Thermal conductivity and management in laser gain materials: A nano/microstructural perspective

Thermal management is one of the most important considerations when designing a solid-state laser system because a portion of the optical pump power is converted to waste heat rather than optical laser power. Thermal gradients in the gain media cause thermal lensing (reducing beam quality) and ultimately thermal stress fracture. Management strategies at the system level include water cooling of laser crystals and the use of highly thermally conductive heat sinks. Figure 1 shows a schematic of an edge pumped laser design where the gain medium is in direct contact with two heat sinks. The large contact area between gain media and heat sinks allows for efficient heat dissipation and high overall laser power.

Regardless of the pumping/cooling scheme, the maximum deliverable laser power scales directly with thermal conductivity, k, of the gain media, so that a tenfold increase in k translates to a 10 times more powerful laser. Thus, the thermal conductivity of the gain media itself plays a crucial role in the overall performance of the laser.

Since Maiman's first demonstration of the ruby laser in 1960,¹ numerous material systems have been investigated as candidates for solid-state laser gain media. Among them, the most widely used host materials include yttrium aluminum garnet (YAG), glass, sapphire, and many more.² With the development in laser technology, the desire to increase laser power has attracted increasing attention. As mentioned previously, the fundamental power limits are given by the thermal conductivity (controlling thermal gradients) and mechanical properties (controlling fracture) leading to the identification and development of host materials with fundamentally superior thermal/mechanical properties.

Figure 2 shows an overview of the room temperature thermal conductivity and Young's modulus of a variety of optical materials, as measures of intrinsic heat transport capability and mechanical robustness. The k values shown are for single crystals or large grained ceramic in order to highlight the highest and, therefore, most promising values. Young's modulus is a key indicator of intrinsic mechanical properties because it is relatively independent of the microstructure unlike fracture toughness and hardness that are highly dependent on material processing. As high thermal conductivity materials such as diamond and AlN are considered for laser applications,^3–7 microstructural engineering on the polycrystalline form of currently used materials is also explored to improve their thermal and mechanical properties. Microstructure is important because some of the highest k materials (Al₂O₃ and AlN) have anisotropic optical properties (birefringence), making light transmission a strong function of grain size. For polycrystalline materials whose grain sizes are comparable to or smaller than relevant light wavelengths, reducing the grain size minimizes light scattering as discussed in Sec. II A. However, larger grain sizes are beneficial for heat conduction since boundaries scatter phonons as discussed in Sec. II B.

A strategy that could prove useful in future high-power laser designs is to develop gain materials with microstructures designed with both optical and thermal performances in mind. An example is shown schematically in Figs. 1(b) and 1(c). In this proposed microstructural design, the grain sizes are highly anisotropic. Along the pumping and lasing optical axes, the grain sizes are in the deep-subwavelength, nanometer regime to reduce light scattering. By contrast along the cooling axis, they have larger grain sizes, in the micrometer regime, in order to minimize phonon scattering along grain boundaries. The purpose of this Perspective article is to discuss in detail the physical factors that determine a polycrystalline ceramic gain media's k. Emphasis will also be placed on the interrelation of thermal properties and optical properties. It is argued that since both depend heavily on the crystal and microstructure of the gain materials, true optimization requires tailoring of structure considering both optical and thermal properties. Central themes will be the microstructure, i.e., the effects of doping and grain boundaries.

Traditionally, single crystals were the state-of-the-art material for laser applications, thanks to the high optical transparency of high-quality single crystals. While single crystal manufacturing is relatively mature after decades of technological advances, certain challenges such as dopant inhomogeneity and optical inhomogeneity caused by facets and cores from a conventional melt-growth method still exist.^27,28 In addition, microstructural defects such as twinning and inclusions can scatter light. On the other hand, polycrystalline optical ceramics provide alternatives to conventional single crystals, but it is not until recently that some polycrystalline ceramic materials were shown to rival their single crystal counterparts in terms of optical transparency.²⁹ With developments in ceramic sintering and densification technologies, novel powder densification approaches allow the fabrication of optical ceramics that are comparable to single crystals,²⁹ outperform single crystals,³⁰ or can be much more easily made as polycrystalline ceramics than single crystals.^31,32

Loss mechanisms in single crystals involve mainly absorption caused by dopants or impurities. Although scattering loss from optical inhomogeneity still exists in single crystals made from conventional melt-growth approach, the loss coefficient can be reduced to a level as low as 1 dB/m for common optical single crystals such as sapphire and YAG.^33,34 On the other hand, light propagation in polycrystalline ceramics suffers from more scattering losses caused by (1) Pores, (2) Secondary phases, and (3) Birefringence, as detailed next.

Most conventional polycrystalline ceramics are opaque or translucent because of residual porosity after processing. Pores are gas (or vacuum) pockets with refractive index, n close to 1, while most ceramics considered for optical applications have refractive indices larger than 1.5. The huge refractive index mismatch $(Δn>0.5)$ between solid and pores causes intense light reflection and refraction. Therefore, conventional ceramics and porcelains often appear white because of the diffusely reflected environmental light.

The second scattering source is secondary phases. As most ceramic fabrication approaches involve densification/sintering of powder, the powder purity and homogeneity become vital for the uniformity of the densified ceramic. If the powder has more dopants/impurities than are soluble in the material lattice (or if the powder has unwanted phases), precipitation and segregation of secondary phases can happen during the densification process. For many materials such as ZrO₂ that go through phase transitions below or near the sintering temperature, secondary phase precipitation also causes inhomogeneity within the polycrystalline ceramic.^35,36 As light transmits across the grain boundary between two different phases, the refractive index mismatch (on the order of $Δn∼0.1$⁠) again causes refraction and scattering of the propagating light.

It is worth noting that for optically isotropic materials, grain boundaries between the same phase do not cause scattering since refractive indices on either side of boundary are the same, regardless of the grain orientations. It has been reported that intergranular films can exist at grain boundaries for many materials³⁷ because of impurities or lattice distortion near the grain boundary, but the thickness of these layers is typically on the order of 1 nm, which is too thin to have significant interaction with electromagnetic waves with much longer wavelengths (on the order of 1 μm for many laser applications). With developments in ceramic densification and sintering technologies, transparency has been achieved for many cubic ceramic materials such as Y₃Al₅O₁₂ (YAG), MgAl₂O₄ (spinel), CaF₂, sesquioxides, and more,^{20,29,30,32,38,39} showing that clean grain boundaries have no negative effect on optical transparency.

With a combination of optically isotropic material and low porosity, the effects of the first two scattering loss mechanisms discussed above can be minimized. However, for optically anisotropic materials with non-cubic crystal structures, birefringence scattering poses a great challenge to the optical application of the non-cubic material in the polycrystalline form. Because of the structural asymmetry in non-cubic materials, the refractive index of the material depends on the crystallographic orientation. A polycrystalline ceramic with an anisotropic structure and randomly oriented grains has discontinuities in refractive indices in the light propagation direction. This small $Δn$ causes Rayleigh–Gans–Debye (RGD) type scattering loss, which reduces transparency in non-cubic ceramics such as polycrystalline Al₂O₃.⁴⁰ 

The in-line transmission of materials with losses from light reflection, scattering, and absorption can be described using contributions of the individual loss mechanisms as⁴¹ 

where $TR$⁠, $TS$⁠, and $TA$ are the transmission after reflection, scattering, and absorption losses, respectively. To decrease scattering losses and broaden material options for optical ceramics, significant efforts have been made to produce ceramics with sub-micrometer grains.⁴² Apetz and van Bruggen used nanocrystalline Al₂O₃ ceramics as an example to study the grain size dependence of non-cubic ceramic in-line transmission, which showed that high in-line transparency can be achieved by reducing the grain size of Al₂O₃ ceramics.⁴² As the ceramic grain size gets well below the wavelength of electromagnetic waves of interest, RGD-type scattering becomes much less efficient, therefore recovering the transparency of the ceramics, as indicated by

where $RIT$ is real in-line transmission, $Rs$ is reflection loss, r is grain size of the ceramic, d is thickness of the ceramic, and $λ$ is the wavelength of light. In this model, only the reflection loss and the scattering loss are considered while the absorption loss is neglected. Equation (2) proposed by Apetz and van Bruggen for alumina clearly shows that reducing the grain size r in non-cubic ceramics improves the in-line transparency.

