Improving LED CCT uniformity using micropatterned films optimized by combining ray tracing and FDTD methods

Although the light-emitting diode (LED) has revolutionized lighting, the non-uniformity of its correlated color temperature (CCT) still remains a major concern. In this context, to improve the light distribution performance of remote phosphor LED lamps, we employ a micropatterned array (MPA) optical film fabricated using a low-cost molding process. The parameters of the MPA, including different installation configurations, positioning, and diameters, are optimized by combining the finitedifference time-domain and ray-tracing methods. Results show that the sample with the upward-facing convex-cone MPA film that has a diameter of half of that of the remote phosphor glass, and is tightly affixed to the inward surface of the remote phosphor glass renders a superior light distribution performance. When compared with the case in which no MPA film is used, the deviation of the CCT distribution decreases from 1033 K to 223 K, and the corresponding output power of the sample is an acceptable level of 85.6%. We perform experiments to verify our simulation results, and the two sets of results exhibit a close agreement. We believe that our approach can be used to optimize MPA films for various lighting applications. ©2015 Optical Society of America OCIS codes: (230.3670) Light-emitting diodes; (220.4000) Microstructure fabrication; (050.1755) Computational electromagnetic methods; (160.2540) Fluorescent and luminescent materials; (290.1483) BSDF, BRDF, and BTDF. References and links 1. N. Thejokalyani and S. Dhoble, “Novel approaches for energy efficient solid state lighting by RGB organic light emitting diodes–A review,” Renew. Sustain. Energy Rev. 32, 448–467 (2014). 2. S. Pimputkar, J. S. Speck, S. P. DenBaars, and S. Nakamura, “Prospects for LED lighting,” Nat. 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Introduction
Solid-state lighting (SSL) devices, such as organic and inorganic light-emitting diodes (OLEDs and LEDs), realized using ecofriendly, energy efficient, and novel "green" technologies, are considered as powerful candidate for future lightings [1].Recently, LEDs have matured from the research and are now commercially deployed owing to their high efficiencies, low energy requirement, short response, and long lifetime [2].In 1994, Nakamura et al. first developed a thermal annealing method for high-efficiency highintensity blue-LED mass production [3].This breakthrough has led to GaN-based blue-light LEDs coated with down-conversion materials, such as aluminate phosphor [4] and quantum dot phosphor [5,6], becoming one of the most popular approaches to realize white-light LEDs [2].LEDs are currently accelerating the revolution in the lighting industry with their applications ranging from displays to general lighting [7].However, LED development still faces several challenges, and achieving uniform correlated color temperature (CCT) at different viewing angles is one of the major challenges.
Remote phosphor LEDs, in which the phosphor layer is separated from the blue-LED chips, have been demonstrated to improve the conversion efficiency and lifetime of phosphor-converted LEDs [8,9], and they are widely used for general lighting applications such as downlights.However, matching the phosphor layout with the blue emission pattern of the LED chip is difficult, which leads to a non-uniform CCT distribution.One approach toward addressing this issue is to optimize the geometries or the particle features of the remote phosphor to improve the CCT distributions by using patterned or shaped phosphor layers [10,11], multi-layer phosphor [12][13][14], nanoparticle-mixed phosphor [15] and new phosphor material [16].A second approach involves the mixing of the LED emissions by using a lens reflector to obtain a uniform CCT distribution [17,18].
In this backdrop, micropatterned array (MPA) optical structures, which can scatter the incident light over a large area, are also potential candidates for ensuring uniform CCT distribution.The patterned sapphire substrate (PSS), which is a typical MPA material with excellent scattering ability and high light extraction efficiency, is widely used in the LED industry [19].The use of PSS as a diffractive optical element can improve the CCT uniformity for remote phosphor applications [20].However, PSS is a high-cost material, and therefore, a mass-producible MPA film fabricated by imprinting a PSS mold has been reported has an alternative.This method can improve the CCT distributions efficiently by employing a chip-on-board LED source [21].Fig. 1(a) illustrates the fabrication processes involved in the proposed approach.First, a liquid-state polymer is coated on the MPA mold by spin coating.As the polymer solidifies, the "negative" microstructures of the MPA mold form a film.A convex mold is used to obtain concave microstructures, and conversely, convex structures can be obtained by using a concave mold.After solidification, the optical film is peeled off from the MPA mold, as shown in Fig. 1(b).The MPA optical film exhibits a variety of optical phenomena including refraction, reflection, diffraction, and interference.Consequently, designing and optimizing such films for a given lighting requirement is rather difficult.Therefore, popular numerical approaches, such as the finite-difference time-domain (FDTD) and ray tracing (RT) have been used for designing optical elements.The FDTD method (based on wave optics) is used to study the propagation of electromagnetic or light waves by solving Maxwell's equations.The FDTD approach can be applied to structures with dimensions of only a few micrometers because of the limitations of computational power.On the other hand, the classical RT method is based on geometrical optics.This method can effectively be used to simulate macrostructures whose size is considerably larger than the incident wavelength.However, in the case of microstructures, whose sizes range to 10 times the incident wavelength, the RT method is invalid because the diffractive effect becomes prominent.In the context of this study, the RT method has also been used to simulate the properties of the phosphor in an LED via the importing of the phosphor's material parameters [11,22,23].As regards the MPA film used for improving the CCT distribution of remote phosphor LEDs, neither the RT nor the FDTD methods can individually be used for simulation.Consequently, several studies in an attempt to combine the FDTD and RT methods have been conducted [24][25][26].
In this study, we employ an asymmetric bidirectional scattering distribution function (BSDF) to combine the FDTD and RT methods by converting the FDTD data into surface property for RT.As regards the study design, we first introduce the detailed simulation method and setup.Subsequently, we use the method to optimize the MPA optical film with regard to the installation configurations, positioning, and diameters for remote phosphor LED lamps.The performances of the MPA film are analyzed by introducing a syntactical evaluation factor, which accounts for both CCT distribution uniformity and output power.Finally, we experimentally determine the optimal MPA film for remote phosphor LED lamps.

