1. Introduction

Cubic sesquioxides are outstanding host crystals for rare-earth ions. They possess a high thermal conductivity, enabling an efficient heat extraction even in high power laser operation. Their comparably low phonon energies suppress non-radiative decay processes, which is of high relevance for mid-infrared lasers. Ho³⁺-, Er³⁺-, Tm³⁺- or Yb³⁺-doped sesquioxide gain materials enabled unprecedented laser performance in continuous wave (cw) and mode-locked laser operation [1]. Unfortunately, due to their very high melting temperatures in excess of 2400°C the growth of these materials is challenging. Therefore – despite previous successful demonstrations of the growth of high quality sesquioxide crystals, e.g., by the heat exchanger method [2] – sesquioxide crystals are not commercially available. In contrast, ceramic sesquioxides can be fabricated at lower temperatures and their commercial availability is increasing.

Upon crystallization from a stoichiometric melt, cubic rare-earth sesquioxides with the composition RE₂O₃ are only formed by rare-earth (RE) elements with atomic numbers Z between 65 (Tb) and 71 (Lu) as well as Y (Z = 39) and Sc (Z = 21) [3,4]. Among these, only Sc₂O₃, Lu₂O₃ and Y₂O₃ are optically inert in the relevant spectral range from the visible to the mid-IR and thus suitable laser host materials. The significantly different atomic radii of the trivalent ions Sc³⁺ (0.75 Å), Lu³⁺ (0.86 Å) and Y³⁺ (0.90 Å) [5] in the 6-fold coordination of the optically active C₂ sites in sesquioxides enable to tune the spectroscopic properties in a wide range. It is evident, that doping ions incorporated into the matrix of Sc₂O₃ with a lattice constant of only 9.86 Å experience a much stronger Coulomb interaction with the ligands than those incorporated into Y₂O₃ with a lattice constant as large as 10.12 Å. As a consequence, the main emission peaks, e.g., of Yb³⁺ found at 1041 nm and 1095 nm in Sc₂O₃ shift to values of 1031 nm and 1076 nm in Y₂O₃.

In mixed sesquioxides, the rare-earth cations of the host material are considered to be mainly randomly distributed on the crystallographic cation sites in the cubic bixbyite structure [6], resulting in inhomogeneous broadening. The resulting spectra combine the spectroscopic properties of the constituents, leading to a significant broadening of the absorption and emission features. These particularities give rise to compositional tuning of the emission bands of rare-earth doped mixed sesquioxide crystals, which is highly desired for ultrafast mode-locked lasers, where a smooth and broad emission band is a prerequisite for achieving shortest pulse durations [7].

Recently, we found the melting points of mixed sesquioxide crystals to be significantly lower than previously reported in the literature, which enables their growth by the Czochralski technique using iridium crucibles [8]. Upcoming ceramic fabrication techniques also enabled to fabricate various mixed sesquioxides doped with Yb³⁺, Tm³⁺, Er³⁺, Nd³⁺ or Ho³⁺. This motivates a review of the previous work in the field of lasers based on rare-earth doped mixed sesquioxides to envisage the potential of this emerging class of gain materials. This work starts with a short introduction into the melting behavior and successful fabrication techniques for mixed sesquioxides as well as the influence of disorder and doping on the thermal conductivity. In the following, we present the spectroscopic and thermal properties of mixed sesquioxides mainly doped with Yb³⁺, Tm³⁺, Er³⁺ and, where available, Ho³⁺ and Nd³⁺. Finally, we review the state of the art on crystalline and ceramic gain materials for continuous wave and ultrafast lasers in this field.

2. Growth and thermal conductivity of mixed sesquioxide crystals

2.1 Crystal growth of mixed sesquioxides

Cubic sesquioxides form complete a ternary solid-solution series according to (Sc_x,Lu_y,Y_z)₂O₃ with x + y + z = 1. For simplicity, the composition of these mixed sesquioxides is also written as Sc_2xLu_2yY_2zO₃, yielding the simple notations YScO₃, LuScO₃ and LuYO₃ for x, y and/or z = ½. Here, we will use this notation (partially violating the alphabetic Hill system [9] for the sake of an easy articulation) exclusively for these three compositions. It should also be noted, that for better comparison, for all compositions the notation was chosen to normalize the host cations to 2, neglecting the doping ion. Consequently, in this work a composition of (Yb_0.1,Sc_0.4,Y_0.5)₂O₃, e.g., is denoted as Yb(10%):(Sc_0.44Y_0.56)₂O₃, indicating that 10% of the host cations in a host crystal with a 4:5 ratio of Sc and Y are replaced by Yb.