This idea of grain size engineering on non-cubic ceramics has been further developed and highly transparent, optically active Al₂O₃ ceramics have been made for potential lasing and lighting applications.^43–46 Similar investigation on higher $Δn$ materials such as AlN has also been made and translucency as well as photoluminescence have been achieved.⁴⁷ It has been shown that in both Al₂O₃ and AlN ceramics, fine grain size and grain boundary abundancy allow higher-than-equilibrium rare earth incorporation compared to single crystals.^44,46,48

An important consideration for rare earth incorporation into host materials is the luminescence lifetime. It is well known that different host lattices and different doping concentrations can result in different luminescence lifetimes, since they change the local environment of dopant ions. Shortened lifetime at high dopant concentrations (known as concentration quenching) is due to dopant agglomeration. In polycrystalline ceramics, dopant segregation can also occur at the grain boundaries shortening the luminescence lifetime. However, it has been reported that it is possible to minimize this effect by optimizing the processing condition and reducing the grain size.⁴⁶ In a polycrystalline ceramic with smaller grain size, grain boundaries have larger volumes and increase the inter-ionic distance between dopants segregated at the grain boundaries, therefore reducing the segregation effect on luminescence lifetime.

Besides the scattering loss mechanisms discussed above, the effect of the microstructure on optical absorption line shape also brings unique properties to optical ceramics compared with single crystals. As Shachar and co-workers discussed, absorption broadening mechanisms in solid optical materials mainly involve Doppler broadening, natural broadening, collision broadening, and inhomogeneous broadening.⁴¹ Doppler broadening originates from the relative velocity between an absorber and the light source, which causes an absorption frequency shift that is commonly known as the blue shift or red shift. In most cases for optical crystals, thermally induced velocities dominate the absorbers' movement relative to the light source. As thermally induced velocities of absorbers have random spatial directions, the net effect of random shifts is Gaussian broadening centered at the transition frequency.

The other two broadening mechanisms, natural broadening and collision broadening, are caused by the fundamental quantum mechanical time-energy uncertainty. As the excited state in a transition has a finite lifetime, the time-energy uncertainty brings an uncertainty to transition energy. The uncertainty propagates linearly to transition frequency and is referred to as natural broadening. Collision broadening has the same origin as natural broadening but with excited state lifetime shortened due to collisions in solids. With a shorter lifetime that translates to a larger energy uncertainty, collision broadening often dominates over natural broadening between these two Lorentzian-shaped broadening mechanisms.

Finally, inhomogeneous broadening originates from the variation of local environment of absorbers. This is especially significant for optical ceramics because they have grain boundaries near which energy levels for absorber transitions can be different from those in an undistorted lattice. Similar to how emission from amorphous optical glasses is broader than more ordered single crystals, polycrystalline optical ceramics can also have more significant inhomogeneous broadening than single crystals. This effect has been demonstrated in polycrystalline Al₂O₃ and makes optical ceramics attractive candidates for certain applications where absorption/emission width is of interest.⁴⁶ 

Doped polycrystalline ceramics are increasing in popularity as gain media in solid-state lasers. When analyzing the thermal conductivity of such materials, it is important to consider the underlying microstructure. Accordingly, in this section, we will present a model consisting of different scattering mechanisms, including grain boundaries and dopants that cause mass defect scattering, and use it to briefly discuss the underlying physics of the microstructural effects on the thermal conductivity of those laser gain materials.

Since typical polycrystalline laser gain media are dielectrics with large bandgaps, phonons are the dominant heat carriers. Therefore, the thermal conductivity of those materials can be calculated using kinetic theory,^49,50

where $Cω$⁠, $vω$⁠, and $Λω$ are, respectively, the spectral heat capacity, group velocity, and mean free path of the phonons, $ω$ is the angular frequency, and the summation accounts for the three acoustic phonon polarizations. $Cω$ and $vω$ are determined entirely by the phonon dispersion relation and as such are relatively straightforward to understand and model as compared to $Λω$⁠. For simplicity, here we are approximating the dispersion relation as isotropic. In addition, we focus on fully dense homogenous materials, such that the effects of the pores and phase inclusions on the thermal conductivity are negligible.

For this idealization of RE-doped polycrystalline laser gain materials, the dominant phonon scattering mechanisms include both intrinsic and extrinsic phenomena. Here intrinsic refers to those scattering physics present in even a high-quality single crystal, namely phonon-phonon (also known as umklapp) scattering and phonon-impurity scattering; for the latter, the “intrinsic” impurities mean the natural isotopic variations of the constituent atoms. Extrinsic scattering refers to phonon scattering at grain boundaries and at mass defects like rare earth (RE) or transition metal dopants. As such, the overall effective mean free path to be used in Eq. (3) can be calculated by combining all relevant scattering mechanisms in parallel using Matthiessen's rule,

where $Λumk,ω$⁠, $Λimp,ω$⁠, $Λgb,ω$⁠, and $Λmd,ω$ are the frequency-dependent mean free paths (MFPs), respectively, due to umklapp, impurity, grain boundary, and mass defect scattering due to the RE dopants.

For undoped single crystal materials, the dominant scattering mechanisms are umklapp and impurity scattering, and the MFPs associated with these scatterings can be determined by fitting simple MFP models to literature k vs temperature (T) data for high-quality single crystals. As an example of this, Fig. 3 shows experimental data⁵¹ for k(T) of single crystal YAG (black filled circles, Yagi 2007), in which k(T) first increases to reach a peak of ∼800 W/m K at ∼25 K and then starts to fall steeply with temperature, up to and beyond room temperature.

The scattering mechanisms dominating these increasing and decreasing k(T) trends, respectively, at low and high temperatures are well understood.^50,52 In the low-temperature limit of single-crystal YAG, phonon-phonon and phonon-impurity scattering both “freeze out” so that $Λumk,ω$ and $Λimp,ω$ both can be approximated as ∞ for practical purposes. In this case, the only remaining phonon scattering is at the physical boundaries of the sample, which classically corresponds to a k(T) power law of T³ due to the Debye heat capacity.⁵³ This physical boundary scattering effect could easily be added to the model of Eq. (4) as another MFP term, $Λbdy$⁠, as is routinely done in other communities.^49,50,54,55 However, this is unimportant for k of polycrystalline laser gain materials for two reasons. First, the grain sizes in these polycrystalline materials are much finer than the overall sample sizes, so that physical boundary scattering is much weaker than grain boundary scattering of phonons. Second, here we are focused on lasing in the more common and practical cases in which the operating temperatures are near or above room temperature, such that the phonon-phonon scattering also dominates the physical boundary scattering.

