304 research outputs found
Surface Integral Method for the Second Harmonic Generation in Metal Nanoparticles
Second harmonic (SH) radiation in metal nanoparticles is generated by both
nonlocal-bulk and local-surface SH sources, induced by the electromagnetic
field at the fundamental frequency. We propose a surface integral equation
(SIE) method for evaluating the SH radiation generated by metal nanoparticles
with arbitrary shapes, considering all SH sources. We demonstrate that the
contribution of the nonlocal-bulk SH sources to the SH electromagnetic field
can be taken into account through equivalent surface electric and magnetic
currents. We numerically solve the SIE problem by using the Galerkin method and
the Rao-Wilton-Glisson basis functions in the framework of the distribution
theory. The accuracy of the proposed method is verified by comparison with the
SH-Mie analytical solution. As an example of a complex-shaped particle, we
investigate the SH scattering by a triangular nano-prism. This method paves the
way for a better understanding of the SH generation process in arbitrarily
shaped nanoparticles and can also have a high impact in the design of novel
nanoplasmonic devices with enhanced SH emission
Spectral theory of electromagnetic scattering by a coated sphere
In this paper, we introduce an alternative representation of the
electromagnetic field scattered from a homogeneous sphere coated with a
homogeneous layer of uniform thickness. Specifically, we expand the scattered
field using a set of modes that are independent of the permittivity of the
coating, while the expansion coefficients are simple rational functions of the
permittivity. The theory we develop represents both a framework for the
analysis of plasmonic and photonic modes and a straightforward methodology to
design the permittivity of the coating to pursue a prescribed tailoring of the
scattered field. To illustrate the practical implications of this method, we
design the permittivity of the coating to zero either the backscattering or a
prescribed multipolar order of the scattered field, and to maximize an electric
field component in a given point of space
Cloaking of Arbitrarily-Shaped Objects with Homogeneous Coatings
We present a theory for the cloaking of arbitrarily-shaped objects and
demonstrate electromagnetic scattering-cancellation through designed
homogeneous coatings. First, in the small-particle limit, we expand the dipole
moment of a coated object in terms of its resonant modes. By zeroing the
numerator of the resulting rational function, we accurately predict the
permittivity values of the coating layer that abates the total scattered power.
Then, we extend the applicability of the method beyond the small-particle
limit, deriving the radiation corrections of the scattering-cancellation
permittivity within a perturbation approach. Our method permits the design of
invisibility cloaks for irregularly-shaped devices such as complex sensors and
detectors
Resonance frequency and radiative Q-factor of plasmonic and dielectric modes of small objects
The electromagnetic scattering resonances of a non-magnetic object much
smaller than the incident wavelength in vacuum can be either described by the
electroquasistatic approximation of the Maxwell's equations if its permittivity
is negative, or by the magnetoquasistatic approximation if its permittivity is
positive and sufficiently high. Nevertheless, these two approximations fail to
correctly account for the frequency shift and the radiative broadening of the
resonances when the size of the object becomes comparable to the wavelength of
operation. In this manuscript, the radiation corrections to the
electroquasistatic and magnetoquasistatic resonances of arbitrarily-shaped
objects are derived, which only depend on the quasistatic current modes. Then,
closed form expressions of the frequency-shift and the radiative Q-factor of
both plasmonic and dielectric modes of small objects are introduced, where the
dependencies on the material and the size of the object are factorized. In
particular, it is shown that the radiative Q-factor explicitly depends on the
multipolar components of the quasistatic modes
Full-wave electromagnetic modes and hybridization in nanoparticle dimers
The plasmon hybridization theory is based on a quasi-electrostatic
approximation of the Maxwell's equations. It does not take into account
magnetic interactions, retardation effects, and radiation losses. Magnetic
interactions play a dominant role in the scattering from dielectric
nanoparticles. The retardation effects play a fundamental role in the coupling
of the modes with the incident radiation and in determining their radiative
strength; their exclusion may lead to erroneous predictions of the excited
modes and of the scattered power spectra. Radiation losses may lead to a
significant broadening of the scattering resonances. We propose a hybridization
theory for non-hermitian composite systems based on the full-Maxwell equations
that, overcoming all the limitations of the plasmon hybridization theory,
unlocks the description of dielectric dimers. As an example, we decompose the
scattered field from silicon and silver dimers, under different excitation
conditions and gap-sizes, in terms of dimer modes, pinpointing the hybridizing
isolated-sphere modes behind them.Comment: Supplemental material available upon reques
Full-wave electromagnetic modes and hybridization in nanoparticle dimers
The plasmon hybridization theory is based on a quasi-electrostatic approximation of the Maxwell’s equations. It does not take into account magnetic interactions, retardation effects, and radiation losses. Magnetic interactions play a dominant role in the scattering from dielectric nanoparticles. The retardation effects play a fundamental role in the coupling of the modes with the incident radiation and in determining their radiative strength; their exclusion may lead to erroneous predictions of the excited modes and of the scattered power spectra. Radiation losses may lead to a significant broadening of the scattering resonances. We propose a hybridization theory for non-Hermitian composite systems based on the full-Maxwell equations that, overcoming all the limitations of the plasmon hybridization theory, unlocks the description of dielectric dimers. As an example, we decompose the scattered field from silicon and silver dimers, under different excitation conditions and gap-sizes, in terms of dimer modes, pinpointing the hybridizing isolated-sphere modes behind them
