Abstract

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 finite-difference 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

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References

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    [Crossref]

2014 (7)

V. K. Kim, A. Zakharov, and V. Chashchin, “Luminophores Based on Aluminum Yttrium Garnet (Review),” Glass. Ceram. 71(1-2), 64–67 (2014).
[Crossref]

Q. Zhang, C.-F. Wang, L.-T. Ling, and S. Chen, “Fluorescent nanomaterial-derived white light-emitting diodes: what's going on,” J. Mater. Chem. C 2(22), 4358–4373 (2014).
[Crossref]

J. McKittrick and L. E. Shea-Rohwer, “Review: Down Conversion Materials for Solid‐State Lighting,” J. Am. Ceram. Soc. 97(5), 1327–1352 (2014).
[Crossref]

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).
[Crossref]

C.-Y. Liu, K.-J. Chen, D.-W. Lin, C.-Y. Lee, C.-C. Lin, S.-H. Chien, M.-H. Shih, G.-C. Chi, C.-Y. Chang, and H.-C. Kuo, “Improvement of emission uniformity by using micro-cone patterned PDMS film,” Opt. Express 22(4), 4516–4522 (2014).
[Crossref] [PubMed]

C. Leiner, W. Nemitz, S. Schweitzer, F. P. Wenzl, P. Hartmann, U. Hohenester, and C. Sommer, “Multiple interfacing between classical ray-tracing and wave-optical simulation approaches: a study on applicability and accuracy,” Opt. Express 22(13), 16048–16060 (2014).
[PubMed]

C. Leiner, S. Schweitzer, F.-P. Wenzl, P. Hartmann, U. Hohenester, and C. Sommer, “A simulation procedure interfacing ray-tracing and finite-difference time-domain methods for a combined simulation of diffractive and refractive optical elements,” J. Lightwave Technol. 32(6), 1054–1062 (2014).
[Crossref]

2013 (7)

C. Leiner, S. Schweitzer, V. Schmidt, M. Belegratis, F.-P. Wenzl, P. Hartmann, U. Hohenester, and C. Sommer, “Multi-scale simulation of an optical device using a novel approach for combining ray-tracing and FDTD,” Proc. SPIE 8781, 87810Z (2013).
[Crossref]

K.-C. Huang, T.-H. Lai, and C.-Y. Chen, “Improved CCT uniformity of white LED using remote phosphor with patterned sapphire substrate,” Appl. Opt. 52(30), 7376–7381 (2013).
[PubMed]

J. Cho, E. F. Schubert, and J. K. Kim, “Efficiency droop in light‐emitting diodes: Challenges and countermeasures,” Laser. Photonics. Rev. 7(3), 408–421 (2013).
[Crossref]

K.-J. Chen, H.-C. Chen, M.-H. Shih, C.-H. Wang, H.-H. Tsai, S.-H. Chien, C. C. Lin, and H.-C. Kuo, “Enhanced Luminous Efficiency of WLEDs Using a Dual-Layer Structure of the Remote Phosphor Package,” J. Lightwave Technol. 31(12), 1941–1945 (2013).
[Crossref]

L. Zong-Tao, T. Yong, L. Zong-Yuan, E. T. Yan, and Z. Ben-Ming, “Detailed Study on Pulse-Sprayed Conformal Phosphor Configurations for LEDs,” J. Disp. Technol. 9(6), 433–440 (2013).
[Crossref]

J. H. Oh, S. J. Yang, and Y. R. Do, “Polarized white light from LEDs using remote-phosphor layer sandwiched between reflective polarizer and light-recycling dichroic filter,” Opt. Express 21(S5Suppl 5), A765–A773 (2013).
[Crossref] [PubMed]

X. Li, J. D. Budai, F. Liu, J. Y. Howe, J. Zhang, X.-J. Wang, Z. Gu, C. Sun, R. S. Meltzer, and Z. Pan, “New yellow Ba0.93Eu0.07Al2O4 phosphor for warm-white light-emitting diodes through single-emitting-center conversion,” Light: Science amd Applications 2(1), e50 (2013).
[Crossref]

2012 (2)

H. C. Chen, K. J. Chen, C. C. Lin, C. H. Wang, H. V. Han, H. H. Tsai, H. T. Kuo, S. H. Chien, M. H. Shih, and H. C. Kuo, “Improvement in uniformity of emission by ZrO₂ nano-particles for white LEDs,” Nanotechnology 23(26), 265201 (2012).
[Crossref] [PubMed]

Z.-Y. Liu, C. Li, B.-H. Yu, Y.-H. Wang, and H.-B. Niu, “Uniform white emission of WLEDs realized by multilayer phosphor with pyramidal shape and inversed concentration distribution,” IEEE Photonic. Tech. L. 24(17), 1558–1560 (2012).
[Crossref]

2011 (2)

S. E. Brinkley, N. Pfaff, K. A. Denault, Z. Zhang, H. B. Hintzen, R. Seshadri, S. Nakamura, and S. P. DenBaars, “Robust thermal performance of Sr2Si5N8: Eu2+: An efficient red emitting phosphor for light emitting diode based white lighting,” Appl. Phys. Lett. 99, 241106 (2011).
[Crossref]

H.-C. Kuo, C.-W. Hung, H.-C. Chen, K.-J. Chen, C.-H. Wang, C.-W. Sher, C.-C. Yeh, C.-C. Lin, C.-H. Chen, and Y.-J. Cheng, “Patterned structure of remote phosphor for phosphor-converted white LEDs,” Opt. Express 19(S4Suppl 4), A930–A936 (2011).
[Crossref] [PubMed]

2010 (2)

2009 (1)

S. Pimputkar, J. S. Speck, S. P. DenBaars, and S. Nakamura, “Prospects for LED lighting,” Nat. Photonics 3(4), 180–182 (2009).
[Crossref]

2008 (1)

Z. Liu, S. Liu, K. Wang, and X. Luo, “Optical analysis of color distribution in white LEDs with various packaging methods,” IEEE Photonic. Tech. L. 20(24), 2027–2029 (2008).
[Crossref]

