Achievement of Possibly Maximum Photosynthetic Performances for Multi-Primary Laser Lighting for Indoor Farming

The artificial lighting based on multiple-primary light-emitting diodes (LEDs) or multiple-primary laser diodes (LDs) makes the diversity of colors by freely and simply adjusting the emission spectra of rays from these semiconductor devices. It brings the possibility that the artificial lighting matches well with the photosynthetic spectral sensitivity curves of most plants including vegetables and fruits on the earth. Via reasonably designing the spectral components of artificial lighting sources based on intelligent optimization algorithms such as genetic algorithm (GA), one can readily achieve the maximum photosynthetic luminous efficacy of radiation (PLER), at the same time with good color rendering properties. In this regard, the IES-TM-30 scores (color fidelity index Rf and color gamut index Rg) suggested by Illuminating Engineering Society of North America (IES) is employed for evaluating the color rendering performances of artificial lighting sources besides the well-known standardized color rendering index (CRI, Ra). Compared with LEDs, the LDs are free from the so-called “efficiency droop” phenomena, thus have shown great superiority over the LEDs. Therefore, the aim of this work is to explore the maximum PLER of multiple-primary laser lighting while ensuring relatively good color rendering properties. Hope that the achieved results could provide a useful guidance for the quick development of this field.


I. INTRODUCTION
I N THIS era, the conventional lighting sources, such as the incandescent lamps and compact fluorescent lamps (CFLs), fail to meet the quickly increasing requirements of smart lighting fields [1], [2], [3], [4]. The intelligent lighting or smart lighting needs flexible and adjustable artificial spectra to match with the diverse applications, such as smart indoor lighting, smart road lighting, and smart plant-growth lighting among others [5], [6], [7]. As a representative candidate of the semiconductors, the GaN-based light-emitting diodes (LEDs), have been proven to surpass the conventional lighting sources for increasing the plant-growth efficiency, due to the outstanding characteristics of spectral tunability for semiconductor-based lighting sources [8], [9], [10]. However, due to the "efficiency droop" phenomena occurring in the GaN-based LEDs when they are operated at high current densities [11], [12], [13], they have not shown superiority in their wide applications, especially in the super-high powered lighting devices.
Many previous studies focus on increasing the photosynthetic performances of lamps while using LEDs [14], [15], [16], [17], [18]. Among them, Li et al. have developed efficient and stable Mn 4+ -activated double perovskite red phosphors for the plant growth applications [14]. The emission of Mn 4+ manifests as multiple sharp narrow-band peaks in the range of 600-750 nm, just meeting the growth requirements (610-720 nm) of plant chlorophyll a and chlorophyll b [15]. Oh et al. have developed the four-package purplish white LEDs based on four-package phosphor-converted monochromatic LEDs for the requirements of attaining high photosynthetic efficiency for the improved growth of plants [16]. Liu et al. have designed and optimized quantum dot (QD) based LEDs according to the photosynthetic action spectrum (PAS), showing better photosynthetic parameters over those of conventional light sources [17]. Recently, we have performed a numerical study on the maximum PLER of multiple-primary LEDs (MPLEDs) containing three, four, and five emission spectral peaks [19]. The color rendering and photosynthetic performances are also compared for different primary numbers in detail.
However, so far, the photosynthetic performances of multipleprimary laser diodes (MPLDs) based lighting have not yet been fully understood. Therefore, we are desired to carry out a relatively full investigation on the possibly maximum photosynthetic luminous efficacy of radiation (PLER), while taking the color rendering properties such as Commission Internationale de l´Eclairage (CIE) color rendering index (CRI, R a ), the special CRI of R 9 (for saturation red color) and R 12 (for saturation blue color), Illuminating Engineering Society of North America (IES) TM-30-18 scores (color fidelity index R f and color gamut index R g ) [20], NIST color quality scale (CQS, Q a ) [21], of the MPLDs into account. In addition, a comparison of color quality and photosynthetic performances between MPLDs and MPLEDs is also done.

