High-power lasers with "superthermal" laser crystals

INTRODUCTION
Since the birth of the laser in 1960, achieving high output power has been one of the eternal themes in the development of laser technology. The process of increasing laser energy is always accompanied by thermal energy, and thermal energy is useless in this process, "laser energy" and "thermal energy" are the highest and lowest quality forms of energy respectively, and the history of the development of high-power laser technology is a history of struggle with "waste heat".

The first ruby laser[1] that marked the birth of lasers in 1960 was a solid-state laser. Solid-state lasers usually use activated ion-doped crystals, ceramics and glass as the gain medium, and their gain medium forms include conventional bulk materials and low-dimensional materials represented by optical fibers. After the birth of solid-state lasers, on the one hand, the wavelength coverage was expanded, from the initial red light to short-wave green light, blue light, ultraviolet, deep ultraviolet development, long wavelength
Lasers have matured and commercialized in the near-infrared and mid-infrared bands, and on the other hand, the laser pulse width has been narrowed from microseconds (μs) to nanoseconds (ns), picoseconds (ps), and femtoseconds (fs), and attosecond (AS) lasers are expected to be engineered [2-3]. The realization of high output power in any application scenario is the common goal of laser technology development [4-6].
With the increase of pump power, the thermal effect inside the gain medium is significantly enhanced, and the heat generated cannot be removed from the medium in time through heat conduction, resulting in an increase in the internal temperature and temperature gradient of the medium, and the thermal lensing effect and stress birefringence effect caused by the internal thermal distortion seriously deteriorate the beam quality and limit the further increase in power [7]. In order to suppress the thermal effect, researchers have designed different types of solid-state lasers, such as heat-capacity lasers, thin-slice lasers, slat lasers, and fiber lasers [8], with the core idea of improving heat dissipation efficiency. In this paper, the working characteristics and research progress of the above solid-state lasers are briefly reviewed. In addition, based on the current theoretical and experimental research on the thermal conductivity (κ) of crystalline materials, from the perspective of improving the thermal conductivity of gain dielectric materials, the thinking and prospect of solving the thermal effect problem are proposed.

1 High-power lasers
1. 1 heat capacity laser
Heat-capacity lasers reduce the thermal distortion of gain materials by separating the working phase of the laser from the heat dissipation phase in time. When the heat capacity laser is working, the gain medium is in an approximately adiabatic environment, and its internal temperature gradient is small, and the resulting thermal distortion is also small. The internal accumulation of waste heat increases the temperature of the gain medium, which must be forced to cool after a period of continuous operation, depending on the thermodynamic properties of the material itself. Because the gain medium does not dissipate heat from the outside during the laser operation stage, its surface temperature is higher than that inside, and the compressive stress on the surface can greatly increase the damage threshold of the medium, and the allowable laser pumping strength is 5 times that of the surface in the state of tension. The output of a heat-capacity laser depends on the product of the gain medium and the temperature range of the laser that it can generate, so it is not only required that the gain dielectric material have a large heat capacity value, but also that the luminescence efficiency of the internally activated ions is less affected by the increase in temperature [9].

As early as 1994, Walters et al. [10] used a heat-capacity laser with flash-pumped rod-shaped neodymium glass as the gain medium to achieve a pulsed laser output with an average power of more than 1 kW and a duration of several seconds, proving the feasibility of the heat-capacity laser scheme. Subsequently, the Lawrence Livermore national laboratory (LLNL) in the United States used large-size Nd3+∶Glass, Nd3+∶Gd3 Ga5 O12 (GGG) crystals, and Nd3+∶Y3 Al5 O12 (YAG) ceramics as the gain medium to carry out the research of solid-state heat-capacity lasers (see Fig. 1) [11]: In 2001, LLNL used flash lamps to pump 9 pieces10 The cm×10 cm Nd3+∶Glass obtained a pulsed laser output with an average power of 13 kW. In 2004, LLNL used a laser diode array to pump four 10cm×10 cm Nd3+:GGG crystals to achieve 45 kW laser output. In 2006, LLNL used a laser diode array to pump five 10 cm × 10 cm Nd3+:YAG ceramics with an output power of up to 67 kW and a pulse duration of 500 ms. By introducing a real-time adaptive optical correction system in the cavity, the beam quality control was within 2 times the diffraction limit, and the laser running time was increased to 5 s [12].

