Optical Anisotropy of Quantum Disks in the External Static Magnetic Field
P. Schillak a and G. Czajkowski a, b
a University of Technology and Life Sciences, al. S. Kaliskiego 7, 85-796 Bydgoszcz, Poland
b Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy
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Received: 7 06 2008;
We show how to compute the optical functions (the complex magneto-susceptibility, dielectric function, magneto-reflection and ellipsometric spectra) for semiconductor quantum disks exposed to a uniform magnetic field in the growth direction, including the excitonic effects. The optical response is calculated for an oblique incidence of the propagating electromagnetic wave and for input waves with different polarization. The method uses the microscopic calculation of nanostructure excitonic wave functions and energy levels, and the macroscopic real density matrix approach to compute the electromagnetic fields and susceptibilities. The electron-hole screened Coulomb potential is adapted and the valence band structure is taken into account in the cylindrical approximation, thus separating light- and heavy-hole motions. The novelty of our approach is that the solution is obtained in terms of known one-particle electron and hole eigenfunctions, since, in the considered nanostructure due to confinement effects accompanied by the e-h Coulomb interaction, the separation of the relative- and center-of-mass motion is not possible. We obtain both the eigenvalues and the eigenfunctions. The convergence of the proposed method is examined. We calculate the magnetooptical functions, including the optical Stokes parameters and ellipsometric functions for the case of oblique incidence. Numerical calculations were performed for InAs (disk)/ GaAs (barrier) disks. A good agreement with experiments was obtained.
DOI: 10.12693/APhysPolA.114.1349
PACS numbers: 71.35.Cc, 71.35.Ji, 73.21.La, 78.20.Ls, 78.67.Hc