Now focusing on the high-temperature regime of undoped single-crystal YAG in Fig. 3, the primary scattering mechanism is phonon-phonon (umklapp) scattering, which classically leads to $k(T)∝T−1$ for $T≳13θD$⁠, where $θD$ is the Debye temperature. Intrinsic impurity scattering will also play a role near the peak in $k(T)$⁠. As such, one can obtain $Λumk,ω$ and $Λimp,ω$ by fitting the single crystal k(T) data to the theoretical model of Eqs. (1) and (2). Yet, it should be noted that two modifications need to be made for Eq. (4) for such fitting process. First, the $Λgb,ω$ and $Λmd,ω$ terms should be ignored, since the MFPs associated with the scatterings from grain boundaries and mass defects like dopants do not exist in the pure single crystals. Second, the additional MFP related to the physical boundary scattering, $Λbdy$⁠, should be added to Eq. (4) since it is important for the low-temperature regime [below the peak in $k(T)$] as mentioned in the previous paragraph. Thus, fitting the full $k(T)$ range for undoped single-crystal YAG will determine $Λumk,ω$⁠, $Λimp,ω$⁠, and $Λbdy$⁠.

For doped polycrystalline materials, the extrinsic mean free paths $Λgb,ω$ and $Λmd,ω$ also play major roles in further limiting the heat transport and can be combined with $Λumk,ω$ and $Λimp,ω$ already determined from the undoped single-crystal. Hence, understanding how grain boundary and mass defect scattering due to dopants affect the thermal conductivity are essential for developing high-power lasers with high k.

In general, polycrystalline materials have smaller thermal conductivities compared to their single crystal counterparts due to phonon scattering by grain boundaries. The magnitude of this k reduction depends on many factors such as the sizes, orientation, and quality of the grain boundaries. Here, for simplicity, we focus on the effects of the average grain size, D. Generally speaking, k decreases with decreasing grain size since $Λgb,ω$ also becomes shorter, typically following $Λgb,ω∝D$⁠.⁵⁶ To give an example, note from Fig. 3 that the measured k values of all the polycrystalline samples⁵¹ are smaller than that of the single crystal, and indeed, k increases monotonically with D due to the phonon scattering by grain boundaries. Furthermore, the maximum thermal conductivities are 64, 99, and 110 W/m K for the polycrystalline YAG with 3, 4, and 7.5 μm grain size at temperatures of 46, 39, and 37 K, respectively.

Similarly, Watari et al.⁵⁷ fabricated two polycrystalline AlN samples with different grain sizes and found that the maximum thermal conductivity increases from 260 to 655 W/m K at a temperature of ∼175 and 90 K, when grain size increases from 5 to 8 μm, respectively. These samples were not intended to be gain materials but serve well for discussion purposes; AlN is discussed in more detail in Sec. III B 4. Note that these polycrystalline AlN samples have much higher thermal conductivities than the polycrystalline YAG due in part to the much larger intrinsic single crystal k value in AlN (e.g., ∼319 W/m K for single-crystal AlN,¹² compared to ∼13 W/m K for single-crystal YAG,⁹ in both cases referring to undoped samples at 300 K). Therefore, ceramic materials with large single crystal thermal conductivities and coarse grain sizes are preferred for developing high-k polycrystalline laser gain media. Note that this is in tension with the material synthesis and optical criteria, which favor fine grain sizes for easier nonequilibrium RE doping and reduced photon scattering (discussed in Sec. III B 2).

Besides phonon scattering by grain boundaries, RE dopants also play an important role in the thermal conductivity of polycrystalline laser gain materials. Figure 4 shows the thermal conductivity of YAG as a function of Nd doping, obtained from Sato et al.⁵⁸ The thermal conductivity decreases with increasing doping concentration, and the k of 5.4 at. % Nd-doped polycrystalline YAG is about 10%–15% smaller than that of the undoped sample for all temperatures shown in Fig. 4. This is because the increased Nd concentrations increase the rate of mass defect scattering, which reduces $Λmd,ω$ and thus k. Therefore, maximizing k requires minimizing the RE doping concentrations, which again is in conflict with the requirements for lasing.

Finally, it is worth noting that $Λgb,ω$ may depend on the phonon transport direction if the material has a highly anisotropic microstructure, for example, needle-like rather than equiaxed grains. In that case, the grain boundary scattering MFPs need to be calculated separately for each different direction of the microstructure.⁵⁹ This anisotropic concept will be briefly explored further in Sec. III C.

In this section, we will discuss the thermal and mechanical properties of a variety of crystalline material systems, either in single crystal or in polycrystal form. Some like YAG are workhorse gain materials while others like the sesquioxides and AlN have the potential to be important in future high-power laser designs because of their high thermal conductivities.

Crystalline materials with cubic crystal structures have the same refractive indices along different crystallographic directions and are therefore optically isotropic. As discussed in Sec. II A, optically isotropic materials do not have birefringence, simplifying orientational considerations in single crystal scenarios. When made in the polycrystalline form, assuming there are no other phases at the grain boundaries, optically isotropic materials do not have discontinuities in refractive index between grains, which makes it easier to achieve optical transparency.

The most used crystalline laser gain medium for solid state lasers is yttrium aluminum garnet Y₃Al₅O₁₂ (YAG) single crystal. Because of the unique combination of cations (Y³⁺ and Al³⁺), the YAG lattice provides two different cation sites for optically active ion substitution. Therefore, the YAG single crystal can be doped with a variety of RE elements such as Nd³⁺, Er³⁺, Tm³⁺, Ho³⁺, which substitutes Y³⁺ in the lattice, and transition metal elements such as Cr³⁺ that substitute Al³⁺, providing a wide selection of emission wavelengths. Because of its relatively good thermal conductivity and mechanical properties compared with many other laser materials such as YVO₄ and glass hosts,^46,62 YAG single crystal remains the material of choice for many high-power laser applications.

With recent developments in ceramic sintering and densification technologies, polycrystalline YAG ceramics attracted much interest because of superior doping capability, dopant homogeneity, and mechanical properties, while still maintaining comparable thermal conductivity as single-crystal YAG.^28,62,63 It has been reported that the polycrystalline/nanocrystalline microstructure of YAG ceramics improves the fracture toughness of the material.^28,64,65 Polycrystalline YAG ceramics were also shown to allow higher doping concentration while maintaining better dopant homogeneity than single crystals.^27,63 Lab-scale polycrystalline Nd:YAG ceramics have been demonstrated with excellent optical quality comparable to single crystals^28,29,66,67 while lasers based on commercial scale polycrystalline Nd:YAG ceramics showed capability of 67 kW (Ref. 68) and >100 kW (Ref. 69) power output.

Temperature-dependent thermal conductivities of undoped/doped single crystal and polycrystalline YAG have been thoroughly studied in the past several decades. Figure 3 shows YAG thermal conductivities measured recently. Ikesue and co-workers found that their heavily doped vacuum sintered 4.8 at. % Nd:YAG polycrystalline ceramic had a room temperature thermal conductivity of 9.4 W m⁻¹ K⁻¹, which is comparable to 10 W m⁻¹ K⁻¹ they measured for a 1 at. % Nd:YAG single crystal.⁶¹ Thermal conductivity above room temperature is of great engineering importance since laser crystals always heat up in working conditions. Xu et al. grew Yb-doped YAG single crystals using the Czochralski method and measured their thermal conductivities up to 500 °C. The thermal conductivity decreased from 5.2 to 3.9 Wm⁻¹ K⁻¹ for 5 at. % Yb:YAG and from 4.6 to 3.8 Wm⁻¹ K⁻¹ for 25 at. % Yb:YAG as temperature increased from room temperature to 500 °C. Heavy doping and high temperature reduce the thermal conductivity as expected (see Sec. II B).⁶⁰ Li and co-workers measured the thermal conductivity of 1 at. % Nd:YAG polycrystal fabricated through vacuum sintering from room temperature up to 600 °C. The thermal conductivity decreases from 9.7 to 4.0 Wm⁻¹ K⁻¹ as temperature increases.²⁸ 

