1. Introduction

Commercial solid-state lighting for general and specialty illumination is currently dominated by light emitting diodes (LEDs). Despite their many advantages over traditional light sources, LEDs still suffer from a significant problem: power droop[1]. Droop implies that an increase in current density results in a lower internal quantum efficiency. This means that when a very high radiant flux is required, it is necessary to use several light emitting diodes so that the overall efficiency is not too low[2], but doing so makes the entire light source larger and more complex. Similarly, when both high optical power and low étendue are necessary, as is the case in high luminance applications, LEDs are at a disadvantage[3]. Several authors have proposed using laser diodes as an alternative to LEDs in this regard[4–6]. Unlike light emitting diodes, laser diodes do not suffer from power droop; their internal efficiency does not change with increasing current density. As such, even light sources with high luminance requirements can be designed with a limited number of high-power laser diodes.

The most significant downside of using laser diodes for general illumination lies in a typical component of white light engines: the colour converting element (CCE). Since solid-state sources emit light with a very narrow bandwidth, they are coupled to luminescent materials to produce white light, typically phosphors or quantum dots. However, the colour conversion efficiency of these materials, their quantum yield (QY), strongly depends on temperature. Specifically, the QY of phosphors decreases as their temperature increases – an effect called thermal quenching[7]. Coupling phosphors with laser diodes typically creates very high temperature gradients inside the CCE[8] due to QY losses and Stokes shift losses. This causes the colour coordinates of the emitted light to shift and can result in non-stable white light systems.

Modelling the optical and thermal properties of colour converting elements simultaneously allows predicting the onset of thermal quenching[9,10]. This can be useful in developing strategies to avoid thermal quenching, while at the same timeoptimizing the performance of laser-based white light sources. This was the rationale for the development of an opto-thermal simulation framework by the authors[11]. In this paper, this simulation framework is used to tackle a very important problem that arises when designing laser-based transmissive white light configurations. Unlike reflective configurations, where the thermal performance is superior due to dissipation at the reflective boundary, transmissive configurations generally havepoor thermal performance[12,13]. This is because most thermal dissipation has to occur at the rather narrow edges of the CCE, which are typically in thermal contact with a heat-sink. In contrast to reflective configurations, transmissive colour converting configurations are more straightforward to implement in the complete lighting fixture.

In this work, the focus is on improving the thermal performance of transmissive configurations. This is a specific case of the much broader problem of thermal management in solid-state lighting[14]. However, instead of considering the usual strategies that involve manipulating the luminescent material’s thermal properties (e.g. using phosphors in glass[15,16] or in novel polymers[17]) or improving the thermal performance of the components used (e.g. using transparent heat-spreaders, optimizing the CCE packaging[18]), a purely optical strategy is considered. The radiation pattern of the laser diode exciting the CCE is shaped to improve thermal dissipation, and the impact on the temperature distribution inside the CCE is investigated. The rationale for this approach is straightforward. Typically, optics are already included between the laser diode(s) and the CCE to, for instance, collimate the beam pattern. As such, modifying the characteristics of these optical components to adjust the beam shaping is a straightforward change that can provide improved opto-thermal performance. A beam pattern that provides thermal benefits is one that concentrates the optical power in the periphery of the CCE. This is the zone with the highest thermal dissipation potential, since the main thermal dissipation mechanism in transmissive configurations is conduction towards this CCE periphery and then towards the heat-sink. By shifting the power density of the excitation radiation towards this zone, the typical sharp temperature gradients that emerge in transmissive configurations, the so-called hot-spots, could be avoided. Using the opto-thermal simulation framework developed, we have studied if the performance of a system under the influence of thermal quenching can be rescued by only tailoring the excitation radiation pattern. In addition, we have investigated if more power can be used to excite the CCE with this approach and, thus, if higher luminance can safely be extracted from the system. Finally, a qualitative evaluation of the obtained simulation results is performed through an experimental verification of the beam shaping concept. In this verification our goal is to investigate the effect that beam shaping has on CCE’s temperature.