2007 (2)

Y. Kawaguchi, K. Nishizono, J.-S. Lee, and H. Katsuda, “Light extraction simulation of surface-textured light-emitting diodes by finite-difference time-domain method and ray-tracing method,” Jpn. J. Appl. Phys. 46(1), 31–34 (2007).
[Crossref]

S. C. Allen and A. J. Steckl, “ELiXIR—Solid-state luminaire with enhanced light extraction by internal reflection,” J. Disp. Technol. 3(2), 155–159 (2007).
[Crossref]

2006 (1)

E. F. Schubert, J. K. Kim, H. Luo, and J. Xi, “Solid-state lighting—a benevolent technology,” Rep. Prog. Phys. 69(12), 3069–3099 (2006).
[Crossref]

2005 (1)

J. K. Kim, H. Luo, E. F. Schubert, J. Cho, C. Sone, and Y. Park, “Strongly enhanced phosphor efficiency in GaInN white light-emitting diodes using remote phosphor configuration and diffuse reflector cup,” Jpn. J. Appl. Phys. 44(21), L649–L651 (2005).
[Crossref]

2004 (1)

K.-S. Kim, T. Gessmann, H. Luo, and E. F. Schubert, “GaInN light-emitting diodes with RuO 2/SiO 2/Ag omni-directional reflector,” Appl. Phys. Lett. 84(22), 4508–4510 (2004).
[Crossref]

2002 (1)

M. Yamada, T. Mitani, Y. Narukawa, S. Shioji, I. Niki, S. Sonobe, K. Deguchi, M. Sano, and T. Mukai, “InGaN-based near-ultraviolet and blue-light-emitting diodes with high external quantum efficiency using a patterned sapphire substrate and a mesh electrode,” Jpn. J. Appl. Phys. 41(Part 2, No. 12B), L1431–L1433 (2002).
[Crossref]

1992 (1)

S. Nakamura, T. Mukai, M. Senoh, and N. Iwasa, “Thermal annealing effects on p-type Mg-doped GaN films,” Jpn. J. Appl. Phys. 31(Part 2, No. 2B), L139–L142 (1992).
[Crossref]

Allen, S. C.

S. C. Allen and A. J. Steckl, “ELiXIR—Solid-state luminaire with enhanced light extraction by internal reflection,” J. Disp. Technol. 3(2), 155–159 (2007).
[Crossref]

Belegratis, M.

C. Leiner, S. Schweitzer, V. Schmidt, M. Belegratis, F.-P. Wenzl, P. Hartmann, U. Hohenester, and C. Sommer, “Multi-scale simulation of an optical device using a novel approach for combining ray-tracing and FDTD,” Proc. SPIE 8781, 87810Z (2013).
[Crossref]

Ben-Ming, Z.

L. Zong-Tao, T. Yong, L. Zong-Yuan, E. T. Yan, and Z. Ben-Ming, “Detailed Study on Pulse-Sprayed Conformal Phosphor Configurations for LEDs,” J. Disp. Technol. 9(6), 433–440 (2013).
[Crossref]

Brinkley, S. E.

S. E. Brinkley, N. Pfaff, K. A. Denault, Z. Zhang, H. B. Hintzen, R. Seshadri, S. Nakamura, and S. P. DenBaars, “Robust thermal performance of Sr2Si5N8: Eu2+: An efficient red emitting phosphor for light emitting diode based white lighting,” Appl. Phys. Lett. 99, 241106 (2011).
[Crossref]

Budai, J. D.

X. Li, J. D. Budai, F. Liu, J. Y. Howe, J. Zhang, X.-J. Wang, Z. Gu, C. Sun, R. S. Meltzer, and Z. Pan, “New yellow Ba0.93Eu0.07Al2O4 phosphor for warm-white light-emitting diodes through single-emitting-center conversion,” Light: Science amd Applications 2(1), e50 (2013).
[Crossref]

Chang, C.-Y.

Chashchin, V.

V. K. Kim, A. Zakharov, and V. Chashchin, “Luminophores Based on Aluminum Yttrium Garnet (Review),” Glass. Ceram. 71(1-2), 64–67 (2014).
[Crossref]

Chen, C.-H.

Chen, C.-Y.

Chen, F.

Chen, H. C.

H. C. Chen, K. J. Chen, C. C. Lin, C. H. Wang, H. V. Han, H. H. Tsai, H. T. Kuo, S. H. Chien, M. H. Shih, and H. C. Kuo, “Improvement in uniformity of emission by ZrO₂ nano-particles for white LEDs,” Nanotechnology 23(26), 265201 (2012).
[Crossref] [PubMed]

Chen, H.-C.

Chen, K. J.

H. C. Chen, K. J. Chen, C. C. Lin, C. H. Wang, H. V. Han, H. H. Tsai, H. T. Kuo, S. H. Chien, M. H. Shih, and H. C. Kuo, “Improvement in uniformity of emission by ZrO₂ nano-particles for white LEDs,” Nanotechnology 23(26), 265201 (2012).
[Crossref] [PubMed]

Chen, K.-J.

Chen, S.

Q. Zhang, C.-F. Wang, L.-T. Ling, and S. Chen, “Fluorescent nanomaterial-derived white light-emitting diodes: what's going on,” J. Mater. Chem. C 2(22), 4358–4373 (2014).
[Crossref]

Cheng, Y.-J.

Chi, G.-C.

Chien, S. H.

H. C. Chen, K. J. Chen, C. C. Lin, C. H. Wang, H. V. Han, H. H. Tsai, H. T. Kuo, S. H. Chien, M. H. Shih, and H. C. Kuo, “Improvement in uniformity of emission by ZrO₂ nano-particles for white LEDs,” Nanotechnology 23(26), 265201 (2012).
[Crossref] [PubMed]

Chien, S.-H.

Cho, J.

