1.Introduction

Sensitization of Nd:YAG laser emission by co-doping with Cr³⁺, with broader and stronger absorption in visible and able to transfer the excitation (ET) to Nd³⁺ was envisaged from the early years of development of the solid-state lasers as a means to improve the performances under broad-band pumping, such as with lamps or solar radiation [1]. However, the melt-grown (Cr-Nd):YAG single crystals do not enable full exploitation of the potential of sensitization since increasing Cr or Nd concentrations C_Cr or C_Nd reduces the quality of crystals and other valence states of Cr, such as + 4 are difficult to avoid; moreover, the large difference of the segregation coefficients of Cr ($\ge$1) and Nd (0.18) modifies the conditions of ET along the crystal. The interest for sensitization was revitalized with the advent of polycrystalline laser materials produced by ceramic techniques [2] that could enable tailoring of the laser material to the specific of the broad-band pumping [3]; however, the accidental scattering sources or defects (color centers, oxygen vacancies, foreign valence states for Cr and so on) shown by some ceramics call for tight quality control. Using (Cr, Nd):YAG ceramics improvement of pulsed or CW laser performances under lamp, solar simulator or real solar pumping was obtained compared with Nd:YAG [4–10], although utilization of large ceramic rods with high scattering losses [11] in a high performance laser setup impaired on such demonstration. Usually these ceramics contained (0.1 at.%Cr, 1at.%Nd) that granted superposition of absorption spectrum with the solar radiation in the range of 23% compared with ~14-15% for 1at.%Nd:YAG. The solar radiation at Earth’ surface (~1 kW/m²) impose utilization of large-surface collectors and concentrators and advanced technical solutions enabled gradual enhancement of the CW laser power to the range of 20 W per m² of collector. Spectroscopic properties and the ET in the (Cr,Nd):YAG ceramics were also investigated and their effect on laser properties was modeled [12–15]. However, the published results and analyses show great scatter, for instance the ET efficiency to 1 at.% Nd varies between 0.54 and 0.88. This paper brings new data based on high-resolution spectroscopy and emission dynamics in YAG ceramics with various C_Cr and C_Nd, including the evaluation of the energy transfer efficiency and their relevance for laser emission and heat generation is discussed.

2. Experiment

Highly transparent (x at.%Cr-y at.%Nd)-doped YAG ceramics (x = 1, 3, and y = 0, 1, 2) were produced by solid–state reaction synthesis followed by vacuum sintering. The absorption spectra were recorded at different temperatures using tungsten halogen lamp, one-meter monochromator, photomultipliers, Ge photodiodes and a Lock-in amplifier, and emission spectra were excited with 10 ns OPO laser at 445 or 590 nm in Cr³⁺ or at 808 nm in Nd³⁺.

