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Abstract
Laser lighting has great potential to be the next generation of general lighting due to its high brightness and directionality. However, the light extraction efficiency and luminous efficiency from the light exit surface are greatly limited since phosphor structure. Here, we design and optimize a phosphor structure by Monte Carlo method (MCM) with optimization algorithm. The results indicate that the optimized Ce:YAG single crystal phosphor is able to improve the extraction efficiency to 0.49, which is much higher than the conventional parallel phosphor. The luminous efficiency of the optimized phosphor can also reach 230 lm/W. In addition, the experiments and simulations show that the extraction efficiency and luminous efficiency will reduce to 0.41 and 190 lm/W if there is scattering in the optimized phosphor. The spatial distribution of the light intensity and thermal stability of the optimized phosphor are also measured. The optimized phosphor is helpful to the design of side heat dissipation structure. In general, the optimized phosphor may play a significant role in the high-flux laser lighting and the method also provides a universal tool for the phosphor design.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
As a new kind of solid-state lighting, laser lighting is expected to become the next generation of general lighting [1,2]. Laser lighting has advantages of high luminous flux, high brightness and small size [3,4]. Compared with the conventional LED (light-emitting diodes) lighting, laser lighting avoids the “efficiency droop” effect and has higher electro-optical efficiency. Particularly in the commercial field, laser headlamps have been used in mass-produced cars [5].
Phosphor converted white laser diode (PC-WLD) is one of the most common way to efficiently achieve high brightness light [6,7], as shown in Fig. 1(a). In PC-WLD, the Ce3+ doped yttrium aluminum garnet (Ce:YAG) single crystal, glass, ceramic and film (with metal or sapphire substrate) phosphors are widely used to meet the need for withstanding high temperature and preventing aging [8,9]. Efficient extraction of light energy from a phosphor is an important issue in PC-WLD, which determines luminous efficiency and brightness. Tang et al. have demonstrated that the conversion efficiency of the phosphor converter can be improved by optimizing the particle (quantum dot) size and distribution inside a phosphor [10]. Ce:YAG composites can provide higher light extraction by adding pores [11,12]. The luminous efficiency of a phosphor with reflective structure is usually higher than that of a transmissive phosphor since it has a surface coating or a metal reflective structure [13,14]. Ma et al. propose a geometric optical design to collect the backward fluorescence to improve the luminous efficiency of the phosphor [15]. Yong et al. use dichroic filters to improve the utilization efficiency of the input laser and the conversion efficiency (about 1.8 times higher than the conventional structure) [16]. Similarly, the dichroic filter is also applied to improve light extraction efficiency in LED lighting [17]. In addition, several methods to improve the light extraction efficiency in the LED lighting can also be applied in laser lighting, such as the LED with roughened surfaces to destroy the total internal reflection [18,19].
Fig. 1. (a) Interaction between pump laser and a conventional parallel phosphor. The excited fluorescence will escape from the sides and bottom of a phosphor, which will cause energy attenuation from the light exit surface. (b) Interaction between pump laser and the optimized phosphor. The fluorescence will be reflected upward on the inclined surfaces and be concentrated on the light exit surface. The reduction of the bottom area is conducive to reducing light leakage. The laser represented by numerous photon packets vertically incident on the phosphor surface in MCM. The blue and yellow dotted lines represent photon packets of laser and generated fluorescence propagating inside a phosphor, respectively.
Currently, reported luminous efficiency of a single crystal with conventional structure is usually in the range from about 100 to 300 lm/W [6,7,9,20]. The luminous efficiency is usually obtained from the light energy emitted from all surfaces of the sample measured inside an integrating sphere, rather than the light energy emitted from the light exit surface. However, this measurement method obviously overestimated the light efficiency. If it is only measured from the light exit surface of a phosphor sample, the efficiency is usually about 100 lm/W [7], which means that the extraction efficiency of the light from the light exit surface is low. The single crystal or ceramic phosphor usually has a parallel structure in a conventional PC-WLD. However, a parallel phosphor usually leads to serious total internal reflection to reduce the extraction efficiency of laser and excited fluorescence [21,22]. The parallel phosphor is also unfavorable to the design of heating dissipation structure owing to the small size of their side surfaces. Hence, the improvement of extraction efficiency and luminous efficiency in laser lighting still faces enormous challenges. In addition, thermal management in laser lighting also has an important impact on lighting efficiency and flux. Although the thermal calculation and thermal management methods of the conventional laser can be applied to laser lighting [23,24], the heat dissipation of the single crystal phosphor still needs to be further studied and improved.
