Exact partial wave expansion of optical beams with respect to arbitrary origin
Exact partial wave expansion of optical beams with respect to arbitrary origin
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DOI：
10.1364/ol.31.002477
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发表时间：
2006-03
期刊：
影响因子：
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通讯作者：
A. Neves;A. Fontes;W. L. Moreira;A. A. de Thomaz-A.;Diogo Burigo de Almeida;L. Barbosa;C. César
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文献类型：
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作者：
A. Neves;A. Fontes;W. L. Moreira;A. A. de Thomaz-A.;Diogo Burigo de Almeida;L. Barbosa;C. César
在计算球形粒子的散射时，入射光束的分波分解是在粒子界面处施加边界条件的第一项任务。坐标的原点必须在粒子的中心，而不是在光束的高度对称位置。这可能是一个相当复杂的问题，特别是当一个完整的矢量衍射描述的电磁场和高度聚焦的激光束，需要在傍轴限制失败。传统的近似技术已被用来向前推进，并获得数值结果。的主要故障依赖于径向依赖的光束形状系数，这限制了这种近似的有效性。在这里我们证明了径向依赖性将出现从立体角积分，以这种方式获得一个精确的，封闭的表达式，没有任何近似，光束形状系数，对于任意形状的光束，起源和偏振，高斯光束的特殊情况。
Partial wave decomposition of incident beams is the first task to be performed to impose boundary conditions at the particle interface in the calculation of the scattering of spherical particles. The coordinate's origin must be in the center of the particle and not at high symmetry positions of the beam. This can be a quite complicated problem, especially when a full vectorial diffraction description of the electromagnetic fields and highly focused laser beams are required where the paraxial limit fails. Traditional approximation techniques have been used to proceed forward and to obtain numerical results. The main fault relies on a radial dependence of the beam shape coefficients, which limits the validity of such approximations. Here we prove that the radial dependence will emerge from the solid angle integration in this way obtaining an exact, closed expression, without any approximation, for the beam shape coefficients, for an arbitrary beam shape, origin and polarization, the special case of a Gaussian beam is presented.