3. Spectroscopic properties of Cr³⁺ and Nd³⁺ in YAG ceramics

3.1. Optical spectra and emission decay of Cr³⁺ in YAG ceramics

The optical spectra of Cr:YAG ceramics show the dominant presence of Cr³⁺, without any obvious evidence for other valences. The absorption spectra of Cr³⁺ are similar to the melt-grown single-crystals [16, 17] and are dominated by the strong and broad (around 70 nm) vibronic bands of the spin-allowed transitions ⁴A₂→⁴T₁ and ⁴A₂→⁴T₂ peaking at ~450 and 590 nm respectively, whereas the spin-forbidden absorption to the lowest excited level ²E is quite weak. Under solar pumping an effective pump wavelength can be defined by taking into account the overlap of solar emission spectrum with the Cr³⁺ absorption spectrum, ${\lambda }_{p,Cr}$~500 nm. At low temperatures the emission is dominated by transitions from the spin-orbit split components R₁ and R₂ (14552 and 14572 cm⁻¹) of ²E, accompanied by electron-phonon satellites superimposed on a vibronic band extending to about 800 nm. With increasing of temperature the lines shift and broaden, and the phonon satellites collect in the broad vibronic band. Additionally, thermallization of levels ⁴T₂ (placed ~800-1000 cm⁻¹ above ²E) and ⁴T₁ makes possible emission from these levels, manifested in broad vibronic bands that superimpose partially on the ²E emission extending it to NIR (to 900 nm range). The emission decay of Cr³⁺ under short pulse (~10 ns) 445 nm excitation depends on temperature and on C_Cr. At 10K detection at energies above ²E for the 1at.%Cr:YAG ceramic evidences a very weak emission with short lifetime (~150 µs) that can be attributed to ⁴T₂, while the R₁ emission shows rise-time consistent with a feeding mechanism with this 150 µs lifetime, reaches a maximum, then decays quasi-exponentially with lifetime ~8.5 ms; this confirms the flow of excitation ⁴T₁ → ⁴T₂ → ²E. Two new satellites (696.7 and 698.6 nm) with intensities increasing with C_Cr, are seen at 10K, with lifetimes 6.84 ms and 3.51 ms which can be suspected to belong to Cr³⁺ pairs or to centers perturbed by impurities or defects were also observed. With increasing temperature the R₁ decay becomes exponential and shortens: at 300K the lifetime for 1 at.%Cr is ~1.65 ms, shorter than reported for the 0.1 at.%Cr crystals; at higher C_Cr the decay becomes non-exponential and accelerates and this evidences energy transfer to traps which could be Cr³⁺ pairs, accidental impurities, Cr⁴⁺ ions (not evidenced) or new perturbed centers introduced by technology. In our samples this reduces the emission quantum efficiency by ~11% and ~30% for 1 and 3 at.% Cr.

3.2. Spectroscopic properties of Nd³⁺ in YAG ceramics

The spectroscopic properties of Nd:YAG ceramics are similar to those of the single crystals [17, 18]. The absorption spectrum contains numerous sharp lines extending to UV and under solar pumping an effective wavelength ${\lambda }_{pNd}$~660 nm can be defined. The emission decay of Nd³⁺ is influenced by the self-quenching due to ET: at weak excitation this is governed by the cross-relaxation (⁴F_3/2, ⁴I_9/2)→(⁴I_15/2, ⁴I_15/2) induced by static interactions (electric dipole-dipole and superexchange) between an excited ion (donor D) and a non-excited Nd³⁺ ion (acceptor A). The ⁴I_15/2 level is further de-excited by fast multiphonon interaction leading to heat generation. The self-quenching modifies the exponential decay with lifetime ${\tau }_D$ to

4. Energy transfer in (Cr,Nd):YAG

Superposition of Cr emission on Nd absorption determines temperature- and C_Nd dependent ET whose characteristics can be inferred from the emission decay of Cr³⁺. At 300K the high-resolution emission t 300 K the spectral resolution the emission decay starts with a very fast drop, dependent on C_Nd (Fig. 1) and after a certain lapse of time evolves to the $t^{1/2}$ dependence (Fig. 2), similar to Cr³⁺ in (Cr,Nd):GSGG [19]. The decay of Cr³⁺ in (1at.%Cr, 1at.%Nd):YAG can be analyzed with Eq. (1): the fast initial drop, sharper than in case of self-quenching of Nd:YAG, can be attributed to superexchange coupling with the Nd³⁺ ions from the 1st (6 sites) and the 2nd (6 sites) coordination spheres, and the subsequent decay is governed by electric d-d interaction with C_DA = 8.5 × 10⁻⁴⁰cm⁶s⁻¹, although the superexcange influences the decay of the third-oder Cr-Nd pairs too; a weak migration-assisted ET with ${\overline{W}}_0$~20 s⁻¹ (%Cr%Nd)⁻¹.is also present. These ET parameters describe the dependence on C_Nd of the decay for 3at.%Cr too. Emission quantum efficiency ${\eta }_{qe}$calculated [20] with these parameters is 0.48 and 0.23 for 1 and 2 at.% Nd, almost independent on C_Cr, leading to ET efficiencies ${\eta }_{ET}$ of 0.52 and 0.77 respectively, with almost 40% contribution from the fast ET due to superexchange.

 

Fig. 1 Emission decay of Cr³⁺ at 300K after 10ns 445 nm pumping: (a) beginning of decay; (b) long time evolution.

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Fig. 2 Evolution of Nd emission under 10 ns 445 nm excitation in (Cr-Nd):YAG ceramics: (a) at short time, (b) on long-time scale.