J. Cho, E. F. Schubert, and J. K. Kim, “Efficiency droop in light‐emitting diodes: Challenges and countermeasures,” Laser. Photonics. Rev. 7(3), 408–421 (2013).
[Crossref]

J. K. Kim, H. Luo, E. F. Schubert, J. Cho, C. Sone, and Y. Park, “Strongly enhanced phosphor efficiency in GaInN white light-emitting diodes using remote phosphor configuration and diffuse reflector cup,” Jpn. J. Appl. Phys. 44(21), L649–L651 (2005).
[Crossref]

Deguchi, K.

M. Yamada, T. Mitani, Y. Narukawa, S. Shioji, I. Niki, S. Sonobe, K. Deguchi, M. Sano, and T. Mukai, “InGaN-based near-ultraviolet and blue-light-emitting diodes with high external quantum efficiency using a patterned sapphire substrate and a mesh electrode,” Jpn. J. Appl. Phys. 41(Part 2, No. 12B), L1431–L1433 (2002).
[Crossref]

Denault, K. A.

S. E. Brinkley, N. Pfaff, K. A. Denault, Z. Zhang, H. B. Hintzen, R. Seshadri, S. Nakamura, and S. P. DenBaars, “Robust thermal performance of Sr2Si5N8: Eu2+: An efficient red emitting phosphor for light emitting diode based white lighting,” Appl. Phys. Lett. 99, 241106 (2011).
[Crossref]

DenBaars, S. P.

S. E. Brinkley, N. Pfaff, K. A. Denault, Z. Zhang, H. B. Hintzen, R. Seshadri, S. Nakamura, and S. P. DenBaars, “Robust thermal performance of Sr2Si5N8: Eu2+: An efficient red emitting phosphor for light emitting diode based white lighting,” Appl. Phys. Lett. 99, 241106 (2011).
[Crossref]

S. Pimputkar, J. S. Speck, S. P. DenBaars, and S. Nakamura, “Prospects for LED lighting,” Nat. Photonics 3(4), 180–182 (2009).
[Crossref]

Dhoble, S.

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).
[Crossref]

Do, Y. R.

Gessmann, T.

K.-S. Kim, T. Gessmann, H. Luo, and E. F. Schubert, “GaInN light-emitting diodes with RuO 2/SiO 2/Ag omni-directional reflector,” Appl. Phys. Lett. 84(22), 4508–4510 (2004).
[Crossref]

Gu, Z.

X. Li, J. D. Budai, F. Liu, J. Y. Howe, J. Zhang, X.-J. Wang, Z. Gu, C. Sun, R. S. Meltzer, and Z. Pan, “New yellow Ba0.93Eu0.07Al2O4 phosphor for warm-white light-emitting diodes through single-emitting-center conversion,” Light: Science amd Applications 2(1), e50 (2013).
[Crossref]

Han, H. V.

H. C. Chen, K. J. Chen, C. C. Lin, C. H. Wang, H. V. Han, H. H. Tsai, H. T. Kuo, S. H. Chien, M. H. Shih, and H. C. Kuo, “Improvement in uniformity of emission by ZrO₂ nano-particles for white LEDs,” Nanotechnology 23(26), 265201 (2012).
[Crossref] [PubMed]

Hartmann, P.

Hintzen, H. B.

S. E. Brinkley, N. Pfaff, K. A. Denault, Z. Zhang, H. B. Hintzen, R. Seshadri, S. Nakamura, and S. P. DenBaars, “Robust thermal performance of Sr2Si5N8: Eu2+: An efficient red emitting phosphor for light emitting diode based white lighting,” Appl. Phys. Lett. 99, 241106 (2011).
[Crossref]

Hohenester, U.

Howe, J. Y.

X. Li, J. D. Budai, F. Liu, J. Y. Howe, J. Zhang, X.-J. Wang, Z. Gu, C. Sun, R. S. Meltzer, and Z. Pan, “New yellow Ba0.93Eu0.07Al2O4 phosphor for warm-white light-emitting diodes through single-emitting-center conversion,” Light: Science amd Applications 2(1), e50 (2013).
[Crossref]

Huang, K.-C.

Hung, C.-W.

Iwasa, N.

S. Nakamura, T. Mukai, M. Senoh, and N. Iwasa, “Thermal annealing effects on p-type Mg-doped GaN films,” Jpn. J. Appl. Phys. 31(Part 2, No. 2B), L139–L142 (1992).
[Crossref]

Katsuda, H.

Y. Kawaguchi, K. Nishizono, J.-S. Lee, and H. Katsuda, “Light extraction simulation of surface-textured light-emitting diodes by finite-difference time-domain method and ray-tracing method,” Jpn. J. Appl. Phys. 46(1), 31–34 (2007).
[Crossref]

Kawaguchi, Y.

Y. Kawaguchi, K. Nishizono, J.-S. Lee, and H. Katsuda, “Light extraction simulation of surface-textured light-emitting diodes by finite-difference time-domain method and ray-tracing method,” Jpn. J. Appl. Phys. 46(1), 31–34 (2007).
[Crossref]

Kim, J. K.

J. Cho, E. F. Schubert, and J. K. Kim, “Efficiency droop in light‐emitting diodes: Challenges and countermeasures,” Laser. Photonics. Rev. 7(3), 408–421 (2013).
[Crossref]

E. F. Schubert, J. K. Kim, H. Luo, and J. Xi, “Solid-state lighting—a benevolent technology,” Rep. Prog. Phys. 69(12), 3069–3099 (2006).
[Crossref]

J. K. Kim, H. Luo, E. F. Schubert, J. Cho, C. Sone, and Y. Park, “Strongly enhanced phosphor efficiency in GaInN white light-emitting diodes using remote phosphor configuration and diffuse reflector cup,” Jpn. J. Appl. Phys. 44(21), L649–L651 (2005).
[Crossref]

Kim, K.-S.

K.-S. Kim, T. Gessmann, H. Luo, and E. F. Schubert, “GaInN light-emitting diodes with RuO 2/SiO 2/Ag omni-directional reflector,” Appl. Phys. Lett. 84(22), 4508–4510 (2004).
[Crossref]

Kim, V. K.

