Instead of using a frequency-dependent refractive index, we propose to use the integrodifferential equation approach to describe reflection and transmission of an ultrashort pulse passing through the system’s boundary. This method, which is an adaptation of the extinction theorem for ultrafast pulses, explicitly follows time and space evolution without the slowly varying envelope approximation. When the duration of the pulse is comparable with the relaxation time, the results differ significantly from those given by the traditional method (Fresnel formulas), especially if the carrier frequency is close to an absorption line. We compare the two approaches, using the data of GaAs in the infrared domain where pulses of only a few cycles are available experimentally. We also work out a method that efficiently includes the background refractive index that originates from electronic transitions.

© 2001 Optical Society of America

[Optical Society of America ]

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