## Interplay between multiple scattering, emission, and absorption of light in the phosphor of a white light-emitting diode |

Optics Express, Vol. 22, Issue 7, pp. 8190-8204 (2014)

http://dx.doi.org/10.1364/OE.22.008190

Acrobat PDF (1218 KB)

### Abstract

We study light transport in phosphor plates of white light-emitting diodes (LEDs). We measure the broadband diffuse transmission through phosphor plates of varying YAG:Ce^{3+} density. We distinguish the spectral ranges where absorption, scattering, and re-emission dominate. Using diffusion theory, we derive the transport and absorption mean free paths from first principles. We find that both transport and absorption mean free paths are on the order of the plate thickness. This means that phosphors in commercial LEDs operate well within an intriguing albedo range around 0.7. We discuss how salient parameters that can be derived from first principles control the optical properties of a white LED.

© 2014 Optical Society of America

## 1. Introduction

1. E. F. Schubert, *Light Emitting Diodes* (Cambridge University, 2006). [CrossRef]

3. H. Bechtel, P. Schmidt, W. Busselt, and B. S. Schreinemacher, “Lumiramic: a new phosphor technology for high performance solid state light sources,” Proc. SPIE **7058**, 70580E (2008). [CrossRef]

8. E. Alerstam, T. Svensson, and S. Andersson-Engels, “Parallel computing with graphics processing units for high-speed Monte Carlo simulation of photon migration,” J. Biomed. Opt. **13**, 060504 (2008). [CrossRef]

9. E. Alerstam, W. C. Y. Lo, T. D. Han, J. Rose, S. Andersson-Engels, and L. Lilge, “Next-generation acceleration and code optimization for light transport in turbid media using GPUs,” Biomed. Opt. Express **1**, 658–675 (2010). [CrossRef]

6. Z. Liu, S. Liu, K. Wang, and X. Luo, “Measurement and numerical studies of optical properties of YAG:Ce phosphor for white light-emitting diode packaging,” Appl. Opt. **49**, 247–257 (2010). [CrossRef] [PubMed]

10. A. Lagendijk and B. A. van Tiggelen, “Resonant multiple scattering of light,” Phys. Rep. **270**, 143–215 (1996). [CrossRef]

13. E. Akkermans and G. Montambaux, *Mesoscopic Physics of Electrons and Photons* (Cambridge University, 2007). [CrossRef]

*ab initio*models over ray tracing is that one obtains fundamental physical insight, starting from the detailed nanostructure of a sample. Moreover, calculating optical properties from a model is computationally much faster than performing a ray tracing simulation.

14. W. L. Vos, T. W. Tukker, A. P. Mosk, A. Lagendijk, and W. L. IJzerman, “Broadband mean free path of diffuse light in polydisperse ensembles of scatterers for white LED lighting,” Appl. Opt. **52**, 2602–2609 (2013). [CrossRef] [PubMed]

*ab initio*model was made without adjustable parameters by using Mie theory. While the model was found to agree well with the experimental results, both the experiment and the model did not include absorption or emission, both of which are quintessential in the functioning of a white LED. The aim of our present paper is to close this gap and understand multiple scattering in a functional phosphor.

10. A. Lagendijk and B. A. van Tiggelen, “Resonant multiple scattering of light,” Phys. Rep. **270**, 143–215 (1996). [CrossRef]

## 2. Light diffusion with energy conversion - observables and optical properties

*T*- also known as diffuse transmission - which is the transmission integrated over all outgoing angles at which light exits from a medium. In general the total transmission contains information on the transport mean free path

*ℓ*, a crucial parameter that describes multiple scattering of light [10

_{tr}10. A. Lagendijk and B. A. van Tiggelen, “Resonant multiple scattering of light,” Phys. Rep. **270**, 143–215 (1996). [CrossRef]

15. D. J. Durian, “Influence of boundary reflection and refraction on diffusive photon transport,” Phys. Rev. E **50**, 857–866 (1994). [CrossRef]

*total relative intensity T*where

_{rel}*I*is the angular integrated light intensity at the exit face of the phosphor plate, and

_{tot}*I*

_{0}is the reference intensity. In our study the reference intensity is chosen to be the integrated incident intensity in the absence of the phosphor plate.