V. K. Kim, A. Zakharov, and V. Chashchin, “Luminophores Based on Aluminum Yttrium Garnet (Review),” Glass. Ceram. 71(1-2), 64–67 (2014).
[Crossref]

Kuo, H. C.

H. C. Chen, K. J. Chen, C. C. Lin, C. H. Wang, H. V. Han, H. H. Tsai, H. T. Kuo, S. H. Chien, M. H. Shih, and H. C. Kuo, “Improvement in uniformity of emission by ZrO₂ nano-particles for white LEDs,” Nanotechnology 23(26), 265201 (2012).
[Crossref] [PubMed]

Kuo, H. T.

H. C. Chen, K. J. Chen, C. C. Lin, C. H. Wang, H. V. Han, H. H. Tsai, H. T. Kuo, S. H. Chien, M. H. Shih, and H. C. Kuo, “Improvement in uniformity of emission by ZrO₂ nano-particles for white LEDs,” Nanotechnology 23(26), 265201 (2012).
[Crossref] [PubMed]

Kuo, H.-C.

Lai, T.-H.

Lee, C.-Y.

Lee, J.-S.

Y. Kawaguchi, K. Nishizono, J.-S. Lee, and H. Katsuda, “Light extraction simulation of surface-textured light-emitting diodes by finite-difference time-domain method and ray-tracing method,” Jpn. J. Appl. Phys. 46(1), 31–34 (2007).
[Crossref]

Leiner, C.

Li, C.

Z.-Y. Liu, C. Li, B.-H. Yu, Y.-H. Wang, and H.-B. Niu, “Uniform white emission of WLEDs realized by multilayer phosphor with pyramidal shape and inversed concentration distribution,” IEEE Photonic. Tech. L. 24(17), 1558–1560 (2012).
[Crossref]

Li, X.

X. Li, J. D. Budai, F. Liu, J. Y. Howe, J. Zhang, X.-J. Wang, Z. Gu, C. Sun, R. S. Meltzer, and Z. Pan, “New yellow Ba0.93Eu0.07Al2O4 phosphor for warm-white light-emitting diodes through single-emitting-center conversion,” Light: Science amd Applications 2(1), e50 (2013).
[Crossref]

Lin, C. C.

K.-J. Chen, H.-C. Chen, M.-H. Shih, C.-H. Wang, H.-H. Tsai, S.-H. Chien, C. C. Lin, and H.-C. Kuo, “Enhanced Luminous Efficiency of WLEDs Using a Dual-Layer Structure of the Remote Phosphor Package,” J. Lightwave Technol. 31(12), 1941–1945 (2013).
[Crossref]

H. C. Chen, K. J. Chen, C. C. Lin, C. H. Wang, H. V. Han, H. H. Tsai, H. T. Kuo, S. H. Chien, M. H. Shih, and H. C. Kuo, “Improvement in uniformity of emission by ZrO₂ nano-particles for white LEDs,” Nanotechnology 23(26), 265201 (2012).
[Crossref] [PubMed]

Lin, C.-C.

Lin, D.-W.

Ling, L.-T.

Q. Zhang, C.-F. Wang, L.-T. Ling, and S. Chen, “Fluorescent nanomaterial-derived white light-emitting diodes: what's going on,” J. Mater. Chem. C 2(22), 4358–4373 (2014).
[Crossref]

Liu, C.-Y.

Liu, F.

X. Li, J. D. Budai, F. Liu, J. Y. Howe, J. Zhang, X.-J. Wang, Z. Gu, C. Sun, R. S. Meltzer, and Z. Pan, “New yellow Ba0.93Eu0.07Al2O4 phosphor for warm-white light-emitting diodes through single-emitting-center conversion,” Light: Science amd Applications 2(1), e50 (2013).
[Crossref]

Liu, S.

Liu, Z.

Liu, Z.-Y.

Z.-Y. Liu, C. Li, B.-H. Yu, Y.-H. Wang, and H.-B. Niu, “Uniform white emission of WLEDs realized by multilayer phosphor with pyramidal shape and inversed concentration distribution,” IEEE Photonic. Tech. L. 24(17), 1558–1560 (2012).
[Crossref]

Luo, H.

E. F. Schubert, J. K. Kim, H. Luo, and J. Xi, “Solid-state lighting—a benevolent technology,” Rep. Prog. Phys. 69(12), 3069–3099 (2006).
[Crossref]

J. K. Kim, H. Luo, E. F. Schubert, J. Cho, C. Sone, and Y. Park, “Strongly enhanced phosphor efficiency in GaInN white light-emitting diodes using remote phosphor configuration and diffuse reflector cup,” Jpn. J. Appl. Phys. 44(21), L649–L651 (2005).
[Crossref]

K.-S. Kim, T. Gessmann, H. Luo, and E. F. Schubert, “GaInN light-emitting diodes with RuO 2/SiO 2/Ag omni-directional reflector,” Appl. Phys. Lett. 84(22), 4508–4510 (2004).
[Crossref]

Luo, X.

McKittrick, J.

J. McKittrick and L. E. Shea-Rohwer, “Review: Down Conversion Materials for Solid‐State Lighting,” J. Am. Ceram. Soc. 97(5), 1327–1352 (2014).
[Crossref]

Meltzer, R. S.

X. Li, J. D. Budai, F. Liu, J. Y. Howe, J. Zhang, X.-J. Wang, Z. Gu, C. Sun, R. S. Meltzer, and Z. Pan, “New yellow Ba0.93Eu0.07Al2O4 phosphor for warm-white light-emitting diodes through single-emitting-center conversion,” Light: Science amd Applications 2(1), e50 (2013).
[Crossref]

Mitani, T.

M. Yamada, T. Mitani, Y. Narukawa, S. Shioji, I. Niki, S. Sonobe, K. Deguchi, M. Sano, and T. Mukai, “InGaN-based near-ultraviolet and blue-light-emitting diodes with high external quantum efficiency using a patterned sapphire substrate and a mesh electrode,” Jpn. J. Appl. Phys. 41(Part 2, No. 12B), L1431–L1433 (2002).
[Crossref]

Mukai, T.

