140 research outputs found
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
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
Nonasymptotic Homogenization of Periodic Electromagnetic Structures: Uncertainty Principles
We show that artificial magnetism of periodic dielectric or metal/dielectric
structures has limitations and is subject to at least two "uncertainty
principles". First, the stronger the magnetic response (the deviation of the
effective permeability tensor from identity), the less accurate ("certain") the
predictions of any homogeneous model. Second, if the magnetic response is
strong, then homogenization cannot accurately reproduce the transmission and
reflection parameters and, simultaneously, power dissipation in the material.
These principles are general and not confined to any particular method of
homogenization. Our theoretical analysis is supplemented with a numerical
example: a hexahedral lattice of cylindrical air holes in a dielectric host.
Even though this case is highly isotropic, which might be thought as conducive
to homogenization, the uncertainty principles remain valid.Comment: 11 pages, 5 figure
Solution of the inverse scattering problem by T-matrix completion. II. Simulations
This is Part II of the paper series on data-compatible T-matrix completion
(DCTMC), which is a method for solving nonlinear inverse problems. Part I of
the series contains theory and here we present simulations for inverse
scattering of scalar waves. The underlying mathematical model is the scalar
wave equation and the object function that is reconstructed is the medium
susceptibility. The simulations are relevant to ultrasound tomographic imaging
and seismic tomography. It is shown that DCTMC is a viable method for solving
strongly nonlinear inverse problems with large data sets. It provides not only
the overall shape of the object but the quantitative contrast, which can
correspond, for instance, to the variable speed of sound in the imaged medium.Comment: This is Part II of a paper series. Part I contains theory and is
available at arXiv:1401.3319 [math-ph]. Accepted in this form to Phys. Rev.
Nonlinear inverse problem by T-matrix completion. I. Theory
We propose a conceptually new method for solving nonlinear inverse scattering
problems (ISPs) such as are commonly encountered in tomographic ultrasound
imaging, seismology and other applications. The method is inspired by the
theory of nonlocality of physical interactions and utilizes the relevant
formalism. We formulate the ISP as a problem whose goal is to determine an
unknown interaction potential from external scattering data. Although we
seek a local (diagonally-dominated) as the solution to the posed problem,
we allow to be nonlocal at the intermediate stages of iterations. This
allows us to utilize the one-to-one correspondence between and the T-matrix
of the problem, . Here it is important to realize that not every
corresponds to a diagonal and we, therefore, relax the usual condition of
strict diagonality (locality) of . An iterative algorithm is proposed in
which we seek that is (i) compatible with the measured scattering data and
(ii) corresponds to an interaction potential that is as
diagonally-dominated as possible. We refer to this algorithm as to the
data-compatible T-matrix completion (DCTMC). This paper is Part I in a two-part
series and contains theory only. Numerical examples of image reconstruction in
a strongly nonlinear regime are given in Part II. The method described in this
paper is particularly well suited for very large data sets that become
increasingly available with the use of modern measurement techniques and
instrumentation.Comment: This is Part I of a paper series containing theory only. Part II
contains simulations and is available as arXiv:1505.06777 [math-ph]. Accepted
in this form to Phys. Rev.
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