An analysis is made of the application a generalized method of eigenmo
des, which is used in steady-state diffraction problems to the theory
of lasers. In the study of open laser cavities the use of this method
makes it possible to avoid difficulties associated with the exponentia
l growth of the field at infinity. The generalized method developed pr
eviously for solving steady-state diffraction problems is extended to
the case of non-steady-state narrow-band processes to construct in the
ordinary way the equations describing the operation of the laser. The
only difference is that the field is expanded in the eigenfunctions t
hat are orthogonal in the region occupied by the active medium. This e
liminates the difficulties associated with the behavior of the made fi
eld at infinity. In addition, in a number of cases the generalized eig
enfunctions (modes) correspond considerably better to the held distrib
ution in the operating laser. (C) 1997 American Institute of Physics.