15,456 research outputs found
Multipole expansion of strongly focussed laser beams
Multipole expansion of an incident radiation field - that is, representation
of the fields as sums of vector spherical wavefunctions - is essential for
theoretical light scattering methods such as the T-matrix method and
generalised Lorenz-Mie theory (GLMT). In general, it is theoretically
straightforward to find a vector spherical wavefunction representation of an
arbitrary radiation field. For example, a simple formula results in the useful
case of an incident plane wave. Laser beams present some difficulties. These
problems are not a result of any deficiency in the basic process of spherical
wavefunction expansion, but are due to the fact that laser beams, in their
standard representations, are not radiation fields, but only approximations of
radiation fields. This results from the standard laser beam representations
being solutions to the paraxial scalar wave equation. We present an efficient
method for determining the multipole representation of an arbitrary focussed
beam.Comment: 13 pages, 7 figure
Electromagnetic multipole theory for optical nanomaterials
Optical properties of natural or designed materials are determined by the
electromagnetic multipole moments that light can excite in the constituent
particles. In this work we present an approach to calculate the multipole
excitations in arbitrary arrays of nanoscatterers in a dielectric host medium.
We introduce a simple and illustrative multipole decomposition of the electric
currents excited in the scatterers and link this decomposition to the classical
multipole expansion of the scattered field. In particular, we find that
completely different multipoles can produce identical scattered fields. The
presented multipole theory can be used as a basis for the design and
characterization of optical nanomaterials
Multipolar origin of bound states in the continuum
Metasurfaces based on resonant subwavelength photonic structures enable novel
ways of wavefront control and light focusing, underpinning a new generation of
flat-optics devices. Recently emerged all-dielectric metasurfaces exhibit
high-quality resonances underpinned by the physics of bound states in the
continuum that drives many interesting concepts in photonics. Here we suggest a
novel approach to explain the physics of bound photonic states embedded into
the radiation continuum. We study dielectric metasurfaces composed of planar
periodic arrays of Mie-resonant nanoparticles ("meta-atoms") which support both
symmetry protected and accidental bound states in the continuum and employ the
multipole decomposition approach to reveal the physical mechanism of the
formation of such nonradiating states in terms of multipolar modes generated by
isolated meta-atoms. Based on the symmetry of the vector spherical harmonics,
we identify the conditions for the existence of bound states in the continuum
originating from the symmetries of both the lattice and the unit cell. Using
this formalism we predict that metasurfaces with strongly suppressed spatial
dispersion can support the bound states in the continuum with the wavevectors
forming a line in the reciprocal space. Our results provide a new way of
designing high-quality resonant photonic systems based on the physics of bound
states in the continuum.Comment: 13 pages, 7 figures, 2 table
A new approach to electromagnetic wave tails on a curved spacetime
We present an alternative method for constructing the exact and approximate
solutions of electromagnetic wave equations whose source terms are arbitrary
order multipoles on a curved spacetime. The developed method is based on the
higher-order Green's functions for wave equations which are defined as
distributions that satisfy wave equations with the corresponding order
covariant derivatives of the Dirac delta function as the source terms. The
constructed solution is applied to the study of various geometric effects on
the generation and propagation of electromagnetic wave tails to first order in
the Riemann tensor. Generally the received radiation tail occurs after a time
delay which represents geometrical backscattering by the central gravitational
source. It is shown that the truly nonlocal wave-propagation correction (the
tail term) takes a universal form which is independent of multipole order. In a
particular case, if the radiation pulse is generated by the source during a
finite time interval, the tail term after the primary pulse is entirely
determined by the energy-momentum vector of the gravitational field source: the
form of the tail term is independent of the multipole structure of the
gravitational source. We apply the results to a compact binary system and
conclude that under certain conditions the tail energy can be a noticeable
fraction of the primary pulse energy. We argue that the wave tails should be
carefully considered in energy calculations of such systems.Comment: RevTex, 28 pages, 5 eps figures, http://www.tpu.ee/~tony/texdocs/, 4
changes made (pp. 2, 4, 22, 24), 2 references adde
Light scattering from disordered overlayers of metallic nanoparticles
We develop a theory for light scattering from a disordered layer of metal
nanoparticles resting on a sample. Averaging over different disorder
realizations is done by a coherent potential approximation. The calculational
scheme takes into account effects of retardation, multipole excitations, and
interactions with the sample. We apply the theory to a system similar to the
one studied experimentally by Stuart and Hall [Phys. Rev. Lett. {\bf 80}, 5663
(1998)] who used a layered Si/SiO/Si sample. The calculated results agree
rather well with the experimental ones. In particular we find conspicuous
maxima in the scattering intensity at long wavelengths (much longer than those
corresponding to plasmon resonances in the particles). We show that these
maxima have their origin in interference phenomena in the layered sample.Comment: 19 pages, 12 figure
Decomposing the scattered field of two-dimensional metaatoms into multipole contributions
We introduce a technique to decompose the scattered near field of
two-dimensional arbitrary metaatoms into its multipole contributions. To this
end we expand the scattered field upon plane wave illumination into cylindrical
harmonics as known from Mie theory. By relating these cylin- drical harmonics
to the field radiated by Cartesian multipoles, the contribution of the lowest
order electric and magnetic multipoles can be identified. Revealing these
multipoles is essential for the design of metamaterials because they largely
determine the character of light propagation. In par- ticular, having this
information at hand it is straightforward to distinguish between effects that
result either from the arrangement of the metaatoms or from their particular
design
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