Due to their high melting points of more than 2350°C, the growth of sesquioxide crystals is challenging and expensive. Among the few crucible materials with sufficiently high melting points, rhenium is the only to sustain the harsh growth conditions. But even rhenium is very sensitive to oxygen ubiquitous in the growth atmosphere of oxide crystals. Moreover, rhenium crucibles are difficult to fabricate and thus very expensive [2]. Therefore, several crucible free growth methods [10–14] as well as thin film growth techniques [15] were utilized in the past for the growth of sesquioxides. Also, the growth at reduced temperatures from the flux [16,17] and in hydrothermal autoclaves [18,19] was investigated in detail. In all cases the crystal quality and/or dimensions remained limited. In recent years, also ceramic fabrication techniques were applied to produce sesquioxides [20–23], and the latter are commercially available meanwhile. Nevertheless, the fabrication of ceramics process is complex, sintering aids like ZrO₂ may affect the laser performance and in general, laser ceramics are more prone to scattering than crystals [24].

Indeed there are various reports on the growth of sesquioxide crystals from rhenium crucibles by different techniques [25,26] including the Czochralski method [27–29]. However, at the required growth temperatures for pure sesquioxides, the growing crystals partially absorb the heat radiation, which causes unfavorable thermal gradients and ends with small crystals of low quality. Up to now, the highest quality sesquioxide crystals were obtained by a directional solidification in the melt, the so-called heat-exchanger method (HEM) [2].

In our recent work, we revisited the melting behavior of mixed sesquioxide crystals [8]. In previous literature the lowest melting point in the binary solid solution series between Y₂O₃ and Sc₂O₃ is reported to be higher than 2150°C [30,31], but our measurements suggest 100°C lower melting temperatures of 2050°C. The refined phase diagram of the binary system Sc₂O₃-Y₂O₃ is shown in Fig. 1(a). The lowest melting temperature is found close to the composition YScO₃, and it remains below 2200°C for any composition between (Sc_0.68Y_0.32)₂O₃ and (Sc_0.3Y_0.7)₂O₂. This range is further limited by a phase transition at Y₂O₃ contents above ∼60 mol%. For such compositions, the melt initially crystallizes in an undesired hexagonal phase and undergoes a solid-state phase transition into the desired cubic phase at temperatures only slightly below the melting point [33]. We found this to severely degrade the quality of Y₂O₃ crystals. Further investigations showed, that higher Y₂O₃ contents may be possible by the admixture of Lu₂O₃, though at any Lu₂O₃ content higher than 20% the melting points exceed 2200°C. The full refined ternary phase diagram is found in [8].

 

Fig. 1. a) Binary phase diagram of the system Sc₂O₃-Y₂O₃. The grey shaded area indicates compositions with melting points below 2200°C. b) Czochralski-grown Yb³⁺(0.4%):YScO₃ [32] and c) Er³⁺(7%):(Sc_0.54Y_0.46)₂O₃ crystal.

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These reduced melting temperatures in a wide range of compositions enabled the growth of mixed sesquioxide crystals by the Czochralski method from iridium crucibles, a technique routinely applied to, e.g., YAG (Y₃Al₅O₁₂) crystals. This should permit the growth of high quality mixed sesquioxide crystals and represents an important step toward a commercial supply of rare-earth doped sesquioxide crystals for ultrafast laser applications. As a proof-of-principle, we demonstrated the growth of large crystals of Er(7%):(Sc_0.54Y_0.46)₂O₃ and Yb(0.4%):YScO₃ shown in Fig. 1(b) and 1(c) with more than 4 cm length and diameters exceeding 1.5 cm. The growth setup was similar to the one for high melting rare-earth scandate crystals [34]. The eccentric growth in the bottom parts of both crystals is often observed during the Czochralski growth of high melting materials and can be avoided by a precise seed orientation and improved thermal gradients by an optimized growth setup.

2.2 Thermal properties of mixed sesquioxides

In dielectrics with no conduction band electrons, the thermal conductivity is mainly determined by phonon propagation. In the case of ion-doped laser crystals, mass-difference phonon scattering must thus be considered; it is intuitive that a heavy doping ion replacing a light cation in the host may act as a phonon scattering center [35]. In consequence, the thermal conductivity can drop significantly with doping ion concentration. As shown in Fig. 2, this effect becomes stronger with increasing mass difference between the doping ion and the host cation: Sc₂O₃ with the lightest host cation with an atomic mass of 45 amu exhibits a huge mass difference compared to 173 amu for Yb³⁺. This leads to a reduction from the undoped thermal conductivity of 18 Wm^-1K^-1 to values around 7 Wm^-1K^-1 for typical Yb³⁺ doping concentrations of 2.5% (∼8×10²⁰ cm^-3). A similar progress with increasing doping is observed for Y₂O₃. In contrast, the thermal conductivity of Lu₂O₃ drops only marginally with doping concentration, which is owed to the low mass difference between Lu³⁺ (175 amu) and Yb³⁺. For Tm³⁺, a similar trend was observed [38] and is thus expected also for other heavy rare-earth doping ions, mainly Ho³⁺ and Er³⁺.

 

Fig. 2. Thermal conductivity vs. Yb³⁺-doping concentration for different sesquioxide and mixed sesquioxide crystals. With data from [36,37]. The data for YScO₃ refers to an Er³⁺-doped sample [8]. Solid lines are fits according to [35].

