Core-mode cutoff for finite-cladding lightguides

Fundamental core-mode `cutoff is a useful concept for tapered `single-mode? lightguides with either a finite cladding surrounded by a lower-index external medium (= `second cladding?) or, equivalently, a raised inner cladding. This cutoff is not acutely sensitive to the external index for reasonable cladding/core diameter ratios. The dependence on core grading is given via universal step core curves and simple moment formulas for both planar guides and fibres. Arbitrary core profiles can be treated; generalisation to higher-order modes is given, and polarisation effects may be included.