Self-induced and induced transparencies of two-dimensional and three-dimensional superlattices

Abstract

The phenomenon of transparency in two-dimensional and three-dimensional superlattices is analyzed on the basis of the Boltzmann equation with a collision term encompassing three distinct scattering mechanisms (elastic, inelastic and electron-electron) in terms of three corresponding distinct relaxation times. On this basis, we show that electron heating in the plane perpendicular to the current direction drastically changes the conditions for the occurrence of self-induced transparency in the superlattice. In particular, it leads to an additional modulation of the current amplitudes excited by an applied biharmonic electric field with harmonic components polarized in orthogonal directions. Furthermore, we show that self-induced transparency and dynamic localization are different phenomena with different physical origins, displaced in time from each other, and, in general, they arise at different electric fields. Typeset using REVT E X 1 1 <X $ 5RPDQRY HW DO ³6HOI LQGXFHG DQG LQGXFHG WUDQVSDUHQFLHV«´ VXEPLWWHG WR 3K\V 5HY % )LJXUH RI J J J J

Electron Bloch oscillations and electromagnetic transparency of semiconductor superlattices in multi-frequency electric fields

“…Account of this mixing in the SLs with the sinusoidal miniband was discussed in Refs. [8,9] for some specific cases.…”

“…In the strong time-periodic electric field with fundamental frequency ω (without the static component), Bragg reflections give rise to nonlinear periodic oscillations with the period of this field and to corresponding quasienergetic minibands [5][6][7][8][9][10][11]. We call these oscillations "ac BOs" to differ from usual BOs occurring in the static field.…”

“…In contrast to the DL, the SIT occurs only after time τ from the field application and can exist for a long time (mach larger than τ) [17,19] and, consequently, has more chances to be observed experimentally. Beyond the τ-approximation, the values of the field at which the DL and the SIT occur can be quite different [8,9,17]. Moreover, at non-periodic biharmonic field, the DL exists and the SIT does not [17].…”

“…Self-induced transparency (SIT) means that at specific magnitudes of high-frequency field the macroscopic electron polarization in the SL becomes small (even vanishes in the limit of rare collisions) and the SL behaves almost like a dielectric with the permittivity of the crystal lattice and relatively small nonlinear absorption. If the SL becomes transparent by means of some applied harmonic field, it can also be transparent for the other harmonic field [9,15,17]. This effect is called induced transparency (IT).…”

“…The mechanisms of the transparency appearing for the SLs with the sinusoidal miniband have been carefully studied in Refs. [8,9]. It was shown that in the single-relaxation-time (τ-) approximation (and in this approximation only!)…”