Eigenmodes in nonnormal optical systems

It is commonly assumed that the modes of optical waveguides and resonators form a complete set of normal modes in the same fashion as in many other physical systems. The equations that govern the propagating or resonant modes in many common optical systems are, however, nonhermitian in character, and as a result the eigenmodes of these systems are not orthogonal to each other and do not comprise a set of “normal modes” in the usual sense of that term. Many of our fundamental concepts related to optical systems and laser physics depend upon the assumed orthogonality of the modes of these systems, and are significantly changed if these modes are not orthogonal. This paper describes and gives physical interpretations for the unusual mathematical and physical properties of nonnormal optical systems, using as examples loss-guided or gain-guided optical waveguides and the resonant modes of unstable optical resonators.