當在介質中運動的帶電粒子速度大於介質中光傳遞的相速度時會產生契忍可夫輻射，當介質為非勻向介質、週期性介質或者左手介質時都會造成契忍可夫輻射有不同的特性。
本論文透過Vorpal利用PIC-FDTD數值模擬方式模擬不同能量的電子束在層狀金屬超穎材料中產生的契忍可夫輻射，並且利用傅立葉轉換得到契忍可夫輻射的頻譜與理論算出的頻段是否相同。利用本篇研究期望可以藉由改變電子束的能量來得到特定頻段的契忍可夫輻射。

Cherenkov radiation is emitted when a charge particle passes through a dielectric medium at the speed faster than the phase velocity of light in that medium. We also can find out there are many different characteristics when charge particle passes through anisotropic medium, periodic medium, left-hand medium.

In this thesis, We use the finite-difference-time-domain(FDTD)method to investigate the different energy electrons emitted Cherenkov radiation in in layered metallic metamaterials and use Fourier transform to get Fourier spectrum. We except to get specific frequency Cherenkov radiation by changing electron energy

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