Method
The FDTD method is used to solve and decompose Maxwell's curl equations into a threedimensional (3D) difference form based on the popularly used Yee cell; the complex electromagnetic field and certain important derived quantities can be obtained as a function of time or frequency in a step-by-step manner [27].Among these quantities, the Poynting vector is a key derived quantity.This vector lies parallel with the wave vector κ  of the source and its magnitude is also proportional to that of the geometrical optical ray.Therefore, it can be used to connect the FDTD and RT methods.For a plane source, the Poynting vector ( S  ) can be calculated as follow: Here, 0 ε and 0 μ denote the permittivity and magnetic permeability, respectively, and E  the electric field.The scattered power (P s ) can be calculated by the following equation: Here, R denotes the radius in spherical coordinates, and θ s and φ s the zenith and azimuth angles of the scattered light, respectively.In the next step, the asymmetric BSDF is applied to transform the results from the FDTD into a boundary form for manipulation by the RT method.The asymmetric BSDF is a function of both the incident and scattering directions, and its value is defined as follow: , ) , , , ) ( , ) cos Here, L s represents the scattering radiance, I i the incident irradiance, Ω the solid angle element, P i the power of the incident light, and θ i and φ i the zenith and azimuth angles, respectively, of the incident light beam.The schematic of the experimental setup of the remote phosphor lamp used in our study is shown in Fig. 3.The setup comprises four parts: a blue LED component with a Lambertian distribution, an MPA optical film, a remote phosphor glass, and three cylinder holders for assembling the remote phosphor glass and the MPA optical film.The cylinder holders can be moved along the axial direction for adjusting the positions of the blue LED, MPA optical film, and remote phosphor glass.The phosphor layer was coated on the outward surface of the glass.In order to reduce the effect of reflection from the internal wall of the cylinder holder, the holder's surface property is set to perfect absorption.The distance between the LED light source and the remote phosphor is set to a constant of 15 mm, and consequently, the zenith angle of the lamp is approximately 120°.This value is equal to the full angle at half maximum of the standard Lambertian distribution.The parameter 'h' in Fig. 3 represents the distance between the LED light source and the MPA optical film.