Yagi and co-workers studied the cryogenic temperature thermal conductivity of pure (not intentionally doped) YAG. While single crystal YAG reaches a maximum thermal conductivity of 800 Wm⁻¹ K⁻¹ around 25 K, the polycrystalline YAG samples they fabricated through vacuum sintering peaked at around 40 K with thermal conductivities between 64 and 110 Wm⁻¹ K⁻¹, depending on the grain size.⁵¹ They showed that YAG with smaller grain size has lower thermal conductivity, especially at low temperatures, which they attributed to grain boundary scattering that reduces the phonon mean free path. In general, YAG polycrystalline ceramics are as thermally conductive as YAG single crystals at and above room temperature. However, at low temperatures, especially when lower than 200 K, YAG polycrystals suffer from grain boundary scattering of phonons, which lead to a lower thermal conductivity compared with single crystals. From a laser design standpoint, the lower k caused by polycrystallinity could be problematic for cryogenically cooled lasers but less so for traditionally cooled designs.

Table I shows a compilation of selected thermal/mechanical studies on YAG single crystals and polycrystalline ceramics. Kaminskii and co-workers vacuum sintered YAG ceramic and showed a nearly fivefold improvement to fracture toughness when compared with a single crystal YAG sample.⁶⁴ Mezeix and Green showed that commercial polycrystalline 1 wt. % Nd:YAG with an average grain size of 2.22 μm has Young's modulus of 287 GPa, which is comparable to the 280 GPa value they measured for a 1 wt. % Nd:YAG single crystal along the <111> direction.⁸ They also measured other elastic constants including shear modulus, bulk modulus, and Poisson's ratio that are comparable between single crystal and polycrystal samples, with fracture toughness 7% higher for the polycrystal.

Subsequent studies also support the possibility of improving fracture toughness of YAG ceramics by reducing the grain size. Li and co-workers showed that their vacuum-sintered Nd:YAG ceramic with 15 μm grain size has 7% higher fracture toughness compared to a single-crystal Nd:YAG sample.²⁸ Sokol and co-workers fabricated a 1 at. % Nd:YAG polycrystal through high-pressure current-activated pressure-assisted densification (CAPAD)⁷⁰ (also referred to as high-pressure spark plasma sintering, HPSPS) and compared with a commercial 1.1 at. % Nd:YAG single crystal and a free sintered 1 at. % Nd:YAG polycrystal with grain size of 26 μm.⁶⁵ They found that the 1 at. % Nd:YAG ceramics they fabricated with grain sizes from 186 nm to 26 μm have comparable Young's modulus and shear modulus when compared with the single crystal, while the 186 nm sample from high-pressure CAPAD showed 22% improvement in Vicker's hardness and 155% improvement in bending strength and thermal shock resistance when compared to the single crystal. The thermal shock enhancement could be especially beneficial for high-power applications since thermal shock is the ultimate failure caused by over pumping of gain media. This would require successful doping of fine grained YAG; although this has not yet been demonstrated, one would not expect doping to reduce fracture toughness.

The sesquioxides Sc₂O₃, Y₂O₃, and Lu₂O₃ have gained increasing interest recently, mainly because of their somewhat higher thermal conductivity compared with state-of-the-art crystalline laser host YAG³¹ as well as their doping compatibility with rare earth elements. These properties combined with their good mechanical properties make sesquioxides great materials for laser host material especially suitable for RE doping.³² Although the improvements of thermal and mechanical properties of sesquioxides over YAG are not remarkably significant compared to Al₂O₃ (discussed in Sec. III B 2), sesquioxides have superior thermal and mechanical properties compared to glass, making them excellent candidates for heavy RE doping applications. However, high-quality sesquioxide single crystals are technologically challenging to synthesize through conventional melt-growth methods due to the high melting temperatures above 2400 °C and requirements for special crucibles.⁷¹ For example, high-quality single crystal Y₂O₃ is especially difficult to grow because its phase transition temperature is below the melting temperature, generating light scattering sources that impair the single crystal optical quality.³² Therefore, great efforts have been made to achieve high-quality sesquioxide polycrystalline ceramics.^32,63,72

Figure 5 shows selected thermal conductivity measurements on sesquioxide single crystals and polycrystalline ceramics. As expected (see Sec. II B), the thermal conductivity of sesquioxides highly depends on dopant concentration since they are often heavily doped. For most compositions, above 90 K, the thermal conductivity of sesquioxides decreases as temperature increases. Table II shows a compilation of recent thermal/mechanical measurements on sesquioxide single crystals and polycrystalline ceramics. More details are discussed in the Secs. III A 2 a–III A 2 c for each sesquioxide.

Despite the technological difficulties in Sc₂O₃ single crystal growth, Czochralski growth of RE³⁺-doped Sc₂O₃ has been accomplished and laser oscillation has been demonstrated in Yb:Sc₂O₃, Nd:Sc₂O₃, Tm:Sc₂O₃, and Er:Sc₂O₃.^73–76 However, the size of the grown single crystal was limited because of the problems discussed above.⁷⁶ The thermal conductivity of an undoped Sc₂O₃ single crystal at room temperature was measured to be 16.5 W m⁻¹ K⁻¹, while 3% Yb:Sc₂O₃ single crystal had a thermal conductivity of 6.6 W m⁻¹ K⁻¹.¹⁷ 

In 2005, Li and co-workers synthesized Sc₂O₃ powder via a precipitation method and fabricated transparent Sc₂O₃ ceramics using vacuum sintering.⁷⁷ Fully dense Sc₂O₃ ceramic was sintered at 1700 °C with a resulting grain size of 9 μm. Thermal conductivities of 1 at. % Yb:Sc₂O₃, undoped Sc₂O₃, and 9 at. % Yb:Sc₂O₃ ceramics were measured by Garrec et al.⁷⁸ and Rand et al.⁷⁹ to be 12.4, 13.2, and 4.57 Wm⁻¹ K⁻¹, respectively. At cryogenic temperature, 1 at. % doped Sc₂O₃ ceramic thermal conductivity peaks around 200 K at 18 Wm⁻¹ K⁻¹.⁷⁸ 

Another key parameter for a robust laser host material is fracture toughness. Gogotsi measured a fracture toughness, K_IC, of 1.49 MPa m^1/2 for Sc₂O₃ ceramic.⁸⁰ Yeheskel and co-workers measured a comparable value of 1.35 MPa m^1/2 for a hot isostatic pressed (HIPed) Sc₂O₃ ceramic.¹⁶ 

Y₂O₃ is the most well-studied material among the sesquioxides. Like Sc₂O₃, single crystal Y₂O₃ was successfully grown using a Czochralski method and laser oscillation was achieved in Tm:Y₂O₃, Nd:Y₂O₃, and Yb:Y₂O₃.^75,81,82 Klein and Croft measured single crystal thermal conductivity of 27 Wm⁻¹ K⁻¹ for undoped Y₂O₃ and 13 Wm⁻¹ K⁻¹ for 1 at. % Nd-doped Y₂O₃ at 300 K.⁹ A more recent study by Peters et al. measured 13.6 Wm⁻¹ K⁻¹ for undoped Y₂O₃ and 7.7 Wm⁻¹ K⁻¹ for 3% Yb:Y₂O₃.¹⁷ Mun and co-workers reported 16.0 Wm⁻¹ K⁻¹ for undoped Y₂O₃ single crystal and 5.4 Wm⁻¹ K⁻¹ for 15 at. % Yb:Y₂O₃ at room temperature.⁸³ In all cases, Y₂O₃ shows comparable or slightly higher thermal conductivity compared with YAG, making it an attractive material for RE-doped laser applications.

