1,042 research outputs found
Inward and Outward Integral Equations and the KKR Method for Photons
In the case of electromagnetic waves it is necessary to distinguish between
inward and outward on-shell integral equations. Both kinds of equation are
derived. A correct implementation of the photonic KKR method then requires the
inward equations and it follows directly from them. A derivation of the KKR
method from a variational principle is also outlined. Rather surprisingly, the
variational KKR method cannot be entirely written in terms of surface integrals
unless permeabilities are piecewise constant. Both kinds of photonic KKR method
use the standard structure constants of the electronic KKR method and hence
allow for a direct numerical application. As a by-product, matching rules are
obtained for derivatives of fields on different sides of the discontinuity of
permeabilities.
Key words: The Maxwell equations, photonic band gap calculationsComment: (to appear in J. Phys. : Cond. Matter), Latex 17 pp, PRA-HEP 93/10
(exclusively English and unimportant misprints corrected
A simple formula for the L-gap width of a face-centered-cubic photonic crystal
The width of the first Bragg's scattering peak in the (111)
direction of a face-centered-cubic lattice of air spheres can be well
approximated by a simple formula which only involves the volume averaged
and over the lattice unit cell, being the
(position dependent) dielectric constant of the medium, and the effective
dielectric constant in the long-wavelength limit approximated
by Maxwell-Garnett's formula. Apparently, our formula describes the asymptotic
behaviour of the absolute gap width for high dielectric contrast
exactly. The standard deviation steadily decreases well below
1% as increases. For example for the sphere filling
fraction and . On the interval , our
formula still approximates the absolute gap width (the relative
gap width ) with a reasonable precision, namely with a standard
deviation 3% (4.2%) for low filling fractions up to 6.5% (8%) for the
close-packed case. Differences between the case of air spheres in a dielectric
and dielectric spheres in air are briefly discussed.Comment: 13 pages, 4 figs., RevTex, two references added. For more info see
http://www.amolf.nl/external/wwwlab/atoms/theory/index.htm
Resonance-Induced Effects in Photonic Crystals
For the case of a simple face-centered-cubic photonic crystal of homogeneous
dielectric spheres, we examine to what extent single-sphere Mie resonance
frequencies are related to band gaps and whether the width of a gap can be
enlarged due to nearby resonances. Contrary to some suggestions, no spectacular
effects may be expected. When the dielectric constant of the spheres
is greater than the dielectric constant of the
background medium, then for any filling fraction there exists a critical
above which the lowest lying Mie resonance frequency falls inside
the lowest stop gap in the (111) crystal direction, close to its midgap
frequency. If , the correspondence between Mie
resonances and both the (111) stop gap and a full gap does not follow such a
regular pattern. If the Mie resonance frequency is close to a gap edge, one can
observe a resonance-induced widening of a relative gap width by .Comment: 14 pages, 3 figs., RevTex. For more info look at
http://www.amolf.nl/external/wwwlab/atoms/theory/index.htm
Photonic Band Gaps of Three-Dimensional Face-Centered Cubic Lattices
We show that the photonic analogue of the Korringa-Kohn-Rostocker method is a
viable alternative to the plane-wave method to analyze the spectrum of
electromagnetic waves in a three-dimensional periodic dielectric lattice.
Firstly, in the case of an fcc lattice of homogeneous dielectric spheres, we
reproduce the main features of the spectrum obtained by the plane wave method,
namely that for a sufficiently high dielectric contrast a full gap opens in the
spectrum between the eights and ninth bands if the dielectric constant
of spheres is lower than the dielectric constant of
the background medium. If , no gap is found in the
spectrum. The maximal value of the relative band-gap width approaches 14% in
the close-packed case and decreases monotonically as the filling fraction
decreases. The lowest dielectric contrast for which a
full gap opens in the spectrum is determined to be 8.13. Eventually, in the
case of an fcc lattice of coated spheres, we demonstrate that a suitable
coating can enhance gap widths by as much as 50%.Comment: 19 pages, 6 figs., plain latex - a section on coated spheres, two
figures, and a few references adde
A superconvergent representation of the Gersten-Nitzan and Ford-Webber nonradiative rates
An alternative representation of the quasistatic nonradiative rates of
Gersten and Nitzan [J. Chem. Phys. 1981, 75, 1139] and Ford and Weber [Phys.
Rep. 1984, 113, 195] is derived for the respective parallel and perpendicular
dipole orientations. Given the distance d of a dipole from a sphere surface of
radius a, the representations comprise four elementary analytic functions and a
modified multipole series taking into account residual multipole contributions.