Experiment and simulation setups
Based on the Mie scattering model, the phosphor particles are assumed to be spherical [23,28].The scatter coefficient is set to 27.54 mm −1 for blue light and 32.63 mm −1 for yellow light.The spherical phosphor particles absorb the blue light (450 nm) strongly and transform it into yellow light (570 nm) that is weakly absorbed by the phosphor.The bulk absorption is set to 5.31 mm −1 for blue light and 0.15 mm −1 for the yellow light.The power conversion efficiency of the phosphor layer is assumed to be 75% in the simulation.During the RT process in this study, a bilinearly interpolated 2D table was used to determine the asymmetric BSDF, which could interpolate the scattering distribution based on specific incident angles.It has been previously reported that the incident angle θ is not significantly affected by the energy distribution [29].Therefore, in this work, the scattering data of the normal incident light was chosen to define the surface property for simplification.It is evident that the scattering areas for the upward-facing MPA configurations are larger than those for the downward-facing MPA configurations.One reason for this difference is that the deflection (due to refraction) angle from silicone to air is larger than that from air to silicone.Further, in the case of the downward-facing MPA configurations, light scattering at angles greater than the critical angle does not exit the silicone film because of total internal reflection at the flat surface of the film.The CCT distributions of the four MPA configurations and for the case without the MPA film are shown in Fig. 5(a).We clearly observe that the use of the MPA film can improve the CCT distributions upon reducing the CCT values of the central area of the light spot, but the improvement degrees are very different for different cases.In practical applications of LED lamps, high output power and high CCT uniformity are two important properties.However, the output power and CCT uniformity properties exhibit a tradeoff relationship for two reasons: one is the objective properties of the MPA films (as explained previously), and the other is the phenomenon of Stokes loss, wherein higher-energy photons are transformed into lower-energy photons [30].In order to determine the optimum configuration for improving the performance of the remote phosphor LED, the light output power (P opt ) and standard deviation of the CCT distribution (σ CCT ) are analyzed using the following equation:

