Coupling of a laser diode to single-mode fiber with an upside-down tapered lens end

We present in detail a simple analysis of the coupling efficiency and possible transverse and angular misalignment losses of a laser diode to single-mode, step-index fiber excitation with an upside-down tapered lens (UDTL) end, drawn by molding the end of a step-index fiber. The analysis employs our recently formulated ABCD matrix for an UDTL and has the advantage of simplicity compared with complicated methods involving cumbersome numerical integrations. Both the analysis and the results should be useful in designing coupling optics that use such lenses in the context of probable misalignments.