CALCULATION OF LIGHT PROPAGATION INSIDE A PLANAR WAVEGUIDE USING A MODIFIED SCALAR DIFFRACTION MODEL. N.A. S. Rodrigues, R. Riva, M. G. Destro, C. Schwab Instituto de Estudos Avançados Centro Técnico Aeroespacial 12231-970 - S.J Campos - SP São José dos Campos - SP S. S. Sato Instituto Tecnológico de Aeronáutica Centro Técnico Aeroespacial São José dos Campos - SP ABSTRACT A numerical model for the mode calculation of strip, waveguide structure, optical resonator is presented. This model adds to the Fox and Li’s approach the kaleidoscopic effect, taking into account the multiple reflections on the sidewalls. It was tested in conventional strip waveguide resonators, resulting in field patterns that agrees quite well with analytical results. It was also applied to hybrid unstable resonators, with results that look correct in the qualitative point of view. 1. Introduction. The diffraction calculation is a powerful tool for laser resonator design since it permits a good insight about many important laser beam parameters, such as: transverse mode intensity distribution, mode evolution, diffraction losses and so on. Since it was first proposed by Fox and Li [1] , the diffraction calculation has been used to calculate transverse modes for many different resonators. The same authors deeply investigated the stable resonator, both in the rectangular and in the circular geometry [2, 3] ; Rensch and Chester [4] , using basically the same idea, investigated the confocal positive branch unstable resonator; considering a thin sheet of gain medium inserted in the resonator, Fox and Li [5] , and more recently Zaidi and MacFarlane [6] ' ,evaluated the effect of the gain saturation on the resonator transverse mode and, virtually, any open resonator configuration can be analyzed using the basic Fox and Li' s idea [7] . The advent of lasers with slab geometry active medium (slab lasers), mainly RF excited C02 lasers, allowed the development of very powerful and very compact systems [8] . This laser active medium geometry determines, however, strongly nonsymmetric resonators since the transverse dimensions of the active medium are very different: in one direction (say, x direction) the sideways are closely spaced in such a way that the resonator can be considered, basically, an ordinary waveguide; in the other direction (y direction), the sidewalls are separated by a bigger distance and, in order to avoid very high order multimode oscillation, a hybrid unstable resonator is often used. The hybrid unstable resonator is diagrammed in Fig. 1: it consists on a guided planar half unstable resonator, with sidewalls both in the x and in the y directions. Rensch and Chester [4] had already studied numerically the problem of the strip unstable resonator, but their results don' t apply to the slab resonator mainly because they did not consider the sidewall effects (kaleidoscopic effect) in their calculations. The diffraction calculation for the slab resonator, in the y direction, meets this difficulty: the reflections on the sideways must be considered in a realistic transverse mode calculation and the basic Fox and Li algorithm is not convenient for such a case. Another aspect has also to be considered: since hybrid unstable resonators are usually designed with small magnifications, the diffraction effects are likely to be very important, making the geometrical foresights too imprecise. So, the aim of this paper is to present an algorithm for slab lasers transverse mode calculations, that, based on a modified Fox and Li treatment, takes the reflections on the sidewalls into account and calculates the propagation equations using FFT techniques, what reduces considerably the computation time. This model is developed considering a strip resonator, what is quite adequate for the slab configuration. 2. Diffraction of light inside a strip waveguide. First of all, it is necessary to consider the light propagation through a generic strip waveguide. Let' suppose the situation diagrammed in Fig. 2: the electric field u(S) is known in the plane S, parallel to the propagation direction there are two reflecting walls, and one wants to calculate the electric field u(S0) in the plane S0. Let' s take one point x in S and one point x0 in S0. The contribution of u(x) on u(x0) has many distinct components: the