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The average phonon propagation length is intrinsically short in materials with a disordered structure. Consequently, even undoped mixed sesquioxides exhibit lower thermal conductivities. However, these do not significantly decrease with doping ion density. Thus, for high doping concentrations, e.g., required for efficient 3 µm lasers based on Er³⁺, their thermal conductivity is not much lower than for other sesquioxides except Lu₂O₃ (see Fig. 2). Also for YAG, the thermal conductivity at such high doping concentrations is only ∼25% higher than for mixed sesquioxides [36]. However, as broad emission bands often result from a disordered structure, the resulting thermal conductivities of mixed sesquioxides on the order of 4 Wm^-1K⁻¹ are still significantly higher than for other host materials for ultrafast lasers such as glasses and even higher than those of some ordered host materials with similarly broad emission like double-tungstates [39].

3. Spectroscopic properties of mixed sesquioxides

The large difference in particular between the lattice constants of Sc₂O₃ (9.86 Å) and Y₂O₃ (10.60 Å) gives rise to modification of the crystal field strength, which results in a considerable shift of absorption and emission peaks of rare-earth dopants. For Lu₂O₃ with a lattice constant of 10.39 Å between that of Sc₂O₃ and Y₂O₃, the effect is somewhat reduced. Mixed sesquioxides combine the absorption and emission features of their constituents, leading to significantly broadened absorption and emission bands. One could expect that the intrinsic disorder of mixed sesquioxides causes a reduced site symmetry, which should in turn reduce the excited state lifetimes. This is, however, not supported by existing work on this topic; instead, the existing lifetime variation is well explained by differences of the lifetimes of the pure constituting sesquioxides [40].

By the choice of a suitable composition, the emission bands can even be tailored to the desired application [41], which is also referred to as ‘compositional tuning’. This can include shifting the emission peak to a desired wavelength [42], but mainly enables to create materials with broad and smooth emission bands suitable for the generation of ultrashort pulses [7]. This concept was mainly applied to Yb³⁺, Tm³⁺, and Er³⁺-doped sesquioxides. The spectroscopic features of sesquioxides doped with these ions will be reviewed in the following, but also for Nd³⁺- [42,43] and Ho³⁺-doped [44,45] sesquioxides preliminary data exist and in particular the latter appears very promising for the generation of ultrashort pulses in the 2 µm spectral range.

It should be noted that for the spectra shown in this review, we assume that there are no differences between the properties of perfect single crystals and perfect ceramics. Potentially existing differences between corresponding publications are rather attributed to sintering aids, impurities and/or unprecise knowledge about sample composition and doping ion density as well as different measuring conditions.

3.1 Ytterbium-doped mixed sesquioxides

Figure 3 shows the absorption and emission spectra of different Yb³⁺-doped pure and mixed sesquioxide crystals. Yb:Sc₂O₃ exhibits the largest transition cross sections and the strongest Stark splitting. This is indicated by the absorption shown in Fig. 3(a) extending to shortest and the emission shown in Fig. 3(g) extending to longest wavelengths. This can be explained by the smallest lattice parameter and cation size (0.75 Å) of Sc₂O₃, both inducing a strong crystal field. The spectra of Yb:Lu₂O₃ are shown in Fig. 3(b) and 3(h). Its lattice parameter and cation size (0.86 Å), are close to the values of Y₂O₃ (0.90 Å), which exhibits the lowest crystal field strength with the smallest Stark splitting and the lowest transition cross sections as shown in Fig. 3(c) and 3(i). As seen later, this trend is maintained for sesquioxides doped with any rare-earth ion.

 

Fig. 3. Absorption (a-f) and emission cross section spectra (g-l) of Yb³⁺-doped pure and mixed sesquioxide crystals. The black lines in the emission spectra represent the emission cross sections in the wavelength range relevant for lasing multiplied by a factor of 3 for better visibility. The data are taken from [52] except for the spectra of Yb:(Sc_0.5Y_0.5)₂O₃, which were measured for this work and the absorption for Yb:Y₂O₃, which was taken from [53].

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The influence of these different crystal fields on the absorption features of Yb³⁺ doped into these host materials shown in Fig. 3(a) to 3(f) is surprisingly low. All absorption peaks around 976 nm vary by less than 1 nm around this value and the largest full width at half maximum (FWHM) does not exceed 3.5 nm even in the inhomogeneously broadened absorption spectra of the mixed Yb³⁺-doped sesquioxide crystals.

In emission, the largest broadening of the lines can be expected from the combination of the strongest and the weakest crystal field, i.e., the host material YScO₃. In fact, its emission bandwidth is so broad, that the FWHM of the emission peak around 1035 nm extends nearly down to 1000 nm, though this broadening is associated with a reduction of the peak emission cross sections.

