Coupling efficiency of single-mode fiber components using GRIN-rod lenses

This article analyzes the characteristics of single-mode fiber (SMF) components using graded-index-rod (GRIN-rod) lenses. The coupling efficiency of the SMF to GRIN-rod lens to SMF coupling system is derived in the general case. The problem is simplified by using the reciprocal field method. All solutions are in closed form. It is found that SMF position tolerance is about 3 μm; the angular tolerance is about 1°. The GRIN-rod lens position tolerance is much less critical while the angular tolerance is extremely small. These tolerances could be much less critical if the fiber is kept near the GRIN-rod lens axis.