Dispersive properties and large Kerr nonlinearities using dipole-induced transparency in a single-sided cavity

We calculate the dispersive properties of a single-sided cavity coupled to a single dipole. We show that when a field is resonant with the dipole and the Purcell factor exceeds the bare cavity reflection coefficient, the field experiences a phase shift relative to reflection from a bare cavity. We then show that optically Stark shifting the dipole resonance with a second field creates large Kerr nonlinearities. An approximate expression for the total number of photons needed to create a phase shift is derived.