Room temperature k of undoped Y₂O₃ polycrystalline ceramic was measured by Fan et al. to be 13 Wm⁻¹ K⁻¹.⁸⁴ For 10 at. % doped Yb:Y₂O₃ heavily doped ceramics, Garrec et al. and Rand et al. reported k = 7 Wm⁻¹ K⁻¹ (Ref. 78) and k = 6.1 Wm⁻¹ K⁻¹ (Ref. 79), respectively, at room temperature. Cryogenic temperature measurements were also conducted in these studies and the thermal conductivity of Y₂O₃ increased by 50%–80% as temperature decreased to 77 K. The thermal conductivities of Nd³⁺-doped Y₂O₃ ceramics at different doping concentrations from room temperature to 800 °C were measured by Zhang et al.³⁹ From room temperature to 800 °C, undoped Y₂O₃ ceramic thermal conductivity dropped from 13.3 to 3 Wm⁻¹ K⁻¹, while the thermal conductivities of Nd³⁺-doped Y₂O₃ ceramics dropped from 4–6 to 2–3 Wm⁻¹ K⁻¹, depending on the doping concentrations.

Kaminskii et al. reported the fracture toughness $KIC$ value for Y₂O₃ single crystal to be 1.0 MPa m^1/2, which is inferior to the YAG single crystal.⁸⁵ While polycrystalline ceramic Y₂O₃ is a great alternative to Y₂O₃ single crystals in terms of material processing, the mechanical properties of Y₂O₃ ceramic are also improved compared with single crystals. Fine-grained Y₂O₃ ceramics with grain sizes of 0.76–11.5 μm from vacuum sintering and HIPing are reported to have improved fracture toughness to 1.0–2.5 MPa m^1/2, varying with different dopant concentrations and grain sizes.^18,39,85 Hardness of Y₂O₃ ceramic also showed 10%–30% improvement over single crystals.^39,85

Lu₂O₃ has the heaviest cation among all the sesquioxides, making the thermal conductivity of undoped Lu₂O₃ lowest among the three. Mix reported room temperature thermal conductivity of Lu₂O₃ single crystal to be 12.2 Wm⁻¹ K⁻¹,⁸⁶ which is lower than that for Sc₂O₃, Y₂O₃, and YAG. However, since the atomic mass of Lu is very close to that of RE dopant elements, Lu₂O₃ thermal conductivity is not much affected by heavy RE doping.³² Measurement by Peters et al. showed that the undoped Lu₂O₃ single crystal has a thermal conductivity of 12.5 Wm⁻¹ K⁻¹, while 3% Yb doping only reduced it to 11.0 Wm⁻¹ K⁻¹, which is much higher than the other two sesquioxides with similar doping concentrations.¹⁷ 

Like Sc₂O₃ and Y₂O₃, polycrystalline Lu₂O₃ ceramics are great fabrication alternative to single crystals. Garrec reported 8 Wm⁻¹ K⁻¹ for thermal conductivity of 1 at. % Yb:Lu₂O₃ polycrystalline ceramic⁷⁸ while Rand reported 11.1 Wm⁻¹ K⁻¹ for 10 at. % Yb:Lu₂O₃,⁷⁹ which is more heavily doped. The discrepancy may be attributed to different grain sizes⁷⁸ and possibly different impurity levels and sample preparation. Nevertheless, these thermal conductivity values are comparable and even higher at certain temperatures compared with RE-doped Sc₂O₃ and Y₂O₃.

Single crystal Lu₂O₃ samples were successfully synthesized through a micropulling-down method,^87,88 laser heated pedestal growth,⁸⁷ and hydrothermal technique.⁸⁹ A laser experiment on a Yb:Lu₂O₃ single crystal has been demonstrated.⁹⁰ But reports on mechanical testing on Lu₂O₃ single crystals are lacking. Kaminskii and co-workers reported micro-hardness and fracture toughness of polycrystalline Lu₂O₃ ceramic $H=12.5GPa$ and $KIC=4.1MPam1/2$⁠.¹⁹ 

Only 4 years after Maiman's first demonstration of the laser using SC ruby in 1960, the first polycrystalline ceramic laser was shown by Hatch and co-workers using hot pressed Dy:CaF₂.⁹¹ CaF₂ is a well-known optical material with a wide transparency window from 0.15 to 9 μm, and growth of large size single crystals is relatively easy.⁹² Thanks to the relatively large ionic radius of Ca²⁺ and the relatively open fluorite structure, CaF₂ can readily accommodate rare earth dopants making it a good laser host material. In recent years, incorporation of various rare earth elements into CaF₂ crystals have been shown for lasing applications, including Tm, Y:CaF₂,⁹³ Tm:CaF₂,⁹² Na, Yb:CaF₂,⁹⁴ Nd, Y:CaF₂,^95–97 and Er, Pr:CaF₂.⁹⁸ Meanwhile, a great research effort has been made to fabricate polycrystalline rare earth-doped CaF₂ ceramic as a simpler approach compared with single crystal growth. Some drivers are a wide transparency window, a lower melting point (compared to oxides), and a low refractive index (∼1.4). Growing interest in RE:CaF₂ was seen in the past decade and Nd:CaF₂,⁹⁹ Nd, Y:CaF₂,¹⁰⁰ Yb:CaF₂,^20,101 Yb,Y:CaF₂,¹⁰² Yb, Er:CaF₂,¹⁰³ Er:CaF₂,^104,105 Tm:CaF₂,¹⁰⁶ Ho:CaF₂,¹⁰⁷ and Eu:CaF₂ (Ref. 108) have all been demonstrated for laser applications.

Figure 6 shows the temperature-dependent thermal conductivity of CaF₂ single crystals and polycrystalline ceramics. Popov and co-workers used a stationary thermal flux method and showed that both naturally existing polycrystalline CaF₂ ceramics and artificially synthesized polycrystalline CaF₂ ceramics have comparable thermal conductivities compared to CaF₂ single crystals, with a room temperature value of around 10.3 Wm⁻¹ K⁻¹.²¹ $3ω$ thermal conductivity measurements from Sarthou et al. support this room temperature result with a 10 Wm⁻¹ K⁻¹ value on an undoped CaF₂ polycrystal.¹⁰⁹ However, as temperature decreases, Popov et al. showed that the thermal conductivity increases up to 245 Wm⁻¹ K⁻¹ at 50 K, while Sarthou et al. measured 73 Wm⁻¹ K⁻¹ at 50 K. This discrepancy may be due to the grain size difference between these two studies. The CaF₂ polycrystals used in the former study have grain size around 100 μm, while in the latter study, the grain size of this specific sample was not reported, but other samples reported in the same study have grain sizes around 200 nm, which is much smaller than that in the former study.

For Yb-doped CaF₂, Akchurin and co-workers showed that a polycrystalline 2.5 at. % Yb:CaF₂ ceramic has comparable thermal conductivity as a single crystal sample with the same doping concentration, both with a room temperature value around 4.7 Wm⁻¹ K⁻¹,²⁰ which is much lower than that of undoped CaF₂ samples mentioned above. Sarthou et al. showed similar result that 1.5–5 at. % Yb doping reduced the thermal conductivity of polycrystalline CaF₂ ceramic to 5.6–3.6 Wm⁻¹ K⁻¹ compared to undoped samples.¹⁰⁹ In general, the thermal conductivity of CaF₂ is slightly lower that of YAG for both single crystals and polycrystalline ceramics.

