Urban spaces and the levels of the historic city

Ponencia presentada a Session 8: Dimensiones psicosociales de la arquitectura y el urbanismo / Psycological dimensions of architecture and plannin

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

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

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

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 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 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