Besides the data shown here for crystals, Pirri and coworkers recently published a series on investigations on different Yb³⁺-doped mixed sesquioxide ceramics. Yb:(Lu_xY_1-x)₂O₃ ceramics with x = 0.11, 0.14 and 0.23 were investigated [46,47], where in some cases ZrO₂ was co-doped as a sintering aid. The reported absorption cross sections are lower for pure Y₂O₃ ceramics than for the corresponding crystals reported here. But as expected from the similar emission features of Yb:Y₂O₃ and Yb:Lu₂O₃ shown in Fig. 3(i) and 3(h), respectively, at such relatively low mixing ratios the influence on the spectral properties is rather low. They further investigated the composition (Sc_xY_1-x)₂O₃ with x = 0.27, 0.51, and 0.74 [48]. In this case, the absorption cross sections for the pure Yb:Y₂O₃ ceramic were similar to the values presented here for crystals. The unexpected result of the largest absorption cross sections found for x = 0.51 in [48] may be caused by inaccuracies caused by the use of too long samples in the transmission measurements. In emission, the results presented in [48] show a continuous shift of the laser relevant emission peaks from 1031 nm to 1039 nm and from 1076 nm to 1088 nm with increasing Sc₂O₃ admixture. This further supports the possibility of compositional tailoring of the emission features to enable shortest pulse durations, which also could be expected from the data shown in Fig. 3(j) to Fig. 3(k).

In addition, several other ceramic compositions in the binary systems Sc₂O₃-Lu₂O₃ [40,49] Lu₂O₃-Y₂O₃ [50,51] were investigated with respect to spectral properties and upper state lifetime of the Yb³⁺ doping ions. The results mainly confirm the largest bandwidths to be found in 50:50-ratio compositions.

3.2 Thulium-doped mixed sesquioxides

Due to their broad emission ranging over more than 300 nm between about 1.75 and 2.15 µm, Tm³⁺-doped sesquioxide materials are highly interesting for the generation of ultrashort pulses in the 2 µm range. This emission bandwidth can be even enhanced in mixed sesquioxides, which have thus been subject of intensive investigations in recent years for crystals as well as ceramics. Traditionally, Tm³⁺-doped materials are pumped via the well-known ‘two-for-one’ pumping mechanism at wavelengths around 800 nm, in which one pump photon can excite two Tm³⁺ ions by the cross relaxation ³H₄ → ³F₄ / ³H₆ → ³F₆ and thus enable two laser photons. As shown in Fig. 4(a) to 4(c), the absorption of pure Tm³⁺-doped sesquioxides is very structured around 800 nm and the choice of a wavelength stable and narrow emission pump source is crucial to meet the narrow absorption lines. In contrast, the absorption in mixed sesquioxides is much broader and less structured, however, at the expense of reduced peak absorption cross sections [see Fig. 4(d) and 4(e)]. The ground state absorption directly into the emitting level ³F₄ is crucial for the determination of the gain cross sections of the 2 µm laser transition, but as seen in Fig. 4(a) to 4(d), the residual absorption at wavelengths longer than 1.8 µm is fairly low, so that all peaks in the emission spectra shown in Fig. 4(g) to 4(l) can be utilized for lasing even at low inversion levels.

 

Fig. 4. Absorption (a-e) and emission cross section spectra (g-l) of Tm³⁺-doped pure and mixed sesquioxide crystals. The data for Tm³⁺-doped Sc₂O₃, Lu₂O₃ and LuScO₃ are taken from [1], the data for Y₂O₃ are from [55]. The data for the 800 nm and 1.6 µm absorption of (Lu_0.5Y_0.5)₂O₃ are extracted from [56] and [57], respectively and the emission cross section data for (Lu_0.5Y_0.5)₂O₃ and (Sc_0.5Y_0.5)₂O₃ are from [58]. For the latter no absorption data were available at the time of writing. The noise-like features in some of the emission spectra between 1.8 µm and 2.0 µm are caused by atmospheric water vapor absorption in this range.

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In recent years, also direct in-band pumping has been shown to be an efficient measure to increase the absorption of Tm³⁺-doped gain media as well as further improving the laser efficiency. Pump sources in the required 1.6 µm wavelength range are still hard to find, but Er³⁺-doped fiber amplifiers have shown their potential for this purpose [54]. The use of mixed sesquioxides somewhat relaxes the requirements for the particular pump wavelength, though at the expense of significantly reduced absorption cross sections which is associated with the broadening of the absorption band. Also in the case of Tm³⁺, this effect increases with increasing difference of the constituents’ lattice constants, as seen by comparing Tm:LuYO₃ in Fig. 4(d) with Tm:LuScO₃ shown in Fig. 4(e).

In the emission spectra shown in Fig. 4(g) to 4(l) it can be seen, that the FWHM emission bandwidth on the order of 60 nm in pure Tm³⁺ sesquioxides is enhanced to more than 100 nm in Tm:YScO₃ around the main peak at 1.9 µm, which supports the generation of sub-50-fs pulses.

