A. Ceramics

The microstructure illustrated in Fig. 3 is homogeneous with mean grain size (mean intercept length) 33 ± 3 μm, but some pores are present, mostly inside grains. Although the processing conditions were analogous to those applied in the preparation of single-doped Yb³⁺:YAG^{Reference Hostaša, Esposito, Alderighi and Pirri11} or Er³⁺:YAG ceramics,^{Reference Cavalli, Esposito, Hostaša and Pedroni12} which exhibited transmittances higher than 77%, in the case of the co-doped samples the measured transmittance at 1100 nm did not exceed 70%. Obviously, the presence of pores or secondary phases causes scattering of light during propagation, and thus leads to low optical transmittance. Occasionally, a secondary YSiO-type phase was observed in the form of a few grains found in the bulk material and grain boundary enrichment identified by transmission electron microscopy–energy-dispersive x-ray spectroscopy (TEM-EDX) [see Figs. 3(b) and 4(a)].

FIG. 3.

SEM micrographs of ceramic samples: fracture surface (a) and polished surface after thermal etching (b).

FIG. 4.

Typical intergranular secondary phase (Y–Si–O) occasionally observed at grain boundaries (a); nanoprobe EDX analysis (here with a 3 nm probe) shows that most of the GBs exhibit Si-enrichment (but no detectable Er³⁺ or Yb³⁺ variation); HRTEM images show generally ‘blurred’ contrasts at GBs, indicating the presence of some SiO₂ segregation as confirmed by EDX analysis on the right (b). Er³⁺ distribution was detectable with high accuracy despite its very low content (0.27 ± 0.04 at.% in the present case).

TEM-EDX results confirm the expected content of Yb³⁺ and Er³⁺ in the material as reported in Table I. Experimental measurements were consistently analyzed by assuming a linear combination of the Yb,Er-doped YAG phase and additional contribution of SiO₂ and Y₂O₃ (the elementary constituents of YSiO-type phases such as Y₂SiO₅ or Y₂Si₂O₇).

TABLE I.

EDX chemical analysis of the Yb,Er-doped YAG ceramic (at.%). The final composition (and sample thickness defining the x-ray absorption factors in the EDX treatment) is obtained with an accuracy of 0.2 at.% by minimizing a quadratic error between experimental atomic contents and calculated ones assuming a linear combination of oxide formulae (Y,Yb,Er)₃Al₅O₁₂, SiO₂, and Y₂O₃.

Consistently with Fig. 3(b), a crystalline secondary phase was occasionally found at a grain boundary as shown in Fig. 4(a). The diffractogram (calibrated with the upper YAG grain) can be indexed as a composite pattern from variants of the γ-Y₂Si₂O₇ phase (space group P2 ₁/c, lattice parameters a = 4.69, b = 10.84, c = 5.58 Å, γ = 96.03°^{Reference Dolan, Harlan, White, Hall, Misture, Bancheri and Bewlay13}). This phase was confirmed by EDX as reported in Table II.

TABLE II.

EDX nanoprobe (2 nm) analysis of the central region of the Y₂Si₂O₇ crystallite from Fig. 4(a). A treatment similar to that performed in Table II leads to an excellent agreement between experimental atomic contents and calculated ones assuming a minor contribution of the YAG matrix (7.8%).

In the perspective to check whether any dopant segregation occurred, several linescans were performed perpendicularly to grain boundaries. A representative example is shown in Fig. 4(b). No variation of either Yb or Er is detected within a dispersion of <0.06 at.% and thus the dopant distribution can be described as homogeneous. Conversely, Si-enrichment was detected at grain boundaries. The absence of a sharp contrast at grain boundary strongly suggests intergranular Si segregation, which is indeed confirmed by the increase of the Si content at the grain boundary position.

