Improvement of the coupling efficiency between LEDs and optical fibers

A truncated spherical lens geometry is evaluated for layered lenses with various index profiles to determine power coupling efficiency between an LED and an optical fiber. The equations for the efficiency calculation through multiple boundaries are discussed, and numerical results are presented for optical fibers with numerical aperture values of 0.14, 0.23, and 0.35. The layered Luneburg profile is found to give the highest efficiency when the lens and fiber have a significantly larger size than the LED. The layered Maxwell fisheye profile is most efficient when the lens, fiber, and LED are of similar radius.