Heat-capacity lasers have two important limitations: (1) the laser beam quality degrades rapidly with the increase of light generation time [13]; (2) The cooling time of the gain medium accounts for 80% of the entire working cycle, which determines that the heat capacity laser cannot work at high frequency, and the working time in seconds is difficult to meet the practical requirements.

1. 2 thin-slice lasers
The gain medium of the thin slice laser is a thin sheet with a thickness of less than 1 mm, which is fixed to a rigid substrate that dissipates heat by solder, and the bottom surface of the contact acts as a cooling surface and also acts as a reflective surface for the laser and pump light, and the other side acts as a high transmission surface. Since the direction of heat flow and the direction of laser propagation are basically the same, the wavefront distortion caused by the temperature gradient can be largely ignored, resulting in a high beam quality laser output. The advantage of thin-slice lasers is that they maintain high beam quality at high power outputs. Thin-slice lasers are available in two types of pumping methods: end-pumping and side-pumping, as shown in Figure 2 [14].

Due to the short propagation distance of light in a single sheet, the gain capacity is limited, and the maximum output power is currently 5 kW [15], and further power increases require the cascade of multiple lamella for amplification (see Figure 3 [16]). In 2000, Stewen et al. [17] achieved a continuous laser output of 647 W in a single Yb3+∶YAG thin slice by end-pumping, and a maximum laser output of 1070 W by combining four thin slices. In 2009, the Boeing Company pumped 10 Yb3+:YAG thin slices to obtain a laser output of 28 kW, with a laser duration of several seconds and a beam mass close to the diffraction limit [18]. The commercial thin-slice laser developed by Trumpf in Germany is capable of producing a continuous laser with a stable output power of 18 kW. Theoretical calculations show that the maximum output power of a single sheet is about 30 kW [15], and it is clear that the current experimental results are still quite far from the theoretical value.

At present, the main problems of thin slice lasers are: (1) high requirements for crystal thin slice processing and welding process; (2) The gain capacity of a single sheet is limited, and the cascade of multiple pieces will make the optical path of the system extremely complex, which requires high precision assembly and adjustment ability of the system.

1. 3 slatted lasers
The slat laser is to process the crystal into a slat, in which the laser travels in a "Z" shape, and the reciprocating and tortuous optical path makes the laser wavefront distortion caused by the temperature gradient in the length and thickness direction of the slat, which is partially homogenized, and the two large sides of the slats are conducive to cooling, thereby reducing the deterioration of the laser quality caused by the thermal effect.

Figure 4 shows the "Thin Zag" type slatted laser designed by Textron [6]. The Thin Zag structure is a "sandwich" structure in which the Nd3+∶YAG ceramic slats are sandwiched between two fused silica windows, and the pump light enters the Nd3+∶YAG ceramic slats from one end through the coupling window, and then the total reflection occurs on the inside of the quartz window, so that the laser propagates to the other end of the slats in the form of a "Z" shape. In 2005, Marsh achieved a laser output of 15 kW with a laser duration of 10 s by connecting two Nd3+∶YAG ceramic slats in series. Subsequently, the company achieved a laser output of 50 kW using two Nd3+:YAG ceramic slats [15]. In February 2010, Marsh achieved the first single-link 100 kW laser output by connecting six laser modules with an output power of 17 kW in series [6].
The main difficulty in the development of slat lasers is that there are many limited factors in the selection of coolant. The refractive index of the coolant should be matched with the gain medium to reduce the loss of the laser at the solid-liquid interface, and it is required to have a low absorption rate for the pump light and the laser. In addition, the difference in thermo-optical coefficient can lead to additional optical distortion of the laser, and different flow states can also affect the laser quality.