3.3 Erbium-doped mixed sesquioxides

The most famous laser transition in Er³⁺-based lasers is the found at 1.5 µm (see Fig. 5). When pumped at wavelengths around 1 µm, this transition requires an efficient energy transfer ⁴I_11/2 → ⁴I_13/2 to populate the emitting level ⁴I_13/2. This is supported by high phonon energies of the host lattice inducing multi-phonon decay [59]. However, due to the comparably low phonon energies of sesquioxide host crystals, this process is inefficient and they are not considered useful for 1.5 µm laser operation under 1 µm pumping. Nevertheless, due to their strong crystal fields, the 1.5 µm transition of Er³⁺-doped laser materials extents to unusually long wavelengths in excess of 1.65 µm, which makes this transition, e.g., interesting for the above mentioned in-band pumping of Tm³⁺-lasers. An alternative pump channel for the 1.5 µm transition of Er³⁺ is direct in-band pumping. As shown in the absorption spectra of Er³⁺-doped sesquioxides and mixed sesquioxides in Fig. 5(a) to 5(f), their main absorption peak in this wavelength range is located at 1535 nm with variations of less than 1 nm around this value.

 

Fig. 5. Absorption cross sections (a-f) and emission cross sections (g-l) of different Er³⁺-doped sesquioxides and mixed sesquioxides in the wavelength range around 1.5 µm. The black curves in the emission cross section spectra show the cross sections multiplied by a factor of 5 for better visibility of the laser relevant emission features. All data are from [60].

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The largest emission peaks are also found at this wavelength, however, due to the strong reabsorption very high inversion densities are required and high laser thresholds can be expected at this wavelength. Thus, lasing at longer wavelengths seems more promising. Also in the case of Er³⁺, the strongest Stark splitting is found in Er:Sc₂O₃ [Fig. 5(g)], leading to an emission extending to nearly 1.7 µm. This splitting is decreasing over Er:Lu₂O₃ to the smallest splitting found in Er:Y₂O₃. Consequently, the mixtures LuScO₃ [Fig. 5(j)] and YScO₃ [Fig. 5(k)] exhibit a strong broadening of the long-wavelength emission around 1.65 µm, which is less pronounced in Er:LuYO₃. The short-wavelength emission around 1.58 µm is less affected by the inhomogeneous broadening in mixed sesquioxide host materials.

Even more promising for applications is the 2.8 µm laser in Er³⁺-doped sesquioxides based on the transition ⁴I_11/2 → ⁴I_13/2. While for 1-µm-pumped 1.5 µm Er³⁺-lasers a strong non-radiative decay process on this transition is desired, the 2.8 µm Er³⁺-laser based on this transition strongly benefits from the comparably low phonon energies of sesquioxide host crystals. Therefore, Er³⁺-doped sesquioxides are among the most efficient laser materials for the generation of laser emission in this wavelength range. Efficient lasers based on the pure sesquioxides Lu₂O₃ [61,62], Sc₂O₃ [63], and Y₂O₃ [64] have been demonstrated based on this transition, the respective absorption and emission cross section spectra are shown in Fig. 6.

 

Fig. 6. Absorption cross sections around 1 µm (a-e) and emission cross sections around 2.8 µm (g-k) of different Er³⁺-doped sesquioxides and mixed sesquioxides. The data for Sc₂O₃, Lu₂O₃ and Er₂O₃ are from [1], those for LuScO₃ are from [65]. Finally, the data for (Lu_0.84Sc_0.16)₂O₃ were kindly provided by the authors of [65]. All emission data are derived by multiplying the fluorescence spectra by λ⁵ according to the Füchtbauer-Ladenburg equation [67].

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To directly populate the upper laser level, pump light at wavelengths around 1 µm is required. As can be seen in Fig. 6(a) to Fig. 6(c), the absorption in this wavelength range is very structured in the pure sesquioxides and the laser efficiency may depend on the absence of excited state absorption at the particular pump wavelength [61]. Interestingly, despite the broadening of the absorption features typical for mixed sesquioxides, the height of the absorption peak around 981 nm remains nearly unaffected by the broadening for Er:(Sc_0.54Y_0.46)₂O₃, a composition very close to Er:YScO₃ [Fig. 6(d)].

One cannot assume a complete absence of non-radiative decay processes for the 2.8 µm transition. Therefore, it is not easy to determine the emission cross sections for this transition and the emission cross sections shown in Fig. 6(g) to 6(k) are shown in arbitrary units. However, for Er:(Lu_0.84Sc_0.16)₂O₃ the peak emission cross section was estimated to be on the order of 1.3 × 10⁻²⁰ cm² [65]. Despite a certain smoothening of the emission around 2.85 µm in the mixed crystals, which is the typical laser wavelength for Er³⁺-doped sesquioxide lasers in this range, the broadening effect appears to be low. It should be noted, that the growth of Er³⁺-doped LuYO₃ crystals by the optical floating zone technique was reported recently [66]. The spectra shown in that work differ considerably from the values shown in Fig. 6 and are thus not discussed.

