A novel scalar (i.e. paraxial) free space radiation mode method is presente
d for calculating the normal incidence facet reflectivity of the main guide
d mode of a step-index optical fibre with generally shaped smooth core. Num
erical results are presented and discussed for several cases of the Nth ord
er super-elliptical core shape, including the circular, elliptical, rectang
ular-type and slab limiting cases.