1,172 research outputs found
Anderson Localization of Polar Eigenmodes in Random Planar Composites
Anderson localization of classical waves in disordered media is a fundamental
physical phenomenon that has attracted attention in the past three decades.
More recently, localization of polar excitations in nanostructured
metal-dielectric films (also known as random planar composite) has been subject
of intense studies. Potential applications of planar composites include local
near-field microscopy and spectroscopy. A number of previous studies have
relied on the quasistatic approximation and a direct analogy with localization
of electrons in disordered solids. Here I consider the localization problem
without the quasistatic approximation. I show that localization of polar
excitations is characterized by algebraic rather than by exponential spatial
confinement. This result is also valid in two and three dimensions. I also show
that the previously used localization criterion based on the gyration radius of
eigenmodes is inconsistent with both exponential and algebraic localization. An
alternative criterion based on the dipole participation number is proposed.
Numerical demonstration of a localization-delocalization transition is given.
Finally, it is shown that, contrary to the previous belief, localized modes can
be effectively coupled to running waves.Comment: 22 pages, 7 figures. Paper was revised and a more precise definition
of the participation number given, data for figures recalculated accordingly.
Accepted to J. Phys.: Cond. Mat
On the Convergence of the Born Series in Optical Tomography with Diffuse Light
We provide a simple sufficient condition for convergence of Born series in
the forward problem of optical diffusion tomography. The condition does not
depend on the shape or spatial extent of the inhomogeneity but only on its
amplitude.Comment: 23 pages, 7 figures, submitted to Inverse Problem
Multiple Projection Optical Diffusion Tomography with Plane Wave Illumination
We describe a new data collection scheme for optical diffusion tomography in
which plane wave illumination is combined with multiple projections in the slab
imaging geometry. Multiple projection measurements are performed by rotating
the slab around the sample. The advantage of the proposed method is that the
measured data can be much more easily fitted into the dynamic range of most
commonly used detectors. At the same time, multiple projections improve image
quality by mutually interchanging the depth and transverse directions, and the
scanned (detection) and integrated (illumination) surfaces. Inversion methods
are derived for image reconstructions with extremely large data sets. Numerical
simulations are performed for fixed and rotated slabs
Coherently tunable third-order nonlinearity in a nanojunction
A possibility of tuning the phase of the third-order Kerr-type nonlinear
susceptibility in a system consisting of two interacting metal nanospheres and
a nonlinearly polarizable molecule is investigated theoretically and
numerically. It is shown that by varying the relative inter-sphere separation,
it is possible to tune the phase of the effective nonlinear susceptibility
\chi^{(3)}(\omega;\omega,\omega,-\omega)2\pi$.Comment: 10 pages 5 figure
Local anisotropy and giant enhancement of local electromagnetic fields in fractal aggregates of metal nanoparticles
We have shown within the quasistatic approximation that the giant
fluctuations of local electromagnetic field in random fractal aggregates of
silver nanospheres are strongly correlated with a local anisotropy factor S
which is defined in this paper. The latter is a purely geometrical parameter
which characterizes the deviation of local environment of a given nanosphere in
an aggregate from spherical symmetry. Therefore, it is possible to predict the
sites with anomalously large local fields in an aggregate without explicitly
solving the electromagnetic problem. We have also demonstrated that the average
(over nanospheres) value of S does not depend noticeably on the fractal
dimension D, except when D approaches the trivial limit D=3. In this case, as
one can expect, the average local environment becomes spherically symmetrical
and S approaches zero. This corresponds to the well-known fact that in trivial
aggregates fluctuations of local electromagnetic fields are much weaker than in
fractal aggregates. Thus, we find that, within the quasistatics, the
large-scale geometry does not have a significant impact on local
electromagnetic responses in nanoaggregates in a wide range of fractal
dimensions. However, this prediction is expected to be not correct in
aggregates which are sufficiently large for the intermediate- and
radiation-zone interaction of individual nanospheres to become important.Comment: 9 pages 9 figures. No revisions from previous version; only figure
layout is change
Spectroscopic studies of fractal aggregates of silver nanospheres undergoing local restructuring
We present an experimental spectroscopic study of large random colloidal
aggregates of silver nanoparticles undergoing local restructuring. We argue
that such well-known phenomena as strong fluctuation of local electromagnetic
fields, appearance of "hot spots" and enhancement of nonlinear optical
responses depend on the local structure on the scales of several nanosphere
diameters, rather that the large-scale fractal geometry of the sample.Comment: 3.5 pages, submitted to J. Chem. Phy
Inversion formulas for the broken-ray Radon transform
We consider the inverse problem of the broken ray transform (sometimes also
referred to as the V-line transform). Explicit image reconstruction formulas
are derived and tested numerically. The obtained formulas are generalizations
of the filtered backprojection formula of the conventional Radon transform. The
advantages of the broken ray transform include the possibility to reconstruct
the absorption and the scattering coefficients of the medium simultaneously and
the possibility to utilize scattered radiation which, in the case of the
conventional X-ray tomography, is typically discarded.Comment: To be submitted to Inverse Problem
Convergence and Stability of the Inverse Scattering Series for Diffuse Waves
We analyze the inverse scattering series for diffuse waves in random media.
In previous work the inverse series was used to develop fast, direct image
reconstruction algorithms in optical tomography. Here we characterize the
convergence, stability and approximation error of the serie
Phonons in a Nanoparticle Mechanically Coupled to a Substrate
The discrete nature of the vibrational modes of an isolated nanometer-scale
solid dramatically modifies its low-energy electron and phonon dynamics from
that of a bulk crystal. However, nanocrystals are usually coupled--even if only
weakly--to an environment consisting of other nanocrystals, a support matrix,
or a solid substrate, and this environmental interaction will modify the
vibrational properties at low frequencies. In this paper we investigate the
modification of the vibrational modes of an insulating spherical nanoparticle
caused by a weak {\it mechanical} coupling to a semi-infinite substrate. The
phonons of the bulk substrate act as a bath of harmonic oscillators, and the
coupling to this reservoir shifts and broadens the nanoparticle's modes. The
vibrational density of states in the nanoparticle is obtained by solving the
Dyson equation for the phonon propagator, and we show that environmental
interaction is especially important at low frequencies. As a probe of the
modified phonon spectrum, we consider nonradiative energy relaxation of a
localized electronic impurity state in the nanoparticle, for which good
agreement with experiment is found.Comment: 10 pages, Revte
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