Laser modes and threshold conditions in N-mirror resonators

Two formal methods for finding laser modes and threshold conditions in laser resonators containing as many as N mirrors are presented. The first method is based on an analysis determining the reflectivity and the transmittivity of an N-mirror system with gain. This is an extension of the classical 2 X 2 matrix method. The second method is based on self-consistency equations for the system and directly yields the circulating fields of the individual resonators. A set of rules has been proved to allow these fields to be calculated directly by means of inspection. The laser oscillation condition for an N-mirror system is found. Examples are given for systems with as many as five mirrors. (C) 1996 Optical Society of America