Exciton polaritons in long-period quantum-well structures

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Abstract
The distribution of the normal frequencies in the complex plane for the exciton polaritons in a finite periodic quantum-well structure is analyzed by matrix-theory methods. Relations governing the sums of the normal frequencies for polariton modes that are even and odd relative to the center of the structure are derived. It is shown in an anti-Bragg structure, whose period equals a quarter of the optical wavelength at the excitonic resonance frequency ω0, that the sets of the natural frequencies corresponding to even and odd solutions transform into one another upon reflection relative to the vertical line ω=ω0. Approximate analytical expressions are found for the natural frequencies of the “long-lived” and “short-lived” polariton modes. The relation between the shape of the optical reflection spectrum and the set of natural frequencies of the system is elucidated.