Here, we propose an optimized phosphor structure that obtained by the Monte Carlo method (MCM) with optimization algorithm. In our design, the structural parameters of the phosphor are optimized by optimization, which based on the evaluation function of MCM simulation. The structure of the optimized phosphor has inclined surfaces to improve the light extraction efficiency from the light exit surface, as shown in Fig. 1(b). The simulation and experimental results demonstrate that the normalized extraction efficiency of the optimized Ce:YAG single crystal phosphor is about 0.49, which is much higher than the conventional phosphor. In addition, the luminous efficiency of the optimized Ce:YAG single crystal phosphor reaches 230 lm/W. The influence of scattering on the final performance of the optimized phosphor is also simulated and studied experimentally. The results demonstrate that the scattering will result in the extraction efficiency of the optimized phosphor being reduced to 0.41 and the luminous efficiency being reduced to 190 lm/W. The inclined phosphor is more convenient for the design of heat dissipation structure and makes heat dissipation structure closer to the highest temperature point. The experimental results show that the center temperature of the crystal sample reduces more than 63% with heat dissipation structure at 1440 mW pump power. In addition, the structure for different lighting requirements can also be obtained by adjusting the evaluation function in the optimization algorithm, which shows its scalability. In general, this optimized design may provide a new way to realize high-flux laser lighting.
2. Method
2.1 Basic optimization process of phosphor
The optimized phosphor, calculated by MCM and optimization algorithm, has the structure of inclined surfaces. MCM can effectively calculate the scattering, propagation and absorption of light (laser and fluorescence) in the phosphor. The optimization algorithm, including local optimization algorithm and global optimization algorithm [25], are used to optimize the phosphor structure based on energy change obtained by MCM. Most notably, the commonly used optimization algorithms can basically meet the requirements of optimization, because the structural parameters of the phosphor are usually few, and the evaluation function is relatively simple. The optimization algorithm described in this section refers to all available optimization algorithms to improve the applicability of this method.
The main optimization process includes following:
- I. Initialize the parameters. The parameters are the initial structure, absorption coefficient, scattering coefficient, refractive index of the phosphor, algorithm iterations number, and algorithm search steps. It is recommended to optimize several times to select the appropriate initial values, since the initial structure has influence on the final structure.
- II. Calculate the evaluation function by MCM. The evaluation function is the light extraction efficiency of the target phosphor. Of course, different evaluation functions can be selected for several optimization needs. The numbers of the photon packet participated in MCM calculation should take into account the requirements of computing time and calculation accuracy. The evaluation function calculated by MCM will be fed back to the optimization algorithm to determine the next parameter change.
- III. Set the termination conditions and iteration numbers. The optimization algorithm is terminated when the iteration reaches the convergence condition or the maximum number of iterations. In addition, the number of iterations need not be set too much, because there are fewer structural parameters.
- IV. Obtain the finial structural parameters. It is recommended to obtain the optimal structure after multiple optimizations. The structure calculated needs to be judged whether it is suitable for machining. Some specially designed structures may be difficult to achieve by existing machining technology.
2.2 MCM applied in inclined phosphor
The pump laser irradiated into a phosphor is simplified to abundant photon packets. The laser packets move randomly and the absorption occurs at a random position in the phosphor due to the scattering effect [26]. The photon packets of fluorescence (fluorescent packets) will generate with the initial energy weight wf at the same position when a laser packet is absorbed (for example, in position (x1, y1, z1) and (x2, y2, z2) in Fig. 2(a)). The initial energy of a generated fluorescent packet wf is given by
where wl is the energy carried by the laser packet when absorbed, η is the net conversion efficiency of a phosphor [26]. Meanwhile, the fluorescent packet is generated with a random direction, which is also the reason for low extraction efficiency in a traditional phosphor [27]. The generated fluorescent packet moves randomly in the phosphor (similar to the laser packet) until its energy is completely absorbed or escapes out of the phosphor. The step length of each random motion s of the laser or fluorescent packet is expressed by where ζ is a random variable, which is uniformly distributed over the interval (0,1), μa and μs are the absorption coefficient and scattering coefficient of the packet, μt is the interaction coefficient which equals μa plus μs.Fig. 2. (a) The interaction between laser, fluorescent packets and the optimized phosphor. The main interactions are as follows: the movement and absorption of laser packets, excitation and movement of fluorescent packets inside a phosphor. (b) The direction changes of packets represented by vectors on an inclined surface of the phosphor. The vectors BA and AC represent the direction of incident light and the direction of reflected light, respectively. The incident and reflection angles are α; the inclined angle of the surface is β. (c) Dimensional representation of an inclined phosphor.