1. 4 Fiber lasers
Fiber lasers use a glass fiber doped with activated ions as the gain medium, relying on gain amplification that can often be hundreds of meters long to achieve high power, and because the fiber has a large specific surface area, it is easy to manage the thermal effect of the fiber at high power output. In addition, fiber lasers are characterized by high beam quality and flexible output because the laser is transmitted in a core with a diameter of tens of microns (see Figure 5) [19]. With the continuous development of double-clad fiber preparation and cladding pumping technology, the output power of fiber lasers is gradually approaching that of lasers with bulk materials as the gain medium. With a simple structure and low quantum loss, Yb3+ quartz fiber is the main gain medium used in high-power fiber lasers. In 2009, IPG used a 1 018 nm laser-pumped Yb3+ fiber to achieve a continuous laser output of 10 kW in a single fiber for the first time, with an output wavelength of 1 070 nm and a quantum loss of less than 5%, based on the same belt pumping technology and MOPA amplification structure [20]. In 2012, the company achieved the first 20 kW single-mode fiber CW laser output, followed by a 120 kW multimode fiber laser output in 2013 [21], and now the company is able to provide industrial-grade 20 kW single-mode and 500 kW multimode fiber lasers, both of which are currently the highest output power of fiber lasers. University of Jena, Germany
Otto et al. calculated that the ultimate output power of a single-fiber Yb3+ fiber laser is about 70 kW, and the current output power is still far from this value [22].

One way to improve the thermophysical performance of the fiber gain medium is to use a single crystal fiber. Compared with quartz glass, crystalline materials have higher thermal conductivity, smaller nonlinear coefficients, and higher damage thresholds, so the theoretical ultimate power of single-crystal fiber lasers is more than one order of magnitude higher than that of traditional quartz fibers [23]. The Charles Fabry laboratory in France used a 1 mm diameter and 40 mm length uncoated Yb:YAG single crystal fiber as the gain medium to achieve a 251 W continuous laser output [24]; Subsequently, the U.S. Army laboratory used diode-pumped double-clad Yb:YAG monocrystalline fibers to achieve a maximum output power of 60 W [25]. At present, there is still a big gap between the output power of single crystal fiber lasers and traditional quartz fiber lasers, which is mainly due to the immaturity of low transmission loss single crystal fiber preparation technology, especially how to achieve the high-quality cladding structure of single crystal fiber is the key bottleneck in the development of single crystal fiber lasers.

It can be seen that in order to solve the problem of thermal effect of laser gain medium under high-power operation, in addition to heat capacity lasers, the main solutions currently used are:
Changing the size and shape of the medium to have a large specific surface area to facilitate heat dissipation, combined with advanced cooling technology to maximize the performance of the material. However, whether it is a thin sheet, slat, or fiber laser, its performance is ultimately limited by the thermal performance of the gain dielectric material itself, and it is a great challenge to further increase the laser power.
2 Ultra-high thermal conductivity laser crystals
In the process of heat transfer, the thermal conductivity of the dielectric material is the most critical physical parameter. Among the currently used laser gain dielectric materials, the thermal conductivity of glass materials is low, and its value is generally lower than that of 1W·m-1· K-1; Crystal materials have high thermal conductivity due to their orderly periodic structure, and the thermal conductivity of laser matrix crystals currently used is relatively high (~30W·m-1· K-1)[26], sesquioxide crystals such as Sc2O3 (16.5W·m-1· K-1), garnet crystals such as YAG (11W·m-1· K-1)[27]。 It can be found that the thermal conductivity of the laser gain dielectric material used at present is higher than that of the general thermal conductive material (~400W·m-1· K-1) is 1~2 orders of magnitude lower, and the thermal conductivity of the gain dielectric crystal is expected to break through the bottleneck of existing materials and obtain higher laser power.

2.1 Common high thermal conductivity crystal materials
Solid dielectric materials mainly transfer heat through phonons, and the thermal resistance comes from the phonon scattering process inside the material, including the scattering between phonons in the material and the scattering of phonon by various structural defects. The intrinsic thermal conductivity of an insulating material is mainly related to the U process of phonon-to-phonon scattering of the material [28], which depends on the microscopic crystal structure of the material and the way in which the atoms that make up the material bond with each other. In 1911, Eucken [29] found for the first time in experiments that diamond has excellent thermal conductivity at room temperature; In 1953, Berman et al. [30] experimentally measured the thermal conductivity of diamond at room temperature
550W·m-1· K-1, which is significantly higher than that of silver with the best thermal conductivity among metal materials (430W·m-1· K-1) and copper (400W·m-1· K-1)。 In the following decades, extensive research was carried out on dielectric materials with high thermal conductivity, and Slack [31-32] summarized the discovered dielectric materials with high thermal conductivity, pointing out that the unit or binary system materials with diamond-like structures exhibit better thermal conductivity properties, including diamond, cubic BN, BP, SiC, BeO, BeS, BAs, AlN, AlP, GaN, GaP, and Si. In addition to excellent thermal conductivity, it is also necessary to meet the requirements of high transmittance in the visible and infrared bands, large-scale preparation of crystals, and high-concentration activation ion doping. Table 1 lists the band gap widths for crystalline materials with high thermal conductivity and the maximum size of crystals that can be prepared at present. It can be seen that diamond, AlN, GaN, and SiC are among these crystals that meet the requirements for both transmission in the visible and infrared bands and large-scale preparation (on the order of centimeters).

