Reflection of THz Radiation by a Superlattice

The dynamics of a charged particle in a superlattice under the action of an external electric field has been the subject of intense research [1–6]. Under different conditions, an electron is predicted to reveal a variety of time-dependent phenomena such as Bloch oscillations [1], Zener tunneling [2], self-induced transparency [3], miniband collapse [4], negative differential conductivity, and absolute negative conductance in photon-assisted tunneling experiments [5], and other effects. In particular, the phenomenon of dynamic localization [6] is quite interesting. In the presence of a high frequency electric field Estd ­ E cossvtd along the growth direction of a superlattice of period d, an electron in a single miniband is predicted in general to drift off. However when the parameter Q ­ eEdyh̄v is a root of the zeroth order Bessel function, the electron is predicted to oscillate with a finite amplitude (in all of the following, we shall set h̄ ­ 1). Such a bounded motion at certain discrete parameter values can be understood in the following simple way: in each half-period of the incident ac field, the electron tries to execute Bloch oscillations. If it completes an integer number of Bloch oscillations before the sign of the field switches, the electron is localized, else it drifts off. This sharp change in transport properties of the electron should be expected to show up in easily measurable optical properties. So far, the only observations of dynamic localization have been in photon-assisted tunneling experiments [5], where one observes the appearance of sidebands with intensity J2 nsQd, and in the parametric suppression of dc current in the presence of an ac field [7]. However, it is difficult to directly measure transport properties because one cannot simply attach electrical contacts to the superlattice and apply a voltage at THz frequencies. The only realistic way of applying THz frequency fields to a superlattice is to place the superlattice in the path of a propagating THz pulse. This argues for a more direct measurement of the optical properties of the superlattice at THz frequencies. With this in mind, we propose in this paper an optical experiment where one measures the THz reflection coefficient of the superlattice. We predict oscillations in the reflection coefficient as a function of the electric field amplitude arising out of dynamic electron localization. Previous theoretical studies of electronic re-