General formula for coupling-loss characterization of single-mode fiber collimators by use of gradient-index rod lenses

A general formula for determining the coupling loss between two single-made fiber collimators with the simultaneous existence of separation, lateral o ffset and angular tilt misalignments, and spot-size mismatch is theoretical ly derived by use of the Gaussian held approximation. Based on this general formula, the formulas for coupling losses that are due to the misalignment of insert separation, lateral offset, and angular tilt are given. The form ula for the coupling loss that is due to Gaussian spot-size mismatch of two single-mode collimators is also given. Good agreement between these formul as and experimental results is demonstrated with gradient-index rod lens-ba sed fiber collimators operating in the 1300 nm band. (C) 1999 Optical Socie ty of America.