M. Yamada, T. Mitani, Y. Narukawa, S. Shioji, I. Niki, S. Sonobe, K. Deguchi, M. Sano, and T. Mukai, “InGaN-based near-ultraviolet and blue-light-emitting diodes with high external quantum efficiency using a patterned sapphire substrate and a mesh electrode,” Jpn. J. Appl. Phys. 41(Part 2, No. 12B), L1431–L1433 (2002).
[Crossref]

S. Nakamura, T. Mukai, M. Senoh, and N. Iwasa, “Thermal annealing effects on p-type Mg-doped GaN films,” Jpn. J. Appl. Phys. 31(Part 2, No. 2B), L139–L142 (1992).
[Crossref]

Nakamura, S.

S. E. Brinkley, N. Pfaff, K. A. Denault, Z. Zhang, H. B. Hintzen, R. Seshadri, S. Nakamura, and S. P. DenBaars, “Robust thermal performance of Sr2Si5N8: Eu2+: An efficient red emitting phosphor for light emitting diode based white lighting,” Appl. Phys. Lett. 99, 241106 (2011).
[Crossref]

S. Pimputkar, J. S. Speck, S. P. DenBaars, and S. Nakamura, “Prospects for LED lighting,” Nat. Photonics 3(4), 180–182 (2009).
[Crossref]

S. Nakamura, T. Mukai, M. Senoh, and N. Iwasa, “Thermal annealing effects on p-type Mg-doped GaN films,” Jpn. J. Appl. Phys. 31(Part 2, No. 2B), L139–L142 (1992).
[Crossref]

Narukawa, Y.

M. Yamada, T. Mitani, Y. Narukawa, S. Shioji, I. Niki, S. Sonobe, K. Deguchi, M. Sano, and T. Mukai, “InGaN-based near-ultraviolet and blue-light-emitting diodes with high external quantum efficiency using a patterned sapphire substrate and a mesh electrode,” Jpn. J. Appl. Phys. 41(Part 2, No. 12B), L1431–L1433 (2002).
[Crossref]

Nemitz, W.

Niki, I.

M. Yamada, T. Mitani, Y. Narukawa, S. Shioji, I. Niki, S. Sonobe, K. Deguchi, M. Sano, and T. Mukai, “InGaN-based near-ultraviolet and blue-light-emitting diodes with high external quantum efficiency using a patterned sapphire substrate and a mesh electrode,” Jpn. J. Appl. Phys. 41(Part 2, No. 12B), L1431–L1433 (2002).
[Crossref]

Nishizono, K.

Y. Kawaguchi, K. Nishizono, J.-S. Lee, and H. Katsuda, “Light extraction simulation of surface-textured light-emitting diodes by finite-difference time-domain method and ray-tracing method,” Jpn. J. Appl. Phys. 46(1), 31–34 (2007).
[Crossref]

Niu, H.-B.

Z.-Y. Liu, C. Li, B.-H. Yu, Y.-H. Wang, and H.-B. Niu, “Uniform white emission of WLEDs realized by multilayer phosphor with pyramidal shape and inversed concentration distribution,” IEEE Photonic. Tech. L. 24(17), 1558–1560 (2012).
[Crossref]

Oh, J. H.

Pan, Z.

X. Li, J. D. Budai, F. Liu, J. Y. Howe, J. Zhang, X.-J. Wang, Z. Gu, C. Sun, R. S. Meltzer, and Z. Pan, “New yellow Ba0.93Eu0.07Al2O4 phosphor for warm-white light-emitting diodes through single-emitting-center conversion,” Light: Science amd Applications 2(1), e50 (2013).
[Crossref]

Park, Y.

J. K. Kim, H. Luo, E. F. Schubert, J. Cho, C. Sone, and Y. Park, “Strongly enhanced phosphor efficiency in GaInN white light-emitting diodes using remote phosphor configuration and diffuse reflector cup,” Jpn. J. Appl. Phys. 44(21), L649–L651 (2005).
[Crossref]

Pfaff, N.

S. E. Brinkley, N. Pfaff, K. A. Denault, Z. Zhang, H. B. Hintzen, R. Seshadri, S. Nakamura, and S. P. DenBaars, “Robust thermal performance of Sr2Si5N8: Eu2+: An efficient red emitting phosphor for light emitting diode based white lighting,” Appl. Phys. Lett. 99, 241106 (2011).
[Crossref]

Pimputkar, S.

S. Pimputkar, J. S. Speck, S. P. DenBaars, and S. Nakamura, “Prospects for LED lighting,” Nat. Photonics 3(4), 180–182 (2009).
[Crossref]

Sano, M.

M. Yamada, T. Mitani, Y. Narukawa, S. Shioji, I. Niki, S. Sonobe, K. Deguchi, M. Sano, and T. Mukai, “InGaN-based near-ultraviolet and blue-light-emitting diodes with high external quantum efficiency using a patterned sapphire substrate and a mesh electrode,” Jpn. J. Appl. Phys. 41(Part 2, No. 12B), L1431–L1433 (2002).
[Crossref]

Schmidt, V.

C. Leiner, S. Schweitzer, V. Schmidt, M. Belegratis, F.-P. Wenzl, P. Hartmann, U. Hohenester, and C. Sommer, “Multi-scale simulation of an optical device using a novel approach for combining ray-tracing and FDTD,” Proc. SPIE 8781, 87810Z (2013).
[Crossref]

Schubert, E. F.

J. Cho, E. F. Schubert, and J. K. Kim, “Efficiency droop in light‐emitting diodes: Challenges and countermeasures,” Laser. Photonics. Rev. 7(3), 408–421 (2013).
[Crossref]

E. F. Schubert, J. K. Kim, H. Luo, and J. Xi, “Solid-state lighting—a benevolent technology,” Rep. Prog. Phys. 69(12), 3069–3099 (2006).
[Crossref]

J. K. Kim, H. Luo, E. F. Schubert, J. Cho, C. Sone, and Y. Park, “Strongly enhanced phosphor efficiency in GaInN white light-emitting diodes using remote phosphor configuration and diffuse reflector cup,” Jpn. J. Appl. Phys. 44(21), L649–L651 (2005).
[Crossref]

K.-S. Kim, T. Gessmann, H. Luo, and E. F. Schubert, “GaInN light-emitting diodes with RuO 2/SiO 2/Ag omni-directional reflector,” Appl. Phys. Lett. 84(22), 4508–4510 (2004).
[Crossref]

Schweitzer, S.

