Extinction theorem for ultrafast pulses

Instead of using frequency dependent refractive index, we propose to use the extinction theorem to describe reflection and transmission of an ultrashort pulse passing through the boundary. When the duration of the pulse is comparable with the relaxation time, the results differ significantly from those given by the traditional method, especially if the carrier frequency is close to an absorbtion line. We compare the two approaches using the data of GaAs in the infrared domain.