Discrete Sources Method Research Articles

Влияние пространственной дисперсии в металлах на оптические характеристики биметаллических плазмонных наночастиц

The problem of diffraction of an electromagnetic plane wave field on a core-shell nanoparticle composed of two plasmon metals is considered. The effect of spatial dispersion in metals on the absorption cross section is investigated on the basis of the Discrete Sources method. Various combinations of core and shell metals: Au@Ag and Ag@Au of spheroidal particles, as well as the effect of elongation and asymmetry of particle geometry on energy absorption are being studied. It was found that taking into account the spatial dispersion, both in the core and in the shell, leads to a significant decrease in the absorption cross section and a shift of the plasmon resonance to the shorter wavelength region.

Discrete sources method for investigation of near field enhancement of core-shell nanoparticles on a substrate accounting for spatial dispersion

Quantum nanoplasmonics attracts increasing interest of researchers since its innovations have great potential for practical applications. Over the past decades, the use of core-shell nanoparticles has gained huge popularity due to the ability to manipulate the materials and sizes of both core and shell to control their plasmonic properties. This circumstance favorably distinguishes them from its homogeneous counterparts. In this paper, based on the Discrete Sources Method, we investigate the effect of spatial nonlocality in a metal shell of a nonspherical core-shell nanoparticle deposited on a glass prism. Our primary goal is to examine the impact of the nonlocal effect on the near-field enhancement and the absorption cross section of the particle. We found that accounting for the interaction of a particle with a prism has a larger influence on the optical characteristics of the near field than on the intensity in the far zone. For excitation of the core-shell particle, both a propagating and an evanescent wave, have been considered. It was found that evanescent wave excitation provides a larger near field enhancement than an exciting propagating wave. Taking into account the nonlocality effect in the metal shell leads to a significant damping of the plasmon resonance amplitude accompanied by a small blue shift.

Discrete Sources Method for Investigation of the Influence of Geometry Asymmetry of Core-Shell Particles Accounting For Spatial Dispersion

In this paper, the Discrete Sources Method has been extended to describe the influence of the geometry asymmetry of a core-shell particle accounting for the effect of spatial dispersion inside the plasmonic metal shell. We found that varying the plasmonic shell thickness has more influence on the near field intensity distribution then on the average enhancement factor. Besides, we demonstrates that the effect of spatial dispersion can decrease the near field intensity up to 60% of its value and it provides a small blue shift.

The Influence of the Asymmetry of the Geometry of a Core–Shell Particle on a Substrate on the Optical Characteristics Accounting for Spatial Dispersion

The problem of excitation of a core–shell particle located on a transparent substrate by a field of an evanescent electromagnetic wave is considered. The particle consists of a dielectric core with a metal nanoplasmonic shell in which spatial dispersion occurs. Based on the Discrete Sources Method, a model has been constructed that considers the influence of the presence of the substrate and nonlocality in a metal on the optical scattering characteristics. The effect of the asymmetry of the particle geometry on the optical characteristics of the near field has been investigated. It was found that the asymmetry of the particle geometry significantly affects the intensity enhancement coefficient, as well as the absorption cross-section.

Analysis of the Influence of Nonlocality on Characteristics of the Near Field of a Layered Particle on a Substrate

The problem of diffraction of the electromagnetic plane wave field on a layered nanoparticle with a metal plasmon layer on the surface of a transparent substrate is considered. Based on the discrete sources method, the influence of spatial nonlocality in a metal on the intensity of the near field and absorption cross section is studied. The cases of particle excitation both by a propagating wave and by a evanescent wave are considered. It is shown that the substrate provides a more significant influence on optical characteristics of the near field than on the intensity in the far zone. It is established that taking into account the nonlocality effect in the metal leads to a significant decrease in the plasmon resonance amplitude with a small shift to the shortwave region.

Application of the Method of Extended Boundary Conditions to the Solution of the Problem of Wave Diffraction by Magnetodielectric Scatterers Having a Compound Geometry

A technique allowing to model scattering characteristics for bodies of arbitrary geometries is suggested on the basis of the method of extended boundary conditions. The scattering characteristics include those ones, which are averaged over orientation angles. The 2D problem of diffraction of a plane wave by dielectric bodies having a complicated geometry of the cut and, in particular, by bodies similar to fractals is considered. The numerical algorithms of the diffraction problem solution on the basis of the systems of integral equations of the first and second kinds are compared. The correctness of the method is confirmed with the help of the verification of the optical theorem fulfillment for various bodies and by comparing with the calculation results obtained by the modified method of discrete sources.

Discrete Sources Method to Solve Nonlocal Scattering Problems in Plasmonic Applications

Current paper presents a comprehensive up-to-date review of one of the most recently developed numerical schemes based on the Discrete Sources Method. The aim of these developments is to implement and justify new efficient mathematical models allowing to accurately simulate response of small plasmonic nanoparticles with scale less than 10 nm to the different types of incident fields. Spatial dispersion effects of the material that are non-negligible at the given scales are incorporated into the numerical technique via Generalized Nonlocal Optical Response approach. Electron energy loss and plane wave scattering problems are considered, with the latter additionally featuring account for the presense of the substrate in the medium. Validity of the obtained results is ensured via a posteriori residual estimation, via comparison of computed scattering properties to the other available simulation techniques, and via comparison to the experimental electron energy loss measurements available in reference literature.

Numerical method for analyzing the near-field enhancement of nonspherical dielectric-core metallic-shell particles accounting for the nonlocal dispersion.