Senoh, M.

S. Nakamura, T. Mukai, M. Senoh, and N. Iwasa, “Thermal annealing effects on p-type Mg-doped GaN films,” Jpn. J. Appl. Phys. 31(Part 2, No. 2B), L139–L142 (1992).
[Crossref]

Seshadri, R.

S. E. Brinkley, N. Pfaff, K. A. Denault, Z. Zhang, H. B. Hintzen, R. Seshadri, S. Nakamura, and S. P. DenBaars, “Robust thermal performance of Sr2Si5N8: Eu2+: An efficient red emitting phosphor for light emitting diode based white lighting,” Appl. Phys. Lett. 99, 241106 (2011).
[Crossref]

Shea-Rohwer, L. E.

J. McKittrick and L. E. Shea-Rohwer, “Review: Down Conversion Materials for Solid‐State Lighting,” J. Am. Ceram. Soc. 97(5), 1327–1352 (2014).
[Crossref]

Sher, C.-W.

Shih, M. H.

H. C. Chen, K. J. Chen, C. C. Lin, C. H. Wang, H. V. Han, H. H. Tsai, H. T. Kuo, S. H. Chien, M. H. Shih, and H. C. Kuo, “Improvement in uniformity of emission by ZrO₂ nano-particles for white LEDs,” Nanotechnology 23(26), 265201 (2012).
[Crossref] [PubMed]

Shih, M.-H.

Shioji, S.

M. Yamada, T. Mitani, Y. Narukawa, S. Shioji, I. Niki, S. Sonobe, K. Deguchi, M. Sano, and T. Mukai, “InGaN-based near-ultraviolet and blue-light-emitting diodes with high external quantum efficiency using a patterned sapphire substrate and a mesh electrode,” Jpn. J. Appl. Phys. 41(Part 2, No. 12B), L1431–L1433 (2002).
[Crossref]

Sommer, C.

Sone, C.

J. K. Kim, H. Luo, E. F. Schubert, J. Cho, C. Sone, and Y. Park, “Strongly enhanced phosphor efficiency in GaInN white light-emitting diodes using remote phosphor configuration and diffuse reflector cup,” Jpn. J. Appl. Phys. 44(21), L649–L651 (2005).
[Crossref]

Sonobe, S.

M. Yamada, T. Mitani, Y. Narukawa, S. Shioji, I. Niki, S. Sonobe, K. Deguchi, M. Sano, and T. Mukai, “InGaN-based near-ultraviolet and blue-light-emitting diodes with high external quantum efficiency using a patterned sapphire substrate and a mesh electrode,” Jpn. J. Appl. Phys. 41(Part 2, No. 12B), L1431–L1433 (2002).
[Crossref]

Speck, J. S.

S. Pimputkar, J. S. Speck, S. P. DenBaars, and S. Nakamura, “Prospects for LED lighting,” Nat. Photonics 3(4), 180–182 (2009).
[Crossref]

Steckl, A. J.

S. C. Allen and A. J. Steckl, “ELiXIR—Solid-state luminaire with enhanced light extraction by internal reflection,” J. Disp. Technol. 3(2), 155–159 (2007).
[Crossref]

Sun, C.

X. Li, J. D. Budai, F. Liu, J. Y. Howe, J. Zhang, X.-J. Wang, Z. Gu, C. Sun, R. S. Meltzer, and Z. Pan, “New yellow Ba0.93Eu0.07Al2O4 phosphor for warm-white light-emitting diodes through single-emitting-center conversion,” Light: Science amd Applications 2(1), e50 (2013).
[Crossref]

Thejokalyani, N.

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).
[Crossref]

Tsai, H. H.

H. C. Chen, K. J. Chen, C. C. Lin, C. H. Wang, H. V. Han, H. H. Tsai, H. T. Kuo, S. H. Chien, M. H. Shih, and H. C. Kuo, “Improvement in uniformity of emission by ZrO₂ nano-particles for white LEDs,” Nanotechnology 23(26), 265201 (2012).
[Crossref] [PubMed]

Tsai, H.-H.

Wang, C. H.

H. C. Chen, K. J. Chen, C. C. Lin, C. H. Wang, H. V. Han, H. H. Tsai, H. T. Kuo, S. H. Chien, M. H. Shih, and H. C. Kuo, “Improvement in uniformity of emission by ZrO₂ nano-particles for white LEDs,” Nanotechnology 23(26), 265201 (2012).
[Crossref] [PubMed]

Wang, C.-F.

Q. Zhang, C.-F. Wang, L.-T. Ling, and S. Chen, “Fluorescent nanomaterial-derived white light-emitting diodes: what's going on,” J. Mater. Chem. C 2(22), 4358–4373 (2014).
[Crossref]

Wang, C.-H.

Wang, K.

Wang, X.-J.

X. Li, J. D. Budai, F. Liu, J. Y. Howe, J. Zhang, X.-J. Wang, Z. Gu, C. Sun, R. S. Meltzer, and Z. Pan, “New yellow Ba0.93Eu0.07Al2O4 phosphor for warm-white light-emitting diodes through single-emitting-center conversion,” Light: Science amd Applications 2(1), e50 (2013).
[Crossref]

Wang, Y.-H.

Z.-Y. Liu, C. Li, B.-H. Yu, Y.-H. Wang, and H.-B. Niu, “Uniform white emission of WLEDs realized by multilayer phosphor with pyramidal shape and inversed concentration distribution,” IEEE Photonic. Tech. L. 24(17), 1558–1560 (2012).
[Crossref]

Wenzl, F. P.

Wenzl, F.-P.

