F. Bassani

Radiative lifetime of free excitons in quantum wells

Abstract We calculate the intrinsic radiative lifetime of excitons in quantum wells arising from the lack of translational invariance along the growth direction. For 100 A wide GaAs-Ga1− x Al x As quantum wells, we compute a lifetime of 25 ps for the lowest heavy-hole exciton at zero in-plane wavevector. Since this is longer than typical thermalization times, the effective radiative decay rate is given by an average over the thermal distribution, resulting in an effective lifetime which increases linearly with temperature. A microscopic calculation of the reflectivity shows that the intrinsic radiative decay rate can also be measured in reflectivity experiments.

Resonant and surface polaritons in quantum wells

SummaryWe show how the breaking of the translational invariance in a quantum well modifies the concept of polariton with respect to that defined for bulk material. Polaritons in quantum wells result from the combination of the exciton states with the radiation field. They are here obtained as the solutions of Maxwell equations with retardation, provided an appropriate nonlocal response function is used for the electric susceptibility, and Maxwell boundary conditions are imposed. We find two types of polaritons depending on the values of the in-plane wavevectorkII: those atkIIω/v cannot be coupled to waves in the barrier. In both cases explicit expressions are given for radiative shifts and radiative broadenings as functions ofkII. Numerical results are obtained for GaAs-Ga1−xAlxAs and for CuCl quantum wells and new experiments are suggested. The existence of resonant and surface polaritons justifies an interpretation of the temperature dependence of the radiative lifetime suggested by the same authors. It also decreases the radiative efficiency in the direction perpendicular to the planes and increases the radiative efficiency parallel to the planes with increasing temperature.

Quantum wire polaritons

SummaryUsing a nonlocal susceptibility with cilindrical symmetry as computed from the microscopic theory, we obtain the exciton-polariton modes in quantum wires, where the translational symmetry is preserved in one direction only. Resonant polaritons, with a finite radiative lifetime, result for

Excitonic polaritons in superlattices

k_\parallel< k_0 = (\omega /c)\sqrt {\varepsilon _\infty }

Exciton-photon coupling in GaAs bulk microcavities

, while wire polaritons with infinite radiative lifetime result fork‖>k0. Dispersion laws and lifetimes are given for all values ofk‖, and the separation between the longitudinal and the nonlongitudinal mode is obtained. Numerical examples are given for GaAs/Ga1−xAlxAs quantum wires.

EMPIRICAL SPDS* TIGHT-BINDING CALCULATION FOR CUBIC SEMICONDUCTORS : GENERAL METHOD AND MATERIAL PARAMETERS

SummaryWe consider the case of a plurality of polariton modes due to the valence band structure, and give a one-dimensional model to compute the optical functions in the exciton frequency range. Interference effects of each mode with itself and with the other modes are identified by a fine structure in the reflectivity spectrum.

Hole subbands in strained GaAs-Ga1-xAlxAs quantum wells: Exact solution of the effective-mass equation.

SummaryThe excitonic energies are computed in superlattices from the poles in the imaginary part of the susceptibility, using an appropriate Greens function expression for the coherent amplitude function of the electron-hole pair. Solving the Maxwell equations, the polariton states are obtained and the optical properties are computed. The procedure includes the effects of coherence between the carriers and the electromagnetic field, and it does not require any type of additional boundary conditions. Detailed calculations in GaAs/Ga1−xAlxAs superlattices show polaritonic effects in the optical properties, in particular a peculiar fine-structure lineshape of then=1 andn=2 hh and lh excitons is obtained. A comparison with similar calculations in bulk GaAs clearly shows the roles of quantum confinement and of anisotropy in the superlattice.

Exchange interaction and polariton effects in quantum-well excitons

SummaryAn analysis of the optical properties of an array of quantum wires of cylindrical shape is presented. Effects of the electromagnetic coupling between the wires are found to be given by additional energy shifts and modified oscillator strengths of the reflectivity peaks with respect to the single-wire exciton polariton ones previously calculated. Numerical values for realistic structures show the importance of these effects. Changes of the lifetimes of the single-wire excitations produced by this electromagnetic coupling are also put into evidence. In particular, the short lifetimes of the two-dimensional exciton-polariton are recovered when the interwire distanceD is smaller than the wavelength λ of light. Stationary, or non-radiative electromagnetic modes are also expected in this close-packed case. These radiative and non-radiative modes therefore show some analogies with those found in two-dimensional systems such as quantum wells.