雷射增益介質利用範圍廣泛，而VORPAL擁有可隨使用者編寫疊代步驟的功能，因此可透過VORPAL來模擬四能級雷射系統，並且可在之後的研究結合表面電漿子，以觀察兩者的交互作用情形。
　　本論文主要討論四能級增益介質系統的原理、疊代方程式、以及FDTD模擬，透過VORPAL這套軟體可以將四能級增益介質系統完整描述，並且更可以討論以表面電漿子驅動四能級增益介質系統，期望在未來可以達成一個可在小尺度下作用的雷射源。

The applications of laser gain medium have been extendedly investigated. Vorpal PIC-FDTD program has a function to implement the iterative solving of differential equations by user writing the solving procedure. Therefore, we can use Vorpal to model the four-level laser gain medium. Furthermore, the interaction between the surface plasmon fields and the gain medium can be examined under this function of VORPAL.
In this thesis, we first examined the iterative equations of a four-level gain medium within the FDTD simulations architecture. Then they are implemented in Vorpal program. Finally, the properties of output power vs. input power for a slab of four-level gain medium are examined and analyzed. In the future, we hope to combine surface plasmon effect and four-level gain medium in VORPAL to model a plasmonic laser.

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