These observations are in agreement with those published in studies dealing with Yb:YAG and the spatial distribution of doping ions and those of the sintering additive. Due to the similar ionic radius of Yb³⁺ and Y³⁺ no segregation of Yb was expected,^{Reference Epicier, Boulon, Zhao, Guzik, Jiang, Ikesue and Esposito14} and Er³⁺ should behave similarly. On the other hand, the segregation of Si-rich phases in YAG ceramics has already been observed, with their presence causing losses in laser efficiency. Recent studies^{Reference Epicier, Malchère, Esposito, Hostaša, Piancastelli, Toci, Vannini, Pirri, Alderighi and Boulon15,Reference Esposito, Epicier, Serantoni, Piancastelli, Alderighi, Pirri, Toci, Vannini, Anghel and Boulon16} show that in the case of Yb³⁺:YAG the segregation of Si-rich phases such as Y₂SiO₅ or Y₂Si₂O₇ on grain boundaries can be reduced by changing the annealing cycle. In the present case, further research in this direction would be required for the optimization of the process.

B. Absorption

The room temperature absorption spectra of YAG: Er³⁺(1%), Yb³⁺(5%) single crystal and polycrystalline ceramic in the UV-visible and in the NIR region are shown in Figs. 5(a) and 5(b), respectively. The observed manifolds are composed of sharp lines having similar bandwidths, with no features ascribable to defect sites. The broadband present in the 240–300 nm region of the spectrum of the ceramic sample is probably due to the secondary phase discussed in the previous section. The UV-visible absorption bands [Fig. 5(a)] can be assigned to transitions from the ⁴I_15/2 ground state of Er³⁺ to its excited levels on the basis of previous literature data^{Reference Gruber, Quagliano, Reid, Richardson, Hills, Seltzer, Stevens, Morrison and Allik17}: many manifolds (14, exactly) contribute to the complicate spectral structure in the high energy region up to 400 nm, whereas the multiplets at longer wave lengths can be easily identified: ²G_9/2 (405 nm), ⁴F_5/2 + ⁴F_3/2 (450 nm), ⁴F_7/2 (490 nm), ⁴S_3/2 + ²H_11/2 (520 nm), ⁴F_9/2 (650 nm), ⁴I_9/2 (800 nm). Only two band systems are present in the NIR region. Two absorption manifolds contribute to form the intense band at about 900 nm: The strong ²F_7/2 → ²F_5/2 transition of Yb³⁺ and the weaker ⁴I_15/2 → ⁴I_11/2 transition of Er³⁺, whereas the system in the 1500 nm region is assigned to the ⁴I_15/2 → ⁴I_13/2 transition of Er³⁺. In Figs. 6(a)–6(f) are reported selected absorption manifolds measured at 4 K in high resolution conditions to verify the number of the Stark components arising from the crystal field splitting of the Er³⁺ and Yb³⁺ excited levels. The spectra of the crystalline and ceramic sample are in excellent agreement between them and accurately reproduce the literature data available for Er:YAG (Ref. Reference Gruber, Quagliano, Reid, Richardson, Hills, Seltzer, Stevens, Morrison and Allik17 for the crystal and Ref. Reference Gruber, Nijjar, Sardar, Yow, Russell, Allik and Zandi18 for the ceramic (50% Er)). It can be observed from Fig. 6(e) that the three ²F_7/2 → ²F_5/2 absorption transitions of Yb³⁺ at 968.1 (zero-phonon line) 940.8 and 916.0 nm, associated with a complex vibronic structure consequent of the relatively strong electron–phonon coupling characteristic of this ion.

FIG. 5.

UV-visible (a) and NIR (b) room temperature absorption spectra of the Er³⁺, Yb³⁺:YAG samples.

FIG. 6.

Selected absorption manifolds measured at 4 K in high resolution conditions.

C. Emission spectroscopy

The NIR emission spectra of the two samples were measured upon excitation at 940 nm, in correspondence with the Yb³⁺ absorption maximum, and are reported in Fig. 7. The spectra are composed of two band systems ascribed to the ²F_5/2 → ²F_7/2 emission of Yb³⁺ ions (950–1100 nm range) and to the ⁴I_13/2 → ⁴I_15/2 emission of Er³⁺ ions (1430–1680 nm range). It can be observed that the Yb³⁺/Er³⁺ emission ratio is larger in the crystal than in the ceramic. Excitation at 940 nm gives rise also to the Er³⁺ upconverted emission in the 550 and 660 nm regions, shown in Figs. 8(a) and 8(b), respectively. In this case, the crystal luminescence is slightly more intense than that of the ceramic. Since the Yb³⁺ absorption coefficient is practically the same for both samples [Fig. 5(c)] we can infer that the excited state dynamics of the investigated material could be in part affected by the morphology, especially by the grain boundaries of the ceramic sample.