A. Related Photosynthetic Parameters
In this section, we introduce the related theory and realization methodology. The photosynthetic performances of MPLDs can be evaluated by a figure of merit (FoM) generally called as photosynthetic luminous efficacy of radiation (PLER, K p ). Here, the PLER can be expressed by where P(λ) is called as the normalized photosynthetic action spectrum, as obviously shown in Fig. 1; S(λ) represents the spectral power distribution (SPD) of MPLDs; K pm = 683 plm/W is the maximum PLER; λ is the wavelength. Higher value of PLER of laser-based lighting sources means that the emitting rays from MPLDs can mostly help increase the photosynthetic efficiency in the growth of plants. Another related useful parameter for describing the photosynthetic performances, denoted as photosynthetic action factor (PAF), can be written as where K m = 683 lm/W is the maximum luminous efficacy of radiation (LER); V(λ) is the CIE photopic sensitivity.
We treat the narrow spectral lines of LDs as the Gaussian shape, thus the Gaussian function can be adopted for the following spectral modelling [19] where λ, λ 0 , and Δλ are wavelength, peak wavelength, and full-width at half maximum (FWHM), respectively; a i varying within the range of (0, 1) is the relative intensity of ith primary color; N is the primary number, and N = 3, 4, and 5, respectively. If increasing the number of LDs in the MPLDs, the cost and device complexity would also increase, too.

B. Color Rendering Performances
With the emerging needs of the color rendering for LEDand LD-based illuminants, many FoMs have been put forward recently, including the NIST color quality scale (Q a ), IES TM-30-18 R f and R g . Because CRI fails to rendering the color fidelity of LED-and LD-based illuminants due to their relatively narrow spectral bandwidths although it is still currently the standardized color metrics for evaluating the color rendering characteristics of white lighting sources [21].

C. Intelligent Optimization Algorithms
We briefly introduce the used intelligent optimization algorithms (IOAs). Inspired by the human intelligence, biological community sociality or natural phenomena, several IOAs have been suggested, including the genetic algorithm (GA), ant colony optimization (ACO), particle swarm optimization (PSO), simulated annealing algorithm (SAA), neural network algorithm (NNA), etc [22], [23]. Most optimization algorithms encounter the same issues, like falling into the local optimum values. Therefore, we run the program many times (more than 50) to solve this issue, to avoid falling into the local optimum values and to find out possibly maximum PLER. We primarily employ GA as the typical candidate of IOAs. The other IOAs can also reach the same effect for this calculation. Three elements are included in the IOAs, which are decision variables, objective functions F, and constraints.
In this optimization, the objective function F can be expressed by Many constraints (penalty conditions) in GA-based optimization are shown as follows: (a) the correlated color temperature (CCT) is set as 2700 K, 3000 K, 3500 K, 4000 K, 4500 K, 5000 K, 5700 K, and 6500 K, respectively. The deviation of CCT (comparison of reference and tested light source) is set as 10 K. (b) The color distance D uv (in the CIE 1960 UCS color space) between the standard and calculated ones is kept within D uv < 0.01. (c) The color rendering index R a is kept of R a > 70 to ensure basically high color rendering property. The flow chart  Fig. 3(a) plots the possibly optimal results concerning on the PLER of three-primary, four-primary, and five-primary LDs under various representative CCTs (from 2700 K to 6500 K, eight CCTs). Clearly observed from it, the PLER appears to be higher for the lower CCT and higher CCT than middle CCT. These trends are in good consistence with that of LEDs [19]. As the CCT is increasing, the optimal PLER decreases first, and then increases. The LD-based devices under CCT of 2700 K has the highest PLER compared to other seven CCTs for all three cases. In addition, the PLER is the highest for five-primary LDs among three cases. This seems to be a little different from the case of LEDs [19], where the PLERs appear to be the highest for the four-primary case. While comparing them under eight CCTs, the minimum PLER is at 5000 K (three-primary LDs), 5000 K (four-primary LDs), and 4500 K (five-primary LDs), respectively. Another information from the figure is that the PLER is nearly close to each other for four-primary LDs and five-primary LDs under relatively low CCTs (for example when CCT ≤ 4000 K), but big difference can be found under high CCTs (when CCT > 4000 K). This fact means that under the low CCTs (warm white light), the LD-based lighting sources exhibit almost the same photosynthetic performances for four-primary LDs and five-primary LDs. In terms of the cost, the four-primary LDs own more potentials for the application in the plant lighting sources. However, when the CCT is high, five-primary LDs have surpassed four-primary LDs in the photosynthetic qualities. Therefore, this above analysis can offer sufficient information and reference for users while employing LD-based illuminants as the plant-growth lighting sources. Fig. 3(b) shows the color rendering index, R a, for three-primary LDs, four-primary LDs, and five-primary LDs, respectively, under eight representative CCTs. The R a is higher than 90 for four-primary LDs and five-primary LDs. This means that if using the multiple-primary LDs for plant-growth lighting sources in the indoor greenhouses, in consideration of the higher requirements of color rendering performances, the four-primary LDs and five-primary LDs are more suitable than three-primary LDs. Fig. 4 clearly shows the calculated SPDs under 2700-6500 K CCTs. Table I lists all the parameters for describing the color and photosynthetic performances. The maximum PLER is about 527.2 plm/W under 2700 K CCT with a 90 CRI for five-primary LDs. For four-primary LDs, this value is about 521.2 plm/W, only 6 plm/W lower than five-primary LDs. It can be noticed that R 9 and R 12 for the LD-based lighting sources are hardly to be higher than 90 comparing with LED-based lighting sources [19]. Moreover, the TM-30 scores for four-primary LDs and five-primary LDs are higher than three-primary LDs. Fig. 5 plots the IES TM-30 icon and distortion for all optimal results under 2700-6500 K. We can see that the deviations for reference and simulation are smaller for four-and five-primary LDs than  I  CALCULATED PARAMETERS INCLUDING THE WAVELENGTH OF PRIMARY COLOR three-primary LDs. In Table I, the optimal wavelengths for threeprimary, four-primary, and five -primary LDs are also provided. We can notice that the optimal wavelengths seem to be different for various CCT cases. In order to achieve good color rendering properties and high PLER values, when the CCT increases from 2700 K to 6500 K, the blue shifts of wavelengths can be found for most colors, except for some wavelengths which change slightly. This fact can be helpful to guide the experimental realization in practical.