*T*is the total transmission in the presence of absorption and

*T*is the ratio of re-emitted intensity to the reference intensity. We can lump multiple scattering with the first step of energy conversion, namely absorption, into one term

_{em}*T*, because in diffusion theory the combined behavior can be readily described simply as lossy diffusive scattering [16

16. N. Garcia, A. Z. Genack, and A. A. Lisyansky, “Measurement of the transport mean free path of diffusing photons,” Phys. Rev. B **46**, 14475–14479 (1992). [CrossRef]

*T*contains information on both the transport mean free path

*ℓ*and the absorption mean free path

_{tr}*ℓ*. The absorption mean free path is the distance it takes for light to be absorbed to a fraction 1/

_{abs}*e*while light performs a random walk in a scattering medium. We note that

*T*remains an integrated measure of the incident light that is

*transmitted*through the phosphor plate.

*T*(

*ℓ*, 1/

_{tr}*ℓ*→ 0) ≡

_{abs}*T*

^{0}(

*ℓ*). In phosphor,

_{tr}*T*

^{0}(

*ℓ*) is an experimentally accessible quantity if we remove the effects of absorption and emission by spectral filtering. From

_{tr}*T*

^{0}(

*ℓ*) the transport mean free path can be deduced, as was studied in Ref. [14

_{tr}14. W. L. Vos, T. W. Tukker, A. P. Mosk, A. Lagendijk, and W. L. IJzerman, “Broadband mean free path of diffuse light in polydisperse ensembles of scatterers for white LED lighting,” Appl. Opt. **52**, 2602–2609 (2013). [CrossRef] [PubMed]

*ℓ*(

_{tr}*λ*) is known, we can use this information to deduce

*ℓ*(

_{abs}*λ*) from

*T*. We assume there is no re-absorption, which is reasonable as the Stokes-shifted light emitted by the phosphor will no longer be in the phosphor absorption band. Therefore by a suitable combination of experiments in different wavelength ranges with excitation filters, we can distinguish the multiple light scattering from diffuse absorption properties in a white LED phosphor.

## 3. Experimental details

17. See catalog at: http://www.lighting.philips.co.uk/pwc_li/gb_en/subsites/oem/fortimo-led-catalogue, retrieved August, 2013.

^{3+}is the most commonly-used compound for remote phosphors and is also employed in Fortimo white LEDs. We investigated five polymer plates (polycarbonate, Lexan 143R) containing YAG:Ce

^{3+}crystalline particles with weight densities ranging through

*ϕ*= 2.0, 2.5, 3.0, 3.5 and 4.0 wt%, the typical densities of phosphor used in Fortimo white LEDs. These phosphor particles are known to have a broad size distribution centered around 10

*μ*m. The emission spectrum of the particles in powder form was measured at Philips Lighting. Plates were fabricated as follows: a powder of YAG:Ce

^{3+}crystals is mixed with polymer by making a compound in the required weight ratio. Next, the compound is shaped into plates (60 mm × 2 mm) by industrial injection molding. The plates have a thickness

*L*= 2.0 mm.

*T*of light we implemented a setup with a white-light source, which in our case is a white LED (Luxeon LXHLMW1D). The spectral range runs from

_{rel}*λ*= 400 nm to 700 nm as shown in Fig. 1(b). The output of such a white LED light source has a spectral range identical to the range of interest, conveniently eliminating the need for additional spectral filters. To measure the total transmission in the absence of absorption

*T*

^{0}, we use a broadband high-pass filter with a cut-off wavelength at 520 nm that removes the blue component of the white-light source.

*I*

_{0}in absence of a sample, and determined the total relative intensity

*T*(

_{rel}*λ*) or the total transmission

*T*(

*λ*) as the ratio of a sample spectrum and a reference spectrum. Reference spectra were frequently collected in between sample spectrum measurements to correct for possible time-dependent changes in the setup. The total relative error in the transmission is estimated to be about 5% percent points, including systematic errors, based on the variations between different measurements.

## 4. Results and discussion

### 4.1. Total transmission

*T*(

_{rel}*λ*) for phosphor plates with increasing phosphor content. For visual clarity we have only plotted

*T*(

_{rel}*λ*) of the lowest (2%) and highest (4%) weight percentages studied. Also for visual clarity we have binned

*T*(

_{rel}*λ*) into 6 nm-wide spectral intervals. The spectra are limited to the range 400 to 700 nm since this is the range where the white light source intensity

*I*

_{0}is significant, see Fig. 1(b). In each spectrum,

*T*(

_{rel}*λ*) exhibits a broad trough between

*λ*= 400 and 510 nm, indicating a strong absorption of blue light by the phosphor.