Scattering inside a phosphor has a significant influence on the packet movement and the final illumination performance. Both laser and fluorescent packet will be scattered when propagating inside a phosphor (the scattering in transparent phosphor is extremely weak). The movement direction of a photon packet is determined by the deflection angle θ and azimuth angle ψ. The phase function p(cosθ) is usually used to describe the angular distribution of scattering energy for the analysis and application of multiple scattering and radiative transfer. It can be reduced to H-G approximation [28] and be expressed by
where g is the anisotropy factor and it is close to 1 in a phosphor [29]. The direction of the scattered packet can be sampled randomly based on the phase function p(cosθ), and cosθ can be expressed as a function of the random number ζ when g > 0, which isThe angle change of each photon when it undergoes random scattering can be calculated. The strong scattering effect will cause the movement direction of photons to be more random, which may increase the probability of photons emitting from the non-illuminating surface of the optimized phosphor, which will also be verified in simulation and experiment.
As shown in Fig. 2(b), the propagation angle change of laser and fluorescent packets at the boundary can be calculated by the reflection law of light beam. To simplify the calculation, a random number is generating to compare with the Fresnel reflection R(β) to determine whether the simulated photon is internally reflected or not [30]. The reflection or transmittance may happen when a laser or florescent packet moves to the inclined surface. The angle of the reflected packet relative to the rectangular coordinate system and that relative to the normal of inclined surfaces of a phosphor determine the direction of the new packet and the energy change of Fresnel reflection, respectively. Other steps that are similar to the conventional MCM will not be repeated here [29,31,32].
2.3 Calculation of extraction efficiency
According to energy conservation theory, the total energy mainly converts to the following parts: I. Fresnel reflection of the pump laser on the incident surface. II. Laser escaped from the light exit surface. III. Fluorescence escaped from the light exit surface. IV. Laser and fluorescent energy escaped from other surfaces. V. Energy lost during photo-conversion inside a phosphor. The extraction efficiency is given by
where Q0 is the total pump energy of laser, Nf is the number of fluorescent packets emitted from the light exit surface, wf is the energy carried by every fluorescent packet emitted from the light exit surface. The total energy is usually normalized to 1. It means that the fluorescent energy measured at the light exit surface is τ W when the pump power is 1 W.As shown in Fig. 2(c), both the top and bottom surfaces are square to simplify the complexity of design. To accurately describe the special structure of a phosphor, we define the parameters bottom length u1, top length u2, thickness u3, absorption coefficient μa, scattering coefficient μa and refractive index n.
3. Results
3.1 Design of optimized phosphor
MCM with optimization algorithm is compiled by the Matlab language and runs on the Windows platform. It should be noted that the stochastic parallel gradient descent (SPGD) algorithm is used to optimize the structure in our simulation [33]. Other optimization algorithms can also be used, since there are few optimization parameters of the phosphor. In order to verify the accuracy and applicability of our design, we select the Ce:YAG single crystal phosphor as the target phosphor, which is widely used in laser lighting due to its strong thermal stability and high conversion efficiency. For convenience, ‘Ce:YAG crystal’ is instead of ‘Ce:YAG single crystal phosphor’ in the following parts. The doping concentration of Ce3+ in the crystal is about 2.0 at%. The absorption coefficient of a pump laser with center wavelength 450 nm is calculated to be about 80 cm−1. The refractive index of the single crystal is 1.84. In addition, the phosphor with different doping concentration and absorption coefficient may also be selected to meet several lighting requirements. The initial structure parameters, search steps and iteration times of the optimization algorithm have influences on the final optical performance. The initial structure with empirical parameters obtained through multiple calculations. The number of iterations is selected as 1000 so that it is large enough to make the optimization converge. A cube structure with the length of 6 mm is selected in the initial structure optimization.
