1,520 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
Comment on "Silver nanoparticle array structures that produce remarkably narrow plasmon lineshapes" [J. Chem. Phys. 120, 10871 (2004)]
In this Comment I discuss two incorrect statements which were made in the
paper "Silver nanoparticle array structures that produce remarkably narrow
plasmon line shapes" [J. Chem. Phys.120, 10871 (2004)] by Zou, Janel, and
Schatz (ZJS). The first statement is about the use of quasistatic approximation
in my earlier work on the similar subject, and the second statement concerns
the possibility of exact cancellation of radiative relaxation in periodical
chains of nanoparticles. The relationship between the quasistatic
approximation, the dipole approximation, and the approximation due to Doyle
[Phys. Rev. B39, 9852 (1989)] which was used by ZJS is clarified. It is shown
that the exact cancellation of radiative relaxation cannot take place in the
particular geometry considered by ZJS.Comment: 3 pages, no figure
Divergence of Dipole Sums and the Nature of Non-Lorentzian Exponentially Narrow Resonances in One-Dimensional Periodic Arrays of Nanospheres
Origin and properties of non-Lorentzian spectral lines in linear chains of
nanospheres are discussed. The lines are shown to be super-exponentially narrow
with the characteristic width proportional to exp[-C(h/a)^3] where C is a
numerical constant, h the spacing between the nanospheres in the chain and a
the sphere radius. The fine structure of these spectral lines is also
investigated.Comment: 9 pages, 4 figure
Experimental demonstration of an analytic method for image reconstruction in optical tomography with large data sets
We report the first experimental test of an analytic image reconstruction
algorithm for optical tomography with large data sets. Using a continuous-wave
optical tomography system with 10^8 source-detector pairs, we demonstrate the
reconstruction of an absorption image of a phantom consisting of a
highly-scattering medium with absorbing inhomogeneities.Comment: 3 pages, 3 figure
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
Can photonic crystals be homogenized in higher bands?
We consider conditions under which photonic crystals (PCs) can be homogenized
in the higher photonic bands and, in particular, near the -point. By
homogenization we mean introducing some effective local parameters
and that describe reflection, refraction
and propagation of electromagnetic waves in the PC adequately. The parameters
and can be associated with a hypothetical
homogeneous effective medium. In particular, if the PC is homogenizable, the
dispersion relations and isofrequency lines in the effective medium and in the
PC should coincide to some level of approximation. We can view this requirement
as a necessary condition of homogenizability. In the vicinity of a
-point, real isofrequency lines of two-dimensional PCs can be close to
mathematical circles, just like in the case of isotropic homogeneous materials.
Thus, one may be tempted to conclude that introduction of an effective medium
is possible and, at least, the necessary condition of homogenizability holds in
this case. We, however, show that this conclusion is incorrect: complex
dispersion points must be included into consideration even in the case of
strictly non-absorbing materials. By analyzing the complex dispersion relations
and the corresponding isofrequency lines, we have found that two-dimensional
PCs with and symmetries are not homogenizable in the higher
photonic bands. We also draw a distinction between spurious -point
frequencies that are due to Brillouin-zone folding of Bloch bands and "true"
-point frequencies that are due to multiple scattering. Understanding
of the physically different phenomena that lead to the appearance of spurious
and "true" -point frequencies is important for the theory of
homogenization.Comment: Accepted in this form to Phys. Rev. B. Small addition in Sec.V
(Discussion) relative to previous version. The title to appear in PRB has
been changed to "Applicability of effective medium description to photonic
crystals in higher bands: Theory and numerical analysis" per the journal
policy not to print titles in the form of question
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