Bragg reflection waveguide

Abstract

The spectral function can be introduced into the transverse wave-number representation of TE modes in a dielectric slab guide. The modified representation provides a connection to the theory of singular ordinary differential equations. By making use of this theory, some exact solutions to novel dielectric slab guides can be found. The Gel’fand–Levitan integral equation is used to construct an example that has the interesting feature that Bragg reflection is used to confine the field.