Controlling of Goos-Hänchen shift via biexciton coherence in a quantum dot

Controlling of the Goos–Hönchen (GH) shifts of the reflected and transmitted probe pulses through a cavity containing four-level GaAs/AlGaAs quantum dot with 15 periods of 17.5 nm GaAs wells and 25-nm Al$_{0.3}$Ga$_{0.7}$As barriers is investigated. Under appropriate conditions, the probe absorption can be converted to the probe gain, therefore the controlling of negative and positive GH shift in the both reflected and transmitted probe beams can be occurred simultaneously. Our obtained results show that the group index of the probe beams could be negative or positive in both reflected and transmitted pulses. Therefore, simultaneous subluminal or superluminal light propagation in reflected and transmitted pulses can be achieved.