Coupling of spherical-surfaced LED and spherical-ended fiber

Abstract
The coupling of a spherical‐surfaced LED and a spherical‐ended fiber is analyzed using a model in which a light source and an aperture stop are on the anterior and posterior focal planes, respectively. The launching efficiency is defined as the ratio of the power launched into a fiber to the optical power generated in the LED. The efficiencies for step‐ and graded‐index fibers are derived. Maximum efficiency can be obtained when d0=dc, where d0 is the emitting diameter and dc is the critical diameter defined by the focal length and the critical angle of the fiber. When d0?dc, the ratio χ of improvement in the efficiency for a spherical‐surfaced LED to that for a flat LED is approximately proportional to the square of the lateral magnification β, which is the image diameter divided by d0. χ?β2 is confirmed experimentally with couplings using spherical‐surfaced and flat LED’s.

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