Abstract

Light extraction efficiency (LEE) from a light-emitting diode is commonly referenced against an isotropic radiator within a dense dielectric medium. However, this description is not necessarily accurate for photonic devices with directional source elements. We therefore derive exact solutions for the LEE of a directive radiating source next to a planar dielectric boundary, accounting for any Fresnel reflections at the interface. These results can be used to validate numerical simulations and to quantify the baseline LEE for different source models. Four variations are explored, including the isotropic radiator, parallel and perpendicular orientations of the Hertzian dipole, and Lambertian scattering. Due to index matching, Fresnel reflections are generally negligible for materials with large escape cones, but reduce LEE by 20 % or more when critical angle is below 25°.

© 2012 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. I. Schnitzer, E. Yablonovitch, C. Caneau, T. J. Gmitter, and A. Scherer, “30 % external quantum efficiency from surface textured, thin-film light-emitting diodes,” Appl. Phys. Lett.63(16), 2174–2176 (1993).
    [CrossRef]
  2. T. Fujii, Y. Gao, R. Sharma, E. L. Hu, S. P. DenBaars, and S. Nakamura, “Increase in the extraction efficiency of GaN-based light-emitting diodes via surface roughening,” Appl. Phys. Lett.84(6), 855–857 (2004).
    [CrossRef]
  3. A. David, H. Benisty, and C. Weisbuch, “Optimization of light-diffracting photonic-crystals for high extraction efficiency LEDs,” J. Disp. Technol.3(2), 133–148 (2007).
    [CrossRef]
  4. C. Wiesmann, K. Bergenek, N. Linder, and U. T. Schwarz, “Photonic crystal LEDs - designing light extraction,” Laser & Photon. Rev.3(2), 262–286 (2009).
    [CrossRef]
  5. J. Vuckovic, M. Loncar, and A. Scherer, “Surface plasmon enhanced light-emitting diode,” IEEE J. Quant. Electron.36(10), 1131–1144 (2000).
    [CrossRef]
  6. T. Yamasaki, K. Sumioka, and T. Tsutsui, “Organic light-emitting device with an ordered monolayer of silica microspheres as a scattering medium,” Appl. Phys. Lett.76(10), 1243–1245 (2000).
    [CrossRef]
  7. E. F. Schubert, Light-Emitting Diodes (Cambridge University Press, 2006).
    [CrossRef]
  8. M. F. Schubert, S. Chhajed, J. K. Kim, and E. F. Schubert, “Polarization of light emission by 460 nm GaInN/GaN light-emitting diodes grown on (0001) oriented sapphire substrates,” Appl. Phys. Lett.91(5), 051117 (2007).
    [CrossRef]
  9. K. B. Nam, J. Li, M. L. Nakarmi, J. Y. Lin, and H. X. Jiang, “Unique optical properties of AlGaN alloys and related ultraviolet emitters,” Appl. Phys. Lett.84(25), 5264–5266 (2004).
    [CrossRef]
  10. W. Lukosz and R. E. Kunz, “Light emission by magnetic and electric dipoles close to a plane dielectric interface. I. Total radiated power,” J. Opt. Soc. Am.67(12), 1607–1615 (1977).
    [CrossRef]
  11. W. Lukosz and R. E. Kunz, “Light emission by magnetic and electric dipoles close to a plane dielectric interface. II. Radiation patterns of perpendicular oriented dipoles,” J. Opt. Soc. Am.67(12), 1615–1619 (1977).
    [CrossRef]
  12. M. Cui, P. Urbach, and D. K. G. de Boer, “Optimization of light extraction from OLEDs,” Opt. Express15(8), 4398–4409 (2007).
    [CrossRef] [PubMed]
  13. D. H. Staelin, A. W. Morgenthaler, and J. A. Kong, Electromagnetic Waves (Prentice Hall, 1998).
  14. J. D. Jackson, Classical Electrodynamics (Wiley, 1999).
  15. F. T. Ulaby, Fundamentals of Applied Electromagnetics (Prentice Hall, 2007).
  16. J. A. Kong, Electromagnetic Wave Theory (EMW Publishing, 2000).
  17. H. Kikuta, S. Hino, and A. Maruyama, “Estimation method for the light extraction efficiency of light-emitting elements with a rigorous grating diffraction theory,” J. Opt. Soc. Am. A23(5), 1207–1213 (2006).
    [CrossRef]
  18. M. G. Moharam and T. K. Gaylord, “Three-dimensional vector coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am.73(9), 1105–1112 (1983).
    [CrossRef]

