Abstract

In this paper formulas are derived that describe the optical efficiency of an LED package consisting of a hemispherical lens placed on the cylinder. The dependence of this efficiency on the H/R ratio and the epoxy coefficient of refraction is calculated. In calculations it is assumed that the semiconductor chip, believed to be the point source of radiation, is mounted on the optical axis of the LED package, and the absorption of nonscattering epoxy is small. As an example, the optical efficiency of the LED with H/R = 2.5 and n = 1.5 is calculated: it is equal to 37.4%.

© 1982 Optical Society of America

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References

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  1. A. M. Kontkiewicz, “Calculations of the Angular Characteristics of Light-Emitting Diodes,” Proceedings of ITE36 (1977) (in Polish).

1977

A. M. Kontkiewicz, “Calculations of the Angular Characteristics of Light-Emitting Diodes,” Proceedings of ITE36 (1977) (in Polish).

Kontkiewicz, A. M.

A. M. Kontkiewicz, “Calculations of the Angular Characteristics of Light-Emitting Diodes,” Proceedings of ITE36 (1977) (in Polish).

Proceedings of ITE

A. M. Kontkiewicz, “Calculations of the Angular Characteristics of Light-Emitting Diodes,” Proceedings of ITE36 (1977) (in Polish).

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Figures (5)

Fig. 1
Fig. 1

Light-emitting diode package.

Fig. 2
Fig. 2

Dependence of the critical H/R ratio [(H/R)cr] on the coefficient of refraction n.

Fig. 3
Fig. 3

Dependence of angle Δθ on H/R ratio (see text).

Fig. 4
Fig. 4

Dependence of the M function on the coefficient of refraction n.

Fig. 5
Fig. 5

Transmitting factor calculated for H/R = 2.5 and n = 1.5

Equations (25)

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α cr = arc sin ( 1 / n ) ,
α = arc sin [ ( H R 1 ) sin θ ]
( H R 1 ) sin θ > 1 n ,
θ s = arc sin R [ R 2 + ( H R ) ] 2 ,
( H / R 1 ) sin θ s = 1 / n ,
( H / R ) cr = 1 + 1 ( n 2 1 ) 1 / 2 ,
T 4 n ( n + 1 ) 2 .
R 0 ( n 1 ) 2 ( n + 1 ) 2 .
θ < θ 0 = arc sin 1 n ( H / R 1 ) .
θ 0 < θ < θ 1 = arc tan 1 H / R 1
θ 1 < θ < θ 2 = 90 ° α cr .
θ 1 < θ < θ 3 = arc tan 3 H / R 1 .
θ < max ( θ 2 , θ 3 )
θ 1 < θ < θ 1 + Δ θ = θ 4 ,
η 1 = T 0 2 π d φ 0 θ 1 I ( θ ) sin θ d θ 0 2 π d φ 0 π / 2 I ( θ ) sin θ d θ ,
η 1 = T 0 2 π d φ 0 θ 0 I ( θ ) sin θ d θ 0 2 π d φ 0 π / 2 I ( θ ) sin θ d θ .
η 1 = 0 2 π d φ 0 θ 1 L 1 ( θ ) I ( θ ) sin θ d θ 0 2 π d φ 0 π / 2 I ( θ ) sin θ d θ ,
L 1 ( θ ) = T η ( θ 0 θ ) .
η ( x ) = 0 for x < 0 1 for x > 0 .
η 2 = 0 2 π d φ θ 1 π / 2 L 2 ( θ ) I ( θ ) sin θ d θ 0 2 π d φ 0 π / 2 I ( θ ) sin θ d θ ,
L 2 ( θ ) = T [ η ( θ 2 θ ) η ( θ θ 4 ) + R 0 η ( θ θ 2 ) η ( θ θ 4 η ( θ 3 θ ) ] .
η = 0 2 π d φ 0 π / 2 L ( θ ) I ( θ ) sin θ d θ 0 2 π d φ 0 π / 2 I ( θ ) sin θ d θ ,
L ( θ ) = L 1 ( θ ) + L 2 ( θ ) .
η L = 0 π / 2 L ( θ ) sin 2 θ d θ .
η L = 0.96 0 26.39 ° sin 2 θ d θ + 37.66 ° 48.19 ° sin 2 θ d θ + 0.04 48.19 ° 63.44 ° sin 2 θ d θ = 0.190 + 0.175 + 0.009 = 0.374 .

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