Dynamic theory of an optical transistor

The amplification of a modulation by an optical transistor is shown to depend on the modulation frequency. At high frequency there is no amplification whereas at low frequency the expected amplification occurs. The critical frequency which separates these two domains depends on the modulation amplitude. These results are derived analytically for purely dispersive optical bistability in the bad cavity case. The modulation can be applied to the holding beam, to the refraction index or to the detuning with similar results for the output field intensity.