2009 (1)

C. Wiesmann, K. Bergenek, N. Linder, and U. T. Schwarz, “Photonic crystal LEDs - designing light extraction,” Laser & Photon. Rev.3(2), 262–286 (2009).
[CrossRef]

2007 (3)

M. F. Schubert, S. Chhajed, J. K. Kim, and E. F. Schubert, “Polarization of light emission by 460 nm GaInN/GaN light-emitting diodes grown on (0001) oriented sapphire substrates,” Appl. Phys. Lett.91(5), 051117 (2007).
[CrossRef]

A. David, H. Benisty, and C. Weisbuch, “Optimization of light-diffracting photonic-crystals for high extraction efficiency LEDs,” J. Disp. Technol.3(2), 133–148 (2007).
[CrossRef]

M. Cui, P. Urbach, and D. K. G. de Boer, “Optimization of light extraction from OLEDs,” Opt. Express15(8), 4398–4409 (2007).
[CrossRef] [PubMed]

2006 (1)

2004 (2)

K. B. Nam, J. Li, M. L. Nakarmi, J. Y. Lin, and H. X. Jiang, “Unique optical properties of AlGaN alloys and related ultraviolet emitters,” Appl. Phys. Lett.84(25), 5264–5266 (2004).
[CrossRef]

T. Fujii, Y. Gao, R. Sharma, E. L. Hu, S. P. DenBaars, and S. Nakamura, “Increase in the extraction efficiency of GaN-based light-emitting diodes via surface roughening,” Appl. Phys. Lett.84(6), 855–857 (2004).
[CrossRef]

2000 (2)

J. Vuckovic, M. Loncar, and A. Scherer, “Surface plasmon enhanced light-emitting diode,” IEEE J. Quant. Electron.36(10), 1131–1144 (2000).
[CrossRef]

T. Yamasaki, K. Sumioka, and T. Tsutsui, “Organic light-emitting device with an ordered monolayer of silica microspheres as a scattering medium,” Appl. Phys. Lett.76(10), 1243–1245 (2000).
[CrossRef]

1993 (1)

I. Schnitzer, E. Yablonovitch, C. Caneau, T. J. Gmitter, and A. Scherer, “30 % external quantum efficiency from surface textured, thin-film light-emitting diodes,” Appl. Phys. Lett.63(16), 2174–2176 (1993).
[CrossRef]

1983 (1)

1977 (2)

Benisty, H.

A. David, H. Benisty, and C. Weisbuch, “Optimization of light-diffracting photonic-crystals for high extraction efficiency LEDs,” J. Disp. Technol.3(2), 133–148 (2007).
[CrossRef]

Bergenek, K.

C. Wiesmann, K. Bergenek, N. Linder, and U. T. Schwarz, “Photonic crystal LEDs - designing light extraction,” Laser & Photon. Rev.3(2), 262–286 (2009).
[CrossRef]

Caneau, C.

I. Schnitzer, E. Yablonovitch, C. Caneau, T. J. Gmitter, and A. Scherer, “30 % external quantum efficiency from surface textured, thin-film light-emitting diodes,” Appl. Phys. Lett.63(16), 2174–2176 (1993).
[CrossRef]

Chhajed, S.

M. F. Schubert, S. Chhajed, J. K. Kim, and E. F. Schubert, “Polarization of light emission by 460 nm GaInN/GaN light-emitting diodes grown on (0001) oriented sapphire substrates,” Appl. Phys. Lett.91(5), 051117 (2007).
[CrossRef]

Cui, M.

David, A.

A. David, H. Benisty, and C. Weisbuch, “Optimization of light-diffracting photonic-crystals for high extraction efficiency LEDs,” J. Disp. Technol.3(2), 133–148 (2007).
[CrossRef]

de Boer, D. K. G.

