We propose to use the resonant nonlinear-wave mixing due to the second-order electron (hole) nonlinearity in the semiconductor asymmetric quantum wells under a femtosecond optical pulse excitation for the generation of the utmost short mid/far-infrared pulses with a fewor even single-cycle duration defined by the pump duration [1,2]. Based on the well-known investigations of the ultrafast coherence relaxation dynamics of the electron and hole states in multiple quantum-well heterostructures, we find a special case of the resonant difference-frequency mixing (within the bandwidth of the pump femtosecond pulse) when the system is left unexcited at the end of the pump pulse. In this case, in the frame of a simple three-level model of step or double quantum wells, the mid/far-infrared coherence excitation may be described analytically. The schematics is given in the Figure for a step quantum well, an essential point being that the mean frequency of the pump pulse is close to the frequencies of the interband transitions, and the width of the pump pulse spectrum is large enough to span the difference between them.On the basis of the analytical solution for a simple Hl-shaped optical pump pulse, we find that one can expect the generation of the utmost short mid/far-infrared pulses with a fewor even single-cycle duration if the proper adjustment of the pump pulse parameters is done. The results of numerical simulations with a finite coherence relaxation included demonstrate that, for typical parameters of Al(ln)GaAs heterostructures, one will get the system to be almost in the initial state, i.e., the coherence oscillations will stop, as soon as the pump pulse ends. We show that an essential shortening of the generated mid/far-infrared pulse due to cut-off of the afterglow rings of the intersubband coherence is quite general effect that takes place for any other smoothly-shaped pump pulse, if its duration and amplitude satisfy a special relation.We analyze emission of the mid/far-infrared pulses for the planar multiple quantum-well structure optically pumped at the Brewster's angle. The explicit formula for the mid/far-infrared electric field is derived, and its peak value is estimated as I V/m (for the Al(ln)GaAs heterostructures) that is high enough for many applications, in particular, in the THz frequency range.
Conduction bandFemtosecond 3 pump pulse Generated mid/far-infrared pulse Valence band A schematic diagram of the three-level system with two electron and one hole levels. The mean frequency of the pump pulse, two dipole allowed interband transitions, and one dipole allowed intersubband transition are shown by arrows.