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Evolution of ⁴F_3/2 Nd³⁺ population after 445 nm short pulse excitation of Cr³⁺ is [21]

The consistency of the evolution of Nd³⁺ emission when pumping in Cr³⁺ with the decay of Cr³⁺ and with intrinsic decay of Nd³⁺ confirms the validity of the ET model used in analysis and shows that the longer evolution of Nd³⁺ emission than its intrinsic decay is caused solely by the slower feeding of excitation by the ET from Cr³⁺. Under non-selective short-pulse excitation with broad-band sources that encompass the absorption of both Cr³⁺ and Nd³⁺, such as Xe flashlamps, the decay contains contributions from both ions, function on C_Cr and C_Nd and thus the contribution of the Nd³⁺ ions excited directly by pump could cancel the rise part of temporal evolution of Nd³⁺ excited by ET from Cr³⁺: the global emission evolution would resemble a conventional decay. However, the “lifetime” of this pseudo-decay has not precise physical meaning and it depends both on C_Cr and C_Nd and on their excitation by pump.

5. The effect of sensitization on laser emission

Sensitization of Nd³⁺ emission under monochromatic pumping ${\lambda }_{pCr}$in Cr³⁺ modifies the small-signal gain coefficient form the value $g_{0Nd}$ when pumping directly in Nd³⁺ (${\lambda }_{pNd}$) to $g_{0Cr-Nd}=\gamma g_{0Nd}$ where $\gamma ={\eta }_{aCr}{\eta }_{ET}{\lambda }_{pNd}/({\eta }_{aNd}{\lambda }_{pCr})$, ${\eta }_{aCr}$ and ${\eta }_{aNd}$ being the absorption efficiencies and the threshold and the slope efficiency for CW laser emission become $P_{thCr-Nd}={\gamma }^{-1}{P}_{thNd}$ and ${\eta }_{slCr-Nd}=\gamma {\eta }_{slNd}$. Efficient sensitization of laser emission (large$\gamma$) assumes high ${\eta }_{aCr}$ and ${\eta }_{ET}$ efficiencies. Higher ${\eta }_{aCr}$ could be obtained increasing C_Cr within limits with reasonable parasitic quenching: C_Crs in the range to 0.7-1 at.%, which increase ${\eta }_{aCr}$ to ~35-50% could be tempting. On the other hand, increased C_Nd would enhance ${\eta }_{ET}$; however, since $P_{thCr-Nd}\propto {({\eta }_{ET}{\eta }_{qe})}^{-1}$, above a certain value of C_Nd the reduction of ${\eta }_{qe}$ could counterbalance the positive effect of ${\eta }_{ET}$ on the laser threshold, although it has no negative effect on slope efficiency, which increases with ${\eta }_{ET}$; additionally, larger C_Nd will increase ${\eta }_{aNd}$, i.e. the contribution of Nd³⁺ ions excited directly by absorption of pump. With our data ${({\eta }_{ET}{\eta }_{qe})}^{-1}$ = 2.4 for 1at.%Nd and 2.24 for 2at.%Nd and thus selection of 2 at.%Nd, which keeps $P_{thCr-Nd}$ similar to 1 at.%Nd but increases ${\eta }_{slCr-Nd}$ with ~48% could prove useful. Under broad-band pumping, when both ions are excited $g_0=g_{0Cr-Nd}+g_{0Nd}=(1+\gamma )g_{0Nd}$ and ${\eta }_a={\eta }_{aCr}+{\eta }_{aNd}$. The modest ${\eta }_{aCr}$ and ${\eta }_{ET}$ efficiencies for the (0.1at.Cr, 1at.%Nd):YAG ceramics can thus explain their limited improvement of the laser performances. Nevertheless, increased Cr and Nd concentrations within the limits discussed above could improve considerably these performances. However, the insufficient optical quality of particular ceramic rods, evidenced by integration sphere and confirmed by laser emission [11] could impede on comparison of performances with the solar pumped Nd:YAG crystal lasers.