Taking the extraction efficiency as the evaluation function, MCM with optimization algorithm is run to optimize phosphor structure for iterations. The extraction efficiency of the initial cube structure is only 0.1. The simulation results indicate that the extraction efficiency can reach to about 0.52 on about the 500-th iteration. The simulated efficiency also has a slight fluctuation (less than 0.03) after reaching the optimization convergence. The final optimized top length, bottom length and thickness are 6.4 mm, 1.4 mm and 5.6 mm. With the number of iterations increases, the bottom length of the phosphor gradually increases and the top length gradually decreases. In general, the optimized structure is able to reduce the fluorescence leakage from the bottom surface and gradually incline the surfaces to lead more energy to reflects to the light exit surface to improve extraction efficiency compared with the conventional structure.
3.2 Experimental verifications of optical performance
In order to verify the optical performance of the designed phosphor, we select structural parameters of the simulation and a 2.0 at% Ce:YAG crystal for experimental measurement. A schematic of the experimental setup and pictures of the Ce:YAG crystal samples are shown in Fig. 3. The size of the machined sample is measured: top length 6.9 mm, bottom length 1.4 mm and thickness 5.6 mm, which includes few machining tolerances. The Ce:YAG crystal (sample 1 in Fig. 3(b)) is a nearly transparent medium. In addition, scattering has an important influence on the light extraction. The light exit surface of the optimized sample (sample 2 in Fig. 3(c)) is roughened to verify the influence of scattering effect. An integrating sphere (Hangzhou Hopoo Light&Color Technology Co., Ltd, model OHSP-350M) is used to measure the pump power and luminous flux. The laser source used in the experiment is a laser diode (LD) with a central wavelength of 450 nm (Beijing Pinafi Laser Technology Co., Ltd, model PNF-450-CW30-AC).
Fig. 3. (a) Schematic of measurement experiment setup of the optimized Ce:YAG crystal. The phosphor is fixed at the entrance of the integrating sphere. The laser with center wavelength 450 nm emitted from the LD module irradiated vertically on the center of the phosphor sample after collimation. An aperture is used to control the size of laser beam. (b) The transparent Ce:YAG crystal sample. Scale bar: 2 mm. (c) The scattering Ce:YAG crystal sample with roughened surface. Scale bar: 2 mm. (d) Top view of optimized Ce:YAG crystal sample when pumped by laser. Scale bar: 1 mm.
The single crystal sample is fixed at the light entrance of the integrating sphere with a fixture, where it will not block the light exit surface. It is worth noting that the light from the sides and bottom of the sample will not enter the integrating sphere and not influence the measurement results. This measurement method will lead to much lower extraction efficiency and luminous efficiency compared with the results measured inside (at center) the integrating sphere. After collimation, the pump laser is vertically incident on the bottom surface of the sample. The aperture is utilized to control the size and shape of the pump beam.
The relationship between the luminous power emitted from the light exit surface of the phosphor sample and the pump power is shown in Fig. 4(a). As can be seen from the experimental results, the luminous power changes linearly with the pump power. Linear equations are used to fit the measured data and the its R-square is 0.998. The slope of the fitting line of the transparent sample is 0.49, which represents the extraction efficiency from the light exit surface. The difference between the measured extraction efficiency and the simulated one (0.52) is only 5.8%. It means that the optimized Ce:YAG crystal designed by our method shows excellent light extraction efficiency. Strong scattering is formed by roughing the light exit surface of the sample. The experimental results demonstrate that the extraction efficiency of the scattering sample with roughened surface is reduced to 0.41, 16.3% lower than that of the transparent sample. That is, scattering from the surface of the optimized phosphor will weaken the energy of extracting light.
Fig. 4. (a) Relationship between pump power and luminous power in the optimized Ce:YAG crystal samples. The slope of the fitting line represents the extraction efficiency. (b) Relationship between pump power and luminous flux in the optimized Ce:YAG crystal samples. The slope of the fitting line represents the luminous efficiency.
In addition, the luminous flux and luminous efficiency of our optimized phosphor are also measured. Figure 4(b) illustrates the relationship between pump power and luminous flux of the transparent and scattering samples. The luminous efficiency in this study is the luminous flux produced by 1 W pump laser. The linear equation is used to fit the measured luminous flux, and the R-square is also 0.998. The slope of the fitting line represents the luminous efficiency, which is 230 lm/W in the transparent sample. In contrast, the luminous efficiency of the scattering sample decreases to 190 lm/W due to the increase of scattering intensity, which will be further discussed in Method 3.3. The results indicate that the luminous efficiency of the optimized phosphor has a significant improvement compared with the conventional parallel phosphor.