4. Laser results with rare-earth doped mixed sesquioxide gain media

Lasing in mixed sesquioxide host materials was reported first in Nd:YScO₃ [68]. Since then, it took more than 30 years before further reports on lasing in mixed sesquioxides were published [69] and only very recently, various publications on lasers based on rare-earth-doped ceramic mixed sesquioxides are found. In the following, we will review the laser results obtained with the laser ions Yb³⁺, Tm³⁺, Er³⁺ as well as Ho³⁺ and Nd³⁺. In all tables, ‘Dop.’ refers to the doping ion concentration with respect to the cation sites, ‘η_slope’ stands for the highest reported slope efficiency rounded to whole percent, ‘P_out’ to the maximum output power (not necessarily obtained at the highest slope efficiency) and ‘λ_las’ refers to the laser wavelength rounded to whole nm, where an interval describes the shortest and longest observed laser wavelength and not necessarily a continuous wavelength tuning range. To illustrate the historical progress, the entries are sorted by publication year.

4.1 Ytterbium-doped mixed sesquioxide lasers

Table 1 shows the laser results obtained up to now with Yb³⁺-doped mixed sesquioxide crystals and ceramics. The first reports on laser operation with mixed Yb³⁺-doped sesquioxides utilized HEM-grown Yb:LuScO₃ crystals in a thin-disk laser configuration [70]. In the same year, the highest output power of any laser based on a mixed sesquioxide host material of 250 W was demonstrated [36]. In both cases, the slope efficiencies exceeded 80%, which demonstrates the potential of these materials for efficient high-power laser operation. Since 2018, various reports on mixed sesquioxide ceramics were published. The highest output powers amount to only 6 W in cw operation [48] and 10 W in 3.5% duty-cycle q-cw thin-disk laser operation [71]. This may be attributed to the end-pumped bulk laser scheme utilized in these reports. However, it is also noted that for ceramics none of the slope efficiencies exceeded 63%. Figure 7(a) shows the laser performance of a Ti:sapphire pumped low power end-pumped bulk Yb:LuScO₃ laser [37] and Fig. 7(b) shows a preliminary result of an Yb:YScO₃ laser pumped by an optically pumped semiconductor laser (OPSL) measured for this work. Both curves indicate, that also at low powers and in end-pumped bulk geometry, high efficiencies can be obtained with Yb³⁺-doped mixed sesquioxide crystals. On the other hand, also in thin-disk geometry, the performance of pure sesquioxide ceramics was found to fall slightly behind the results obtained with crystals [72].

 

Fig. 7. a) Laser characteristics of a Ti:sapphire pumped Yb:LuScO₃ laser utilizing different output coupler transmissions T_oc [37] and b) Laser characteristics of an OPSL-pumped Yb:YScO₃ at T_oc = 3.4%.

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Table 1. Continuous wave laser results obtained with Yb³⁺-doped mixed sesquioxides.

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While here one can only speculate about the reasons for the lower efficiency of ceramic based mixed sesquioxide lasers, it is likely associated with considerable scattering losses at grain boundaries for 1 µm laser radiation and/or loss processes associated to possible sintering aids such as ZrO₂. Notably, also the doping concentrations of the Yb³⁺-doped mixed sesquioxide ceramics investigated hitherto are fairly high and in the range where detrimental effects were observed in high-inversion lasing schemes like the thin-disk laser setup [37].

All mode-locked laser results obtained with Yb³⁺-doped mixed sesquioxide crystals up to now utilized crystals. An overview on these results is shown in the upper half of Table 2, in which τ_pulse stands for the pulse duration, f_rep for the repetition rate and P_av for the average output power. Pulses as short as 74 fs were generated in an end-pumped bulk SESAM mode-locked resonator based on Yb:LuScO₃ as the gain medium [75]. Not much longer pulses at, however, two orders of magnitude higher average power of 5.1 W were obtained in thin-disk geometry with the same host material [76]. The results obtained with Yb:(Lu_0.33Sc_0.33Y_0.33)₂O₃ of 101 fs at 4.6 W of average power are very comparable, but, notably, the ternary composition does not seem to be a significant advantage in terms of ultrafast pulse generation. However, sub-100-fs results were obtained with pure Yb³⁺-doped sesquioxide crystals [77] and more recently even sub-30-fs pulses were generated with Yb:YAG [78] in Kerr-lens mode-locked thin-disk laser setups utilizing self-phase modulation for spectral broadening to generate the spectral bandwidth required for such short pulses. These results give rise to the hope, that even shorter pulse durations are possible with mixed Yb³⁺-doped sesquioxide crystals or ceramics once they are available in suitable quality and size. This could be enabled by to their extremely broad gain regions as evidenced by the laser tuning curve of Yb³⁺-doped sesquioxides shown in Fig. 8, extending from below 1000 nm to above 1100 nm.

 

Fig. 8. Wavelength tuning curves of 0.2 mm thick sesquioxide disks in the thin-disk laser setup under 32 W of pump power at an output coupler transmission of 0.4% [37].

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Table 2. Mode-locked laser results obtained with Yb³⁺- and Tm³⁺-doped mixed sesquioxides.