FIG. 7.

NIR emission of the investigated samples, measured upon excitation at 940 nm. The spectra are normalized with respect to the Er³⁺ maximum emission.

FIG. 8.

Upconversion luminescence spectra of the Er³⁺ ions in the green (a) and the red region (b) measured upon excitation at 940 nm.

Figure 9(a) shows the decay profiles of the ⁴I_13/2 → ⁴I_15/2 emission of Er³⁺:YAG crystal and ceramic. Both are single exponential with decay times of 7.48 ms in the former and 8.34 ms in the latter case. The radiative lifetime of the ⁴I_13/2 level, estimated by the Judd–Ofelt analysis of the absorption spectrum, is 7.59 ms,^{Reference Cavalli, Esposito, Hostaša and Pedroni12} consistent with both experimental values, especially in consideration of the intrinsic error (±20%) of the Judd–Ofelt approach. It also has to be noted that the decay profiles present rise times in consequence of the Er³⁺ excitation ‘via’ ET from Yb³⁺. The evaluated time constants are 0.48 ms for the single crystal and 0.50 ms for the ceramic, well consistent with the decay times of Yb³⁺, whose decay curves are reported in Fig. 9(b). They are again single exponential. The decay time of the Yb³⁺²F_5/2 excited state is 474 µs in the single crystal and 461 µs in the ceramic. They are significantly shorter than the decay times of the single-doped Yb³⁺:YAG, usually of the order of 1 ms [Ref. Reference Yoshikawa, Boulon, Laversenne, Canibano, Lebbou, Collombet, Guyot and Fukuda19], in consequence of the ET to the Er³⁺ ions.^{Reference Zhou, Zhang, Huang, Wang, Li, Liu, Jiang, Pan and Guo2} The analysis of the mechanisms involved in this process is complex and requires systematic measurements as function of the doping concentration. This is beyond the scope of the present paper.

FIG. 9.

Luminescence decays of the (a) Er³⁺⁴I_13/2 and (b) Yb³⁺²F_5/2 metastable states at room temperature in the single-crystal (A) and the ceramic (B).

In conclusion, the main difference in the emission behavior of the crystal and ceramic samples concerns the Yb³⁺/Er³⁺ emission ratio. A probable explanation of this difference might come from the presence of the γ-Y₂Si₂O₇ phase in the ceramic and the Si-enrichment as detected at grain boundaries by TEM-EDX. Some considerations can however be of help to organize the future work in this connection. First of all, the Yb³⁺ excitation at 940 nm triggers several nonradiative processes: The Yb³⁺ to Er³⁺ ET, the migration among Yb³⁺ ions, responsible for the radiation trapping effect, and various mechanisms involving excited Er³⁺ ions like multiphonon relaxation, upconversion, back transfer to Yb³⁺. Possible differences in the local concentrations of the doping ions in the two samples can be reasonably excluded for Yb³⁺ in crystals^{Reference Świrkowicz, Skórczakowski, Jabczyński, Bajor, Tymicki, Kaczmarek and Łukasiewicz20} as well as in ceramic,^{Reference Epicier, Boulon, Zhao, Guzik, Jiang, Ikesue and Esposito14} but the information about the Er³⁺ ion is lacking, then this is a point to take into consideration. Regarding the grain size, it can have a significant effect on the decay time (and likely on the emission intensity) of Yb³⁺ when of the order of the nanometers.^{Reference Amami, Hreniak, Guyot, Zhao and Boulon21} This is not the case, since the grains constituting the ceramic sample are of about 30 μm in size (see Section III. A). The relatively higher intensity of the Yb³⁺ emission band in Fig. 7 can be accounted for by considering (i) a major efficiency of the Yb³⁺ to Er³⁺ transfer in the ceramic, compatible in part (but not to a sufficient extent) with the shorter decay time of Yb³⁺; (ii) a major efficiency of the Er³⁺ to Yb³⁺ back transfer in the crystal, compatible in part with the shorter decay time of Er³⁺; (iii) the transmittance of the ceramic sample, that is relatively low (of the order of 70%) and increases with the wave length (even if it was not measured in the 1500 nm region).