DenBaars, S. P.

T. Fujii, Y. Gao, R. Sharma, E. L. Hu, S. P. DenBaars, and S. Nakamura, “Increase in the extraction efficiency of GaN-based light-emitting diodes via surface roughening,” Appl. Phys. Lett.84(6), 855–857 (2004).
[CrossRef]

Fujii, T.

T. Fujii, Y. Gao, R. Sharma, E. L. Hu, S. P. DenBaars, and S. Nakamura, “Increase in the extraction efficiency of GaN-based light-emitting diodes via surface roughening,” Appl. Phys. Lett.84(6), 855–857 (2004).
[CrossRef]

Gao, Y.

T. Fujii, Y. Gao, R. Sharma, E. L. Hu, S. P. DenBaars, and S. Nakamura, “Increase in the extraction efficiency of GaN-based light-emitting diodes via surface roughening,” Appl. Phys. Lett.84(6), 855–857 (2004).
[CrossRef]

Gaylord, T. K.

Gmitter, T. J.

I. Schnitzer, E. Yablonovitch, C. Caneau, T. J. Gmitter, and A. Scherer, “30 % external quantum efficiency from surface textured, thin-film light-emitting diodes,” Appl. Phys. Lett.63(16), 2174–2176 (1993).
[CrossRef]

Hino, S.

Hu, E. L.

T. Fujii, Y. Gao, R. Sharma, E. L. Hu, S. P. DenBaars, and S. Nakamura, “Increase in the extraction efficiency of GaN-based light-emitting diodes via surface roughening,” Appl. Phys. Lett.84(6), 855–857 (2004).
[CrossRef]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Wiley, 1999).

Jiang, H. X.

K. B. Nam, J. Li, M. L. Nakarmi, J. Y. Lin, and H. X. Jiang, “Unique optical properties of AlGaN alloys and related ultraviolet emitters,” Appl. Phys. Lett.84(25), 5264–5266 (2004).
[CrossRef]

Kikuta, H.

Kim, J. K.

M. F. Schubert, S. Chhajed, J. K. Kim, and E. F. Schubert, “Polarization of light emission by 460 nm GaInN/GaN light-emitting diodes grown on (0001) oriented sapphire substrates,” Appl. Phys. Lett.91(5), 051117 (2007).
[CrossRef]

Kong, J. A.

D. H. Staelin, A. W. Morgenthaler, and J. A. Kong, Electromagnetic Waves (Prentice Hall, 1998).

J. A. Kong, Electromagnetic Wave Theory (EMW Publishing, 2000).

Kunz, R. E.

Li, J.

K. B. Nam, J. Li, M. L. Nakarmi, J. Y. Lin, and H. X. Jiang, “Unique optical properties of AlGaN alloys and related ultraviolet emitters,” Appl. Phys. Lett.84(25), 5264–5266 (2004).
[CrossRef]

Lin, J. Y.

K. B. Nam, J. Li, M. L. Nakarmi, J. Y. Lin, and H. X. Jiang, “Unique optical properties of AlGaN alloys and related ultraviolet emitters,” Appl. Phys. Lett.84(25), 5264–5266 (2004).
[CrossRef]

Linder, N.

C. Wiesmann, K. Bergenek, N. Linder, and U. T. Schwarz, “Photonic crystal LEDs - designing light extraction,” Laser & Photon. Rev.3(2), 262–286 (2009).
[CrossRef]

Loncar, M.

J. Vuckovic, M. Loncar, and A. Scherer, “Surface plasmon enhanced light-emitting diode,” IEEE J. Quant. Electron.36(10), 1131–1144 (2000).
[CrossRef]

Lukosz, W.

Maruyama, A.

Moharam, M. G.

Morgenthaler, A. W.

D. H. Staelin, A. W. Morgenthaler, and J. A. Kong, Electromagnetic Waves (Prentice Hall, 1998).

Nakamura, S.

T. Fujii, Y. Gao, R. Sharma, E. L. Hu, S. P. DenBaars, and S. Nakamura, “Increase in the extraction efficiency of GaN-based light-emitting diodes via surface roughening,” Appl. Phys. Lett.84(6), 855–857 (2004).
[CrossRef]

Nakarmi, M. L.