2. Methods

2.1. Simulations

The previously mentioned opto-thermal simulation framework was used for all the modelling results. This tool simulates the variation in temperature inside the CCE due to quantum yield losses and Stokes shift losses. It takes all thermal dissipation effects (i.e. convection, radiation and conduction) and thermal material properties into account when simulating the temperature distribution. The coupling between optical and thermal effects ensures that the simulated variation in temperature continuously updates the CCE’s quantum yield distribution and vice-versa. In this way, the framework accurately describes thermal quenching while allowing the simulation of any relevant optical metrics, such as the extracted luminance or colour uniformity of the light produced by the system. More details about this tool can be found in the original article[11]. In this work, the framework is used to analyze how the optical performance varies for different transmissive configurations with varying laser radiant flux and beam shapes.

A cross-section depiction of the chosen transmissive design can be found in Fig. 1. It consists of a cylindrical CCE in contact with a heat-sink at its periphery. A uniform dispersion of YAG:Ce phosphor powder in a transparent plate of PMMA is considered as the CCE. The phosphor’s optical properties (absorption and scattering coefficient, scatter phase function, quantum yield and emission spectrum) and thermal dependencies were obtained and estimated from previous work[19,11]. The CCE’s geometry is fixed: it has a diameter of 1 cm and it is 2 mm thick. A refractive index of $n=1.49$ was assumed for the CCE. The phosphor concentration is optimized such that the system emits white light with colour coordinates CIE$\mathrm{x},\mathrm{y}=\left(0.339,0.331\right)$ and CCT $=5200$ K. The converting element is excited at its anterior surface by a $450\pm 3$ nm blue laser diode. The exiting surface is optically coupled to a N-BK7 glass (refractive index $n=1.52$) compound parabolic concentrator (CPC) to improve light extraction.

 

Fig. 1 Depiction of a cross-section of the transmissive configuration that is considered in the opto-thermal simulations. Blue light is incident from the left towards a CCE that is thermally connected to a heat-sink at its periphery. A CPC is in optical contact with the outgoing surface of the CCE to improve light extraction.

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Thermally, the heat-sink is modelled as a hollow aluminum cylinder in which the CCE is embedded. It has a diameter of 5 cm and the same thickness as the CCE. Its outer surface is assumed to be at a fixed temperature of $T={27}^{°}$ C. Natural convection is assumed at the outer surfaces of the CCE and the heat-sink, which is modelled using a heat transfer coefficient of h = 8 W/(m²K) and surrounding temperature of $T_s={25}^{°}$ C[20]. The thermal contact between the CCE and the heat-sink is assumed to be perfect. Because the thermal dissipation between the CCE and the glass CPC is assumed to be small, the CPC is not included in the thermal simulations and its thermal boundary is modelled with a low heat transfer coefficient h = 1 W/(m²K). The thermal properties for the materials used in the model were obtained from the COMSOL material library environment[21].

The main variable in this study is the shape of the exciting radiation pattern. The objective is to take advantage of the higher dissipation potential at the periphery of the CCE. Because the system is axially symmetric, the beam pattern is tailored by varying its radial irradiance distribution while ensuring that the incident excitation beam remains collimated. The radial shaping function is given by Eq. (1), with $\tilde{r}=r/R$ as the radial distance r normalized by the radius R of the CCE. This function can be manipulated by changing the shape function’s degree, or order, n. This function is similar to the dual hollow Gaussian function typically used to obtain uniform temperature distributions in material processing[22].

Power distributions which are increasingly more skewed towards the edges of the CCE can be obtained by increasing the shaping function order n. This is demonstrated in Fig. 2 which shows some examples of this shaping function and corresponding irradiance distributions at the surface of the CCE. The shaping function is converted into a density function by normalizing it by its integral which is then used to model the irradiance distribution of the collimated laser diode beam. In practice, a refractive beam shaping optic with two rotationally-symmetric lens surfaces can be designed to convert the original beam pattern of a laser diode with high spatial coherence into the desired beam shape[23,24].

 

Fig. 2 Shaping function plot (left) for three shaping function orders. Irradiance distribution at the CCE’s excitation surface, in $\mathbf{W}/{\mathbf{m}}^2$, for (middle) n = 2 and (right) n = 6.

