurements of the pumped volume of the material, where the highest temperatures are reached. In this paper, we demonstrate, for the first time to our knowledge, temperature measurements of the pumped region inside an Yb³⁺ doped crystal (Yb³⁺:CALGO) during laser action. This is obtained by recording the green emission from erbium impurities which is known as an accurate temperature monitor [12–15]. Er³⁺ visible luminescence results from efficient successive energy transfers between Yb³⁺ and Er³⁺ ions, a process called APTE (Addition de Photons par Transfert d’Energie) or ETU (Energy Transfer Upconversion) [16, 17]. The use of Er³⁺ upconverted emission in the green spectral region, instead of directly recording Yb³⁺ fluorescence [18], allows one to completely eliminate diffused light from pump and stimulated emission which may strongly perturb Yb³⁺ spontaneous emission spectrum. It is also a general method for Yb³⁺ doped materials since Er³⁺ is a very common impurity of Yb³⁺, these rare earth ions having close electronic configurations (respectively 4f¹¹ and 4f¹³).

2. Experiments

The experimental set-up for measurements during laser action is shown in Fig. 1. Orthogonally to a plano-concave laser cavity containing a 2 at%Yb³⁺:CALGO single crystal, two lenses collected visible emission on the entrance slit of a 25 cm Jobin-Yvon spectrometer equipped with a photomultiplier. A Schott BG 18 filter blocked infrared light around 1 μm. With that set of lenses, an image of the crystal was obtained on the input of the spectrometer with a magnification of 1.5. Translation of the first lens translated the crystal image on the spectrometer slit. Thus, the sample could be scanned in order to analyze the temperature profile along the pumped zone. With slits 500 μm wide, the temperature was averaged over a pumped zone approximately described by a cylinder of 100 μm radius and 330 μm length. The pump source was a Coherent 890 titanium sapphire (Ti-Sa) laser tuned to 980 nm. For Er³⁺ luminescence calibration, the same set-up (without the laser cavity) was used with a thin sample glued with thermal grease to a regulated heating plate allowing us to set sample temperature between 40 °C and 250 °C. This sample was only 1 mm thick, with a 1 cm² surface in contact with the heating plate to improve heat transfer. Moreover, to ensure low thermal loading by the Ti-Sa excitation, the pump power was limited to 500 mW. In these conditions, temperature measurements by erbium luminescence (see below) showed no dependence on laser power. We then concluded that the sample temperature was that of the regulated plate, within the measurement accuracy of +/− 2°C (see below).

 

Fig. 1 Experimental setup for erbium green emission measurements during laser action.

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3. Results and discussion

3.1. Visible emissions in Yb:CALGO and temperature calibration

Visible emissions recorded in Yb³⁺:CALGO in the 440–600 nm range under 980 nm excitation are presented in Fig. 2 and are similar to those found in other Yb³⁺ doped materials [19]. A broad line centered at 500 nm corresponds to the cooperative emission of ytterbium ions (²F_5/2,²F_5/2) → (²F_7/2,²F_7/2) [20] as confirmed by the calculation of the infrared emission (²F_5/2 → ²F_7/2) convolution (Fig. 4, inset). The emission peaking at 470 nm is attributed to thulium ions (¹G₄ → ³H₆ transition), which are also a common impurity of Yb³⁺ ions. Tm³⁺ ions are excited from Yb³⁺ ions through a three step upconversion process [17,21]. Erbium ion emissions (²H_11/2,⁴S_3/2 → ⁴I_15/2 transitions) are observed between 520 and 570 nm.

 

Fig. 2 Emission spectra in the blue-green spectral range of Yb³⁺ :CALGO under 980 nm excitation at three different temperatures. The spectra are normalized to the line denoted by a star.

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Fig. 4 Yb³⁺:CALGO visible fluorescence spectrum at 100 °C. Dashed line: Gaussian line-shape fit to Yb³⁺ cooperative luminescence. Er³⁺ intensities are evaluated at 530 and 550 nm (denoted by A and B respectively). Inset: Yb³⁺ infrared emission convolution (solid line) and fit by a Gaussian lineshape (dotted line).

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Er³⁺ excitation proceeds by a first energy transfer from an excited ytterbium ion: (⁴I_15/2(Er³⁺),² F_5/2(Yb³⁺)) → (⁴I_11/2(Er³⁺),² F_7/2(Yb³⁺)) (see Fig. 3). This is much more efficient than direct Er³⁺ absorption at 980 nm, which is negligible compared to Yb³⁺ one since erbium concentration is much lower than ytterbium one (see below). In a second step, an energy transfer from an excited Yb³⁺ ion to an already excited Er³⁺ ion in the ⁴I_11/2 multiplet can take place, resulting in a Er³⁺ ion in the ⁴F_7/2 multiplet: (⁴I_11/2(Er³⁺),² F_5/2(Yb³⁺)) → (⁴F_7/2(Er³⁺),² F_7/2(Yb³⁺)). After a fast non radiative relaxation, the ⁴S_3/2 and ²H_11/2 multiplets are finally populated and emissions occur at about 550 nm (⁴S_3/2 →⁴ I_15/2) and 530 nm (²H_11/2 →⁴ I_15/2) (Fig. 3). Typical distances for efficient energy transfer between rare earth ions are on the order of a few nanometers, leading to energy diffusion lengths on the order of 1 μm [22, 23], which is negligible compared to the excited volumes in laser experiments. Erbium fluorescence may therefore be safely assumed to originate from the infrared excited volume. In laser experiments, this volume could be different from the laser mode one. In these two volumes, Yb³⁺ excited state populations and therefore Er³⁺ ones can be significantly different. Temperatures deduced from Er³⁺ fluorescence will therefore correspond to an average over these volumes.