^{3+},

*T*(

_{rel}*λ*) includes light absorption and re-emission. To distinguish the contributions, we first measured the spectral range of YAG:Ce

^{3+}emission, shown in Fig. 2(b). We see that the emission has an onset at

*λ*

_{1}= 490 nm and extends to all longer wavelengths. Therefore we can already conclude with Eq. 2 that for short wavelengths

*λ*≤

*λ*

_{1}, the total transmission

*T*is equal to the total relative intensity:

*T*(

*λ*≤

*λ*

_{1}) =

*T*(

_{rel}*λ*≤

*λ*

_{1}). The equivalence of

*T*(

_{rel}*λ*≤

*λ*

_{1}) and

*T*(

*λ*≤

*λ*

_{1}) is illustrated in Fig. 2(a) by the overlap of the red and green symbols.

*λ*

_{2}= 520 nm. Such a filter prevents blue light from exciting the phosphor, and thus corresponds to zero emitted intensity:

*T*= 0. Hence at long wavelengths

_{em}*λ*>

*λ*

_{2}(= 520 nm) the total transmission is equal to the total relative intensity:

*T*(

*λ*>

*λ*

_{2}) =

*T*(

_{rel}*λ*>

*λ*

_{2}). The total relative intensity in the presence of the filter is shown as red diamonds in Fig. 2(a) for the 4 wt% YAG:Ce

^{3+}plate. Thus by combining the measurements of

*T*(

*λ*) for

*λ*<

*λ*

_{1}and

*λ*>

*λ*

_{2}, we obtain the total transmission of a phosphor-containing diffuser plate for the entire visible spectral range, with the exception of the 30-nm interval between

*λ*

_{1}and

*λ*

_{2}as is shown in Fig. 2(a). (We have chosen

*λ*

_{2}so that there is some overlap with the YAG:Ce

^{3+}absorption band [6

6. Z. Liu, S. Liu, K. Wang, and X. Luo, “Measurement and numerical studies of optical properties of YAG:Ce phosphor for white light-emitting diode packaging,” Appl. Opt. **49**, 247–257 (2010). [CrossRef] [PubMed]

18. L. G. Van Uitert, D. A. Pinnow, and J. C. Williams, “Photoluminescent conversion of laser light for black and white and multicolor displays. 1: Materials,” Appl. Opt. **10**, 150–153 (1971). [CrossRef] [PubMed]

*T*(

*λ*).)

*T*(

_{rel}*λ*) and

*T*(

*λ*) in Fig. 2(a), we see that

*T*(

_{rel}*λ*) is significantly higher than

*T*(

*λ*) in the wavelength range 520 <

*λ*< 700 nm as a result of emitted light. Apparently, the shape of the emitted spectrum

*I*(

_{em}*λ*) agrees well with the input spectrum of the white source

*I*

_{0}(

*λ*), resulting in a nearly wavelength-independent

*T*(

_{em}*λ*) shown in Fig. 2(a). We conclude that since the relative total intensity for

*λ*>

*λ*

_{2}in Fig. 1 is enhanced by the phosphor emission, only measuring the relative total intensity does not allow us to characterize light scattering in phosphors with emission.

^{3+}content of 2 wt% and 4 wt%. We observe a decreasing

*T*(

*λ*) with increasing phosphor density. In the range

*λ*>

*λ*

_{2}this behavior is intuitively reasonable as the scattering strength is expected to increase with the density of the phosphor particles that act as scatterers. In the range

*λ*<

*λ*

_{1}(= 490 nm) the total transmission is affected by absorption of light in the YAG:Ce

^{3+}phosphor; as is evident from the spectral shape with a minimum at

*λ*= 460 nm.

