當一帶電粒子以超過光速在此介質中的速度經過一介質時，會發出輻射，此幅射即為契忍可夫幅射，隨著經過的介質特性不同，契忍可夫幅射的特性也會隨之改變。

本論文透過模擬軟體Meep來模擬不同的電子束能量下，多層膜中的契忍可夫幅射的群速度及相速度的角度變化關係。比較傅立葉轉換後得到的頻譜及透過色散關係算出的能帶圖之間的關係，並期望以此推算出不同能量區間的契忍可夫幅射特性。

An electron beam passing through a medium with the speed faster than the phase velocity of the light in the medium will emit the Cherenkov radiation. Recently, the Cherenkov radiation in metal gratings, in negative refraction index medium, and in metal film are also observed.

In this work, the Cherenkov radiations in metal-dielectric multilayers are investigated by finite-difference-time-domain (FDTD) simulation. The metal-dielectric multilayers have an anisotropic relative permittivity and hence the wave propagation properties in longitudinal and parallel directions are different from each other. The threshold energy of electron beam, the frequency ranges, the propagation directions and the angles of Cherenkov radiations in metal-dielectric multilayers strongly depend on metal-dielectric multilayers band structures.

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