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To investigate the effect of different beam shapes on the opto-thermal performance it is necessary to excite the CCE with different laser radiant flux values for different shaping functions, and compare the simulated optical and thermal performance to a baseline case. In this study, the uniform illumination of the CCE surface is considered as the baseline case. From a thermal point of view this is already an improvement when compared to illuminating the CCE with a Gaussian irradiance distribution. To takea wide range of cases into account, the simulations were run on a grid of parameters, with laser radiant flux $P_i\in {\left[2,12\right]}_{11}$ W and shaping function degree $n\in {\left[2,12\right]}_7$. For simplicity the baseline case is described as n = 0. For each parameter pair, the opto-thermal simulation is run until an opto-thermal steady-state is reached. That is, the value of the temperature does not change after successive opto-thermal simulation iterations implying that further iterations will not change the quantum yield of the CCE nor the optical performance of the system. In this study, possible temperature degradation effects of the CCE host material were not considered.

2.2. Experimental verification

To evaluate if the general trend observed in the simulations is also found in practice, an experimental verification of the beam shaping concept was also conducted. The specific goal for these experiments was to investigate if using beam shaping could avoid the formation of a hot-spot across the CCE’s surface and, thus, reduce its overall temperature.

A Necsel Blue $44510$ W laser was used as a light source in the experiments. It emits a Gaussian shaped beam pattern with a central wavelength of 445 nm. To perform the necessary beam shaping, a free-form lens was designed using a recently developed algorithm[25] to transform the laser’s Gaussian beam shape to the rotationally symmetric annular pattern used in the simulations. A shaping function with n = 4 was chosen for the design of the lens, which was then manufactured out of PMMA. A depiction of the designed lens and the fabricated prototype can be found in Fig. 3. For the CCE, a luminescent plate was manufactured using a mixture of YAG:Ce phosphor powder and UV-curable resin (Sadechaf UVAcryl 2305), which was cured inside a hole drilled in an aluminum plate which acted as a heat-sink. A concentration of 5% weight by weight of phosphor powder to resin was used. A close-up image of this sample is shown in Fig. 3. The CCE hasa diameter of 1 cm and has the same thickness as the aluminum plate, i.e. 3 mm. The aluminum plate is 20 by 10 cm, which is much larger than the CCE. The temperature at the surface of the CCE that is optically excited, i.e. the surface facing thelaser source, was measured with a FLIR A65sc thermal camera. To confirm that the heat-sink temperature variation was small throughout the experiments, a PT100 thermocouple was thermally attached to the heat-sink and monitored.

 

Fig. 3 Images of (left) the designed beam shaping lens and (middle) the fabricated prototype. A picture (right) of the CCE sample in the aluminum plate.

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The experimental procedure consisted of exciting the CCE with the blue laser diode, either directly or through the beam shaping lens, and measuring the temperature distribution at its surface with the thermal camera when a steady-state was reached. The experiment, with and without lens, was repeated when the laser diode emitted a radiant flux of 3 W, 5 W and 7 W.

An additional experiment was performed to assess the impact of the beam shaping lens on the optical power efficiency. An integrating sphere connected to a spectrometer (Newport 74055 MS260i) was introduced into the experimental setup and positioned in close proximity to the CCE sample to capture most of its converted and scattered light in the forward hemisphere, i.e. the transmitted light. The measurements were performed at low excitation powers, 1 W and 2 W, to minimize temperature effects and repeated to have an estimate of the measurements’ variance. The experimental procedure consisted of first measuring the radiant flux of light emitted by the sample with and without beam shaping lens. Then, the same procedure was repeated without the CCE sampleto get a reference radiant flux for each case. With these measurements the difference in optical efficiency resulting from using the beam shaping lens can be investigated.