D. Considerations on the required population inversion

It can be noticed that the lasing action can be rather difficult to achieve in the Yb:Er:YAG system. The Er laser transition at 1550–1650 nm (between the levels ⁴I_13/2 → ⁴I_15/2) is affected by ground state absorption, that is the population in the ground level absorbs the laser radiation itself. Therefore, a large fraction of the population has to be excited to the upper laser level just to overcome the ground level absorption. An estimate of the single-pass small signal gain G provided by an excited fraction of population β is given by the following relation:

(1)$$G = {N_{{\rm{Er}}}}I\left[ {{\sigma _{\rm{E}}}\beta - \left( {1 - \beta } \right){\sigma _{\rm{A}}}} \right]\quad ,$$

where N _Er is the density of the Er atoms in the matrix (1.38 × 10²⁰ cm⁻³), l is the sample length (2 mm), σ_E and σ_A are the emission and the absorption cross section at the lasing wave length, respectively, and β is the value of the excited population fraction averaged over the whole laser mode volume in the sample.

To achieve laser emission, the small signal gain must be

(2)$$G \,\ge\, {L \mathord{\left/ {\vphantom {L 2}} \right. \kern-\nulldelimiterspace} 2}\quad ,$$

where L(<<1) are the round trip cavity losses.

In the system under consideration, lasing has been observed at 1645 nm,^{Reference Schweizer, Jensen, Heumann and Huber3} and more recently at 1615 nm^{Reference Zhu, Tang, Duan, Luo and Zhang22} whereas the peak emission cross section is located at about 1531 nm. Another possible candidate for lasing could be the transition at 1631 nm. The corresponding cross section values are listed in Table III (after Schweizer et al.³). With the data from Table III, the values of the small signal gain for increasing inverted population fraction can be calculated (see Fig. 10).

TABLE III.

Values of the absorption (σ_A) and emission (σ_E) cross sections used for the calculation of the small signal gain.

FIG. 10.

Calculated population inversion needed to achieve laser threshold with assumed losses of 9% (green dashed line) for emission at 1531, 1615, 1631, and 1645 nm.

In general, it can be seen that for low to moderate population inversion (and thus low losses), the transition at 1645 nm and at 1615 nm are favored for laser oscillation, whereas the transition at 1631 nm features a smaller gain. It can be also seen that a positive gain for the transition at 1531 nm can be obtained only for very high values of inversion fraction, exceeding 0.5. This analysis is consistent with the results provided by Zhu et al.,^{Reference Zhu, Tang, Duan, Luo and Zhang22} where simultaneous laser action was observed at 1615 and 1645 nm, with similar output power, using output couplers with very low transmission. Our analysis indicates indeed that lasing at these two wave lengths should occur with similar pump threshold and overall efficiency (even though the power balance between the two lines can be influenced by differences in the output mirror transmission at the two wave lengths). On the other hand, Zhu et al. observed laser action neither at 1531 nm nor at 1631 nm, indicating that the required inversion is higher than that needed for lasing at 1615 nm and 1645 nm.

Furthermore, this analysis shows that for the length and doping level of tested samples lasing action can be achieved only for low cavity losses. For instance, if we consider the case of a sample placed perpendicularly in the cavity (where the overall round trip losses L are at least due to two Fresnel reflection (2 × 8%) plus the output coupling (e.g., 2%)) a small signal gain value G > 0.09 is required (horizontal dashed line in Fig. 10), corresponding to a population inversion of about 0.6 to achieve laser threshold both at 1645 and at 1531 nm. Even in the case of crystal placed at the Brewster angle, residual losses can amount to some percent, still requiring an inversion fraction of ∼0.4. With this combination of sample length and doping, lasing at 1645 and at 1615 nm becomes impossible for losses higher than L/2 > 0.15, and laser action becomes impossible at 1531 nm as well for losses higher than L/2 > 0.35.

In the case of the ceramic material, this evaluation shows that scattering losses can have a dramatic impact on the laser action of this system: For instance, in the case depicted in Fig. 10(a), further single pass scattering loss of only 5% (dash-dotted horizontal line) would almost forbid the lasing action at 1615 and at 1645 nm, and it would rise the inversion threshold to about 0.73 for lasing at 1531 nm.