### 4.2. Transport mean free path

16. N. Garcia, A. Z. Genack, and A. A. Lisyansky, “Measurement of the transport mean free path of diffusing photons,” Phys. Rev. B **46**, 14475–14479 (1992). [CrossRef]

19. P. D. García, R. Sapienza, J. Bertolotti, M. D. Martín, Á. Blanco, A. Altube, L. Viña, D. S. Wiersma, and C. López, “Resonant light transport through Mie modes in photonic glasses,” Phys. Rev. A **78**, 023823 (2008). [CrossRef]

*T*is equal to: The total transmission

*T*(

*L*,

*λ*) is a function of the thickness of the plate

*L*and the wavelength

*λ*.

*R*(

_{s}*λ*) is the specular reflectivity of the incident light from the front surface. As the phosphor density is relatively low, the specular reflectivity is mainly determined by the refractive index of the polymer matrix. Previous measurements show that in the visible regime, the specular reflectivity is low, between 4 and 5% [14

14. W. L. Vos, T. W. Tukker, A. P. Mosk, A. Lagendijk, and W. L. IJzerman, “Broadband mean free path of diffuse light in polydisperse ensembles of scatterers for white LED lighting,” Appl. Opt. **52**, 2602–2609 (2013). [CrossRef] [PubMed]

*z*is the distance within the medium at which a source of isotropically emitted light is taken to be positioned, and is 2/3

_{p}*ℓ*for diffuse incident light and

_{tr}*ℓ*for collimated normal-incident light. The extrapolation length

_{tr}*z*is the distance outside the boundary at which the diffuse intensity decreases to zero [20] and it equals The reciprocal absorption mean free path

_{e}*α*is equal to

*α*= 1/

*ℓ*, where

_{abs}*ℓ*is the diffuse absorption length. In the absence of absorption the extrapolation length

_{abs}*z*

_{0}is well-described by where

*R̄*is the angle- and polarization-averaged reflectivity [21

21. A. Lagendijk, R. Vreeker, and P. de Vries, “Influence of internal reflection on diffusive transport in strongly scattering media,” Phys. Lett. A **136**, 81–88 (1989). [CrossRef]

*n*= 1.5 typical of a polymer the average diffuse reflectivity is equal to

*R̄*= 0.57 [22

22. J. X. Zhu, D. J. Pine, and D. A. Weitz, “Internal reflection of diffusive light in random media,” Phys. Rev. A **44**, 3948–3959 (1991). [CrossRef] [PubMed]

*ℓ*and secondly the absorption mean free path

_{tr}*ℓ*as a function of wavelength

_{abs}*λ*and phosphor density. Using the Taylor series expansion for sinh(

*x*), we first write Eq. (3) in the limit of low absorption (

*α*<< 1) as As a result, Eq. (3) converges to the standard expression for the total transmission

15. D. J. Durian, “Influence of boundary reflection and refraction on diffusive photon transport,” Phys. Rev. E **50**, 857–866 (1994). [CrossRef]

*z*=

_{p}*ℓ*, as the incident light is collimated.

_{tr}*λ*>

*λ*

_{2}), the transport mean free path can be found by applying Eq. (7). Plotting

*ℓ*as a function of

_{tr}*λ*(Fig. 3), we see firstly that the mean free path decreases with increasing phosphor density. Thus, scattering increases with increasing density, as expected. We also see that there is generally more scattering for blue than red light, a trend consistent with that observed for ensembles of highly poly-disperse non-absorbing nano-particle scatterers [14

**52**, 2602–2609 (2013). [CrossRef] [PubMed]

*ℓ*is only weakly dependent on wavelength [23

_{tr}23. J. Gómez Rivas, R. Sprik, C. M. Soukoulis, K. Busch, and A. Lagendijk, “Optical transmission through strong scattering and highly polydisperse media,” Europhys. Lett. **48**, 22–28 (1999). [CrossRef]

24. O. L. Muskens and A. Lagendijk, “Broadband enhanced backscattering spectroscopy of strongly scattering media,” Opt. Express **16**, 1222–1231 (2008). [CrossRef] [PubMed]

*ℓ*as a linear function of

_{tr}*λ*from 450 to 700 nm, the most important spectral range for white LEDs. Such a linearity was also observed in the study of LED diffuser plates with highly polydisperse ensembles of scatterers reported in Ref. [14

**52**, 2602–2609 (2013). [CrossRef] [PubMed]

*λ*< 530 nm, and diffusion theory is used to find the transport mean free path

*ℓ*. For the strongest scattering sample of 4 wt% YAG:Ce

_{tr}^{3+}, the mean free path increases by a factor 1.4 in the spectral range between 450 and 650 nm. This reveals that the observed scattering is not in the Rayleigh regime, which has a

*λ*

^{4}scaling of the scattering cross section that would correspond to an increase by a factor of 4 [25, 26].