3. Results and discussion

3.1. Simulations

The first important result of the simulation study is the variation of the maximum and mean temperature inside the CCE for each simulated $\left\{n,P_i\right\}$ pair, which is shown in Fig. 4. In the baseline case, i.e. uniform illumination (n=0), the temperature rises sharply at higher excitation powers. With illumination shaping functions that are more skewed towards the periphery (i.e. increasing n), the temperature inside the CCE becomes significantly lower for similar incident powers. The difference between the maximum and mean temperatures inside the CCE also decreases as n increases, which is clearly illustrated in Fig. 5. The cross-sections of the temperature at the CCE front surface become much flatter when more skewed shaping functions are used. This is in stark contrast to the typical case of a transmissive laser-based white light configuration where a hot-spot exists in the center of the CCE.

 

Fig. 4 Results for several shaping functions and optical excitation powers showing the (left) maximum temperature and (right) the mean temperature inside the CCE (in degree Celsius).

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Fig. 5 Cross-sections of the temperature at the front surface of the CCE for different shape functions when the system is excited with (left) 5 W and (right) 9 W.

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While the improvement of the thermal performance through beam shaping is encouraging, the main goal is to improve the optical performance. To evaluate the optical performance, an optical power efficiency P_f is calculated as $P_f=P_e/P_i$, with P_e being the radiant flux emitted from the output of the CPC and P_i the excitation radiant flux that is incident on the CCE. This value is shown for all simulations in Fig. 6. Without thermal quenching, the output radiant flux should increase linearly with increasing incident power and the resulting efficiency should be constant. For the baseline case, at moderate excitation powers, a constant power efficiency of $0.475$ is obtained. However, after a certain point the efficiency decreases sharply due to thermal quenching. This is a direct consequence of the lower quantum yield value inside the CCE: more optical power is lost as heat instead of being converted to useful visible radiation. A second consequence of thermal quenching is the shift in the color point of the generated light towards blue. Also in Fig. 6, the effect of the beam shaping is clearly visible. For instance, a uniform illumination (n=0) with 10 W of incident power results in a power efficiency of only $0.269$, while a power efficiency of $0.472$ is obtained for the same incident power, but with a beam shaping order of n = 4. In other words, the onset of thermal quenching at 10 W can be avoided by using a n = 4 beam shape pattern.

 

Fig. 6 Results of the simulations showing (left) the power efficiency P_f and (right) the relative luminance extracted compared to n = 0 at P_i = 1 W.

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When discussing the optical performance, there are two remaining aspects that are important. One is the possible luminance that can be produced by the system. The simulated relative maximum luminance emitted from the system is shown in Fig. 6. This is calculated by normalizing the maximum luminance simulated for each case by the luminance emitted in the base case for a 1 W incident power. Looking at the maximum relative luminance produced by the system for the baseline case and comparing it to the maximum relative luminance obtained when using n = 6, an increase from $3.35$ to $5.32$ is found. That is, by using the beam shaping technique it is possible to extract a 60% higher peak luminance value from the laser-based light system. The other performance related aspect deals with the colour uniformity of the light produced by the system. As beam patterns increasingly more skewed are used, the colour mixing may also change and negatively impact the colour uniformity. During the simulations, the average $d{u}^{\text{'}}{v}^{\text{'}}$ in the far-field was found to be in the interval $\left[0.0040,0.0073\right]$, which is acceptable for most applications.

A final important remark regarding this beam shaping technique is that the results are highly dependent on the system’s boundary conditions. That is, beam patterns with more optical power near regions with good thermal dissipation will always result in improved thermal performance, but the magnitude of the impact on this performance will depend on the geometry of the system, material properties of the CCE and the heat-sink used. Optimizing these parameters for a specific system can be done in a manner similar to the analysis described, as long as a reliable opto-thermal simulation framework is used. Since the goal of this study was solely to show the potential of the beam shaping idea, a more extensive study of its impact for different system characteristics is beyond the scope of this paper and left as future work.