C. Leiner, S. Schweitzer, F.-P. Wenzl, P. Hartmann, U. Hohenester, and C. Sommer, “A simulation procedure interfacing ray-tracing and finite-difference time-domain methods for a combined simulation of diffractive and refractive optical elements,” J. Lightwave Technol. 32(6), 1054–1062 (2014).
[Crossref]

C. Leiner, S. Schweitzer, V. Schmidt, M. Belegratis, F.-P. Wenzl, P. Hartmann, U. Hohenester, and C. Sommer, “Multi-scale simulation of an optical device using a novel approach for combining ray-tracing and FDTD,” Proc. SPIE 8781, 87810Z (2013).
[Crossref]

Wu, D.

Xi, J.

E. F. Schubert, J. K. Kim, H. Luo, and J. Xi, “Solid-state lighting—a benevolent technology,” Rep. Prog. Phys. 69(12), 3069–3099 (2006).
[Crossref]

Yamada, M.

M. Yamada, T. Mitani, Y. Narukawa, S. Shioji, I. Niki, S. Sonobe, K. Deguchi, M. Sano, and T. Mukai, “InGaN-based near-ultraviolet and blue-light-emitting diodes with high external quantum efficiency using a patterned sapphire substrate and a mesh electrode,” Jpn. J. Appl. Phys. 41(Part 2, No. 12B), L1431–L1433 (2002).
[Crossref]

Yan, E. T.

L. Zong-Tao, T. Yong, L. Zong-Yuan, E. T. Yan, and Z. Ben-Ming, “Detailed Study on Pulse-Sprayed Conformal Phosphor Configurations for LEDs,” J. Disp. Technol. 9(6), 433–440 (2013).
[Crossref]

Yang, S. J.

Yeh, C.-C.

Yong, T.

L. Zong-Tao, T. Yong, L. Zong-Yuan, E. T. Yan, and Z. Ben-Ming, “Detailed Study on Pulse-Sprayed Conformal Phosphor Configurations for LEDs,” J. Disp. Technol. 9(6), 433–440 (2013).
[Crossref]

Yu, B.-H.

Z.-Y. Liu, C. Li, B.-H. Yu, Y.-H. Wang, and H.-B. Niu, “Uniform white emission of WLEDs realized by multilayer phosphor with pyramidal shape and inversed concentration distribution,” IEEE Photonic. Tech. L. 24(17), 1558–1560 (2012).
[Crossref]

Zakharov, A.

V. K. Kim, A. Zakharov, and V. Chashchin, “Luminophores Based on Aluminum Yttrium Garnet (Review),” Glass. Ceram. 71(1-2), 64–67 (2014).
[Crossref]

Zhang, J.

X. Li, J. D. Budai, F. Liu, J. Y. Howe, J. Zhang, X.-J. Wang, Z. Gu, C. Sun, R. S. Meltzer, and Z. Pan, “New yellow Ba0.93Eu0.07Al2O4 phosphor for warm-white light-emitting diodes through single-emitting-center conversion,” Light: Science amd Applications 2(1), e50 (2013).
[Crossref]

Zhang, Q.

Q. Zhang, C.-F. Wang, L.-T. Ling, and S. Chen, “Fluorescent nanomaterial-derived white light-emitting diodes: what's going on,” J. Mater. Chem. C 2(22), 4358–4373 (2014).
[Crossref]

Zhang, Z.

S. E. Brinkley, N. Pfaff, K. A. Denault, Z. Zhang, H. B. Hintzen, R. Seshadri, S. Nakamura, and S. P. DenBaars, “Robust thermal performance of Sr2Si5N8: Eu2+: An efficient red emitting phosphor for light emitting diode based white lighting,” Appl. Phys. Lett. 99, 241106 (2011).
[Crossref]

Zong-Tao, L.

L. Zong-Tao, T. Yong, L. Zong-Yuan, E. T. Yan, and Z. Ben-Ming, “Detailed Study on Pulse-Sprayed Conformal Phosphor Configurations for LEDs,” J. Disp. Technol. 9(6), 433–440 (2013).
[Crossref]

Zong-Yuan, L.

L. Zong-Tao, T. Yong, L. Zong-Yuan, E. T. Yan, and Z. Ben-Ming, “Detailed Study on Pulse-Sprayed Conformal Phosphor Configurations for LEDs,” J. Disp. Technol. 9(6), 433–440 (2013).
[Crossref]

Appl. Opt. (2)

Appl. Phys. Lett. (2)

S. E. Brinkley, N. Pfaff, K. A. Denault, Z. Zhang, H. B. Hintzen, R. Seshadri, S. Nakamura, and S. P. DenBaars, “Robust thermal performance of Sr2Si5N8: Eu2+: An efficient red emitting phosphor for light emitting diode based white lighting,” Appl. Phys. Lett. 99, 241106 (2011).
[Crossref]

K.-S. Kim, T. Gessmann, H. Luo, and E. F. Schubert, “GaInN light-emitting diodes with RuO 2/SiO 2/Ag omni-directional reflector,” Appl. Phys. Lett. 84(22), 4508–4510 (2004).
[Crossref]

Glass. Ceram. (1)

V. K. Kim, A. Zakharov, and V. Chashchin, “Luminophores Based on Aluminum Yttrium Garnet (Review),” Glass. Ceram. 71(1-2), 64–67 (2014).
[Crossref]

IEEE Photonic. Tech. L. (2)

Z.-Y. Liu, C. Li, B.-H. Yu, Y.-H. Wang, and H.-B. Niu, “Uniform white emission of WLEDs realized by multilayer phosphor with pyramidal shape and inversed concentration distribution,” IEEE Photonic. Tech. L. 24(17), 1558–1560 (2012).
[Crossref]

Z. Liu, S. Liu, K. Wang, and X. Luo, “Optical analysis of color distribution in white LEDs with various packaging methods,” IEEE Photonic. Tech. L. 20(24), 2027–2029 (2008).
[Crossref]

J. Am. Ceram. Soc. (1)

J. McKittrick and L. E. Shea-Rohwer, “Review: Down Conversion Materials for Solid‐State Lighting,” J. Am. Ceram. Soc. 97(5), 1327–1352 (2014).
[Crossref]

