Theoretical Capture Efficiency

The intensity of light emitted by an LED is greatest in the direction perpendicular to its surface. The EZ290 data sheet shows the irradiance of the LED varying approximately as the cosine of the angle from the normal to the LED surface. If we place a fiber with numerical aperture a above the LED, so that it is perpendicular to the LED surface, and the fiber is large enough that all the light emitted by the LED enters the core of the fiber, we see that light within an angle φ = arcsin(a) of the fiber axis will propagate by total internal reflection down the length of the fiber. The following calculation shows how the fraction of the LED power output propagating down the fiber will vary with φ

We have fibers with numerical aperture 0.37, for which we obtain φ = 22°. Of the light entering the core of such a fiber from the LED, we expect only 14% to propagate down the fiber. If the fiber is too small in diameter to cover the entire LED surface we expect our capture efficiency will be even lower.