Polarizability tensor and Kramers-Heisenberg induction

A general expression for the semiclassical, nonrelativistic linear polarizability of an arbitrary volume element V has been derived in the long wavelength approximation. The derivation starts from the expectation value of the dipole strength, as in the original Kramers-Heisenberg paper about optical scattering by atoms. The main requirements underlying the present approach are a separate non-Hermitian part of the Hamiltonian and a frequency dependent damping, which is zero for the static case. Resonant and antiresonant exponentials are both found to be necessary to obtain a proper static response. It is concluded that even parity for the damping has to be preferred from the theoretical point of view, although odd and asymmetric parity yield virtually the same polarizability. The electromagnetic response can still be written in terms of a single complex frequency, in agreement with the requirements of electrodynamics. The resulting expression is suited for the treatment of nonisotropic system

Rayleigh scattering from single-site polysylane adsorbed on silicon: Theory

An ordered set of dipoles with mutual interaction in the close vicinity of a dielectric surface is studied. The solution of that particular theoretical problem is given rigorously both for the static and dynamic case. It can serve as a description of the polysylane molecules formed at the surface of silicon by means of HOMOCVD or sputtering in a hydrogen atmosphere. The theory can be used to describe the optical behaviour of those molecules, like first the Rayleigh scattering and next also the photoluminescence of those molecules

Anisotropic off-normal incidence optical reflection from GaP (110) surfaces

This article contains a theoretical study for off-normal incidence surface induced optical anisotropy (SIOA). The discrete dipole approximation was used to calculate the off-normal incidence optical response of slabs. By means of the two slab approach those results were converted to semi-infinite reflectivities. The calculated ellipsometric parameter δΔ shows large variations near the Brewster angle, but only the p-polarized reflection has a clearly increased SIOA sensitivity. So experimentally a straightforward determination of ΔRp should be preferred. Advantages have to be sought in the optical observation of surface state related phenomena at subbandgap conditions

Exact solution of the optical response of thick slabs in the discrete dipole approach

The recently developed double cell technique, which describes the optical response of an arbitrary semi-infinite dielectric crystal taking into account internal field effects, is extended to include the response of thick slabs. The surface sensitivity of the first technique is fully retained. The implications of the internal field effects on the microscopy of these thick slabs are examined for three simple model systems. Further, we investigated under which conditions deviations from classical Fresnel-behaviour are to be expected and how important these corrections are

Structural contribution to the anisotropic reflection from the Si (110) surface

For a single plane of dipoles of arbitrary configuration the optical reflection has been calculated, using the screened discrete dipole model. Results differ from continuum approaches. Further the results show that the experimentally observed reflection anisotropy has besides the dominating intrinsic contribution, also a structural on

SSHG of uniaxial molecules: Phenomena near brewster's angle

The nonlinear optical behaviour of a crystalline adlayer of unidirectionally oriented macromolecules at a substrate is studied by means of the discrete dipole model. Polar and azimuthal dependence of the second harmonic pp-reflectance is investigated at the fundamental and second harmonic frequencies. The influence of the anisotropic linear properties of the adlayer turns out to be essential

More efficient computation of the complex error function

Gautschi has developed an algorithm that calculates the value of the Faddeeva function w(z) for a given complex number z in the first quadrant, up to 10 significant digits. We show that by modifying the tuning of the algorithm and testing the relative rather than the absolute error we can improve the accuracy of this algorithm to 14 significant digits throughout almost the whole of the complex plane, as well as increase its speed significantly in most of the complex plane. The efficiency of the calculation is further enhanced by using a different approximation in the neighborhood of the origin, where the Gautschi algorithm becomes ineffective. Finally, we develop a criterion to test the reliability of the algorithm's results near the zeros of the function, which occur in the third and fourth quadrants

Magneto-optical response of layers of semiconductor quantum dots and nanorings

In this paper a comparative theoretical study was made of the magneto-optical response of square lattices of nanoobjects (dots and rings). Expressions for both the polarizability of the individual objects as their mutual electromagnetic interactions (for a lattice in vacuum) was derived. The quantum-mechanical part of the derivation is based upon the commonly used envelope function approximation. The description is suited to investigate the optical response of these layers in a narrow region near the interband transitions onset, particularly when the contribution of individual level pairs can be separately observed. A remarkable distinction between clearly quantum-mechanical and classical electromagnetic behavior was found in the shape and volume dependence of the polarizability of the dots and rings. This optical response of a single plane of quantum dots and nanorings was explored as a function of frequency, magnetic field, and angle of incidence. Although the reflectance of these layer systems is not very strong, the ellipsometric angles are large. For these isolated dot-ring systems they are of the order of magnitude of degrees. For the ring systems a full oscillation of the optical Bohm-Ahronov effect could be isolated. Layers of dots do not display any remarkable magnetic field dependence. Both type of systems, dots and rings, exhibit an outspoken angular-dependent dichroism of quantum-mechanical origin