Full-wave analytical solution of second-harmonic generation in metal nanospheres
We present a full-wave analytical solution for the problem of second-harmonic
generation from spherical nanoparticles. The sources of the second-harmonic
radiation are represented through an effective nonlinear polarization. The
solution is derived in the framework of the Mie theory by expanding the pump
field, the nonlinear sources and the second-harmonic fields in series of
spherical vector wave functions. We use the proposed solution for studying the
second-harmonic radiation generated from gold nanospheres as function of the
pump wavelength and the particle size, in the framework of the Rudnick-Stern
model. We demonstrate the importance of high-order multipolar contributions to
the second-harmonic radiated power. Moreover, we investigate the p- and s-
components of the SH radiation as the Rudnick-Stern parameters change, finding
a strong variation. This approach provides a rigorous methodology to understand
second-order optical processes in metal nanoparticles, and to design novel
nanoplasmonic devices in the nonlinear regime.Comment: 16 pages, 10 figure
Electromagnetic modes and resonances of two-dimensional bodies
The electromagnetic modes and the resonances of homogeneous, finite size,
two-dimensional bodies are examined in the frequency domain by a rigorous full
wave approach based on an integro-differential formulation of the
electromagnetic scattering problem. Using a modal expansion for the current
density that disentangles the geometric and material properties of the body the
integro-differential equation for the induced surface (free or polarization)
current density field is solved. The current modes and the corresponding
resonant values of the surface conductivity (eigen-conductivities) are
evaluated by solving a linear eigenvalue problem with a non-Hermitian operator.
They are inherent properties of the body geometry and do not depend on the body
material. The material only determines the coefficients of the modal expansion
and hence the frequencies at which their amplitudes are maximum (resonance
frequencies). The eigen-conductivities and the current modes are studied in
detail as the frequency, the shape and the size of the body vary. Open and
closed surfaces are considered. The presence of vortex current modes, in
addition to the source-sink current modes (no whirling modes), which
characterize plasmonic oscillations, is shown. Important topological features
of the current modes, such as the number of sources and sinks, the number of
vortexes, the direction of the vortexes are preserved as the size of the body
and the frequency vary. Unlike the source-sink current modes, in open surfaces
the vortex current modes can be resonantly excited only in materials with
positive imaginary part of the surface conductivity. Eventually, as examples,
the scattering by two-dimensional bodies with either positive or negative
imaginary part of the surface conductivity is analyzed and the contributions of
the different modes are examined
Volume Integral Formulation for the Calculation of Material Independent Modes of Dielectric Scatterers
In the frame of volume integral equation methods, we introduce an alternative
representation of the electromagnetic field scattered by a homogeneous object
of arbitrary shape at a given frequency, in terms of a set of modes independent
of its permittivity. This is accomplished by introducing an auxiliary
eigenvalue problem, based on a volume integral operator. With this modal basis
the expansion coefficients of the scattered field are simple rational functions
of the permittivity of the scatterer. We show, by studying the electromagnetic
scattering from a sphere and a cylinder of dimensions comparable to the
incident wavelength, that only a moderate number of modes is needed to
accurately describe the scattered far field. This method can be used to
investigate resonant scattering phenomena, including plasmonic and photonic
resonances, and to design the permittivity of the object to pursue a prescribed
tailoring of the scattered field. Moreover, the presented modal expansion is
computationally advantageous compared to direct solution of the volume integral
equation when the scattered field has to be computed for many different values
of the dielectric permittivity, given the size and shape of the dielectric
body
Magnetoquasistatic resonances of small dielectric objects
A small dielectric object with positive permittivity may resonate when the free-space wavelength is large in comparison with the object dimensions if the permittivity is sufficiently high. We show that these resonances are described by the magnetoquasistatic approximation of the Maxwell's equations in which the normal component of the displacement current density field vanishes on the surface of the particle. They are associated to values of permittivities and frequencies for which source-free quasistatic magnetic fields exist, which are connected to the eigenvalues of a magnetostatic integral operator. We present the general physical properties of magnetoquasistatic resonances in dielectrics with arbitrary shape. They arise from the interplay between the polarization energy stored in the dielectric and the energy stored in the magnetic field. Our findings improve the understanding of resonances in high-permittivity dielectric objects and provide a powerful tool that greatly simplifies the analysis and design of high-index resonators
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