K. B. Nam, J. Li, M. L. Nakarmi, J. Y. Lin, and H. X. Jiang, “Unique optical properties of AlGaN alloys and related ultraviolet emitters,” Appl. Phys. Lett.84(25), 5264–5266 (2004).
[CrossRef]

Nam, K. B.

K. B. Nam, J. Li, M. L. Nakarmi, J. Y. Lin, and H. X. Jiang, “Unique optical properties of AlGaN alloys and related ultraviolet emitters,” Appl. Phys. Lett.84(25), 5264–5266 (2004).
[CrossRef]

Scherer, A.

J. Vuckovic, M. Loncar, and A. Scherer, “Surface plasmon enhanced light-emitting diode,” IEEE J. Quant. Electron.36(10), 1131–1144 (2000).
[CrossRef]

I. Schnitzer, E. Yablonovitch, C. Caneau, T. J. Gmitter, and A. Scherer, “30 % external quantum efficiency from surface textured, thin-film light-emitting diodes,” Appl. Phys. Lett.63(16), 2174–2176 (1993).
[CrossRef]

Schnitzer, I.

I. Schnitzer, E. Yablonovitch, C. Caneau, T. J. Gmitter, and A. Scherer, “30 % external quantum efficiency from surface textured, thin-film light-emitting diodes,” Appl. Phys. Lett.63(16), 2174–2176 (1993).
[CrossRef]

Schubert, E. F.

M. F. Schubert, S. Chhajed, J. K. Kim, and E. F. Schubert, “Polarization of light emission by 460 nm GaInN/GaN light-emitting diodes grown on (0001) oriented sapphire substrates,” Appl. Phys. Lett.91(5), 051117 (2007).
[CrossRef]

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

Schubert, M. F.

M. F. Schubert, S. Chhajed, J. K. Kim, and E. F. Schubert, “Polarization of light emission by 460 nm GaInN/GaN light-emitting diodes grown on (0001) oriented sapphire substrates,” Appl. Phys. Lett.91(5), 051117 (2007).
[CrossRef]

Schwarz, U. T.

C. Wiesmann, K. Bergenek, N. Linder, and U. T. Schwarz, “Photonic crystal LEDs - designing light extraction,” Laser & Photon. Rev.3(2), 262–286 (2009).
[CrossRef]

Sharma, R.

T. Fujii, Y. Gao, R. Sharma, E. L. Hu, S. P. DenBaars, and S. Nakamura, “Increase in the extraction efficiency of GaN-based light-emitting diodes via surface roughening,” Appl. Phys. Lett.84(6), 855–857 (2004).
[CrossRef]

Staelin, D. H.

D. H. Staelin, A. W. Morgenthaler, and J. A. Kong, Electromagnetic Waves (Prentice Hall, 1998).

Sumioka, K.

T. Yamasaki, K. Sumioka, and T. Tsutsui, “Organic light-emitting device with an ordered monolayer of silica microspheres as a scattering medium,” Appl. Phys. Lett.76(10), 1243–1245 (2000).
[CrossRef]

Tsutsui, T.

T. Yamasaki, K. Sumioka, and T. Tsutsui, “Organic light-emitting device with an ordered monolayer of silica microspheres as a scattering medium,” Appl. Phys. Lett.76(10), 1243–1245 (2000).
[CrossRef]

Ulaby, F. T.

F. T. Ulaby, Fundamentals of Applied Electromagnetics (Prentice Hall, 2007).

Urbach, P.

Vuckovic, J.

J. Vuckovic, M. Loncar, and A. Scherer, “Surface plasmon enhanced light-emitting diode,” IEEE J. Quant. Electron.36(10), 1131–1144 (2000).
[CrossRef]

Weisbuch, C.

A. David, H. Benisty, and C. Weisbuch, “Optimization of light-diffracting photonic-crystals for high extraction efficiency LEDs,” J. Disp. Technol.3(2), 133–148 (2007).
[CrossRef]

Wiesmann, C.