Another weakness of CaF₂ compared with YAG is its inferior mechanical robustness. Akchurin and co-workers measured the fracture toughness K_IC of the CaF₂ single crystal and polycrystalline ceramics from different sintering approaches. They found out that the single crystal has a K_IC value of 0.45 MPa m^1/2, which is significantly lower than that of single crystal YAG, while CaF₂ ceramic prepared using hot-press showed nearly 50% improvement compared to the single crystal and other ceramics prepared using the hot forming method, with a K_IC value of 0.65 MPa m^1/2.²⁰ The lower thermal conductivity and fracture toughness of CaF₂ compared with YAG makes it more vulnerable to thermally induced fracture in HEL applications. However, with its lower melting point, wider transparency window, and wider absorption and emission spectra of dopant RE, CaF₂ is one of the best laser materials in certain aspects such as diode pumping and short pulse generation, that is also relatively easy to manufacture.

Materials without cubic structural symmetry can have different refractive indices along different crystallographic directions and, therefore, are referred to as optically anisotropic materials. Common crystal structures like hexagonal and tetragonal have two different refractive indices and are referred to as birefringent materials. Unlike optically isotropic materials discussed above, birefringent materials require orientational considerations in single crystal applications. Also, when made as polycrystalline ceramics, birefringent scattering can cause transmission loss between adjacent grains (see Sec. II A), making it much more difficult to achieve high transparency. However, the excellent thermal and mechanical properties of some anisotropic materials, such as Al₂O₃ and AlN, promise such significant performance improvement over any currently used isotropic material that great research efforts are being made to overcome the aforementioned challenges.

One of the most widely used non-cubic rare earth laser host materials is yttrium orthovanadate (YVO₄). With its tetragonal structure, YVO₄ is birefringent and has a high $Δn>0.2$ across the visible and infrared spectrum. Early in 1966, O'Conner showed in a spectroscopic study that Nd:YVO₄ could become an important laser system.¹¹⁰ In 1977, Tucker and co-workers measured the stimulated emission cross section in Nd:YVO₄ and found out it is superior to Nd:YAG.¹¹¹ In 1987, Fields, Birnbaum, and Fincher demonstrated the first diode laser pumped Nd:YVO₄ laser and showed it has a lower lasing threshold and comparable slope efficiency compared with a similar Nd:YAG laser.¹¹² 

Despite the superior absorption/stimulated emission cross section and gain of Nd:YVO₄ compared with Nd:YAG, it suffers from a lower thermal conductivity and mechanical toughness. Sato and Taira reported thermal conductivities of 9.0 and 12.0 Wm⁻¹ K⁻¹ along the a-axis and c-axis, respectively, in the Nd:YVO₄ single crystal.¹¹³ Lower values around 5.2 Wm⁻¹ K⁻¹ have also been reported in numerous works.^114–116 A recent study on Nd:YVO₄ amplifier crystals by Salem and co-workers showed that its fracture toughness is 0.48 MPa m^1/2, which makes it much more brittle than Nd:YAG.¹¹⁷ 

As discussed above, reducing the grain size in ceramics can improve their fracture toughness and, hence, potentially outperform their singe crystal counterparts. However, this approach is currently not suitable for YVO₄. The large $Δn$ over 0.2 in YVO₄ can cause intense light refraction between adjacent grains in a YVO₄ polycrystalline ceramic, which will lead to a loss of transparency to the ceramic (see Sec. II A). Therefore, the use of YVO₄ in optical applications is currently limited to single crystals, which are more vulnerable to thermally induced failure compared to YAG single crystals and ceramics.

Single-crystal Al₂O₃ (sapphire) has a long history as the transition metal doped laser gain material, including the very first laser demonstrated, Cr-doped ruby.¹ Titanium-doped sapphire (Ti:Al₂O₃) is currently the most widely used tunable laser material¹¹⁸ and has enabled numerous scientific and technological innovations. Al₂O₃ has a much higher thermal conductivity (30–35 Wm⁻¹ K⁻¹)¹¹ compared with YAG (10–14 Wm⁻¹ K⁻¹)⁹ at room temperature, allowing more efficient heat extraction and lower temperature gradients in the laser crystal. Moreover, Al₂O₃ (alumina) is a well-known structural ceramic that has an impressive fracture stress of 3.5 MPa m^1/2.¹¹⁹ The thermal shock resistance of Al₂O₃ is more than 20 times higher than that of YAG, making it a great host material for high-power applications.⁴⁶ Together with its high hardness and good chemical stability over a large temperature range, Al₂O₃ is one of the most robust candidates for the laser gain material.

Since its first demonstration in 1982 by Moulton,¹²⁰ titanium-doped sapphire has been the leading material for tunable lasers. The Ti:sapphire laser offers wavelength tunability over a wide wavelength range (700–1100 nm)¹²¹ as well as capability of ultrafast femtosecond pulse generation. The importance of Ti:sapphire laser technology can be easily recognized with the crucial role it played in high-impact research such as femtochemistry (Zewail, Nobel Prize, 1999), the frequency comb technique (Hall and Hänsch, Nobel Prize, 2005), and chirped pulse amplification (Mourou and Strickland, Nobel Prize, 2018).

Despite the excellent thermal and mechanical properties of Al₂O₃ and scientific/commercial success of Ti:Al₂O₃ lasers, the doping of Al₂O₃ single crystal has been relatively limited to several transition metals such as Ti and Cr. Unlike the YAG lattice having large Y³⁺ sites to accommodate RE³⁺ dopants, the Al₂O₃ lattice only has smaller Al³⁺ sites that are energetically unfavorable for RE³⁺ to substitute. This leads to the low equilibrium solubility of RE³⁺ in Al₂O₃ single crystals $(∼10−3at.%)$⁠,¹²² which makes it difficult, if not impossible, to produce RE³⁺-doped Al₂O₃ single crystals that contain enough RE³⁺ for practical laser applications.

Alternatives to Al₂O₃ single crystals include powders, thin films, and polycrystalline ceramics. Random lasing in RE-doped Al₂O₃ powders was achieved by Rand and co-workers.^123,124 RF-magnetron sputtering¹²⁵ and pulsed laser deposition (PLD)^126,127 showed success in RE incorporation into Al₂O₃ thin films with measurable photoluminescence (PL). Nd:sapphire thin films with Nd concentrations of 0.3–2 at. % were reported by Waeselmann and co-workers.^128–130 These achievements show the possibility of RE incorporation into Al₂O₃ structures through non-equilibrium approaches. However, with powders losing the thermal and mechanical advantages of Al₂O₃ and thin films hard to scale up, bulk RE-doped Al₂O₃ materials are still needed for potential higher power applications.

Polycrystalline Al₂O₃ ceramic, on the other hand, provides the possibility of RE incorporation and bulk material scalability, while maintaining the excellent thermal and mechanical properties at the same time.¹¹⁹ In 2013, Sanamyan et al. reported synthesis and densification of Er³⁺:Al₂O₃ ceramic showing PL from Er³⁺.⁴³ In the same year, Penilla et al. reported visible wavelength PL in Tb³⁺:Al₂O₃ ceramic with a preliminary thermal conductivity measurement of 30 Wm⁻¹ K⁻¹.⁴⁴ In 2018, Penilla and co-workers conducted gain experiments on Nd:Al₂O₃ ceramic, marking the possibility of RE-doped Al₂O₃ ceramic being used as laser gain media.⁴⁶ In both works, the higher than equilibrium RE concentration was attributed to the non-equilibrium densification technique and the abundant grain boundaries in nanocrystalline ceramics. However, thermal and mechanical characterization were lacking in the RE:Al₂O₃ works mentioned above.