2.1.1 Diamond crystals
Diamond is the crystal material with the highest thermal conductivity found so far, and its thermal conductivity at room temperature is as high as 2200W·m-1· K-1, at 340~2500nm
The wavelength band has high transmittance and high mechanical strength, and is regarded as the "ultimate laser crystal" material. With the advancement of crystal preparation technology, it is now possible to artificially synthesize centimeter-level diamond single crystals. Due to the small radius of carbon atoms constituting diamond, the doping studies mainly focus on B, N, P, S, Ge, Si, Sn [59-64], which are elements with small ionic radius
There are research reports in this area. In 1996, Jamison et al. [65] used chemical vapordeposition (CVD) to prepare diamond crystals doped with Ti3+, Nd3+, Cr3+, and Er3+ by low-energy ion implantation, with a doping concentration of about 1×1013 ions/cm3, and realized pulsed laser oscillation in Er3+-doped diamond samples. In 1998, Shiomi et al. [66] first used microwave plasma
Diamond crystal films were prepared by bulk chemical vapor deposition (microwavePCVD, MPCVD), and then Er3+-doped diamond crystals were successfully prepared by ion implantation, with a doping concentration of about 1×1019 ions/cm3 and a doping depth of only 1.5 μm
B can significantly increase the luminous intensity of Er3+. At present, the research on the use of diamond as a laser gain medium is mainly in the field of color center laser [67] and Raman laser [68], and there are no reports on activating ion-doped diamond lasers.

2. 1. 2 SiC crystals
SiC has the same crystal structure as diamond, so many of its physical properties are similar to diamond, such as high mechanical strength, high melting point, and high thermal conductivity. In fact, SiC is currently the bulk single crystal material with thermal conductivity second only to diamond among crystals that can be prepared in large sizes. The demand for SiC crystals for high-energy electronic devices has greatly promoted the progress of crystal fabrication technology, and researchers have successfully grown high-quality 4H-SiC single crystals with a diameter of 200 mm by physical vapor transport (PVT) method. There are two main methods for SiC crystal doping: (1) using raw materials containing doped ions for crystal growth, which has the advantage of simple process and uniform doping, but is limited by raw materials;
(2) In the process of crystal growth, additional gas containing doped ions is introduced and incorporated by the method of co-crystallization, which has the advantage of large degree of freedom, but the introduction of doped gas will increase the complexity of crystal growth, and the uniformity of doping is affected by the difficulty of accurate control of the pressure of the doping atmosphere. Tairov et al. [69] recrystallized Sc3+∶SiC single crystals from Sc3+-doped SiC raw materials, and found that the concentration limit of Sc3+ doping was 2 ~3 ×1017ions/cm3.
Otherwise, inclusions of the second phase will appear in the crystal. Kozanecki et al. [70] prepared Er3+∶SiC single crystals by ion implantation, and found that co-doped O2- could change the local structure of the Er3+ light-emitting center. The research on rare earth-doped SiC lasers has not yet been reported.