J. Disp. Technol. (2)

L. Zong-Tao, T. Yong, L. Zong-Yuan, E. T. Yan, and Z. Ben-Ming, “Detailed Study on Pulse-Sprayed Conformal Phosphor Configurations for LEDs,” J. Disp. Technol. 9(6), 433–440 (2013).
[Crossref]

S. C. Allen and A. J. Steckl, “ELiXIR—Solid-state luminaire with enhanced light extraction by internal reflection,” J. Disp. Technol. 3(2), 155–159 (2007).
[Crossref]

J. Lightwave Technol. (2)

J. Mater. Chem. C (1)

Q. Zhang, C.-F. Wang, L.-T. Ling, and S. Chen, “Fluorescent nanomaterial-derived white light-emitting diodes: what's going on,” J. Mater. Chem. C 2(22), 4358–4373 (2014).
[Crossref]

Jpn. J. Appl. Phys. (4)

S. Nakamura, T. Mukai, M. Senoh, and N. Iwasa, “Thermal annealing effects on p-type Mg-doped GaN films,” Jpn. J. Appl. Phys. 31(Part 2, No. 2B), L139–L142 (1992).
[Crossref]

M. Yamada, T. Mitani, Y. Narukawa, S. Shioji, I. Niki, S. Sonobe, K. Deguchi, M. Sano, and T. Mukai, “InGaN-based near-ultraviolet and blue-light-emitting diodes with high external quantum efficiency using a patterned sapphire substrate and a mesh electrode,” Jpn. J. Appl. Phys. 41(Part 2, No. 12B), L1431–L1433 (2002).
[Crossref]

Y. Kawaguchi, K. Nishizono, J.-S. Lee, and H. Katsuda, “Light extraction simulation of surface-textured light-emitting diodes by finite-difference time-domain method and ray-tracing method,” Jpn. J. Appl. Phys. 46(1), 31–34 (2007).
[Crossref]

J. K. Kim, H. Luo, E. F. Schubert, J. Cho, C. Sone, and Y. Park, “Strongly enhanced phosphor efficiency in GaInN white light-emitting diodes using remote phosphor configuration and diffuse reflector cup,” Jpn. J. Appl. Phys. 44(21), L649–L651 (2005).
[Crossref]

Laser. Photonics. Rev. (1)

J. Cho, E. F. Schubert, and J. K. Kim, “Efficiency droop in light‐emitting diodes: Challenges and countermeasures,” Laser. Photonics. Rev. 7(3), 408–421 (2013).
[Crossref]

Light: Science amd Applications (1)

X. Li, J. D. Budai, F. Liu, J. Y. Howe, J. Zhang, X.-J. Wang, Z. Gu, C. Sun, R. S. Meltzer, and Z. Pan, “New yellow Ba0.93Eu0.07Al2O4 phosphor for warm-white light-emitting diodes through single-emitting-center conversion,” Light: Science amd Applications 2(1), e50 (2013).
[Crossref]

Nanotechnology (1)

H. C. Chen, K. J. Chen, C. C. Lin, C. H. Wang, H. V. Han, H. H. Tsai, H. T. Kuo, S. H. Chien, M. H. Shih, and H. C. Kuo, “Improvement in uniformity of emission by ZrO₂ nano-particles for white LEDs,” Nanotechnology 23(26), 265201 (2012).
[Crossref] [PubMed]

Nat. Photonics (1)

S. Pimputkar, J. S. Speck, S. P. DenBaars, and S. Nakamura, “Prospects for LED lighting,” Nat. Photonics 3(4), 180–182 (2009).
[Crossref]

Opt. Express (4)

Opt. Lett. (1)

Proc. SPIE (1)

C. Leiner, S. Schweitzer, V. Schmidt, M. Belegratis, F.-P. Wenzl, P. Hartmann, U. Hohenester, and C. Sommer, “Multi-scale simulation of an optical device using a novel approach for combining ray-tracing and FDTD,” Proc. SPIE 8781, 87810Z (2013).
[Crossref]

Renew. Sustain. Energy Rev. (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).
[Crossref]

Rep. Prog. Phys. (1)

E. F. Schubert, J. K. Kim, H. Luo, and J. Xi, “Solid-state lighting—a benevolent technology,” Rep. Prog. Phys. 69(12), 3069–3099 (2006).
[Crossref]

Other (1)

S. D. Gedney, “Introduction to the Finite-difference Time-domain (FDTD) Method for Electromagnetics,” Synthesis Lectures on Computational Electromagnetics (Academic, 2011).

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Figures (10)

Fig. 1
Fig. 1 (a) Schematic of imprinting of a patterned sapphire substrate (PSS) mold for micropatterned array (MPA) optical film fabrication, (b) photograph of MPA optical film.
Fig. 2
Fig. 2 Atomic force microscopy (AFM, top panel) and scanning electron microscopy (SEM, bottom panel) photographs of the micropatterned array (MPA) structure. (a) Concave cone surface, (b) Convex cone surface. Finite-difference time-domain (FDTD) simulation setups for (c) downward-facing convex-cone MPA, (d) upward-facing convex-cone MPA, (e) downward-facing concave-cone MPA and (f) upward-facing concave-cone MPA.
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.
Fig. 5
Fig. 5 (a) Correlated color temperature (CCT) distributions on the receiving screen, (b) Popt, σCCT, and F values of micropatterned array (MPA) films with different configurations.
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) Popt, σCCT, 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. 9
Fig. 9 (a) Correlated color temperature (CCT) distributions for different diameters of the micropatterned array (MPA) films. (b) Popt, σCCT, and F values for these MPA-film diameters.
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.

Equations (4)

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S = κ ε 0 μ 0 | E | 2
P s ( θ s , φ s )= S ( θ s , φ s ) R 2 sin( θ s )d θ s d φ s
BSDF( θ i , φ i , θ s , φ s )= d L s ( θ s , φ s ) d I i ( θ i , φ i ) = P s /Ω P i cos θ s
F= P opt / σ CCT

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