In order to further verify the extraction efficiency of the optimized design, the light extraction efficiency on the light exit surface is compared with that of the conventional parallel single crystal. As shown in Fig. 5(a), the simulated extraction efficiency obtained by a Ce:YAG crystal with parallel structure from the light exit surface is about 0.11, which means that most of the energy escapes from the side and bottom surfaces of the parallel phosphor (size: 10 mm × 10 mm × 1 mm). For comparison, due to the design of the inclined structure, the simulation and experimental extraction efficiency of the optimized sample reached 0.49, which is a huge improvement.
Fig. 5. (a) The simulated and measured extraction efficiency obtained by the optimized Ce:YAG crystal and the sample with a conventional parallel structure. (b) Measured spectrum of the optimized sample when pumped by a blue laser. (c) The measured spatial illuminance distribution of the optimized Ce:YAG crystal in diagonal direction A and B. (d) The measured spatial illuminance distribution of the optimized Ce:YAG crystal in Horizontal and vertical directions. The measurement distances are 23 cm, 32 cm, 48 cm.
Figure 5(b) illustrates the measured spectrum of the optimized sample. It can be seen from the results that there are less laser components in the illumination light. The correlated color temperature (CCT) of the illumination light is 4111 K. It is necessary to adjust the spectral distribution and CCT effectively through adding blue laser source to meet different lighting requirements.
Measured spatial intensity distribution of the light emitted from the light exit surface of the optimized phosphor are illustrated in Fig. 5(c) and (d). The measurement results show that the light distribution in horizontal and vertical directions are basically symmetrical, and the two diagonal directions are also symmetrical. Emitted light basically presents nearly Gaussian distribution in space and presents a flat top distribution at the center angle in diagonal directions. In addition, the spatial intensity distribution measured in the horizontal and vertical directions also has a similar phenomenon. However, the spatial intensity in the two directions is not perfectly consistent due to the machining error or measurement error of optimized single crystal. The intensity of light distribution also decreases significantly with the measurement distance increases. The illuminance at the four corners of the measuring surface is less than that at the center and sides.
3.3 Influence of phosphor scattering
The scattering of a phosphor, usually determined by scattering coefficient μs, has a great influence on the packet propagation and light extraction efficiency. The influence of the scattering on the optimized Ce:YAG crystal is simulated and analyzed. As shown in Fig. 6(a), the escaping light in bottom, side and light exit surfaces of the optimized phosphor is simulated by MCM under different scattering coefficients.
Fig. 6. (a) Influence of scattering on the escaping energy of fluorescence on each surface of the optimized phosphor. Light will escape from the bottom, side and light exit surfaces. (b) The light energy emitted from the exit surface of the optimized phosphor. The samples are I. the ideal transparent sample, II. the sample with the measured scattering coefficient of 0.3 cm−1, and III. the experimental sample, respectively.
As you can see from the results, the normalized energy of fluorescence obtained from the light exit surface will decrease with the increase of scattering. When the scattering coefficient reaches to 30 cm−1, the normalized energy from light exit surface is less than 0.1. A lot of energy escapes from the sides with the increase of scattering coefficient. The light energy escaping from the four sides reaches 0.54 when the scattering coefficient is 40 cm−1. In addition, the light escaping from the bottom caused by scattering increases slowly due to its small area (1.4 mm × 1.4 mm).
In order to further study the influence of the internal scattering of the optimized phosphor on the extraction efficiency, we measure the scattering coefficient of the experimental transparent sample and carry out the simulation (shown in Fig. 6(b)). The scattering coefficient of transparent sample is about 0.3 cm−1 measured by collimation method [34]. Although the measurement of scattering coefficient has errors, it has little influence on the final conclusion. It can be seen from the results in Fig. 6(b) that the scattering in the transparent optimized phosphor will slightly reduce the light energy extracted from the exit surface, which may also be the reason for the deviation between the experimental result and the simulation one.
The main reasons for the phenomena are that the increase of scattering coefficient destroys the reflection direction of light on the designed surfaces of the optimized phosphor and causes strong back-scattering, leading to the reduction of light emitted from the light exit surface. The difference in extraction efficiency between transparent and scattering phosphor is verified in experiments (shown in Fig. 4).
