Optical Anisotropy of Quantum Disks in the External Static Magnetic Field

Abstract

We show how to compute the optical functions (the complex magneto-susceptibility, dielectric function, magneto{re°ection and ellipsometric spec-tra) for semiconductor quantum disks exposed to a uniform magnetic fleldin the growth direction, including the excitonic efiects. The optical responseis calculated for an oblique incidence of the propagating electromagneticwave and for input waves with difierent polarization. The method uses themicroscopic calculation of nanostructure excitonic wave functions and en-ergy levels, and the macroscopic real density matrix approach to computethe electromagnetic flelds and susceptibilities. The electron{hole screenedCoulomb potential is adapted and the valence band structure is taken intoaccount in the cylindrical approximation, thus separating light- and heavy--hole motions. The novelty of our approach is that the solution is obtainedin terms of known one-particle electron and hole eigenfunctions, since, in theconsidered nanostructure due to conflnement efiects accompanied by the e{hCoulomb interaction, the separation of the relative- and center-of-mass mo-tion is not possible. We obtain both the eigenvalues and the eigenfunctions.The convergence of the proposed method is examined. We calculate themagnetooptical functions, including the optical Stokes parameters and ellip-sometric functions for the case of oblique incidence. Numerical calculationswere performed for InAs (disk)/ GaAs (barrier) disks. A good agreementwith experiments was obtained.PACS numbers: 71.35.Cc, 71.35.Ji, 73.21.La, 78.20.Ls, 78.67.Hc