34 research outputs found
Virtual Singular Scattering of Electromagnetic Waves in Transformation Media Concept
If a scatterer and an observation point (receive) both approach the so-called near field zone of a source of electromagnetic waves, the scattering process becomes singular one which is mathematically attributed to the spatial singularity of the free space Green function at the origin. Starting from less well known property of left-handed material slab to transfer the singularity of the free space Green function by implementing coordinate transformation, we present a phenomenon of virtual singular scattering of electromagnetic wave on an inhomogeneity located in the volume of left – handed material slab. Virtual singular scattering means that a scatterer is situated only virtually in the near field zone of a source, being, in fact, positioned in the far field zone. Such a situation is realized if a scatterer is embedded into a flat Veselago’s lens and approaches the lens’s inner focus because a slab of Veselago medium produces virtual sources inside and behind the slab and virtual scatterer (as a source of secondary waves) from both slab sides. Considering a line-like dielectric scatterer we demonstrate that the scattering efficiency is proportional to product of singular quasistatic parts of two empty space Green functions that means a multiplicative quasistatic singularity of the Green function for a slab of inhomogeneous Veselago medium. We calculate a resonance value of the scattering amplitude in the regime similar to the known Mie resonance scattering
Anisotropic multiple scattering in diffuse media
The multiple scattering of scalar waves in diffusive media is investigated by
means of the radiative transfer equation. This approach amounts to a
resummation of the ladder diagrams of the Born series; it does not rely on the
diffusion approximation. Quantitative predictions are obtained, concerning
various observables pertaining to optically thick slabs, such as the mean
angle-resolved reflected and transmitted intensities, and the shape of the
enhanced backscattering cone. Special emphasis is put on the dependence of
these quantities on the anisotropy of the cross-section of the individual
scatterers, and on the internal reflections due to the optical index mismatch
at the boundaries of the sample. The regime of very anisotropic scattering,
where the transport mean free path is much larger than the scattering
mean free path , is studied in full detail. For the first time the
relevant Schwarzschild-Milne equation is solved exactly in the absence of
internal reflections, and asymptotically in the regime of a large index
mismatch. An unexpected outcome concerns the angular width of the enhanced
backscattering cone, which is predicted to scale as
, in contrast with the generally
accepted law, derived within the diffusion approximation.Comment: 53 pages TEX, including 2 tables. The 4 figures are sent at reques
Resonant scattering in a strong magnetic field: exact density of states
We study the structure of 2D electronic states in a strong magnetic field in
the presence of a large number of resonant scatterers. For an electron in the
lowest Landau level, we derive the exact density of states by mapping the
problem onto a zero-dimensional field-theoretical model. We demonstrate that
the interplay between resonant and non-resonant scattering leads to a
non-analytic energy dependence of the electron Green function. In particular,
for strong resonant scattering the density of states develops a gap in a finite
energy interval. The shape of the Landau level is shown to be very sensitive to
the distribution of resonant scatterers.Comment: 12 pages + 3 fig