Figure 7 shows selected thermal conductivity measurements on Al₂O₃ single crystals and polycrystalline ceramics. Burghartz and Schulz measured 33 Wm⁻¹ K⁻¹ at room temperature and 125 Wm⁻¹ K⁻¹ at 100 K for single crystal sapphire.¹³¹ Xie and co-workers measured the thermal conductivity of 99% and 92% dense alumina ceramics between 20 and 400 K and reported 15.3 and 12.5 Wm⁻¹ K⁻¹, respectively, at room temperature, which is significantly lower than single crystal sapphire measurements.¹³² However, Penilla and co-workers measured transparent 250 nm grain size Al₂O₃ fabricated though CAPAD and reported 30 Wm⁻¹ K⁻¹ at room temperature, which is comparable to single crystals.⁴⁴ 

Table III shows more selected thermal/mechanical measurements on Al₂O₃ single crystals and polycrystalline ceramics. Smith et al. reported 25.9–32.8 Wm⁻¹ K⁻¹ for free sintered Al₂O₃ ceramic with grain sizes between 1.5 and 20 μm,¹³³ showing that Al₂O₃ ceramics with the well-controlled impurity level and minimal porosity have comparable thermal conductivity as single crystal sapphire at room temperature. Tani and co-workers fabricated Al₂O₃ ceramics with grain sizes of 6.2–60.1 μm through hot press with subsequent HIP annealing and reported fracture toughness between 3.0 and 3.9 MPa m^1/2. Fracture toughness of free sintered Al₂O₃ ceramics was measured between 3.5 and 6.5 MPa m^1/2 for samples with a grain size of 0.2–60 μm.^134,135 The variation may depend on grain shape and processing conditions.^134,135 Yao and co-workers observed grain size independent fracture toughness of 3.4 MPa m^1/2 in vacuum-sintered Al₂O₃ with a grain size of 0.3–3 μm.¹¹⁹ In all cases, Al₂O₃ is more mechanically robust and thermally conductive than YAG and sesquioxides.

Fluorapatite (FAP) is a naturally existing phosphate mineral with chemical formula Ca₅(PO₄)₃F and hexagonal structural symmetry. Artificially grown fluorapatite was demonstrated as the laser host material early in the 1960s,¹³⁶ but it was not until the 1990s that it attracted more attention with the technological advances in laser diodes as the pumping source.^24,137 In the work of Zhang et al., single-crystal Nd³⁺:FAP was grown and exhibited excellent lasing parameters including low optical loss, high absorption/emission cross sections, and low lasing threshold.¹³⁷ In the same year, Payne and co-workers demonstrated lab-grown Yb³⁺:FAP single crystal that has high emission and absorption cross sections as well as high slope efficiency.²⁴ 

As a laser host material, fluorapatite does not have the best thermal and mechanical properties compared to other crystalline hosts. Faure and co-workers grew FAP single crystals using the Czochralski technique and measured the optical and thermal properties.²⁶ They showed that Ca₅(PO₄)₃F single crystals have a thermal conductivity of 2–2.4 Wm⁻¹ K⁻¹ depending on the crystallographic orientation. The birefringence $Δn$ was 0.003. This result is comparable to Payne and co-workers' measurement on Yb:FAP, where they measured a thermal conductivity of 1.9–2.1 Wm⁻¹ K⁻¹ and a $Δn$ of 0.002.²⁴ Payne et al. also reported the fracture toughness K_1C of the Yb:FAP single crystal to be 0.48 MPa m^1/2. The thermal conductivity and mechanical toughness of fluorapatite are significantly lower than that of YAG, making it a less viable option for high power applications.

Despite the inferior thermal and mechanical properties of fluorapatite, it has attracted growing research attention in the past decade. With its hexagonal structure and a smaller $Δn$ than Al₂O₃, FAP is a perfect material to demonstrate highly transparent ceramics from an optically anisotropic material by controlling the orientation or the size of the grains in the ceramic. In 2010, Akiyama, Sato, and Taira fabricated highly transparent Nd:FAP and Yb:FAP ceramics by magnetic alignment with subsequent free sintering followed by hot isostatic pressing.¹³⁸ In the next year, they successfully demonstrated lasing using the Nd:FAP ceramic.¹³⁹ In 2014, the same group demonstrated a laser experiment with the Yb:FAP ceramic they fabricated using the same approach.¹⁴⁰ 

In 2019, Furuse, Horiuchi, and Kim fabricated highly transparent Nd:FAP laser ceramic through CAPAD without any grain alignment step.¹⁴¹ With a grain size as small as 140 nm, they were able to achieve a remarkable loss coefficient of 0.18 cm⁻¹ at 1.06 μm. This work from Furuse et al. marks the first verification of lasing in randomly oriented ceramics made from optically anisotropic materials. The experimental verification of lasing in a non-cubic ceramic opens the possibility to other non-cubic materials that unlike FAP have great thermal and mechanical potential.

Aluminum nitride (AlN) has long been known for its remarkably high thermal conductivity around 285 Wm⁻¹ K⁻¹,¹² which is close to some of the most conductive metals such as silver and copper (∼400 Wm⁻¹ K⁻¹), and 1–2 orders of magnitude higher than the oxide/fluoride-based materials discussed above. Besides the impressive thermal conductivity, AlN is suitable for optical applications such as lighting and lasing because of its wide bandgap of 6.2 eV.¹⁴² Given the bandgap and lattice phonon energy, the AlN single crystal allows light transmission over a wide optical range from 200 nm to 6 μm in wavelength, making it a promising material for window and lighting applications.

Photoluminescence, stimulated emission, and lasing in transition metal-doped AlN have also been reported recently.^5,6 But these works were based on AlN powders, AlN thin films, and AlN microfibers, which are not readily amenable for scaling up or high-energy applications. AlN also suffers from the similar challenges as Al₂O₃ that rare earth incorporation into the AlN lattice can be especially difficult because of the low equilibrium solubility of relatively large rare earth ions in the AlN lattice. Ishikawa et al. reported the synthesis of Ce-doped AlN single crystals, but the dopant concentration was relatively low (<0.1 at. %).¹⁴³ 

Like the polycrystalline Al₂O₃ case, polycrystalline AlN ceramics have been widely studied as an alternative to single crystals. High thermal conductivity AlN ceramics have been obtained by Watari, Nakano, and co-workers.^57,144 The effect of Y₂O₃ additive for AlN ceramic sintering has been thoroughly discussed in order to improve the ceramic thermal conductivity.^57,145,146 Moreover, there is recent work on AlN for light emitting applications; incorporation of Ce, Nd, Tb, and Er into AlN ceramics has been achieved and photoluminescence studies presented.^3,4,48,147 Note that these studies report emission characteristic of RE³⁺ ions that are typically used in lasing. Similar to the polycrystalline Al₂O₃ ceramics discussed in Sec. III B 2, polycrystalline AlN ceramics showed potential for higher RE doping concentration. Wieg and co-workers demonstrated that it is possible to incorporate higher RE concentration into polycrystalline AlN ceramics compared to single crystals and the RE segregation at the grain boundaries can be minimized with proper dopant and host powder processing.^47,48

Figure 8 shows selected temperature-dependent thermal conductivity results for AlN single crystals and polycrystalline ceramics. Slack measured 285 Wm⁻¹ K⁻¹ at room temperature and above 2000 Wm⁻¹ K⁻¹ near 40 K for a AlN single crystal and estimated an astonishing 60 000 Wm⁻¹ K⁻¹ peak value near 30 K for hypothetically “pure” AlN with no oxygen impurity.¹² Watari and co-workers free sintered an AlN ceramic with a grain size of 8 μm and measured room temperature thermal conductivity of 272 Wm⁻¹ K⁻¹.⁵⁷ However, the low-temperature thermal conductivity was significantly lower than that of a single crystal because of the point defect and grain boundary scattering of phonons. Wieg et al. fabricated 0.5 at. % Tb:AlN with a grain size of 4.3 μm through CAPAD and measured 94 Wm⁻¹ K⁻¹ at room temperature.⁴⁷ The high thermal conductivity despite phonon scattering from grain boundaries and dopant atoms indicates the great potential of AlN ceramics for lighting and lasing applications.

