Electric-field-tunable laser emission by photon-assisted tunneling

rate equations has been performed by considering perturbations of the carrier densities about steady state values. That analysis predicts a resonance in the modulation response at a frequency, o, which may be identified as the maximum modulation frequency (MMF) of the device. It is noted that because of the picosecond electron lifetimes that are characteristic of such structures, the estimated MMF is of order 1 THz. It is further observed that such carrier lifetimes are typically of the same order as the photon lifetime, T ~ . Here, in contrast with interband semiconductor lasers, there is a fine balance between the contributions of the resonance frequency and damping factor in the determination of the maximum modulation frequency. In consequence it is found that the MMF does not increase monotonically as a function of the optical output power of the laser. The dependence of the modulation response on the laser output power is illustrated in Fig. 2, where the existence of an optimum optical output power to achieve the maximum modulation frequency is demonstrated. In general numerical solutions of the rate equations are required to elicit the modulation response and the outcome of such calculations will be presented. It is noted, however, that for devices in which a single tunneling time, T , is applicable ie where T~ = T~~ = T ~ ~ , an analytcal expression for that optimum output power can be found and the corresponding MMF is written explicitly as