Intraband polarization as the source of degenerate four-wave mixing signals in asymmetric semiconductor quantum well structures

Abstract

We have developed a formalism for calculating the coherent response of asymmetric semiconductor quantum well structures to ultrashort optical pulses. We work in an excitonic basis and include exciton-exciton interactions via the long-wavelength portion of the excitonic intraband polarization. We apply this formalism to the calculation of degenerate four-wave mixing intensities of a biased semiconductor superlattice and find that many aspects of the four-wave mixing signals are most naturally interpreted as directly resulting from the scattering of excitons off of the intraband polarization grating. We furthermore develop an extremely accurate method of factoring the dynamical equations that does not suffer from the problem encountered by the semiconductor Bloch equations in the Hartree-Fock approximation.

The Interplay of Intraband and Interband Polarization in the Ultrafast Response of Biased Semiconductor Superlattices

“…excitonic effects -are taken into account [2,3,6,7]. These effects are particularly strong for low to moderate electric fields where the WSL energy spacing is comparable to the binding energy of the 1s excitons.…”

“…The dynamical behavior of electrons and holes in BSSLs have been investigated both theoretically [1][2][3][4][5][6][7] and experimentally [7][8][9][10] by a large number of authors. The basic intraband dynamics can be understood in terms of the stationary states of non-interacting electrons in the superlattice potential in the presence of a uniform, along-axis static electric field, F .…”

“…For single beam experiments, these equations still hold with κ 2 = κ 1 . In deriving this Hamiltonian, we have neglected the exchange interaction (which is valid for the densities considered) and have approximated the exciton-exciton interaction via a dipole-dipole interaction [2].…”

“…There has been considerable interest in recent years in the development of a clear theoretical understanding and treatment of the nonlinear optical response of semiconductor nanostructures to ultrashort optical pulses [1][2][3][4][5][6][7]. One common approach to this problem has been to expand the response in powers of the optical field [2,4,[5][6][7].…”

“…One common approach to this problem has been to expand the response in powers of the optical field [2,4,[5][6][7]. This approach has been very successful for the treatment of many different nonlinear effects.…”