C. Wiesmann, K. Bergenek, N. Linder, and U. T. Schwarz, “Photonic crystal LEDs - designing light extraction,” Laser & Photon. Rev.3(2), 262–286 (2009).
[CrossRef]

Yablonovitch, E.

I. Schnitzer, E. Yablonovitch, C. Caneau, T. J. Gmitter, and A. Scherer, “30 % external quantum efficiency from surface textured, thin-film light-emitting diodes,” Appl. Phys. Lett.63(16), 2174–2176 (1993).
[CrossRef]

Yamasaki, T.

T. Yamasaki, K. Sumioka, and T. Tsutsui, “Organic light-emitting device with an ordered monolayer of silica microspheres as a scattering medium,” Appl. Phys. Lett.76(10), 1243–1245 (2000).
[CrossRef]

Appl. Phys. Lett. (5)

I. Schnitzer, E. Yablonovitch, C. Caneau, T. J. Gmitter, and A. Scherer, “30 % external quantum efficiency from surface textured, thin-film light-emitting diodes,” Appl. Phys. Lett.63(16), 2174–2176 (1993).
[CrossRef]

T. Fujii, Y. Gao, R. Sharma, E. L. Hu, S. P. DenBaars, and S. Nakamura, “Increase in the extraction efficiency of GaN-based light-emitting diodes via surface roughening,” Appl. Phys. Lett.84(6), 855–857 (2004).
[CrossRef]

M. F. Schubert, S. Chhajed, J. K. Kim, and E. F. Schubert, “Polarization of light emission by 460 nm GaInN/GaN light-emitting diodes grown on (0001) oriented sapphire substrates,” Appl. Phys. Lett.91(5), 051117 (2007).
[CrossRef]

K. B. Nam, J. Li, M. L. Nakarmi, J. Y. Lin, and H. X. Jiang, “Unique optical properties of AlGaN alloys and related ultraviolet emitters,” Appl. Phys. Lett.84(25), 5264–5266 (2004).
[CrossRef]

T. Yamasaki, K. Sumioka, and T. Tsutsui, “Organic light-emitting device with an ordered monolayer of silica microspheres as a scattering medium,” Appl. Phys. Lett.76(10), 1243–1245 (2000).
[CrossRef]

IEEE J. Quant. Electron. (1)

J. Vuckovic, M. Loncar, and A. Scherer, “Surface plasmon enhanced light-emitting diode,” IEEE J. Quant. Electron.36(10), 1131–1144 (2000).
[CrossRef]

J. Disp. Technol. (1)

A. David, H. Benisty, and C. Weisbuch, “Optimization of light-diffracting photonic-crystals for high extraction efficiency LEDs,” J. Disp. Technol.3(2), 133–148 (2007).
[CrossRef]

J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. A (1)

Laser & Photon. Rev. (1)

C. Wiesmann, K. Bergenek, N. Linder, and U. T. Schwarz, “Photonic crystal LEDs - designing light extraction,” Laser & Photon. Rev.3(2), 262–286 (2009).
[CrossRef]

Opt. Express (1)

Other (5)

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

D. H. Staelin, A. W. Morgenthaler, and J. A. Kong, Electromagnetic Waves (Prentice Hall, 1998).

J. D. Jackson, Classical Electrodynamics (Wiley, 1999).

F. T. Ulaby, Fundamentals of Applied Electromagnetics (Prentice Hall, 2007).

J. A. Kong, Electromagnetic Wave Theory (EMW Publishing, 2000).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

A current density J is radiating light from within a dense dielectric medium. Light that falls within the escape cone defined by θc has the potential to escape the LED. The inset shows the surface of integration Ω for evaluating Prad. The exact geometry for Ω is arbitrary, just so long as it encloses the current element defined by J.

Fig. 2
Fig. 2

Intersection between the plane of incidence (POI) and the planar dielectric boundary at z = a. The POI is defined by the vectors and , with a unit normal vector .

Fig. 3
Fig. 3

Light extraction efficiency calculated for both antireflective (AR) and Fresnel reflective (FR) surfaces. The three source conditions are (1) isotropic radiator with equal TE/TM polarization weights, (2) a parallel-oriented Hertzian dipole, and (3) a perpendicularly-oriented Hertzian dipole.

