Fresnel reflection from a cavity with net roundtrip gain

A planewave incident on an active etalon with net roundtrip gain may be expected to diverge in field amplitude, yet applying the Fresnel formalism to Maxwell's equations admits a convergent solution. We describe this solution mathematically and provide additional insight by demonstrating the response of such a cavity to an incident beam of light. Cavities with net roundtrip gain have often been overlooked in the literature, and a clear understanding of their behavior yields insight to negative refraction in nonmagnetic media, a duality between loss and gain, amplified total internal reflection, and the negative-index lens.