2. 1. 3 AlN/GaN crystals
AlN and GaN belong to group III.-V. wide bandgap semiconductor materials and are now playing an important role in diode lighting and photoelectric detection. The thermal conductivity of both crystals was in the range of 200 W·m-1· K-1 and above, and have a wide transmission band in the visible and infrared bands, and the transmission range of AlN extends to the ultraviolet band. Due to their high melting points (AlN-2800 °C, GaN-2 300 °C), these two materials are generally grown by vapor phase epitaxy (VPE) or PVT method, which has high growth cost and limited crystal growth size. Rare earth doped GaN/AlN crystals in
Extensive research has been obtained over the past 30 years. In 1994, Wilson et al. [71] prepared Er3+-doped GaN and AlN crystal films by molecular beam epitaxy (MBE) growth combined with ion implantation, and measured their fluorescence spectra in the near-infrared band for the first time. Since then, the luminescence properties of Eu3+, Pr3+, Tm3+, Tb3+, Nd3+, and Ce3+-doped GaN/AlN crystals and the microstructure of doped ions in the crystals have been studied and reported [72-75]. In 2004, Park et al. [76-77] achieved a laser oscillation output of 620 nm for the first time in Eu3+-doped GaN crystal films, and found that there were mainly two different cell Eu3+ stimulated emission processes in the crystal. Lorenz et al. demonstrated that high-temperature annealing can effectively repair doping
lattice damage caused by ion implantation into AlN crystals; Usov et al. [78] proposed that multiple ion implantation and annealing of GaN/AlN crystals could increase the doping concentration of rare earth ions. Due to the large difference between rare earth ions and crystal matrix ions, crystal doping is mainly achieved with the help of MBE and ion implantation technology, so a large number of studies are mainly focused on single crystal thin film samples. In 2014, Ishikawa et al. [79] adopted temperature at high pressure (6.5 GPa).
Ce3+-doped AlN single crystals were successfully grown by degree gradient method, and it was observed that the Ce3+ in the crystals was dispersed and occupied by the Al ion lattice, and no Ce3+ ion clusters were formed by scanning transmission electron microscopy (STEM-HAADF). This method provides a new way for the preparation of large-size rare earth doped GaN/AlN-body single crystals.

It can be seen that these high thermal conductivity crystal materials have some common characteristics: first, these crystals are composed of low atomic number elements. The atomic radius is small, and rare earth ions are difficult to incorporate, which often needs to be achieved by high-cost methods such as ion implantation, and the amount of incorporation is limited. Due to the large mismatch between the radius of matrix ions and rare earth ions, the thermal conductivity of the crystal itself will be significantly reduced after incorporation, which needs further research. In addition, the interatomic bonding inside the crystal is dominated by covalent bonds, and the crystal melting point is high, which cannot be prepared by the traditional melt method or solution method, and the preparation of large-size crystals faces the problems of high cost and difficulty. Therefore, the practical application of high thermal conductivity crystals as laser matrix crystals still needs to be further developed in crystal preparation and doping technology.

2. 2 Ultra-high thermal conductivity exploration
For laser crystal materials currently in use, there are a number of measures that can be taken to further improve their thermal conductivity during operation, including reducing the crystal operating temperature, optimizing the doping scheme, and isotope purification.
2. 2. 1 Reduce the temperature of the medium
The thermal conductivity of dielectric crystals generally shows an inverted V-shaped trend of first increasing and then decreasing with temperature, and the κ-T curve has a maximum value. For the vast majority of dielectric crystals, the maximum value corresponds to an extreme temperature of less than 100 K, and above the extreme temperature, the thermal conductivity of the material decreases with the increase of temperature, and there are differences in the decline rate of different materials (see Fig. 6(a)) [28,31,80], and the decrease in thermal conductivity is mainly caused by the stronger interphonon scattering in the material at the increased temperature. Among them, the thermal conductivity of sapphire (Sapphire) is most significantly affected by temperature, and its thermal conductivity even exceeds that of diamond at low temperatures [28]. Aggarwal et al. [81] systematically studied the temperature variation of thermal conductivity of various laser crystals in the range of 100 ~300 K (see Fig. 6(b)), and when the temperature drops from 300 K to 100, YAG, Lu3 Al5 O12 (LuAG), and YAlO3 are studied (YAP)、LiYF4 (YLF)、LiLuF4 (LuLF)、BaY2 F8 (BYF) KGd(WO4)2 (KGW)、KY(WO4 2 (KYW) thermal conductivity increased by 312%, 206%, 455%, 357%, 397%, 177%, 162% and 174%, respectively; In addition, the incorporation of rare earth ions weakens the effect of temperature on thermal conductivity. If the working temperature of the laser crystal can be reduced to about 100 K, the thermal effect of the material will be effectively improved.