3.2. Experimental proof-of-concept

The experimental temperature tests were focused on investigating the shape of the temperature distribution at the surface of the CCE facing the laser source with and without the beam shaping lens. In Fig. 7 the surface temperature is shown for both cases when the laser was emitting 7 W of optical power. Without the lens the typical hot-spot formation in the center of the CCE is observed. With the beam shaping lens the hot-spot is avoided and a more uniform temperature distributionis seen across the CCE surface. To clearly demonstrate the differences in the temperature distribution for the case with and without beam shaping lens, the cross-sections of the thermal images are shown in Fig. 8. With no beam shaping, the temperature distribution shows a sharp gradient: the typical hot-spot scenario. When the lens is introduced, the cross-sections become much flatter. This is verified in all the experiments performed and is in agreement with the trend shown in thesimulations. More importantly, the maximum temperature at the surface of the CCE dropped from $58.3$ to $32.3$ degrees Celsius when using the beam shaping lens with 7 W of optical power: a significant reduction in temperature of 26 degrees Celsius.

 

Fig. 7 Thermal image captured after temperature stabilization for the experiment with the laser diode emitting 7 W (left) without using the free-form lens and (right) with the free-form lens. The CCE’s periphery is delineated in blue.

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Fig. 8 Comparison of the cross-sections of the thermal images captured for experiments with and without the beam shaping lens with the laser diode emitting (left) 3 W, (middle) 5 W and (right) 7 W.

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This temperature focused experimental verification is not meant to be a comprehensive validation of the simulation results, as not all experimental conditions fully match the modelled domain. Despite that, it is still important to note some relevant limitations that lead to the mismatch observed between the measured temperature and the temperature predicted from the simulations when using the beam-shaping lens. The major reason for this mismatch are the optical losses due to the lens and an additional aperture that was introduced between the laser diode and CCE, in both cases, to improve collimation. The losses due to the lens were estimated to be around 12% and a further 59% for the aperture. Considering these losses, the estimated radiant flux that reaches the CCE becomes $1.1$ W, $1.8$ W and $2.5$ W, for the case with the lens, and $1.2$ W, $2.1$ W and $2.9$ W without the lens. The influence of the amount of phosphor powder on the thermal conductivity of the CCE is also pertinent to the mismatchobserved. The thermal conductivity of the host material is very low, $k=0.22$ W/(m.K), while the phosphor powder has a thermal conductivity of $k=13$ W/(m.K). This means that a 5% loading of phosphor powder can double the average thermal conductivity of the CCE which was not taken into account in the simulations. These and other minor effects are the main reasons for the differences in magnitude between the simulated and measured temperature values when using the beam shaping lens. Those limitations notwithstanding, the experimental data verifies that the beam shaping effect has a significant impact on the temperature inside the CCE.

The results of the remaining experimental test, to investigate the effect of the beam shaping lens on the optical power efficiency, can be found in Table 1. The optical power efficiency as previously defined was calculated from measurement data, with P_e being the radiant flux measured with the CCE sample between the laser source and the integrating sphere, with andwithout beam shaping lens, and P_i the reference radiant flux measured without the CCE sample in the optical path. Unlike the simulations, these experiments did not include a dielectric CPC which decreases the extraction efficiency and, thus, the optical power efficiency measured.

Table 1. Optical power efficiency calculated from experimental measurements.

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Comparing the optical power efficiency results obtained, the beam shaping lens decreases optical power efficiency by $12.4$ % on average. We estimate this difference to be mainly due to small mismatches between the beam pattern produced with the lens andthe area of the sample, reducing the amount of light incident on the sample. This is the result of small imperfections in the beam shaping lens prototype that could be mitigated by an improved lens manufacturing and polishing process.

4. Conclusion

In this work, the influence that shaping the beam pattern of a laser diode can have on the thermal and optical performance of a laser-based white light configuration with a colour-converting element was investigated. It was shown that beam shaping can help in avoiding the onset of thermal quenching and the subsequent drop in optical performance. This permits significantly increasing the peak luminance that can be extracted from such a system while guaranteeing stable white light production. An experimental, qualitative, verification of the beam shaping concept was performed and it showed that the beam shaping idea can significantly reduce the temperature inside a CCE.

This method provides a very straightforward way to implement a thermal management solution to enhance the light output of laser-based white light sources. While this work is focused on a specific transmissive configuration, the beam-shaping concept can beapplied to a much wider range of configurations.