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4.2 Tm³⁺ doped mixed sesquioxide lasers

When Tm³⁺ lasers are pumped around 800 nm for 2-µm lasing, one could believe that their efficiency is limited to ∼40% due to the large energetic difference between pump and laser photons and the corresponding low Stokes efficiency. However, due to the previously mentioned two-for-one pumping scheme, Tm³⁺ can theoretically reach slope efficiencies of up to 80%. In fact, when the energetic positions of the involved energy levels are resonant for the required cross relaxation process and the doping ion density is sufficient, such efficiencies are reached in the experiment [87]. Also in pure sesquioxides the two-for-one pumping process of Tm³⁺ is very efficient, enabling slope efficiencies of up to 67% and nearly 50 W of cw output power [88].

Table 3 lists the cw laser results obtained with Tm³⁺-doped mixed sesquioxides. The first laser of this kind was based on a LuScO₃ crystal as the host material. Under Ti:sapphire pumping, this laser delivered an output power of 0.71 W at a high slope efficiency of 55% [38], revealing that the cross-relaxation process can also be efficient in mixed sesquioxides. The laser characteristics for the optimum output coupler transmission of 2.9% as well as a wavelength tuning curve extending from 1961 nm to 2115 nm, where T_oc slightly increased with wavelength, are shown in Fig. 9. In a later result utilizing a higher doped crystal and thus benefiting from higher gain, this tuning range was further extended to wavelengths as long as 2141 nm [81]. These results are still below the tuning range obtained with Tm:Lu₂O₃ of more than 200 nm between 1922 nm and 2134 nm [38,89]. The latter results were, however, obtained under significantly higher pump power.

 

Fig. 9. a) Continuous wave laser performance of a 7.7 mm long Tm(1%):LuScO₃ laser emitting at ∼ 2.1 µm.

b) Spectral tunability the same laser at ∼1.3 W of absorbed pump power utilizing a birefringent filter [38].

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Table 3. Continuous wave laser results obtained with Tm³⁺-doped mixed sesquioxides.

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The first report also remains the most efficient Tm³⁺-doped mixed sesquioxide laser up to now, despite several reports on ceramic mixed sesquioxide Tm³⁺-lasers published recently. But in particular with (Lu_0.8Sc_0.2)₂O₃ ceramics very good results with up to 40% of slope efficiency and significantly higher output power of up to 11 W were obtained [90]. In conclusion, the difference between the cw performance of ceramics and crystals is lower than for Yb³⁺-doped mixed sesquioxides, which may be explained by the strong λ^-4 wavelength dependency of Rayleigh scattering and correspondingly reduced scattering losses. The good performance of Tm³⁺-doped mixed sesquioxides is also evidenced by the fact, that – in contrast to the Yb³⁺-doped compounds – several reports on mode-locked Tm³⁺-doped ceramics exist. These are listed in the lower part of Table 2. The first reports on fs-pulse generation utilizing Tm³⁺-doped mixed sesquioxides were obtained when mode-locking at 2 µm was still exotic. The pulse durations below 200 fs [80] were among the shortest in this wavelength range at the time. However, meanwhile, ceramics outperformed crystals and sub-60-fs pulses, which are among the shortest ever generated around 2 µm, were reported for different mixed sesquioxide ceramics [84–86]. A recent work shows that there may even be potential to further shorten the pulse duration: By combining a Tm:Lu₂O₃ ceramic sample and a Tm:Sc₂O₃ crystal in one resonator, pulses as short as 41 fs at 42 mW of output power were realized [94].

4.3 Er³⁺-, Nd³⁺- and Ho³⁺- doped mixed sesquioxide lasers

Table 4 lists the laser results obtained with mixed sesquioxide crystals and ceramics doped with Er³⁺, Nd³⁺ or Ho³⁺. In fact, the motivation of the early work on Er³⁺-doped mixed sesquioxide crystals was to shift their emission peaks to wavelengths suitable for the detection of greenhouse gases [60]. This was obtained already at low mixing ratios, thus the corresponding laser results under pumping with laser diodes at 1532 nm and listed in Table 4 are not representative for the performance of Er³⁺-doped mixed sesquioxides at ∼1.6 µm. Further reports on this laser transition in mixed sesquioxides do not exist, thus its full potential still needs to be revealed.

Table 4. Continuous wave laser results obtained with Er³⁺-, Nd³⁺, and Ho³⁺-doped mixed sesquioxides