 

Fig. 3 Energy level diagrams of Er³⁺ and Yb³⁺ ions, energy transfers occurring in the up-conversion process (curved lines), non radiative relaxations (dotted lines) and green emissions (thick lines).

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Er³⁺ concentration is estimated to be ≈10 ppm (1.25 × 10¹⁷ ions/cm³), based on the purity of the starting materials. At this level, Er³⁺ has a negligible effect on Yb³⁺ excited state population, as can be deduced from data obtained in CaYAlO₄, a close isostructural compound [24,25]. In this host, the lifetimes of erbium ⁴I_11/2 and ytterbium ²F_5/2 multiplets are very close (435 μs and 420 μs respectively), leading to a thermalisation between these levels in the codoped material [24]. The corresponding relative decrease in ²F_5/2 population is therefore approximately equal to the Er³⁺ to Yb³⁺ concentration ratio, i.e. 1/2000. The second energy transfer from Yb³⁺ to Er³⁺, which populates ²H_11/2 and ⁴S_3/2 multiplets (Fig. 3), has a rate of C = 2.5 × 10⁻¹⁶ cm³s⁻¹ [24]. For a given population N of the ⁴I_11/2 multiplet, this transfer will add a term CN to Yb³⁺ relaxation rate (W = 2380 s⁻¹). Setting N to half of erbium concentration, we find a maximum rate of CN = 16 s⁻¹, so CN ≈ W/150. This also shows that a two-or three-fold increase in Er³⁺ concentration (e.g. by intentional doping) should be possible without significantly affecting Yb³⁺ excited state population. This may be useful to get a larger Er³⁺ green emission compared to Yb³⁺ cooperative one.

Populations N in the ⁴S_3/2 and ²H_11/2 multiplets (denoted by l and h respectively) obey Boltzmann thermal equilibrium:

Since transition oscillator strengths are unknown, temperature measurements require a calibration, i.e. recording Er³⁺ emission spectra as a function of temperature. As seen in Fig. 2, Yb³⁺ cooperative emission partly overlaps Er³⁺ one in the 520–540 nm range. This was taken into account by modeling cooperative emission by a Gaussian lineshape. Indeed the latter is a very good fit to Yb³⁺ infrared emission convolution (see inset in Fig. 4). The absence of sharp features in the cooperative emission is due to Yb³⁺ very broad infrared emission in CALGO [6]. In other materials, a more detailed modeling of cooperative emission may be necessary. In order to further minimize errors due to cooperative emission, temperature was then calibrated by measuring emission peak intensity ratios at 530 and 550 nm (A and B arrows, Fig. 4), subtracting cooperative emission contribution. Possible changes in cooperative emission shape and/or intensity as a function of temperature or laser excitation intensity was therefore taken into account.

A plot of the intensity ratio between 530 and 550 nm peak emission intensities versus crystal temperature is presented in Fig. 5, showing a good agreement with an exponential law (Eq. (1)), although the latter is in principle only valid for integrated intensities. This result is in agreement with the limited change in erbium emission shapes observed in this temperature range (Fig. 2). The fitted value for ΔE in Eq. 1 is 750 cm⁻¹, corresponding to the value deduced from emission mean energies. The fitted exponential curve was then used to deduce temperatures from peak intensity ratios, with an accuracy of ±2°C. This value was limited by the pump laser intensity fluctuations and the spectrum acquisition time on the spectrometer. It could be improved by using a CCD detector and laser diode excitation.

 

Fig. 5 ²H_11/2 and ⁴S_3/2 emission intensity ratios as a function of temperature (squares) and exponential fit (solid line).

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3.2. Temperature measurements during laser action

Temperatures of a 2 at%Yb:CALGO were measured from erbium green emissions ratio with or without laser action taking place in the crystal, using Fig. 1 setup. The sample had a section of 4 × 4mm² and a thickness of 1.8 mm. Only one side of the crystal was in contact with a mount using a plastic layer for thermal insulation. The contact area between the layer and the crystal was small so that heat exchanges occurred mainly between the crystal and the surrounding air. This was necessary to generate high enough temperatures from the limited power (up to 2W at 980 nm) delivered by the Ti-Sa laser. Fig. 6 shows the temperature recorded at the center of the sample (with respect to thickness and averaged over a small volume, see Experimental section) as a function of pump power. In the investigated power range, 63 % of the incident pump power was absorbed. Thanks to thermal insulation, temperatures as high as 110 °C were reached. These were similar to those measured at the surface of the same material with 83 W of pump power but with the latter inserted in a copper mount which allows for high heat transfer [26].

