高斯雷射光束在自由空間下的傳播已經被探討很多年，大多數的人所了解的高斯光束都是經由近軸近似的方式所得到的結果，卻忽略了近軸近似這個方法僅限於小角度的傳播。雷射初始束腰大小與高斯光束波長的關係為區分近軸近似和非近軸近似條件的重要指標，如果腰束與波長大小相當，高斯光束的發散角度則會變大，近軸近似的方法則無法運用在大角度的情況下。本篇論文提出新的方法來達到非近軸近似修正的效果，我們從波動方程式開始，並利用空間頻率表示法與光學轉換函數，得到高斯光束在非近軸近似條件下的精確解，最後利用Matlab 做數值分析，並藉由改變腰束寬度與傳播距離觀察其變化，從模擬結果可以看到，當高斯光束波長與腰束的比例介於3 ≤ k?0 ≤ 12之間時，近軸近似與非近軸近似的高斯光束有1%至13%的差異。

Gaussian light beam propagation in free space has been a popular research topic due to its wide application. The propagation of the Gaussian laser beam in free space can be properly depicted by Maxwell’s wave equation. All the existed solutions of the wave equation are mostly under the paraxial approximation, i.e. the propagation of light is limited to a small angle deviation from the optic axis. In this thesis, we propose a novel approach to solve the wave equation without the paraxial approximation and have derived an analytic representation for the Gaussian light beam. We start with the wave equation and use the angular spectrum representation and the optical transfer function to obtain the exact representation of the Gaussian beam under non-paraxial approximation. A set of simulation results provided to check the validity of our approach and compare the difference between the solution under the paraxial approximation.

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