强聚焦laser光束的多极展开
Multipole expansion of strongly focussed laser beams
摘要：
入射辐射场的多极展开--也就是将场表示为矢量球面波函数的和--对于理论光散射方法如T矩阵方法和广义洛伦兹-米氏理论（GLMT）是必不可少的。一般来说，理论上很容易找到任意辐射场的矢量球面波函数表示。例如，一个简单的公式可以得到入射平面波的有用情况。激光束存在一些困难。这些问题不是球面波函数展开的基本过程中的任何缺陷的结果，而是由于激光束在其标准表示中不是辐射场，而只是辐射场的近似。这是由于标准激光束表示是傍轴标量波动方程的解。本文提出了一种确定任意聚焦光束多极表象的有效方法。
英文摘要：
Multipole expansion of an incident radiation field - that is, representation of the fields as sums of vector spherical wavefunctions - is essential for theoretical light scattering methods such as the T-matrix method and generalised Lorenz-Mie theory (GLMT). In general, it is theoretically straightforward to find a vector spherical wavefunction representation of an arbitrary radiation field. For example, a simple formula results in the useful case of an incident plane wave. Laser beams present some difficulties. These problems are not a result of any deficiency in the basic process of spherical wavefunction expansion, but are due to the fact that laser beams, in their standard representations, are not radiation fields, but only approximations of radiation fields. This results from the standard laser beam representations being solutions to the paraxial scalar wave equation. We present an efficient method for determining the multipole representation of an arbitrary focussed beam.
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