Şahin Erdem, Onural Levent
Department of Electrical and Electronics Engineering, Bilkent University, Bilkent, Ankara, Turkey.
J Opt Soc Am A Opt Image Sci Vis. 2013 Mar 1;30(3):527-36. doi: 10.1364/JOSAA.30.000527.
We present a local Gaussian beam decomposition method for calculating the scalar diffraction field due to a two-dimensional field specified on a curved surface. We write the three-dimensional field as a sum of Gaussian beams that propagate toward different directions and whose waist positions are taken at discrete points on the curved surface. The discrete positions of the beam waists are obtained by sampling the curved surface such that transversal components of the positions form a regular grid. The modulated Gaussian window functions corresponding to Gaussian beams are placed on the transversal planes that pass through the discrete beam-waist position. The coefficients of the Gaussian beams are found by solving the linear system of equations where the columns of the system matrix represent the field patterns that the Gaussian beams produce on the given curved surface. As a result of using local beams in the expansion, we end up with sparse system matrices. The sparsity of the system matrices provides important advantages in terms of computational complexity and memory allocation while solving the system of linear equations.
我们提出了一种局部高斯光束分解方法，用于计算由曲面上指定的二维场引起的标量衍射场。我们将三维场写为朝着不同方向传播且其束腰位置取在曲面上离散点处的高斯光束之和。通过对曲面进行采样来获得束腰的离散位置，使得位置的横向分量形成规则网格。与高斯光束相对应的调制高斯窗函数放置在穿过离散束腰位置的横向平面上。通过求解线性方程组来确定高斯光束的系数，其中系统矩阵的列表示高斯光束在给定曲面上产生的场模式。由于在展开中使用了局部光束，我们最终得到稀疏的系统矩阵。在求解线性方程组时，系统矩阵的稀疏性在计算复杂度和内存分配方面提供了重要优势。