*λ*= 460 nm at the absorption maximum of phosphor. First of all, we see that the sample thickness is 2 to 3 times that of the transport mean free path. We conclude that light is completely randomized as it traverses the thickness of the plate, and that the densities of phosphor optimized for use in white LED components are in a regime of moderate multiple scattering. Secondly, we find that

*i.e.*, phosphor is the main contributor to scattering in our samples. This is reasonable as our samples contain no added scatterers.

*ℓ*≃

*L*), in other words the samples are moderately in the multiple scattering regime, it is relevant to wonder if it is justified to invoke diffusion theory. In Refs. [27

27. M. B. van der Mark, M. P. van Albada, and A. Lagendijk, “Light scattering in strongly scattering media: multiple scattering and weak localization,” Phys. Rev. B **37**, 3575–3592 (1988). [CrossRef]

*i.e.*, for weak multiple scattering, the diffusion theory agrees to better than 10% with the exact results. In addition, simulations of the diffuse transmission of samples with widely varying thickness show that the diffusion approximation is in surprisingly good agreement with the exact results, even for a sample thickness of the order of the mean free path [15

15. D. J. Durian, “Influence of boundary reflection and refraction on diffusive photon transport,” Phys. Rev. E **50**, 857–866 (1994). [CrossRef]

29. P.-A. Lemieux, M. U. Vera, and D. J. Durian, “Diffusing-light spectroscopies beyond the diffusion limit: the role of ballistic transport and anisotropic scattering,” Phys. Rev. E **57**, 4498–4515 (1998). [CrossRef]

### 4.3. Absorption mean free path

*ℓ*and

_{tr}*T*(

*λ*) for

*λ*<

*λ*

_{2}= 530 nm, and all other parameters in Eq. (3) are also known. Therefore we can deduce the absorption mean free path

*ℓ*, using a procedure outlined in detail in the Appendix. The resulting inverse absorption lengths as a function of phosphor density are shown in Fig. 5. We see that

_{abs}*ℓ*≈ 2.5

_{abs}*ℓ*. This implies that the phosphor particles scatter light more strongly than they absorb light. This might seem counter-intuitive, as we normally think of phosphor only in terms of its function in color conversion. Our results show that physically, phosphor is in fact first and foremost a

_{tr}*scattering*material.

^{3+}. The asymptotic behavior of

*T*(

*L*,

*λ*) in Eq. (3) results in a small variation of

*λ*at regions of high absorption, as discussed in greater length in the Appendix. Both Figs. 5 and 6 indicate that across the absorption band,

*ℓ*≃

_{abs}*L*. From Fig. 5 we can clearly see that the optimal phosphor densities arrived at by trial-and-error coincides with a value of

*ℓ*that ranges from being slightly less to slightly greater than the sample thickness

_{abs}*L*. This is intuitively sensible, as luminaires are optimized for the generation of diffuse blue light and an optimal, but not total, conversion to yellow light. Therefore the optimal diffuse white illumination is best accomplished for

*ℓ*comparable to

_{abs}*L*.

*a*that is defined as

*a*=

*σ*/(

_{sc}*σ*+

_{sc}*σ*), where

_{abs}*σ*and

_{sc}*σ*are the scattering and absorption cross-sections [20]. We find that the albedo is 0.7 ± 0.1 for

_{abs}*λ*= 460 nm. This result is independent of phosphor density, as we would expect in the case where scattering and absorption are single-particle properties (Fig. 7). The albedo allows us to place the optical behavior of phosphor doped polymers in relation to other complex photonic media. Traditionally, investigations of multiple light scattering have focused on systems with a high albedo of

*a*> 0.98. A very low albedo, as observed here, is rarely encountered in light scattering, typically in systems of truly black particles [26]. The results we present here thus represent one of the few systems studied with low albedo. Besides the phosphor component of white LEDs, possible applications where this kind of low-albedo system is interesting include paint, printing [30

30. W. Meulebroeck, Y. Meuret, S. Heyvaert, and H. Thienpont, “The experimental characterization of the absorption and scatter properties of photopolymers,” Proc. SPIE **8439**, 84391Z (2012). [CrossRef]