Results and discussion
Here, F represents the evaluating factor.The larger is the value of F, the better is the synthetic performance of the remote phosphor lamp.The P opt , σ CCT , and F values of the four configurations are shown in Fig. 5(b).The MPA films are positioned on the inward surface of the remote phosphor glass.With respect to the synthetic evaluating factor F, the upwardfacing MPA film configurations exhibit a considerably better performance than that in the case without the MPA film.On the other hand, the downward-facing MPA configurations exhibit a poorer performance than that in the case without the MPA film.One reasonable explanation for this difference is the existence of a thin layer of air between the MPA structures and the remote phosphor glass for the downward-facing sample configurations; the consequent large refractive index difference between the silicone and air leads to a reduced amount of light exiting the MPA film.This poor transmission property in the case of the downward-facing MPA configuration samples leads to poor excitation of the peripheral phosphor, thereby degrading the CCT distribution despite the downward-facing MPA films having good scattering properties.For the upward-facing MPA film samples, the flat side of the film is tightly affixed to the inward surface of the remote phosphor; there is no air gap layer that prevents the transmission of light from the silicone to the glass.Among the four configurations, the upward-facing convex-cone MPA film configuration exhibits superior performance with both high output power and uniform CCT distribution.The evaluating factor F for this sample is 2.20 times of that obtained without using of the MPA film.In the following experiments, we select the upward-facing convex-cone MPA film configuration for lamp applications.The CCT distributions, P opt , σ CCT , and F of the upward-facing convex-cone MPA configuration are shown in Fig. 6 for various h values.We observe that the MPA film affixed to the inward surface of the remote phosphor glass (h = 15 mm) exhibits outstanding CCT distribution uniformity and acceptable light output power.When compared with the case in which no MPA film is used, the σ CCT value of the film affixed to the inward surface of the remote phosphor glass decreases from 1033 K to 384 K, and the CCT at the center of the light spot decreases from 7538 K to 5488 K.However, the output power is 83% of that obtained in the absence of the MPA film.When the MPA film is raised from the inward surface of the remote phosphor glass by 3 mm, the CCT distribution immediately reduces as σ CCT rises to 941 K. Simultaneously, the output power decreases to approximately 60%.Subsequently, with decrease in h, the σ CCT and output power values vary indistinctively.
The following conclusions can be drawn from these results: (1) the MPA film that is tightly affixed to the inward surface of the remote phosphor glass (thus, eliminating the intermediary air layer) is the optimal choice among all the cases discussed.However, the presence of an air layer between the MPA film and the glass leads to light being suppressed in the silicone owing to total internal reflection.Only a small amount of light is observed within a small escape angle.Therefore, the total power reduces sharply and the intensity at the center is larger than that at the periphery.(2) The use of the MPA film can reduce the CCT values both at the center and periphery of the light spot, and the CCT reduction at the center is significant.This is because the MPA film can scatter blue light from the normal direction over a large angle.Thus, the intensity of the central area of blue light is reduced strongly and that of the peripheral blue light is enhanced slightly.(3) The use of the MPA film does not always improve the CCT distribution.For example, when h is 3 mm, the resulting CCT distribution is poorer than that obtained without the use of the MPA film.This interesting result is also attributed to the scattering property of the MPA film.In the general case, as shown in Fig. 7(a), a light beam with a large zenith angle β will directly reach point A on the phosphor.However, for the MPA film cases, the intensity of light at point A is reduced, and a portion of the original light is scattered to the center of the remote phosphor layer, as shown in Fig. 7(b).Thus, the intensity of the central blue-light spot of the lamp is enhanced and that of the peripheral blue-light ring of the lamp is reduced.With reduction in h, the zenith angle β increases, thereby leading to more light impinging the MPA film, which in turn increases the intensity of the central blue-light spot.The MPA film can be considered as an optical element that focuses light beams, particularly for light beams with large zenith angles.Consequently, we can infer the possibility of an optimal MPA film with a suitable diameter for lamp applications.The bluelight distributions shown in Fig. 8 support this inference.As the diameter of the MPA film decreases from 50 mm to 25 mm (half of the diameter of the remote phosphor glass), the "focusing" effect reduces.When the diameter is approximately 25 mm, the central blue light spot and the peripheral blue light ring exhibit nearly equal distributions, and the blue light at the periphery exhibits a large zenith angle.We observe that the MPA film with a diameter of approximately 25 mm is the optimal choice.As the diameter decreases from 25 mm to 5 mm, the intensity of the central blue light spot decreases gradually.Moreover, the zenith angle also decreases gradually owing to the prominent scattering ability of the MPA film at small zenith angles.
The CCT distributions after blue photon-energy down-conversion and bulk scattering by the phosphor for different diameters of the upward-facing convex-cone configuration are shown in Fig. 9.As expected, the highest syntactical evaluating factor F, which is 3.96 times of that obtained for the sample without MPA films, corresponds to the upward-facing convex-cone MPA film configuration with a diameter of 25 mm.The output power in this case is in an acceptable level of 85.6% of that obtained without the MPA film, and its σ CCT value of 223 K is also the lowest among the cases compared.We also note that the CCT distributions are similar to the blue-emission distributions compared with Fig. 8; however, the degree of variation in the CCT distribution is not as significant as that of the blue emission.For example, for the MPA film with d = 25 mm, the intensity of the blue emission at a distance of ± 0.3 m is only about 60% of the peak value; the CCT difference between the central position of the light spot and a distance of ± 0.3 m from this center is only 4%.This is because the phosphor particles scatter and mix the blue and yellow emissions simultaneously leading to a uniform light distribution.Without loss of generality, we can further state that the diameter of MPA film must be half of that of the lamp for application in remote phosphor LED downlights.Moreover, the CCT at the outermost area is constant at approximately 4500 K, which corresponds to the formation of a yellow ring.However, the intensity at this area is so low that the yellow ring is nearly invisible in practical applications.Most of the emission energy concentrates within an emission angle of 100°, and therefore, the central light spot is the actual area of concern.In this work, the radius of the central light spot is approximately 0.6 m, which is the area for which the MPA film is optimized.Finally, we fabricated, applied, and evaluated the optimized MPA film.The experiment and simulation results exhibit a close agreement, as shown in Fig. 10.The differences between the simulations and experiments appear mainly because of the following reasons: (1) the use of high-accuracy meshing is very time-consuming in FDTD simulations, but loweraccuracy simulations lead to the introduction of larger errors.(2) The phosphor particles are considered as simplified spheres based on the Mie theory, which does not lead to accurate simulation of the actual scattering properties of the phosphor.(3) In the FDTD simulation, all the microstructures were assumed to be identical; however, fabrication errors inevitably exist in practice, particularly for large-area films.
We believe that our approach can significantly contribute to the development of LEDs for a variety of general lighting applications.

