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Numerical Solution of Large Non-Hermitian Eigenvalue Problem Arising from Model of Vertical Cavity Surface Emitting Laser Array

  • Nikolay N. Elkin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2542)

Abstract

Modal behavior of a 2-D (square lattice geometry) antiguided vertical cavity surface emitting laser (VCSEL) array was studied numerically. The background of the numerical model of VCSEL array is scalar diffraction theory and 3-D bidirectional beam propagation method. Resonator modes were found as eigen-functions of the socalled round-trip operator which transforms the transverse distribution of electro-magnetic field when light have a round-trip in the device. The round-trip operator after corresponding discretization becomes a linear non-hermitian operator in a complex linear large dimensional space. Using the Arnoldi algorithm, a number of array optical modes were found. In calculations, both Fourier and space variable descriptions of beam propagation were combined. Calculations were made for various spacing length between elements and a size of the array. 4x4 and 10x10 laser arrays were studied numerically. Array optical modes having different symmetry properties were found. They include in-phase mode with constant phase over the array, out-of-phase mode with alternating phase between elements and modes with mixed symmetry. Conditions are found for favorable lasing of the in-phase mode providing high laser beam quality.

Keywords

Krylov Subspace Absorb Boundary Condition Laser Array Vertical Cavity Surface Emit Laser Mixed Symmetry 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Nikolay N. Elkin
    • 1
  1. 1.State Science Center Troitsk Institute for Innovation and Fusion Research(TRINITI)Troitsk Moscow RegionRussia

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