31. J. R. Nagel and M. A. Scarpulla, “Enhanced absorption in optically thin solar cells by scattering from embedded dielectric nanoparticles,” Opt. Express **18**, A139–A146 (2010). [CrossRef] [PubMed]

*u′*,

*v′*coordinates in this color space, as shown in Fig. 8. Spectral data of a reference light source is used as the initial starting point

*u′*= 0.21,

_{i}*v′*= 0.30. This is convolved with our total transmission data to give new final values

_{i}*u′*,

_{f}*v′*as a function of phosphor density. In this way, we effectively describe a white LED with a remote phosphor in a simple way. Increasing phosphor density increases

_{f}*u′*,

_{f}*v′*. For our choice of reference light source, increasing the density of phosphor in the phosphor plates creates a color point sequence which crosses the Planckian locus or black-body line at a color temperature of 5000 K. The color temperature of a white LED is of utmost importance to its application. Our work establishes a physics-based connection between a white LED with a certain

_{f}*u′*,

*v′*color point, and its displacement in this color space with the addition of scatterers or absorbers. By disentangling the roles of absorption and scattering into fundamental physical parameters based on diffusion theory, we now have a way to predict shifts in

*u′*,

_{f}*v′*due to changes in

_{f}*ℓ*and

_{tr}*ℓ*. This offers a practical method to model changes in chromaticity in the phosphor of a white LED from a relatively straightforward measurement of the total transmission, and will be considered further in future research.

_{abs}## 5. Summary and outlook

^{3+}in a polycarbonate matrix, a widely employed production method for white LED modules. We measured the total relative intensity over the visible wavelength range, and extracted from this measurement the total transmission. Employing photonic diffusion theory, we obtained from the total transmission the transport mean free path. The transport mean free path, which fundamentally characterizes the diffuse transport of light, is studied as a function of phosphor density. In addition we have experimentally differentiated the optical roles of phosphor in multiple scattering and absorption. This enabled us to obtain the absorption mean free path which characterizes the color conversion of light in the phosphor plates.

*u′*,

*v′*color space.

## Appendix: Finding the absorption mean free path

*λ*<

*λ*

_{2}= 530 nm, we begin with the analytical solution for the total transmission Eq. (3). As a result of the analysis of Fig. 2 and the extrapolation of the transport mean free path into the absorption region, we know

*ℓ*(

_{tr}*λ*<

*λ*

_{2}). From the initial experimental data presented in Fig. 1, we also know

*T*(

*λ*<

*λ*

_{2}). Thus we are left with only one unknown quantity in Eq. (3): the absorption mean free path

*ℓ*(

_{abs}*λ*<

*λ*

_{2}).

*T*and the inverse absorption mean free path

*ℓ*(

_{tr}*λ*= 460) nm. We can therefore find the specific inverse absorption mean free path that corresponds to the experimentally obtained total transmission

*T*(

*λ*= 460) nm (Fig. 1). This procedure for extracting the absorption mean free path from total transmission data allows us to obtain inverse absorption mean free paths as a function of phosphor density, plotted in Fig. 5.

*T*(

*L*,

*λ*) asymptotically approaches a limiting value of

*T*(

*L*,

*λ*) stems from the extrapolation length in the presence of absorption

*z*, given in Eq. (4). The quantity

_{e}*z*diverges if the absorption mean free path

_{e}*ℓ*becomes smaller than the extrapolation length without absorption

_{abs}*z*

_{0}. We can see that in Eq (5), when 1 −

*αz*

_{0}> 1, the logarithmic part of Eq. (4) becomes divergent. In other words, Eq. (3) is unphysical for very strong absorption compared to scattering, or

*ℓ*>>

_{tr}*ℓ*. For our samples we do not reach this regime; as we have shown, the optimal balance of scattering and absorption in white LED phosphors is when the two mean free paths are nearly commensurate. In our case, the asymptotic behavior of

_{abs}*T*(

*L*,

*λ*) results in a small variation of

*λ*at regions of high absorption such as at

*λ*= 460 nm, the absorption peak of our data. The broadband spectral dependence of the inverse absorption mean free path for

*λ*<

*λ*

_{2}is shown in Fig. 6.