3.4 Experimental verifications of thermal stability
Heat generates in the phosphor via the Stokes shift when the pump laser interacts with the phosphor. Of special note is that this section mainly discusses the thermal management and temperature change of the optimized phosphor. Usually, the feedback between the optical and thermal performance also has an important impact on the thermal management and light efficiency. The opto-thermal simulation and analysis of phosphor in laser lighting can refer to [35]. The optimized phosphor has a certain thickness to facilitate the design of heat dissipation structure on the sides.
As shown in Fig. 7(a), the optimized phosphor is fixed in the heat sink, and the measured temperatures of the two conditions when the pump power is 1440 mW. The heat sink is made of brass in which the heat is quickly dissipated by water. In addition, the indium foil is sandwiched between the heat sink and the sample to improve the heat dissipation effect. In order to verify the thermal stability of the inclined structure, the maximum temperatures of the sample with the heat sink under different incident pump power are measured and compared with that in the air. The maximum temperature of the phosphor is generally at the incidence position of pump laser [36]. The maximum temperatures appear at the incident position of the pump laser, and the measured temperatures are 78.7 °C and 29.0 °C, respectively.
Fig. 7. (a) Experimental setup of thermal measurement of the optimized sample and the measured temperatures in 1440 mW pump power. (b) The measured temperatures of the optimized sample in the air and with the heat sink under different pump power.
The temperatures of the sample in the air and with the heat sink under different pump power are illustrated in Fig. 7(b). the measured temperature of the sample with a heat dissipation structure can be close to the room temperature under the low pump power (< 1000 mW). The experimental results show that the temperature of the sample with heat dissipation structure decreases by 63% at the pump power 1440 mW. The temperature of the sample can be significantly reduced by the dissipation structure. More importantly, the heat dissipation structure is on the sides of the sample so as not to influence the propagation of illumination light.
4. Discussion
In summary, the results show that the optimized Ce:YAG crystal phosphor used in laser lighting designed by MCM with optimization algorithm has a much higher extraction efficiency and luminous efficiency than the conventional phosphor. The extraction efficiency of optimized Ce:YAG crystal can reach 0.49, which is considerably higher than that of the conventional parallel phosphor. The difference of results between simulation and experiment is only 5.8% in terms of extraction efficiency. Moreover, the luminous efficiency of the optimized Ce:YAG crystal can reach 230 lm/W, which means that less energy consumption is achieved. The experimental results also show that strong scattering will significantly reduce the extraction efficiency. At the same time, the sample with inclined surfaces is more conducive to the design of heat dissipation structure, and greatly reduces its working temperature.
In addition, the proposed method also has the capability to apply to optimize different kinds of phosphors (glass, ceramic and film) with strong applicability. The evaluation function can also be the light flux, total energy or correlated color temperature when optimized by MCM and algorithm. The phosphor structure under several lighting requirements can be designed and optimized efficiently. The selection of evaluation function can meet the optimization under different lighting requirements. The method has theoretical significance for the design of high flux and high efficiency laser lighting. In future, this phosphor still needs lighting optical design and heat dissipation structure to achieve a wider range of commercial lighting applications.
Acknowledgments
The authors thank Zhensong Wan for his valuable suggestions on the revision of this paper. They also thank the reviewers for their insightful comments.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. C. Cozzan, G. Lheureux, N. O’Dea, E. E. Levin, J. Graser, T. D. Sparks, S. Nakamura, S. P. DenBaars, C. Weisbuch, and R. Seshadri, “Stable, Heat-Conducting Phosphor Composites for High-Power Laser Lighting,” ACS Appl. Mater. Interfaces 10(6), 5673–5681 (2018). [CrossRef]
2. J. J. Wierer and J. Y. Tsao, “Advantages of III-nitride laser diodes in solid-state lighting,” Phys. Status Solidi A 212(5), 980–985 (2015). [CrossRef]
3. G. B. Nair, H. C. Swart, and S. J. Dhoble, “A review on the advancements in phosphor-converted light emitting diodes (pc-LEDs): Phosphor synthesis, device fabrication and characterization,” Prog. Mater. Sci. 109, 100622 (2020). [CrossRef]
4. C. Y. Ma and Y. G. Cao, “Phosphor converters for laser driven light sources,” Appl. Phys. Lett. 118(21), 210503 (2021). [CrossRef]
