Relation between three mode field half-width definitions for single-mode planar waveguide and application to splice-loss evaluation

Two moment-related definitions for the mode-field half-width (MFHW) of a planar optical waveguide with an arbitrary index profile are proposed, and their relationships to the MFHW based on a Gaussian least-mean-square fit are derived. Various formulas for calculating splice loss for two identical planar waveguides under transverse offset and axial tilt are presented, including accurate formulas based on transmission coefficient, approximate formulas based on various MFHW definitions, and error formulas for using them both. Numerical data for symmetrical step-index slab waveguides show that for small misalignments, splice losses calculated from moment MFHWs are more accurate than those from the Gaussian MFHW, and error formulas can be used to obtain conservative estimates