使用數值模擬的方式來分析一個光學系統一直以來都是一個很重要的課題，因為數值模擬不只可以在進行實驗之前先評估實驗的可行性，更可以在實驗之後和實驗結果進行比對以分析兩者的差距來源並進行修正，如此一來不只可以確定數值模擬方法的正確性，更可以確定實驗結果的準確性以及可信度。
用來分析一已知入射光場被粒子所散射的方法有很多種，而根據粒子的尺寸和波長的比例可以大致上分成三個區塊，分別是粒子尺寸遠大於波長、粒子的尺寸接近波長以及粒子的尺寸遠小於波長。由於本篇論文所討論的範圍主要是落在粒子的尺寸接近波長的這一區塊，且以球形介電質粒子為主要討論的對象。考慮到運算時間，因此可選用的方法有：（1）適用在任意場型及任意形狀的粒子上的Discrete Dipole Approximation（DDA） method及（2）適用在特定的場型及特定粒子形狀的Mie theory。但考量日後亦會探討特殊雷射光鉗捕捉任意形狀粒子的情況，故本論文選用了DDA method為計算方法。
本篇論文的主要目的即是要使用DDA method去分析球形粒子落在一由恩司─高斯光束（Ince-Gaussian Beams, IGBs）所組成的光渦流陣列雷射光束（Vortex Array Laser Beams）下的受力情形，並藉由改變此球狀粒子和光渦流陣列雷射光束的相對位置、改變恩司─高斯光束的模態以及改變粒子的大小以觀察不同的光渦流陣列雷射光束入射不同大小的球狀粒子所造成的橫向力的分布，最後將會展示粒子由不同路徑進入到光渦流陣列雷射光束的光場時感受的力學位能變化。

Using numerical simulations to analyze an optical system is always an important issue, since one can estimate the possibility of an experiment before doing it. Besides, with the comparison between numerical simulations and experiments, we can find the difference between them. It helps us to correct the bugs of experiments or numerical calculations, and thus adds credibility of experimental or numerical results both.
There are many methods can find the light scattered by particles. Depending on the size of particles, we can classify the problems into three categories: particles’ size is much larger than the wavelength, particles’ size is approaching to the wavelength, and particles’ size is much smaller than the wavelength. This paper focuses on the problem of second category; that is, finding the light scattered by a spherical dielectric particle with size approaching to the wavelength. Moreover, considering the length of computing time, two methods can be chose: (a) Discrete dipole approximation (DDA) method, which can calculate light scattered by particles of any shape with arbitrary incident electromagnetic fields, and (b) Mie theory, which can calculate light scattered by particles of several specific shapes with some specific incident electromagnetic fields. This paper chose the DDA method as main numerical method for the reason that we will discuss light scattered by particles with arbitrary shapes in the future.
The main purpose of this thesis is using the DDA method to analyze the resultant force acting on a spherical particles with an incident vortex array laser beam that constructed by Ince-Gaussian beams (IGBs). The resultant transverse force acting on particles with several different situations are considered in this study, such as: the particle’s relative position, the mode of IGBs, and the size of the particle. At last, this study shows the mechanical potentials of the vortex array laser beam while passing a particle through the field via different paths.

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