5. A. B. S Weber and C Amann, “Laser Light in the BMW I8,” ATZ worldwide (2014).
6. J. Xu, A. Thorseth, C. Xu, A. Krasnoshchoka, M. Rosendal, C. Dam-Hansen, B. Du, Y. Gong, and O. B. Jensen, “Investigation of laser-induced luminescence saturation in a single-crystal YAG:Ce phosphor: Towards unique architecture, high saturation threshold, and high-brightness laser-driven white lighting,” J. Lumin. 212, 279–285 (2019). [CrossRef]
7. J. Xu, Y. Yang, Z. Guo, D. D. Corell, B. Du, B. Liu, H. Ji, C. Dam-Hansen, and O. B. Jensen, “Comparative study of Al2O3-YAG:Ce composite ceramic and single crystal YAG:Ce phosphors for high-power laser lighting,” Ceram. Int. 46(11), 17923–17928 (2020). [CrossRef]
8. N. Rondelez, N. Ganguly, W. Ryckaert, and Y. Meuret, “Laser-diode-driven high-luminance white light source with sediment phosphors and optimal opto-thermal performance,” Opt. Lett. 47(18), 4692–4695 (2022). [CrossRef]
9. Y. Zhang, J. Liu, Y. Zhang, H. Yang, Y. Yu, Q. He, X. Liang, Y. Liu, and W. Xiang, “Robust YAG:Ce single crystal for ultra-high efficiency laser lighting,” Journal of Rare Earths (2021).
10. Y. Tang, H. Lu, J. Li, Z. Li, X. Du, X. Ding, and B. Yu, “Improvement of optical and thermal properties for quantum dots WLEDs by controlling layer location,” IEEE Access 7, 77642–77648 (2019). [CrossRef]
11. B. Ratzker, A. Wagner, S. Kalabukhov, and N. Frage, “Controlled pore growth for enhanced photoluminescence of ceramic phosphors,” Scr. Mater. 202, 114008 (2021). [CrossRef]
12. Y. Liang, Y. Zhang, H. Yang, Y. Zhang, J. Zhang, L. Wang, X. Liang, J. Zhong, and W. Xiang, “The excellent luminous efficiency and high thermal stability of phosphor-in-glass for high-power laser,” Appl. Phys. Lett. 119(3), 033303 (2021). [CrossRef]
13. J. Xu, L. Wang, W. Gu, Z. Jiang, X. Chen, B. Hu, B. Du, H. Ji, C. Dam-Hansen, and O. B. Jensen, “Emitting area limitation via scattering control in phosphor film realizing high-luminance laser lighting,” J. Eur. Ceram. Soc. 42(2), 608–615 (2022). [CrossRef]
14. K. Fujioka, K. Yagasaki, T. Sawada, H. Minemoto, H. Fuji, and K. Yamamoto, “AlN–Ce-doped yttrium aluminum garnet composite ceramic phosphor for high-power laser lighting,” Opt. Mater. 121, 111507 (2021). [CrossRef]
15. Y. Ma and X. Luo, “Small-divergent-angle uniform illumination with enhanced luminance of transmissive phosphor-converted white laser diode by secondary optics design,” Opt. Lasers Eng. 122, 14–22 (2019). [CrossRef]
16. Y. Tang, Y. Liang, X. Ding, Q. Wu, and B. Yu, “A laser-driven phosphor converted system with enhanced optical efficiency by using light-recycling dichroic filters,” J. Lumin. 223, 117180 (2020). [CrossRef]
17. J. H. Oh, S. J. Yang, and Y. Rag, “Polarized white light from LEDs using remote-phosphor layer sandwiched between reflective polarizer and light-recycling dichroic filter,” Opt. Express 21(S5), A765–A773 (2013). [CrossRef]
18. G. Li, W. Wang, W. Yang, Y. Lin, H. Wang, Z. Lin, and S. Zhou, “GaN-based light-emitting diodes on various substrates: a critical review,” Rep. Prog. Phys. 79(5), 056501 (2016). [CrossRef]
19. Y. J. Sung, M.-S. Kim, H. Kim, S. Choi, Y. H. Kim, M.-H. Jung, R.-J. Choi, Y.-T. Moon, J.-T. Oh, H.-H. Jeong, and G. Y. Yeom, “Light extraction enhancement of AlGaN-based vertical type deep-ultraviolet light-emitting-diodes by using highly reflective ITO/Al electrode and surface roughening,” Opt. Express 27(21), 29930 (2019). [CrossRef]
