Moving mirrors and time-varying dielectrics

The spectral distribution of light generated by a finite cavity with one moving mirror is compared with that produced by a fixed cavity containing a time-varying dielectric. In both cases a motion over a finite time interval is considered. Although the moving mirror is usually considered to be an idealization for the time-varying dielectric, there are qualitative differences in the spectra produced. The spectral distribution for the moving mirror case behaves as 1/n³, while that for the time-varying dielectric behaves on average as 1/n⁴ but is rapidly oscillating.