Single-mode fiber-to-single-mode fiber coupling efficiency and tolerance analysis: comparative study for ball, conic and GRIN rod lens coupling schemes using Zemax Huygen's integration and physical optics calculations

Abstract

In this work, numerical coupling efficiency calculations comparing single-mode fiber (SMF) to SMF coupling schemes using uncoated single ball, conic and graded-index (GRIN) rod lenses are discussed. The reported fiber coupling efficiency (FCE) calculations were performed using Huygens integral and Gaussian beam physical optics propagation (GBPOP) features in Zemax®. The Huygens integral method results indicate that the FCE for ball, conic and GRIN rod single uncoated lenses (without accounting for Fresnel reflection and bulk absorption effects) can reach with the optimal lens and fiber parameters 91.11% (N-BK7 glass), 99.68% (N-BK7 glass) and 96.58%, respectively. In comparison, the calculated FCE for uncoated N-BK7 glass ball lens using the GBPOP method was 87.22% (without accounting for Fresnel reflections and bulk absorption effects). Furthermore, FCE calculations for ball lenses made out of sapphire, fused silica, S-LAH79 and N-LASF9 glass are given. The calculated deviation between the GBPOP and Huygens integral methods is <0.5%. Finally, tolerance analysis for each lens coupling scheme relating FCE to the tilts and the decentering of the lens and the two fibers is provided. The tolerance analysis calculations indicate that decentering of fibers and the single lens has the highest impact on the FCE values. Finally, FCE results suggest that the GRIN lens coupling scheme is the most sensitive scheme to misalignment and the ball lens scheme is the least sensitive to misalignment.