A general formalism describing the supermodes of an array of N identical, circulantly coupled resonators is presented. The symmetry of the problem results in a reduction of the N coupled integral equations to N decoupled integral equations. Each independent integral equation defines a set of single-resonator modes derived for a hypothetical resonator whose geometry resembles a member of the real array with the exception that all coupling beams are replaced by feedback beams, each with a prescribed constant phase. A given array supermode consists of a single equivalent resonator mode appearing repetitively in each resonator with a prescribed relative phase between individual resonators. The specific array design chosen for example is that of N adjoint coupled confocal unstable resonators. The impact of coupling on the computer modeling of this system is discussed and computer results for the cases of two- and four-laser coupling are presented.
S. S. Townsend, S. S. Townsend,
"Modeling Of Supermodes In Coupled Unstable Resonators", Proc. SPIE 0642, Modeling and Simulation of Optoelectronic Systems, (25 November 1986); doi: 10.1117/12.975480; https://doi.org/10.1117/12.975480