Optimized mode coupling condition for high-efficiency step-index to graded-index multimode fiber fusion splicing

In recent years, graded-index multimode fibers (GRIN-MMFs) have been extensively studied in fields such as beam self-cleaning and geometric parametric instability due to their unique spatiotemporal nonlinear effects. The splicing of step-index fibers (SIFs) to GRIN-MMFs is a critical unresolved engineering issue in fiber technology. However, the different mode field distribution between GRIN-MMFs and conventional SIFs leads to mode mismatch at splicing. Based on the principles of mode field size adaptation and mode matching for GRIN-MMF splicing, this work theoretically analyzes the coupling efficiency of splicing SIFs to GRIN-MMFs. We propose a mode-matching condition under a slight mode-field size mismatch. The condition states that an extremum in splicing efficiency is reached when the normalized frequency VGRIN-MMF = VSIF ​. The highest splicing efficiency obtained in the experimental validation is 97.65% when the condition VGRIN-MMF ≥ VSIF is met. The systematic analysis verifies the optimal fiber parameters and splicing strategy for high-efficiency multimode splicing, providing a theoretical basis and parameter selection method for splicing SIFs to GRIN-MMFs.