20. A. Salimian, J. Silver, G. R. Fern, H. Upadhyaya, A. Metcalfe, T. G. Ireland, P. Harris, and R. Haghpanahan, “Investigating the Emission Characteristics of Single Crystal YAG When Activated by High Power Laser Beams,” ECS J. Solid State Sci. Technol. 5(10), R172–R177 (2016). [CrossRef]
21. X. Liu, X. Qian, Z. Hu, X. Chen, Y. Shi, J. Zou, and J. Li, “Al2O3-Ce:GdYAG composite ceramic phosphors for high-power white light-emitting-diode applications,” J. Eur. Ceram. Soc. 39(6), 2149–2154 (2019). [CrossRef]
22. Y. Yuan, D. Wang, B. Zhou, S. Feng, M. Sun, S. Zhang, W. Gao, Y. Bi, and H. Qin, “High luminous fluorescence generation using Ce:YAG transparent ceramic excited by blue laser diode,” Opt. Mater. Express 8(9), 2760 (2018). [CrossRef]
23. Y. Ma, Y. Shen, L. Xu, T. Zhou, W. Lin, Q. Gao, and Y. Wu, “High-power continuous-wave dual-wavelength diode-pumped Yb: YAG slab amplifier with temperature-dependent effects,” Appl. Phys. B 123(10), 258 (2017). [CrossRef]
24. Y. Shen, M. Gong, E. Ji, X. Fu, and L. Sun, “Spatial dynamic thermal iteration model for 888 nm end-pumped Nd: YVO4 solid-state laser oscillators and amplifiers,” Opt. Commun. 383, 430–440 (2017). [CrossRef]
25. G. Venter, “Review of optimization techniques,” Encyclopedia of Aerospace Engineering (Wiley, 2010).
26. L. Wang, S. L. Jacques, and L. Zheng, “MCML—Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47(2), 131–146 (1995). [CrossRef]
27. J. Liao, H. Rao, W. Wang, X. Wan, L. Zhou, D. Zhou, X. Wang, and Q. Lei, “Optical simulation of phosphor layer of white LEDs,” J. Semicond. 34(5), 053008 (2013). [CrossRef]
28. L. G. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941). [CrossRef]
29. A. Krasnoshchoka, A. K. Hansen, A. Thorseth, D. Marti, P. M. Petersen, X. Jian, and O. B. Jensen, “Phosphor material dependent spot size limitations in laser lighting,” Opt. Express 28(4), 5758–5767 (2020). [CrossRef]
30. S. A. Prahl, “A Monte Carlo model of light propagation in tissue,” Proc. SPIE 10305, 1030509 (1989). [CrossRef]
31. S. David, T. E. Kidger, E. Chatzizyrli, D. Kracht, J. Neumann, R. Lachmayer, and N. Tinne, “Opto-thermal simulation model for optimizing laser-excited remote phosphor systems,” in Illumination Optics V, (2018).
32. J. R. Howell, “The Monte Carlo method in radiative heat transfer,” (1998). [CrossRef]
33. M. A. Vorontsov and V. P. Sivokon, “Stochastic parallel-gradient-descent technique for high-resolution wave-front phase-distortion correction,” J. Opt. Soc. Am. A 15(10), 2745–2758 (1998). [CrossRef]
34. L. Wang and S. L. Jacques, “Error estimation of measuring total interaction coefficients of turbid media using collimated light transmission,” Phys. Med. Biol. 39(12), 2349 (1994). [CrossRef]
35. N. Rondelez, A. Correia, W. Ryckaert, H. De Smet, D. Cuypers, and Y. Meuret, “Efficient transmissive remote phosphor configuration for a laser-driven high-luminance white light source,” Opt. Express 30(4), 5107–5120 (2022). [CrossRef]
36. Y. Shen, W. Zhang, M. Gong, Y. Meng, Y. Wang, and X. Fu, “Four-dimensional thermal analysis of 888 nm pumped Nd: YVO4 dual-rod acousto-optic Q-switched laser,” Appl. Sci. 7(5), 470 (2017). [CrossRef]