6. Heat generation in sensitized systems

Heat generation can be characterized by the fraction of absorbed power transformed into heat (the heat load coefficient) ${\eta }_h$. In presence of laser emission for the Nd³⁺ ions excited by direct absorption ${\eta }_h^{Nd}=1-{\eta }_l({\lambda }_p/{\lambda }_l)-(1-{\eta }_l){\eta }_{qe}({\lambda }_p/{\overline{\lambda }}_{fNd})$ involves contribution of the ions that de-excite or do not de-excite by laser emission, delineated by the laser emission efficiency ${\eta }_v={\eta }_v(1-P_{th}/P)$, where ${\eta }_v$ is the overlap integral of laser mode and pumped volume; ${\overline{\lambda }}_{fNd}$ is the effective luminescence wavelength (1038 nm for Nd:YAG). In case of Cr- sensitization both the Cr³⁺ ions not involved in ET and the sensitized Nd³⁺ ions contribute and ${\eta }_h^{Cr-Nd}=1-(1-{\eta }_{ET})({\lambda }_{pCr}/{\lambda }_{fCr})-{\eta }_{ET}[{\eta }_l({\lambda }_{pCr}/{\lambda }_l)+(1-{\eta }_l){\eta }_{qe}({\lambda }_{pCr}/{\overline{\lambda }}_{fNd})]$. For instance, in case of solar pumping of a 1064 nm CW Nd:YAG laser with ${\eta }_l$ = 0.8 the calculated ${\eta }_h^{Nd}$ is 0.402 for 1at.% Nd and 0.430 for 2at.%Nd for direct solar pumping of Nd³⁺-only doped YAG, whereas sensitization with Cr determines ${\eta }_h^{Cr-Nd}$ = 0.419 and 0.503, respectively. In the solar-pumped lasers, where Cr³⁺ and Nd³⁺ are pumped simultaneously the global generated heat is $P_h={\eta }_h^{Nd}{P}_{aNd}+{\eta }_h^{Cr,Nd}P{}_{aCr}$ and a global heat load coefficient can be defined as ${\eta }_h=P_h/P_a$, with $P_a=P_{aNd}+P{}_{aCr}$: ${\eta }_h$ takes thus values between ${\eta }_h^{Nd}$ and ${\eta }_h^{Cr-Nd}$. The laser emission studies on broad-band pumped (0.1at.%Cr, 1at.% Nd):YAG ceramics did not evidence, except for misinterpretation of data in some works (such as for those given in Fig. 9 of Ref. 5), obvious effects of heat generation; this is not really surprising since a rough estimation indicates an enhancement less than 2% for ${\eta }_h$ and thus the enhancement of $P_a$ by ~65% leads to increase of $P_h$ by ~67% compared with 1at.%Nd:YAG for the same incident power, which could be accommodated by experiment. Nevertheless, heat generation remains the largest challenge when increasing the doping concentrations: with the calculated ${\eta }_h$ = 0.41 and 0.37 for (0.7 - 1at.%Cr, 1at.%Nd) and (0.7 - 1at.%Cr, 2at.%Nd) the enhanced $P_a$ (by ~4.3 and ~5.3 times) will increase strongly$P_h$ and impede on power scaling and this would impose special requirements for the laser material and for laser design in order to control the thermal field.

7. Conclusion

High temporal resolution of the emission decay of Cr³⁺ and Nd³⁺ in (Cr,Nd):YAG ceramics evidences that the energy transfer from Cr³⁺ is determined by the joint contribution of superexchange and of electric dipole interaction. The calculated energy transfer efficiency depends on C_Nd (0.52 for 1at.%Nd and 0.77 for 2at.%Nd) and is almost independent on C_Cr. Increased C_Cr enhances the absorption of solar radiation, although parasitic de-excitation could limit the useful range. This study infers that increasing C_Cr and C_Nd within certain limits (to 0.7-1 at.% and 2 at.% respectively) could increase strongly the efficiency of the solar-pumped laser emission. At the same time the enhanced heat generation would impose special care in the design of the laser active component and in the design of the laser resonator and of pumping configuration. It also argues that the effects of the accidental low optical quality of particular rods could not act as argument against utilization of (Cr,Nd):YAG ceramics in construction of solar-pumped lasers and asks for tighter control of the possible loss sources.