Mode-field-half-widths of two kinds of planar single-mode waveguides

In this paper, we derive the analytic formulae of the Laplacian mode-field-half-width (MFHW) and the near-field second moment MFHW for nonsymmetric step-index planar single mode optical waveguides and symmetric planar single mode optical waveguides with the Epstein-index.<>