Analytical results for the confinement factor of antiguides

A dielectric waveguide with a core index lower than the cladding index can support guided modes if there is a sufficiently high gain in the core, in this letter, an analytical expression for the confinement factor (defined as the fraction of the intensity present in the core) for such antiguides is derived. Based on this result it is also shown that the number of modes in an antiguide increases super-linearly with the waveguide dimension, and a simple result for the scaling law is derived.