B. The Comparison of LDs and LEDs
Because the LDs have much narrower FWHMs than LEDs, so the optimal PLER would behave differently. Fig. 6 compares the optimal PLER between MPLDs and MPLEDs with threeprimary, four-primary, and five-primary colors, respectively. Mostly, the optimal PLER is mostly higher for MPLDs than MPLEDs for all cases. This indicates that the light emitted by MPLDs is more helpful to improve the photosynthetic efficiency in the plant growth than MPLEDs.
Also, it can be seen that as the CCT increases, the MPLDs' PLER first decreases sharply and then increases slowly. In contrast, the PLER of MPLEDs changes very slightly. Under 2700 K CCT, the PLER of MPLDs is much higher than that of MPLEDs. Particularly, this PLER difference between fiveprimary LDs and five-primary LEDs is the most, which is about 50 plm/W. However, when the CCT is at 4500 K, there is not much difference between them. So both can be used in the indoor farming. But under other CCTs, it is strongly recommended to use MPLDs.
Apart from these, the difference between the PLER of threeprimary LDs and three-primary LEDs is relatively small. In order to reduce the cost, we can choose three-primary LEDs. In addition, we also compare the color qualities between MPLDs and MPLEDs from the previous work [19]. The color rendering properties are better for the latter than the former, which can be found from the color rendering values as well as the IES TM-30 icon and distortion for all results. Nonetheless, the R a of MPLDs is sufficiently high for the wide application in the indoor lighting.

IV. CONCLUSION
In summary, this article aims for investigating the maximum PLER of multiple-primary laser diodes (MPLDs). It is carried out by using the common genetic algorithms (GA). A comparison between the multiple-primary LDs and multiple-primary LEDs has also been done. Some useful results can be concluded for the reference of fabricating the high-performance plant-growth lighting sources by using LDs, as follows: 1) the maximum PLER is about 527.2 plm/W under 2700 K CCT with a 90 CRI for five-primary LDs. 2) The PLER appears to be higher for the lower CCT and higher CCT than middle CCT, and this fact is quite similar to that of LEDs. At the same time, the PLER is nearly close to each other for four-primary LDs and five-primary LDs under relatively lower CCTs (for example when CCT ≤ 4000 K), but big difference can be found for higher CCTs (when CCT > 4000 K). 3) The optimal PLER is higher for multiple-primary LDs than multiple-primary LEDs for most cases. 4) R 9 and R 12 for multiple-primary LDs are hardly to be higher than 90 comparing with multiple-primary LEDs. The above works are mostly concentrating on the spectral optimization of multiple-primary laser diodes. In the future, if the LDs would be used as the plant-growth light sources, reasonable optical designing and thermal management of the LDs should be done.