Transient optical reflectivity from bounded nonlocal media

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Abstract
This paper considers the problem of reflection of a finite-duration optical pulse incident normally on a semi-infinite nonlocal medium. The light frequency is assumed to lie in the vicinity of an exciton-polariton resonance. The reflected pulse is found to have transients associated with its leading and trailing edges. It is shown that spatial dispersion enhances reflected transients when the laser frequency is at resonance with the exciton polariton. For the case of CdS and GaAs semiconductors, the transient intensities are about 10% of the incident intensity at a time 0.1 psec after the trailing edge of the reflected pulse and remain about 1% even after several picoseconds. We have obtained explicit expressions for the transient part of the reflected field and evaluated them numerically under certain simplifying assumptions; analytical results are presented in some limiting cases of interest. The theory predicts a crossover from exponential to inverse power-law decay rate of transient reflectivity; this occurs at a characteristic time of the order of 1 psec for CdS and GaAs crystals.