Leaky modes of circular slab waveguides: modified Airy functions

Circular slab waveguides are conformally mapped into straight waveguides. In the outer cladding region with monotonously increasing index profile, modified Airy functions of traveling-wave form are introduced to express the leaky mode. Field distributions and losses calculated by the proposed method are compared with those obtained by the Wentzel-Kramers-Brillouin method.