Effect of radius of curvature of a convex interface on the light output power of light-emitting diode package with double-layered encapsulant

We investigate the effect of the radius of curvature, R, of a convex interface on the light output power of an light-emitting diode package. The encapsulation layers consist of two layers, with refractive indices of 1.41 and 1.53. By using a geometrical calculation and 3-D ray-tracing simulation, we quantify the effect of R on the light extraction efficiency (LEEec) by examining the escape cone and the Fresnel reflection loss. The increase in the LEEec is explained with respect to the change of the incident angle and the re-extraction of the reflected rays at the curved interface.