Conclusion
In this study, cone-shaped micropatterned array (MPA) optical films were applied to remote phosphor LED lamps to improve their CCT distributions.An asymmetric bidirectional scattering distribution function (asymmetric BSDF) was used to combine the finite-difference time domain (FDTD) and ray tracing (RT) methods, and the resulting method was applied to optimize the MPA optical films.We determined that transmittance and scattering exhibit a tradeoff relationship.Therefore, we syntactically evaluated the performance of the MPA films.Our results showed that an upward-facing convex-cone MPA film with a diameter of 25 mm (half of that of the remote phosphor glass) that is tightly affixed to the inward surface of the remote phosphor glass exhibits a superior performance with both a uniform CCT distribution and acceptable output power.In comparison with the case in which the MPA film was not used, the CCT distribution deviation of the optimal sample decreased from 1033 K to 223 K, and the output power corresponding to this sample was an acceptable level of 85.6%.We believe that our approach that combines the FDTD and RT methods is efficient for optimizing MPA films, and the application of such optimized MPA films can significantly contribute to the development of high-quality remote phosphor LED lamps.
In future, we plan to apply MPA films on free-form surfaces to improve the lighting output.We believe that our findings will significantly contribute to the development of LED lighting applications.

Figures 2 (
Figures 2(a) and 2(b) show the atomic force microscopy (AFM) and scanning electron microscopy (SEM) photographs of the concave (depressions in the film) and convex (raised projections) cone-shaped MPA structures studied in this work.The convex or concave coneshaped MPA structures are hexagonally arranged on one side of a silicone film.Each structure has a height of approximately 1.5 μm and a base diameter of approximately 2.8 μm.In the FDTD simulation part, a 3D simulation region, which contains the minimized period structure of the MPA, was selected.Here, we remark that the contour for the molding is based on the actual structure.A simulated plane wave source with a domain wavelength of 455 nm was positioned at the top side of the simulation region.The perfectly matched layer (PML) boundary condition was applied to the top and bottom sides of the simulation region along the z direction.The PML could absorb the light transmitted through the MPA optical film, which is equivalent to the transmitted light propagating towards the infinite far field.The Bloch boundary condition for periodic structures was used for the other four sides along the x and y directions.The concave-and convex-cone MPA optical films can be arranged along two directions: the surface with the MPA structures facing up and down, as shown in Figs.2(c)-2(f).

Fig. 3 .
Fig. 3. Schematic cross-sectional view (left) and axonometric view (right) of the remote phosphor LED lamp.(Note: the hexagonal distributed light spots on the MPA film on the right of this figure are based on the actual photographs.)

Fig. 4 .
Fig. 4. (a)-(d) Cross-sectional electric field distributions of different installation configurations of micropatterned array (MPA) films.(e)-(f) Corresponding far field light distributions of normally incident light beams passing through different MPA film configurations.

Figures 4 (
Figures 4(a)-4(d) show the FDTD results of the cross-sectional electric field distributions for the four MPA sample configurations mentioned in the previous section.The transmittance performances for the upward-or downward-facing MPA film configurations are very different.Light waves are not easily transmitted through the downward-facing MPA film configurations, as shown in Figs.4(a) and 4(c).Most of the light is restricted to the silicone layer and reflected backward.This is because light propagates from the denser medium to the rarer medium in this case, and therefore, light waves are mostly reflected at the interface.When a light wave propagates to the conical tip, wherein the structure scale approximates the

Fig. 6 .
Fig. 6.(a) Correlated color temperature (CCT) distributions of the upward-facing convex-cone micropatterned array (MPA) film configuration for different h values.(b) P opt , σ CCT , and F values of this configuration for different h values.

Fig. 7 .
Fig. 7. Illustration of light incident on remote phosphor (a) without and (b) with the MPA film.(Note: the scattering lights absorbed by the holders are represented by dash lines)

Fig. 8 .
Fig. 8. Illustration of distribution of the blue emission for different diameters of the MPA film.

Fig. 10 .
Fig. 10.Experimental and simulated correlated color temperature (CCT) distributions for remote phosphor downlights with/without optimized MPA film.The inset shows the photographs of the actual light spots.