Fig. 4
Fig. 4

Light extraction efficiency for diffuse light from a Lambertian source. The black curve indicates perfect antireflection (AR) while the dashed red curve accounts for Fresnel reflections (FR) at the dielectric interface.

Fig. 5
Fig. 5

Light extraction efficiencies for optically dense dielectrics with shallow critical angle. Black curves indicate perfect antireflection (AR) while the dashed red curves account for Fresnel reflections (FR) at the dielectric interface.

Tables (1)

Tables Icon

Table 1 Percent light extraction efficiencies for some common indices of refraction found in various LEDs. Comparisons are made between perfectly antireflective (AR) surfaces and Fresnel-reflective (FR) surfaces.

Equations (39)

Equations on this page are rendered with MathJax. Learn more.

θ c = sin 1 ( ε r 2 ε r 1 ) ,
S = 1 2 { E × H * } ,
P rad = Ω S ( x , y , a ) d Ω ,
LEE = 1 P rad S ( x , y , a ) z ^ d x d y .
x = a tan θ cos ϕ ,
y = a tan θ sin ϕ .
LEE = 1 P rad 0 2 π 0 π / 2 S ( θ , ϕ ) z ^ ( a 2 sec 2 θ tan θ ) d θ d ϕ .
S t ( θ , ϕ ) = S i ( θ , ϕ ) T ( θ , ϕ ) ,
LEE = 1 P rad 0 2 π 0 π / 2 T ( θ , ϕ ) S i ( θ , ϕ ) z ^ ( a 2 sec 2 θ tan θ ) d θ d ϕ .
LEE = 1 P rad 0 2 π 0 π / 2 T ( θ , ϕ ) S i ( θ , ϕ ) ( a 2 sec θ tan θ ) d θ d ϕ .
G ( θ , ϕ ) = S i ( θ , ϕ ) P rad / 4 π r 2 .
LEE = 1 4 π 0 2 π 0 π / 2 T ( θ , ϕ ) G ( θ , ϕ ) sin θ d θ d ϕ .
T ( θ , ϕ ) = { 1 , θ < θ c 0 , otherwise .
LEE = 1 4 π 0 2 π 0 θ c sin θ d θ d ϕ .
LEE = 1 cos θ c 2 .
J ( r ) = p J 0 δ ( r r 0 ) ,
G ( θ , ϕ ) = 3 2 sin 2 θ .
G | | ( θ , ϕ ) = 3 2 ( 1 sin 2 θ cos 2 ϕ ) .
LEE = 1 2 + 1 16 [ cos ( 3 θ c ) 9 cos θ c ] ,
LEE | | = 1 2 1 32 [ 15 cos θ c + cos ( 3 θ c ) ] .
1 3 ( LEE + 2 LEE | | ) = 1 cos θ c 2 ,
E = E T E + E T M .
cos ψ = | E T E | | E | .
S i = S T E + S T M ,
cos 2 ψ = | S T E | | S i | .
S t = T T E S T E + T T M S T M ,
S t = S i ( T T E cos 2 ψ + T T M sin 2 ψ ) .
T ( θ , ϕ ) = T T E ( θ ) cos 2 ψ + T T M ( θ ) sin 2 ψ .
cos ψ = n ^ e ^ .
n ^ = k ^ × z ^ | k ^ × z ^ | .
r ^ = x ^ sin θ cos ϕ + y ^ sin θ sin ϕ + z ^ cos θ .
n ^ = x ^ sin ϕ y ^ cos ϕ ,
E ( r , θ , ϕ ) = θ ^ j ω μ J 0 sin ( θ ) e j k r 4 π r .
cos ψ = ϕ ^ θ ^ .
E ( r , θ , ϕ ) = ( cos θ cos ϕ θ ^ sin ϕ ϕ ^ ) j ω μ J 0 e j k r 4 π r .
cos ψ = sin ϕ .
G ( θ , ϕ ) = 4 cos θ ( 0 θ π / 2 ) .
LEE = sin 2 θ c .
LEE = 0 θ c [ T T E ( θ ) + T T M ( θ ) ] sin θ cos θ d θ .

Metrics