2. 2. 2 Doping optimization
Defects in the crystal also scatter phonons, resulting in a decrease in the thermal conductivity of the material. For laser crystals, the additional doping of activated ions is itself a point defect, and its effect on the thermal conductivity of the laser crystal is also the most important. Due to the differences in the atomic mass and ionic radius of the incorporated activated ions and the substituted matrix ions, these differences disrupt the integrity of the crystal lattice, and the distortion field induced by them increases the scattering probability in phonon propagation, thereby reducing the thermal conductivity of the material, and the greater the difference, the greater the effect on the thermal conductivity. Taking Yb3+-doped laser crystals as an example [82], YAG and GGG crystals have similar garnet structures, and YAG crystals (13.4 W·m-1· K-1) was higher than that of GGG crystal (9.0 W·m-1· K-1), because the atomic mass and ionic radius of Yb3+ and Gd3+ are close but quite different from Y3+, the thermal conductivity of YAG crystals decreased significantly after Yb3+ doping
GGG crystals have less impact; Romain describes the effect of atomic mass differences on thermal conductivity by introducing δ mass difference factor using equation (1):

where: Mi is the mass of the atom in the crystal that occupies the substituted site; i stands for atomic species; ci represents the number of lattice occupancy of class I atoms; a0 is the average interion.
Distance; κ0 is the thermal conductivity of the undoped crystal.
Therefore, the difference of ions should be fully considered when designing laser crystals to reduce the influence of doping on thermal conductivity. In addition, for the systems with strong interaction between ions represented by Er3+ and Tm3+ doped laser crystals, the doping concentration can be effectively reduced on the basis of ensuring the laser performance of the materials through the reasonable selection of matrix crystals, so as to reduce the influence of doped ions. Su et al. [83-85] used the spontaneous agglomeration of Er3+/Tm3+ in fluorite crystals CaF2/SrF to prepare Er/Tm∶CaF2/SrF2 crystals with high laser efficiency and a doping concentration 1~2 orders of magnitude lower than that of other crystals.

2. 2. 3 Isotope purification
In addition to defects, the presence of isotope atoms in the crystal also scatters phonons, resulting in a decrease in the thermal conductivity of the material. At present, the specific mechanism of phonon scattering by isotope atoms needs to be improved, and it is generally believed that isotope atoms affect the thermal conductivity of materials by affecting the N process of phonon scattering. Experiments have shown that isotope purification can improve the thermal conductivity of materials, and this effect is more significant at low temperatures: after isotope purification (12C99.9%), the thermal conductivity of diamond (12C98.9%) is increased by 50% at room temperature and 5 times at 104 K [86]; After isotope purification (70Ge 99.99%), the thermal conductivity of germanium single crystal (70Ge 96.3%) increased by 20% at room temperature and 8 times increased at 15 K [87]; The thermal conductivity of GaAs crystals (71Ga, 39.89%) was isotopically purified (71Ga99.4%), which increased by 5% at room temperature and 13% at 100 K[88]. After isotope purification (28Si 92.2%), the thermal conductivity of silicon single crystal (28Si 92.982%) increased by 10% at room temperature and 8 times at 26 K [89]; BP Crystal (11B80.1%). After isotope purification (11B99%), the thermal conductivity at room temperature increased by 10% [46]. In 2020, Chen et al. [90] reported that isotopically purified cubic BN achieved more than 1600 W·m-1· The ultra-high thermal conductivity of K-1 is 95% higher than that before purification, and the thermal conductivity is second only to diamond. At present, the work in this area is still in the basic research stage, and it is expected that the thermal conductivity of materials will be greatly improved on the basis of isotope purification and low-temperature refrigeration technology.

2. 3 Research on new materials with high thermal conductivity
Theorists and experimentalists have been searching for new materials with high thermal conductivity on the basis of constructing accurate theoretical models of material thermal conductivity. In 1965, Julian et al. [91] derived the expression κ of the thermal conductivity of crystals by rationally simplifying the Peierls equation that describes the thermal transport process of crystals, that is, the phonon collision term ignores the scattering above the action of three phonons and only considers the forces between the nearest neighbors:

where: B is a constant; M
(2) the average atomic mass of the crystal; δ is the cube root of the volume occupied by an average atom; θ is the Debye temperature; T is the temperature; γ is Green's Eisen constant. Experiments show that the formula can fit the thermal conductivity of rare gas crystals at high temperatures. In 1973, Slack [31-32] extended the formula to polyatomic systems (see Fig. 7) and summarized the materials with high thermal conductivity that have been studied, and proposed that materials with high thermal conductivity should have the following characteristics: (1) low atomic mass; (2) simple crystal structure; (3) strong bonding between atoms; (4) The non-harmonic characteristics of lattice vibration are weak.
In 2007, Broido et al. [92] calculated the force constant between Si and Ge atoms in a crystal based on density functional theory, and solved the phonon transport equation by iterative solution with this as the only input, and calculated the thermal conductivity of Si and Ge with an error of less than 5% compared with the experimental value, as shown in Figure 8. The calculation results show that the contribution of optical phonon to the thermal conductivity of Si and Ge is only 5% and 8%, respectively, but more importantly, the optical phonon also provides an additional phonon scattering channel, that is, the scattering process of two acoustic phonons colliding to generate an optical phonon. In 2013, Lindsay et al. [38] used a similar method (considering only the three-phonon process) to calculate the thermal conductivity of BX (X=N, P, As, Sb) and found that the thermal conductivity of BAs crystals did not conform to the empirical law of Slack (Fig. 9(a)), and the thermal conductivity at room temperature was about 2000 W·m-1· K-1。 Through the calculation of the phonon spectrum, it is found that the high thermal conductivity is due to the large mass ratio of As to B and its strong covalent bond, which makes the large band gap between the acoustic branch and the optical branch of the phonon spectrum, and the scattering process of two acoustic phonon collisions to generate an optical phonon is inhibited, and the three acoustic branches are bound together, so that the scattering process of two acoustic phonon collisions to generate an acoustic phonon is also inhibited (see Fig. 9(b)). Subsequently, it was also confirmed that the thermal conductivity of BAs crystals was about 1 140 W·m-1· K-1 [35,93], much higher than BP (400 W·m-1· K-1) and BN (768 W·m-1· K-1), which further confirms the theory
Correctness of predictions. In 2018, Tian et al. [37] introduced the four-phonon scattering process into the calculation of thermal conductivity, and found that the influence of four-phonon scattering on the thermal conductivity of BAs is also quite obvious. K-1 was reduced to 1260 W·m-1· K-1, thus bringing the theoretical calculated value closer to the experimental value.

With the deepening of the understanding of the thermal conductivity of materials and the gradual improvement of theoretical calculation methods, researchers have discovered BAs crystals, which are of the same magnitude as diamond, and thus established the internal correlation between the phonon dispersive spectral structure and thermal conductivity of materials. Based on the understanding of the important role of higher-order phonon scattering in heat conduction, Tian [37,94] proposed the concept of phonon band engineering, arguing that this method can break through the traditional theoretical standards and open up a new way to discover materials with high thermal conductivity. It is expected that these research results will provide new research methods for the discovery of ultra-high thermal conductivity materials: new materials with characteristic phonon dispersion structures can be prepared by designing materials, so as to obtain new materials with high thermal conductivity; Or through high-throughput measurements or calculations of phonon dispersive spectroscopy of existing substances, materials with high thermal conductivity can be screened.

3 Conclusion and outlook
In order to improve the thermal effect of laser gain materials under high-power operation, heat capacity lasers, thin slice lasers, slat lasers and fiber lasers have appeared successively, among which the slat laser has achieved a laser output of 100 kilowatts. With laser beam combining technology, fiber lasers have a single-mode output power of 60 kW and are moving towards 100 kW, showing great application potential.
The thermal conductivity of gain dielectric materials is the key factor limiting the further improvement of laser power, and it is also very important for the lightweight, miniaturization and practical application of high-energy lasers. For existing laser gain crystals, reducing the operating temperature of the dielectric material, optimizing the doping scheme, and isotope purification can improve the thermal conductivity of the material to varying degrees. In addition, the development of high thermal conductivity crystals represented by diamond-like crystals as laser gain materials is expected to increase the thermal conductivity of the gain medium by 1~2 orders of magnitude on the existing basis, which requires further improvement of related crystal preparation and doping technology. Recently, the phonon band engineering proposed by researchers provides a new research method for the development and search of materials with ultra-high thermal conductivity, and combined with high-throughput computing, new crystal materials with high thermal conductivity and excellent optical properties may be discovered, which is expected to solve the core technical bottleneck faced by high-power lasers and improve the output power of existing laser systems.