## Acknowledgments

## References and links

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3. | H. Bechtel, P. Schmidt, W. Busselt, and B. S. Schreinemacher, “Lumiramic: a new phosphor technology for high performance solid state light sources,” Proc. SPIE |

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6. | Z. Liu, S. Liu, K. Wang, and X. Luo, “Measurement and numerical studies of optical properties of YAG:Ce phosphor for white light-emitting diode packaging,” Appl. Opt. |

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13. | E. Akkermans and G. Montambaux, |

14. | W. L. Vos, T. W. Tukker, A. P. Mosk, A. Lagendijk, and W. L. IJzerman, “Broadband mean free path of diffuse light in polydisperse ensembles of scatterers for white LED lighting,” Appl. Opt. |

15. | D. J. Durian, “Influence of boundary reflection and refraction on diffusive photon transport,” Phys. Rev. E |

16. | N. Garcia, A. Z. Genack, and A. A. Lisyansky, “Measurement of the transport mean free path of diffusing photons,” Phys. Rev. B |

17. | See catalog at: http://www.lighting.philips.co.uk/pwc_li/gb_en/subsites/oem/fortimo-led-catalogue, retrieved August, 2013. |

18. | L. G. Van Uitert, D. A. Pinnow, and J. C. Williams, “Photoluminescent conversion of laser light for black and white and multicolor displays. 1: Materials,” Appl. Opt. |

19. | P. D. García, R. Sapienza, J. Bertolotti, M. D. Martín, Á. Blanco, A. Altube, L. Viña, D. S. Wiersma, and C. López, “Resonant light transport through Mie modes in photonic glasses,” Phys. Rev. A |

20. | A. Ishimaru, |

21. | A. Lagendijk, R. Vreeker, and P. de Vries, “Influence of internal reflection on diffusive transport in strongly scattering media,” Phys. Lett. A |

22. | J. X. Zhu, D. J. Pine, and D. A. Weitz, “Internal reflection of diffusive light in random media,” Phys. Rev. A |

23. | J. Gómez Rivas, R. Sprik, C. M. Soukoulis, K. Busch, and A. Lagendijk, “Optical transmission through strong scattering and highly polydisperse media,” Europhys. Lett. |

24. | O. L. Muskens and A. Lagendijk, “Broadband enhanced backscattering spectroscopy of strongly scattering media,” Opt. Express |

25. | H. C. van de Hulst, |

26. | C. F. Bohren and D. R. Huffmann, |

27. | M. B. van der Mark, M. P. van Albada, and A. Lagendijk, “Light scattering in strongly scattering media: multiple scattering and weak localization,” Phys. Rev. B |

28. | M. B. van der Mark, Propagation of Light in Disordered Media: A Search for Anderson Localization, Ph.D. thesis (University of Twente, 1990). |

29. | P.-A. Lemieux, M. U. Vera, and D. J. Durian, “Diffusing-light spectroscopies beyond the diffusion limit: the role of ballistic transport and anisotropic scattering,” Phys. Rev. E |

30. | W. Meulebroeck, Y. Meuret, S. Heyvaert, and H. Thienpont, “The experimental characterization of the absorption and scatter properties of photopolymers,” Proc. SPIE |

31. | J. R. Nagel and M. A. Scarpulla, “Enhanced absorption in optically thin solar cells by scattering from embedded dielectric nanoparticles,” Opt. Express |

32. | D. Malacara, |

**OCIS Codes**

(160.5690) Materials : Rare-earth-doped materials

(230.3670) Optical devices : Light-emitting diodes

(290.1990) Scattering : Diffusion

(290.4210) Scattering : Multiple scattering

(290.5850) Scattering : Scattering, particles

(330.1715) Vision, color, and visual optics : Color, rendering and metamerism

**ToC Category:**

Optoelectronics

**History**

Original Manuscript: November 28, 2013

Revised Manuscript: February 24, 2014

Manuscript Accepted: February 24, 2014

Published: April 1, 2014

**Citation**

V. Y. F. Leung, A. Lagendijk, T. W. Tukker, A. P. Mosk, W. L. IJzerman, and W. L. Vos, "Interplay between multiple scattering, emission, and absorption of light in the phosphor of a white light-emitting diode," Opt. Express **22**, 8190-8204 (2014)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-7-8190

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