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Er³⁺-doped pure sesquioxides are among the best suited host materials for the generation of laser radiation in the 3 µm wavelength range [61]. Therefore, mixed sesquioxide hosts might be very suitable host materials, too. However, it was not before 2021, when corresponding results were published for the first time. An 11.8 mm long Er³⁺-doped (Sc_0.46Y_0.54)₂O₃ crystal pumped at 970.5 nm by an OPSL delivered a slope efficiency of up to 19% under 1:1 chopped pumping at a maximum on-time q-cw output power of 0.44 W [32] (see Fig. 10). Another recent report even obtained a slope efficiency of 42% with an Er³⁺-doped (Lu_0.84Sc_0.16)₂O₃ ceramic [65]. The sample under investigation in this report was rather short, reducing the absorption efficiency and limiting the cw output power to 0.34 W. Nevertheless, the efficiency reported in [65] is higher than the Stokes efficiency of ∼34% between the 0.98 µm pump and the 2.85 µm laser and even higher than the best results obtained with Er³⁺:Lu₂O₃ crystals in this wavelength range. This is enabled by an upconversion process depopulating the lower laser level ⁴I_13/2 and partly repopulating the emitting level [61, 95], which may become more resonant for a suitably tailored crystal field and points toward a high potential of mixed sesquioxides with compositions close to Lu₂O₃ to even further enhance the performance of Er³⁺-doped sesquioxide lasers in the 3 µm range. It should be noted, that at this long laser wavelength, the influence of scattering can be expected to be very low. This makes ceramics possibly the material class of choice for this wavelength range, as also evidenced by recent reports on highly efficient 6.7 W of 2.8 µm laser output from pure Er³⁺-doped sesquioxide ceramics [96].

 

Fig. 10. : Laser characteristics of a q-cw-pumped Er:(Sc_0.46Y_0.54)₂O₃ laser emitting at 2715 nm.

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As seen in the lower lines of Table 4, only few reports exist on Nd³⁺- or Ho³⁺-doped mixed sesquioxide lasers. An early report concentrated on compositional tuning of the emission peak of a Nd:(Lu_xSc_1-x)₂ laser to a desired wavelength [42]. Again, the Sc₂O₃ content in the final laser crystal was very low and amounted to only 9%. Nevertheless, this ground state laser operating at 953 nm enabled a good slope efficiency of 47%. The only other report on a mixed Nd³⁺-doped sesquioxide laser obtained nearly 500 mW of output power at the high-gain 4-level-laser transition of a Nd:LuYO₃ ceramic, however, at a slope efficiency of only 6% [43], which is attributed to the low quality of the sample utilized for these experiments and not considered to be an intrinsic feature of Nd³⁺-doped mixed sesquioxides. For Ho³⁺-doped mixed sesquioxides, besides an early report on an Yb, Ho:(Y_0.89La_0.11)₂O₃ laser with only 2.7% slope efficiency [97], which due to the La³⁺-admixture is not part of the ternary system under investigation here, only a rather preliminary result on a Ho:(Lu_0.58Sc_0.42)₂O₃ exists. In that work, cw and q-cw slope efficiencies of 1.6% and 7.6% at 29 mW and 187 mW of output power in the 2.1 µm range were obtained, respectively, under diode pumping. An improved performance was observed under Tm³⁺-laser pumping at 1946 nm. In this case, the slope efficiency amounted to 25% at, however, only 20 mW of output power [45]. Also in this case, a better performance can be expected by the future use of samples with better optical quality.

5. Conclusion and outlook

We reviewed the spectroscopic and laser properties of rare-earth doped mixed cubic sesquioxide crystals and ceramics in the ternary system Lu₂O₃-Sc₂O₃-Y₂O₃. Their disordered structure leads to a significant inhomogeneous broadening of the gain bandwidth, which is an essential property for the generation and amplification of ultrashort pulses. Even though this disorder is accompanied by a degradation of the thermal properties, the thermal conductivity at the doping concentrations typically required for efficient lasing remains higher than in many other broad-band gain materials.

The reduced melting point of various compositions in the binary system Sc₂O₃-Y₂O₃ enables the growth of high quality mixed sesquioxide crystals by the Czochralski method from iridium crucibles. Ceramic fabrication techniques at temperatures well below the melting point are also well suited for these cubic host materials and enable to fabricate arbitrary compositions in the full ternary solution-series of mixed sesquioxides doped with Yb³⁺, Tm³⁺, Er³⁺, Nd³⁺ or Ho³⁺.

At the current state of the art, the laser performance of Yb³⁺-doped mixed sesquioxide ceramics falls back considerably behind their crystalline counterparts. This may be attributed to losses induced by the sintering aids routinely mixed into ceramic starting materials or an increased scattering rate in the near-infrared spectral range around 1 µm. In contrast, the laser performance of Tm³⁺-doped mixed sesquioxide ceramics is close to the efficiencies obtained with crystals and Er³⁺-doped mixed sesquioxide ceramics even enabled laser efficiencies higher than those obtained with pure sesquioxide crystals, which is likely to be supported by the lower scattering losses for the Er³⁺ laser transition around 3 µm.

Crystalline as well as ceramic fabrication techniques enable the growth of rare-earth doped laser samples with dimensions sufficient for high-power thin-disk lasers and slab amplifiers. Given the performance already demonstrated with Yb³⁺-doped mixed sesquioxides, these host materials are believed to be suitable for the generation and amplification of sub-50-fs pulses in the 100-W-class output power range in the 1 µm and even in the 2 µm range. For Er³⁺-doped mixed sesquioxides an appropriate choice of the composition may increase the rate for the upconversion process from the lower laser level required for efficient lasing on the 3 µm transition.