Is the spatially averaged spectrum equal to the global spectrum?

Abstract

Near-field optical spectroscopy and microscopy give access to excitations that cannot be revealed in the far zone. In order to investigate these remarkable differences, we present a theoretical analysis of the local optical properties of semiconductor quantum wells including the effects of disorder arising from interface fluctuations. The far-field absorption spectrum is compared with spatially averaged absorption spectra calculated at different spatial resolutions. We find that summing up local optical spectra does not reproduce the global spectrum in contrast to findings at diffraction-limited resolutions.Near field microscopy and spectroscopy provide direct information on the spatial and energy distribution of light emitting nanometric centers [1-5] of semiconductor quantum structures. Moreover near field spectroscopy offers unique attributes in addition to high spatial resolution which might be explored in future experiments. For instance, the presence of optical fields with high lateral spatial frequencies able to excite surface states with high k-vectors not accessible by far-field optical excitations allows the possibility to confine the optical excitation to a very small volume below the diffraction limit. As a consequence optical spectra of homogeneous surface systems can display remarkable differences in the near and far zones [6,7]. These spectral changes are caused by the loss of evanescent modes (corresponding to modes with high lateral spatial frequencies) in the far zone. They have been analyzed theoretically in ideal disorder-free surface systems where in-plane k-vectors are good quantum numbers.Here we analyze, in a realistic surface system affected by disorder effects, these additional opportunities of near-field spectroscopy. To what extent these spectral changes are detectable in real systems affected by disorder and imperfections? Are spatially averaged near-field spectra equal to far-field spectra? In order to isolate spectral changes due to excitation of states not accessible by far-field optical probes, we compare far-field absorption spectra with spatially averaged absorption spectra [8]. These averaged spectra are composed summing up local spectra obtained centering the confined illuminating beams on a fine mesh of points on the quantum well plane and they are calculated at different spatial resolutions. Our analysis is performed on quantum wells (QWs). Interface fluctuations in QWs result in an effective 2D (two-dimensional) spatially correlated random potential that tends to localize the center of mass (COM) motion of excitons [9,10] and produces an inhomogeneous Gaussian-like absorption line [11,12]. Inhomogeneities and disorder effects give rise to surface quantum states, eventually localized, with mixed in-plane k-vectors (the in-plane k-vector is no more a good quantum number).

Time and spatially resolved photoluminescence of quantum structures with interfacial roughness: a theoretical description

“…This state, owing to cancellation effects in ( ) is sufficiently confined as compared to the spatial extension of 2 ( ) ψ R , detecting near-field emission from this state becomes possible. Moreover the level occupation of this dark-state is larger than that of the first energy state [12], at the opposite to what predicted by the Boltzmann distribution. The observed inverted occupations origin from the symmetry-suppression of radiative decay of the dark-state ( 2 0 r = ) due to cancellation effects [10,12].…”

“…Moreover the level occupation of this dark-state is larger than that of the first energy state [12], at the opposite to what predicted by the Boltzmann distribution. The observed inverted occupations origin from the symmetry-suppression of radiative decay of the dark-state ( 2 0 r = ) due to cancellation effects [10,12]. Such interpretation is further confirmed by the fact that the emission from the center of the dot decays before than that from its sides (see Fig.…”