Coupling efficiency of surface-emitting LED's to single-mode fibers

Using coherent-mode representation, the light emission of a surface-emitting LED (SELED) with a Lambertian far-field and a uniform near-field intensity is expressed by coherent modes. The coupling efficiency of the SELED to a single-mode fiber is calculated as the weighted sum of the coupling efficiencies of the coherent modes to the fiber mode. The absolute maximum achievable efficiency is found to be the inverse of the number of the coherent modes, and is equal to (
\lambda^{2}/\pi A
), where
A
is the LED emission area and λ is the emission wavelength. This efficiency can be obtained by butt coupling if the LED area
A
is about equal to or larger than the fiber mode size. The theoretical prediction agrees well with published experimental data.