Besides the excellent thermal conductivity, AlN also exhibits good mechanical properties. Table IV shows more thermal/mechanical measurements on AlN single crystals and polycrystalline ceramics. Yonenaga et al. reported the fracture toughness of single-crystal AlN as $K1C=0.5MPam1/2$⁠,¹⁴⁸ which is lower than that of YAG and Al₂O₃. However, more mechanical testing on free sintered polycrystalline AlN ceramics has been done and measured fracture toughness values were reported between $2.9and3.3MPam1/2$ (Refs. 146, 149, and 150) with varying sintering additives. Wieg and co-workers reported fracture toughness between $4.2and5.0MPam1/2$ for AlN ceramics densified using CAPAD with different Tb doping concentrations.⁴⁷ The high thermal conductivity combined with high fracture toughness of AlN ceramic gives it a thermal shock resistance $Rs$ as high as $52000Wm−1$⁠, which is more than 60 times higher than that of Nd:YAG single crystals.⁴⁷ 

As discussed in Secs. II A and II B, one of the grand challenges in developing high-power laser media from polycrystalline ceramics is the competing thermal and optical effects. To address this issue, in a theoretical study, Mishra et al.⁵⁹ proposed to use anisotropic microstructured materials and further allowed for the possibility that thermal transport and light transmission could occur in independent directions from each other. Specifically, the authors explored these concepts by modeling 1 at. % Ti-doped polycrystalline AlN and Al₂O₃, with the anisotropic microstructures having two principal axes along the ab and c directions as shown in Fig. 9. As discussed in Sec. II, the primary phonon and photon scattering mechanisms for such materials around room temperature and above are grain boundaries, active dopants, and umklapp scattering. Considering those scatterings, the authors calculated the thermal conductivity and light extinction coefficient (loss coefficient) of their proposed microstructures for transport in both ab- and c-directions. It should be expected that the thermal and light transport properties are direction-dependent due to the anisotropy of the aligned columnar grain microstructures with an aspect ratio r = l₂/l₁ as shown in Fig. 9.

In order to quantify the lasing performance, the authors further developed an anisotropic figure of merit (FOM) by combining the simple kinetic theory and Rayleigh–Gans–Debye (RGD) models for the thermal conductivity and light scattering calculations, similar to the models introduced above in Secs. II A and II B. The FOM needs to be maximized to realize high lasing power without overheating. This model captures the competing thermal and optical effects in AlN and Al₂O₃ laser media, including some interesting direction-dependent phenomena.

Figure 10 shows the calculated FOM for AlN while considering different grain boundary dimensions and thermal and light transport directions.⁵⁹ Similar observations were reported for Al₂O₃ but are omitted here for brevity. From these calculations, it can be seen that the highest FOM values for AlN, exceeding 5 W/K, are obtained for needle-like grains (r > 10) with c-direction thermal transport and ab-direction light transmission. On the other hand, if the grains have a disk-like shape $(r≪1)$⁠, high FOMs can also be obtained (FOM > 2.5 W/K) when the thermal transport is in ab-direction and light transmission is in c-direction, as seen in panel (b). In both cases, it is not a coincidence that the highest FOMs are found for light propagation along the fine-grained direction, namely in the ab direction for needlelike grains [bottom-right of panel (c)] and in the c direction for pancake-like grains [top-left of panel (b)]. This is expected due to the much easier light propagation when the grain sizes in the propagation direction are much smaller than the wavelength, i.e., the Rayleigh regime.

Thus, a major conclusion of the modeling by Mishra et al.⁵⁹ is that materials with highly anisotropic microstructures are a promising pathway to further improve the lasing performance by designing the light and thermal transport to be in orthogonal directions. They also noted how different materials call for optimizing different parameters to best maximize their FOMs and thus laser powers, since the FOMs of different materials can be limited by two distinct effects (thermal and optical). For instance, AlN has an excitingly high intrinsic thermal conductivity (nearly two orders of magnitude higher than YAG) but also an unfortunately high birefringence, making its FOM highly sensitive to the light scattering in polycrystalline samples.

One important path toward increasing the FOM of AlN would be to ensure highly aligned crystallites in the microstructure. The calculations of Fig. 10 assumed an average grain misalignment angle of $χ=10°$⁠, and the modeling showed that in a limiting regime $FOM∝χ−4$⁠. Thus, reducing $χ$ from $10°$ to $5°$⁠, for example, has the potential to increase AlN's FOM more than tenfold. Indeed, in the best case when optical scattering is negligible, it is tantalizing to recognize that the theoretical maximum FOM, and thus lasing power output, for AlN exceeds that of YAG by more than an order of magnitude. However, realizing this exciting possibility in practice would require great care in preparing samples with exquisitely aligned needlelike grains.

Single crystal and glass-based gain media have been the unrivaled standards for high-power solid-state lasers for decades. However, the flexibility offered by polycrystalline ceramics makes them ever more promising alternatives especially for high-power applications. Recognized advantages of ceramics include improved fracture toughness and flexibility in manufacturing. Less discussed are the enticing possibilities of intentionally designed gradient doping that could lead to more optimized thermal profiles.

Comparison of the materials reviewed here show only modest improvements of thermal conductivity compared to YAG for optically isotropic ceramics (See Figs. 2 and 5 and Table II). However, the anisotropic materials, alumina and AlN, can have significant thermomechanical benefits. However, the birefringent scattering poses important challenges in creating materials with very low optical loss. Despite the complications introduced by birefringence, the tremendous thermomechanical advantage, directly translating to increased power, of alumina and AlN makes them very promising for high-power applications. It is possible that concepts of leveraging judiciously designed anisotropic microstructures (see Fig. 1 and Sec. III C) could pave the way for promising materials to be used in future high-powered lasers.

The effects of microstructure on transparency and thermal conductivity of polycrystalline ceramics were discussed to explore future laser gain materials with superior pumping capability. The thermal conductivity and fracture toughness of the most promising crystalline material candidates were reviewed. Since cubic laser materials such as YAG and sesquioxides exhibit limited thermal conductivity, the use of non-cubic materials with intrinsically much higher thermal conductivity and outstanding mechanical toughness, such as Al₂O₃ and AlN, can be a key to future high-power lasers. To achieve high optical transparency as well as high thermal conductivity, the microstructure with aligned high aspect ratio grains (rods or disks) can be especially beneficial. Meanwhile, the fracture toughness enhancement demonstrated by polycrystalline ceramics compared to single crystals could be especially beneficial for increasing laser power since thermal shock is the ultimate failure caused by over pumping of gain media.

Funding of this work by the Office of Naval Research and the Directed Energy Joint Technology Office is most gratefully acknowledged.

We have no conflicts of interest to disclose.

The data that support the findings of this study are available from the corresponding author upon reasonable request.