Bidirectional Beam Propagation Method Applied for Lasers with Multilayer Active Medium N. N. Elkin, A. P. Napartovich, D. V. Vysotsky State Science Center Troitsk Institute for Innovation and Fusion Research(TRINITI), 142190, Troitsk Moscow Region, Russia, elkin@triniti.ru Abstract. The vertical external cavity surface emitting laser (VEC- SEL) as a typical example of laser with multilayer active medium is considered. The round-trip operator technique is presented in the given paper based on the bidirectional beam propagation method (BiBPM). Similarly to traditional Fox-Li technique our method not requires ex- plicit calculation of matrix of the round-trip operator and suits perfectly to Krylov subspace methods of linear algebra. The presented method is extended in natural way to non-linear case taking into account light- medium interaction. The results of modeling of a VECSEL with a reso- nant array of quantum wells are presented. 1 Introduction Optical devices that have piecewise continuous gain and index distributions along the main propagation direction are widespread. A resonant heterostructure of an array of quantum wells (QW) is of practical interest for application in VECSELs. The steady-state oscillating modes of a laser are described by non-linear partial differential equations containing eigenvalues. Book [1] can be recommended as the general work on the solution of nonlinear eigenvalue problems. However, it should be noted that the theory of nonlinear eigenvalue problems is far from com- pletion. The multilayer medium in the laser cavity complicates considerably the mathematical modeling because of partial reflections from the layer interfaces. For the first time, the applications of BiBPM for laser devices [2] were restricted by linear eigenvalue problem neglecting influence of the light beam on gain and index of the active medium. The eigenvalue problems for a non-hermitian matrix of high dimension were solved numerically in [2]. Next, the BiBPM combined with the round-trip operator technique was developed for self-consistent solution of wave field and material equations [3]. The Krylov subspace methods [4] applied in [3] to calculate the eigenfunctions of the linear wave equation is considerably more effective in comparison with the matrix method [2]. In present paper the modification of the algorithm [3] was applied for a VECSEL with a resonant array of quantum wells. Modeling of a VECSEL using diffraction theory approximation and taking into account diffusion equations for charge carriers in QWs was performed for the first time to our knowledge.