 

Fig. 6 Internal temperature of a 2 at%Yb³⁺:CALGO under 980 nm excitation as a function of pump power with (triangles) or without (squares) laser action. The sample is thermally isolated.

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By slightly misaligning the output mirror we could perform the same experiment without laser action. The temperatures obtained are higher than those observed under laser action, reaching 112 °C instead of 104 °C at the maximum pump power. The mean fluorescence wavelength (1004 nm) is significantly smaller than the laser emission one (1040 nm), which should result in a higher thermal load and therefore higher temperatures during laser action. However, non radiative relaxations (mainly energy transfers to traps) of the excited state decrease when laser action takes place because of stimulated emission [27]. This has the effect of reducing the thermal load compared to the non lasing case. In our experiments, the latter effect seems to dominate over the fluorescence and laser wavelength difference. Another process which has to be taken into account at high pump intensities is Yb³⁺ absorption saturation [29]. Since stimulated emission decreases saturation, absorption tends to be larger during laser action, which in turn increases the thermal load. In our experiments, transmitted pump power showed a linear dependence on input power, so that no saturation occurred. However, it may explain the higher temperature measured during laser action, compared to the case without laser action, in Ref. [26], where high pump powers were used.

In the limit of a high intracavity laser intensity, it can be considered that non radiative relaxations are negligible and that the thermal load is directly proportional to the quantum defect, η_laser = 5.7% in our case [27]. Without laser action, the thermal load due to non radiative relaxations adds to the one due to the difference between pump and mean fluorescence wavelengths. The latter corresponds to a quantum defect of η_fluo = 2%. Fig. 6 shows that the thermal loads with and without laser action are similar, which leads to a quantum efficiency of ≈ 96 % for Yb^{3+ 2}F_5/2 excited multiplet. This value is in reasonable agreement with Yb³⁺ lifetime measurements which gives a quantum efficiency of 93 ± 5 % [28]. Yb³⁺ quantum efficiency includes the effect or Er³⁺ impurities, which therefore contribute to the thermal load. However, from estimations given in section 3.1, the corresponding decrease in Yb³⁺ quantum efficiency should not exceed 1 %, even taking into account the relatively small quantum efficiencies of the ⁴I_11/2 and ⁴S_3/2 multiplets, 17 % and 43 % respectively [25]. The contribution of Yb³⁺ quantum defect to the thermal load during laser action was confirmed by changing the cavity output mirror, in order to obtain a shorter laser emission wavelength (1013 nm). This should decrease the thermal load and we indeed observed a 13 % decrease in crystal temperature at maximum pump power.

To check the validity of the temperature measurement, a simple simulation was run using a finite element program, assuming that the thermal load during laser action was only due to the quantum defect. Simulation parameters included the sample dimensions and quantum defect given above, as well as the absorption coefficient (0.99 cm⁻¹ at 980 nm), the pump beam waist (100 μm) and the crystal mean thermal conductivity (k = 6.5 Wm⁻¹K⁻¹ [6]). Experimental temperatures could be reproduced with a heat transfer coefficient for all sample sides of 17 Wm⁻²K⁻¹). Although we could not measure the latter value, it is consistent with published values [11].

Finally, temperature was measured along the cavity axis at 2 W pump power (Fig. 7) using a 5 mm long crystal. A significant difference (10 ±4 °C) can be observed between points located at 0.7 and 4.3 mm from the side where the pump beam entered the crystal. The decrease of the temperature with increasing distance from the input face simply reflects the corresponding decrease of the absorbed pump power. Since the Rayleigh length of the pump beam was 3 cm, we did not expect to see a temperature minimum inside the sample [4].

 

Fig. 7 Internal temperature variation in a 2 at%Yb³⁺:CALGO under 980 nm excitation (2 W pump power) as a function of the distance from the input face. The sample is thermally isolated. The solid line is a guide for the eyes.

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4. Conclusion

Temperature measurements of the pumped volume of an ytterbium doped material under laser action have been demonstrated. This was obtained by recording green emission from Er³⁺ impurities excited from Yb³⁺ ions by upconversion. Temperatures are deduced from the ratio between erbium emissions at 530 and 550 nm and a calibration performed between 40 and 250 °C. Experiments were performed on a Yb³⁺:CaGdAlO₄ crystal with or without laser action and at different pump powers and laser emission wavelengths. These results can be explained by relating the thermal load to quantum defect, mean fluorescence wavelength and Yb³⁺ quantum efficiency. Measuring temperatures of the pumped volume of a material can complement those obtained by using thermal cameras which can only access surface temperatures in oxide materials. This method could be extended to other laser materials as long as Er³⁺ green upconverted emission is larger than Yb³⁺ cooperative emission. Small intentional Er³⁺ doping could be used for this purpose.