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首页> 外文会议>5th International Conference on Numerical Methods and Applications NMA 2002, Aug 20-24, 2002, Borovets, Bulgaria >Numerical Solution of Large Non-Hermitian Eigenvalue Problem Arising from Model of Vertical Cavity Surface Emitting Laser Array
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Numerical Solution of Large Non-Hermitian Eigenvalue Problem Arising from Model of Vertical Cavity Surface Emitting Laser Array

机译：垂直腔面发射激光阵列模型引起的大非Hermitian特征值问题的数值解

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摘要

Modal behavior of a 2-D (square lattice geometry) anti-guided 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 so-called 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.
机译：数值研究了二维（方格几何）反导垂直腔表面发射激光器（VCSEL）阵列的模态行为。 VCSEL阵列数值模型的背景是标量衍射理论和3-D双向光束传播方法。发现谐振器模式是所谓的往返算子的本征函数，当光在设备中往返时，该算子会转换电磁场的横向分布。相应离散化之后的往返算子在复杂的线性大维空间中成为线性非埃尔米特算子。使用Arnoldi算法，发现了许多阵列光学模式。在计算中，结合了光束传播的傅立叶描述和空间变量描述。针对元素之间的各种间隔长度和数组大小进行了计算。对4x4和10x10激光阵列进行了数值研究。发现具有不同对称特性的阵列光学模式。它们包括在阵列上具有恒定相位的同相模式，在元件之间具有交替相位的异相模式以及具有混合对称性的模式。发现了有利于提供高激光束质量的同相模式激光发射的条件。

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