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Surface plasmon coupling with radiating dipole for enhancing the emission efficiency of a light-emitting diode

Yang Kuo, Shao-Ying Ting, Che-Hao Liao, Jeng-Jie Huang, Chih-Yen Chen, Chieh Hsieh, Yen-Cheng Lu, Cheng-Yen Chen, Kun-Ching Shen, Chih-Feng Lu, Dong-Ming Yeh, Jyh-Yang Wang, Wen-Hung Chuang, Yean-Woei Kiang, and C. C. Yang

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Abstract

The experimental demonstrations of light-emitting diode (LED) fabrication with surface plasmon (SP) coupling with the radiating dipoles in its quantum wells are first reviewed. The SP coupling with a radiating dipole can create an alternative emission channel through SP radiation for enhancing the effective internal quantum efficiency when the intrinsic non-radiative recombination rate is high, reducing the external quantum efficiency droop effect at high current injection levels, and producing partially polarized LED output by inducing polarization-sensitive SP for coupling. Then, we report the theoretical and numerical study results of SP-dipole coupling based on a simple coupling model between a radiating dipole and the SP induced on a nearby Ag nanoparticle (NP). To include the dipole strength variation effect caused by the field distribution built in the coupling system (the feedback effect), the radiating dipole is represented by a saturable two-level system. The spectral and dipole-NP distance dependencies of dipole strength variation and total radiated power enhancement of the coupling system are demonstrated and interpreted. The results show that the dipole-SP coupling can enhance the total radiated power. The enhancement is particularly effective when the feedback effect is included and hence the dipole strength is increased.

©2011 Optical Society of America

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Figures (12)
Fig. 1
Fig. 1 Geometry of the dipole-NP system, including a spherical Ag NP with radius R centered at the coordinate origin and a radiating dipole located at (0, 0, a), which is represented by an arrow.

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Fig. 2
Fig. 2 Spectral dependencies of | p | / p 0 on wavelength in the case of x-oriented dipole for a = 40, 60, 80, 100, and 120 nm.

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Fig. 3
Fig. 3 Dipole-NP distance dependencies of the maximum | p | / p 0 and the corresponding wavelength in the case of x-oriented dipole.

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Fig. 4
Fig. 4 Spectral dependencies of | p | / p 0 on wavelength in the case of z-oriented dipole for a = 40, 60, 80, 100, and 120 nm.

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Fig. 5
Fig. 5 Dipole-NP distance dependencies of the maximum | p | / p 0 and the corresponding wavelength in the case of z-oriented dipole.

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Fig. 6
Fig. 6 Spectral dependencies of total radiated power enhancement ratio on wavelength in the case of x-oriented dipole for a = 40, 60, 80, 100, and 120 nm.

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Fig. 7
Fig. 7 Dipole-NP distance dependencies of the maximum total radiated power enhancement ratio and the corresponding wavelength in the case of x-oriented dipole. Both the results under the conditions with the feedback effect (wF) and without this effect (w/oF) are plotted.

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Fig. 8
Fig. 8 Spectral dependencies of total radiated power enhancement ratio on wavelength in the case of z-oriented dipole for a = 40, 60, 80, 100, and 120 nm.

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Fig. 9
Fig. 9 Dipole-NP distance dependencies of the maximum total radiated power enhancement ratio and the corresponding wavelength in the case of z-oriented dipole. Both the results under the conditions with the feedback effect (wF) and without this effect (w/oF) are plotted.

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Fig. 10
Fig. 10 Spectral dependencies of g(λ) for the cases of x- and z-oriented dipoles at a = 40 nm.

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Fig. 11
Fig. 11 Radiation patterns of the dipole-NP system in the case of x-oriented dipole at the wavelengths of 520.7 ((a) and (b)), 571.2 ((c) and (d)), and 610 nm ((e) and (f)) when a is equal to 40 nm. Parts (a), (c), and (e) ((b), (d), and (f)) demonstrate the patterns when the azimuth angle is 0 (π/2). Three radiation patterns are plotted in each part, including the cases with the feedback effect (black solid curve) and without the feedback effect (blue dashed curve), and the case of the dipole alone (red dash-dotted curve). The two arrows of opposite orientations in each part represent the radiating dipole and the dominating mirror dipole of LSP resonance in the Ag NP.

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Fig. 12
Fig. 12 Radiation patterns of the dipole-NP system in the case of z-oriented dipole at 450 (a), 523.6 (b), 587.2 (c), and 634.7 nm (d) when a = 40 nm. In this situation, the two effective dipoles are roughly in the same orientation.

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Equations (9)

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E → ( s ) = z ^ p ¯ z E 0 f z
E → ( s ) = x ^ p ¯ x E 0 f x
f z = ∑ n = 1 ∞ n ( n + 1 ) a n h n ( 1 ) ( k b a ) ,
f x = ∑ n = 1 ∞ 2 n + 1 2 { α n ( d r h n ( 1 ) ( k b r ) d r ) r = a + β n h n ( 1 ) ( k b a ) } ,
a n = − i ( 2 n + 1 ) k b a h n ( 1 ) ( k b a ) ( ε ¯ j n ( k m R ) ( d r j n ( k b r ) d r ) | r = R − j n ( k b R ) ( d r j n ( k m r ) d r ) | r = R ) ( ε ¯ j n ( k m R ) ( d r h n ( 1 ) ( k b r ) d r ) | r = R − h n ( 1 ) ( k b R ) ( d r j n ( k m r ) d r ) | r = R ) ,
α n = − i k b a ( d r h n ( 1 ) ( k b r ) d r ) | r = a { ε ¯ ( d r j n ( k b r ) d r ) | r = R j n ( k m R ) − j n ( k b R ) ( d r j n ( k m r ) d r ) | r = R ε ¯ ( d r h n ( 1 ) ( k b r ) d r ) | r = R j n ( k m R ) − h n ( 1 ) ( k b R ) ( d r j n ( k m r ) d r ) | r = R } ,
β n = − i k b 3 a 3 h n ( 1 ) ( k b a ) { ( d r j n ( k b r ) d r ) | r = R j n ( k m R ) − j n ( k b R ) ( d r j n ( k m r ) d r ) | r = R ( d r h n ( 1 ) ( k b r ) d r ) | r = R j n ( k m R ) − h n ( 1 ) ( k b R ) ( d r j n ( k m r ) d r ) | r = R } ,
ζ = | f i | | 1 + A f i 1 + B ζ 2 | .
p i = p 0 1 + A f i 1 + B ζ 2 .
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