N.А. Ignatov - Engineer, JSC «Almaz-Antey». E-mail: ignatovnicita@mail.ru М.А. Ogar - Head of Department, JSC «Almaz-Antey». E-mail: mogar@inbox.ru

In powerful flowing gas lasers, in view of the considerable cost of manufacturing of cooled mirrors of the resonator, and also its ex-perimental working off, the problem of numerical modeling of processes in the resonator has a major urgency. The purpose of the given operation is carrying out of the comparative analysis of the basic computational methods of labile optical resonators powerful fast flow lasers. At resonator calculation there is a problem of an evaluation of allocation of an electromagnetic field (or complex amplitude - CA) in a resonator concavity. The method of radial matrixes at calculation CA is one of the most simple, but thus insufficiently exact because does not consider an appearance of diffraction which can affect considerably allocation of an electromagnetic field in a resonator concavity. Electromagnetic field in the resonator in the diffraction approximation in steady state it is possible to calculate by means of the equation of Helmholtz. In the given operation we have considered two modes of its solution: by means of an evaluation of its common decision - Fresnel-Kirchhoffs integral and a finite-difference method. At a numerical solution of Fresnel-Kirchhoffs integral by means of fast transformation of Fourier (FFT) it is possible to reduce an amount of fulfilled operations to ~N2-lnN, but there is a restriction on a pitch size on longitudinal coordinate (distance between reading planes). Thus, for calculation of labile resonators with major numbers of Fresnel (NФ≈100) this method does not approach, as the distance between reading surfaces should be too major, that in turn strongly worsens accuracy of calculation of the resonator with the active medium having a high amplification factor. In turn the finite-difference method allows to make small enough pitch on longitudinal coordinate that allows to calculate labile resonators with major numbers of Fresnel. For a finite-difference method we have considered some profile boards: implicit Krank-Nikolsons plan, it is longitudinal the traversal plan and the «mixed» plan combining implicit and explicit profile boards. Each method has both the advantages and the shortages. Therefore each method is good at a solution of the problems, for example, for definition of allocation CA in a long-range band the method of solution of Fresnel-Kirchhoffs integral by means of a FFT most will approach. However it is necessary to score, that a method of finite differences, with use of the longitudinal-cross-section difference plan it is universal enough. With its help it is possible to calculate labile resonators of various configurations, including multipass, ring, with major numbers of Fresnel, the strong in homogeneities of the active medium etc.

 

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