The analytic functions could be arranged hierarchically according to decreasing
singularity at the short distance limit d ---> 0, ranging from d^{-3} over
d^{-1} to ln (d/a). The alternative representations exhibit drastically
improved convergence properties. On keeping mere residual dipole contribution
of the modified multipole series, the representations agree with the converged
rates on at least 99.9% for all distances, arbitrary particle sizes and
emission wavelengths, and for a broad range of dielectric constants. The
analytic terms of the representations reveal a complex distance dependence and
could be used to interpolate between the familiar d^{-3} short-distance and
d^{-6} long-distance behaviors with an unprecedented accuracy. Therefore, the
representations could be especially useful for the qualitative and quantitative
understanding of the distance behavior of nonradiative rates of fluorophores
and semiconductor quantum dots involving nanometal surface energy transfer in
the presence of metallic nanoparticles or nanoantennas. As a byproduct, a
complete short-distance asymptotic of the quasistatic nonradiative rates is
derived. The above results for the nonradiative rates translate
straightforwardly to the so-called image enhancement factors Delta, which are
of relevance for the surface-enhanced Raman scattering.Comment: 30 pages including 6 figure
How many orthonormal bases are needed to distinguish all pure quantum states?
We collect some recent results that together provide an almost complete
answer to the question stated in the title. For the dimension d=2 the answer is
three. For the dimensions d=3 and d>4 the answer is four. For the dimension d=4
the answer is either three or four. Curiously, the exact number in d=4 seems to
be an open problem
Persistent currents in multicomponent Tomonaga-Luttinger liquid: application to mesoscopic semiconductor ring with spin-orbit interaction
We study persistent currents in semiconductor ballistic rings with spin-orbit
Rashba interaction. We use as a working model the multicomponent
Tomonaga-Luttinger liquid which arises due to the nonparabolic dispersion
relations of electrons in the rings with rather strong spin-orbit coupling.
This approach predicts some new characteristic features of persistent currents,
which may be observed in experimental studies of semiconductor ballistic rings.Comment: 13 pages, 8 figure
ОЦІНКА РІВНЯ НАВАНТАЖЕННЯ ТЕРИТОРІЇ ГОЩАНСЬКОГО РАЙОНУ РІВНЕНСЬКОЇ ОБЛАСТІ ВІД ПОЛІГОНІВ І ЗВАЛИЩ ВІДХОДІВ
In Ukraine, the cheapest technology for waste collection to organized landfills and landfills continues to prevail. This is harmful to the environment.Untimely removal of solid waste worsens the sanitary condition of settlements, can cause diseases and epidemics. At the same time, solid waste is a source of secondary resources, which necessitates a scientific approach to the choice of means of their disposal and utilization in relation to the specific conditions of settlements of Ukraine.The description of the problem at the state level is mainly reduced to the annual regional report on the state of the environment, and as rightly noted by domestic scientists, is limited to data on the number and area of landfills, the amount of waste placed in specially designated areas. But this "standard" presentation of information does not allow to fully characterize the environmental consequences of the existing waste situation. Another group of scientists, after analyzing the state of waste storage, concluded that the introduction of landfill monitoring system will: analyze the location of landfills, not only in relation to settlements – cities, towns and villages, cottages, etc., as well as features of geosystems in the areas of these landfills, the state of landfills, the causes of spontaneous combustion of garbage, threats to engineering structures at landfills, the conditions in which waste is stored. It should be noted that the assessment of the impact on the environment and the contribution to the formation of the level of environmental safety of environmental sources of solid waste are engaged in the identification of unauthorized landfills based on remote sensing materials and multispectral space images, health impact assessments of people , the consequences of soil pollution adjacent to landfills, as well as integrated assessments of the actual and potential impact of solid waste on the environment.The article calculated the environmental safety categories of waste disposal sites of the Hoshcha district of the Rivne region. The assessment of the level of load of the territory It was established that the load level is average, while the majority of the studied objects are classified as dangerous. The results obtained indicate the existing environmental hazard in the area.В Україні продовжує переважати найбільш дешева з можливих технологій – вивіз відходів на організовані полігони й звалища, при цьому вплив такого підходу завдає шкоду навколишньому середовищу. В статті визначено категорії екологічної безпеки місць видалення відходів Гощанського району Рівненської області та проведено оцінку рівня навантаження території. З’ясовано, що рівень навантаження є середнім, однак більшість досліджуваних об’єктів належать до категорії небезпечних, що свідчить про існуючу екологічну небезпеку в районі
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