Switching pulses for an optical transistor

We study the characteristics of a rectangular pulse used to switch an optical transistor. Three regimes appear. (i) For low intensity pulses, the pulse duration and area decrease exponentially with increasing holding intensity. (ii) For high intensity pulses, the pulse duration and area decrease linearly with increasing holding intensity. (iii) For a holding intensity near the transition region, the only constraint is on the pulse area and not on its duration or intensity separately.