Over the last few decades, dielectric core and metallic plasmonic shell (Die@Me) nanoparticles have found a wide variety of applications. The trend to reduce the thickness of the metallic coating requires to account for the influence of the nonlocal dispersion on the spectral response of such nanoparticles. In this paper, we use the discrete sources method and the generalized nonlocal optical response model to describe the nonlocality within the plasmonic metal shell. We found that the variation of the plasmonic shell thickness and the elongation of the nonspherical core-shell particle can enlarge the near-field enhancement and the absorption cross section by an order of magnitude. Besides, we show that the nonlocal dispersion can decrease the field enhancement in the wavelength domain up to 2.5 times with a small blue-shift of about 5 nm.

Application of the Method of Continued Boundary Conditions to the Solution of the Problem of Wave Diffraction on Scatterers of Complex Geometry Located in Homogeneous and Heterogeneous Media

A method that allows modeling the scattering characteristics of bodies of arbitrary geometry has been proposed on the basis of the method of continued boundary conditions. The paper considers a two-dimensional problem of plane wave diffraction on dielectric bodies with complex cross-section geometry—in particular, on fractal-like bodies. Numerical algorithms for solving the diffraction problem based on systems of integral equations of the first and second kind have been compared. The method has been generalized to the problem of diffraction on a cylindrical body located in a homogeneous magnetodielectric half-space. The correctness of the method was confirmed by checking the fulfillment of the optical theorem for different bodies and by comparing with the results of calculations obtained by a modified method of discrete sources.

Investigation of the influence of the electromagnetic interaction between volume bodies on the scattering field characteristics

Using the method of discrete sources, we solve the problem of scattering of an electromagnetic wave by a structure composed of two closely adjacent perfectly conducting triaxial ellipsoids. The solution was realized as a computer code. Using this code, we investigated the influence of the electromagnetic interaction of ellipsoids located at different distances on the scattering field characteristics. Some numerical results are presented.

Анализ влияния нелокальности на характеристики ближнего поля слоистой частицы на подложке

The problem of electromagnetic plane wave scattering by a layered nanoparticle with a metal plasmon shell deposited on the surface of a transparent substrate is considered. Using the Discrete Source Method, the influence of spatial nonlocality in a metal layer on the near-field intensity and absorption cross section is investigated. The particle excitation by both a propagating and evanescent wave are considered. It is shown that the substrate has a more significant effect on the optical characteristics of the near field than on the intensity in the far zone. It was found that taking into account the nonlocal effect in the metal leads to a significant decrease in the plasmon resonance amplitude with a small blue shift.

Method for Analyzing the Influence of the Quantum Nonlocal Effect on the Characteristics of a Plasmonic Nanolaser

Based on the discrete source method, a rigorous approach has been developed and implemented that allows one to analyze light scattering by models of resonators of plasmonic nanolaser (SPASER). This approach takes into account all features of the boundary value problem for the Maxwell system, including the interaction of the resonators with the prism surface and the nonlocal screening effect, which is treated in the framework of the generalized nonlocal optical response (GNOR) model. It is shown that a resonator model with a dielectric core and a plasmonic shell has significant advantages over a layered model with a plasmonic core. The conditions are established under which the field can be enhanced by several orders of magnitude. It is shown that taking into account the GNOR leads to a decrease in the field intensity by 50%.

Simulation of light scattering and electron energy loss (EELS) by small spatially dispersive plasmonic nanodimers

Despite the tremendous progress in the field of nanoplasmonics, complex plasmonic nanostructures such as dimers still present a significant challenge for proper numerical characterization. In particular, for the particles which size is smaller than electron mean free path in metals it is necessary to account for effects of spatial nonlocality in simulations. To address these problems a new mathematical model based on the Discrete Sources Method was developed and corresponding computer model was implemented. It enables one to successfully resolve the problem of accounting for spatial dispersion effects, which is especially important in the systems with very small gap and particle size, and it retains all key features of the Discrete Sources numerical approach including flexibility and a posteriori error estimation. We compute such scattering characteristics as electron energy loss probability and total scattered field intensity of nanodimers as one typically has to rely on methods of both optical and electron spectroscopy to experimentally investigate these structures. The developed model also allows to simultaneously consider several external excitations of the plasmonic system, including both electron and plane wave, in order to obtain more information about the system and to significantly speed up computational performance.

Применение метода продолженных граничных условий к решению задачи дифракции волн на рассеивателях сложной геометрии, расположенных в однородной и неоднородной средах

Based on the method of continued boundary conditions, a technique is proposed that allows modeling the scattering characteristics for bodies of arbitrary geometry. The two-dimensional problem of the diffraction of a plane wave by dielectric bodies with complex section geometry, in particular, by fractal-like bodies, is considered. Comparison of numerical algorithms for solving the diffraction problem based on systems of integral equations of the 1st and 2nd kind is carried out. The method is generalized to the problem of diffraction by a cylindrical body located in a homogeneous magnetodielectric half-space. The correctness of the method is confirmed by checking the fulfillment of the optical theorem for various bodies and by comparing it with the results of calculations obtained by the modified method of discrete sources.

Influence of the Nonlocal Effect on the Optical Properties of Nonspherical Plasmonic Semiconductor Nanoparticles

Noble metals are commonly used as plasmon materials because of their high density of free electrons, but semiconductor materials are also becoming of interesting in this field because its electron density can be varied by doping. Metal nitrides can be an alternative to noble metals because of their low absorption loss and high electron density. Among others, TiN and ZrN seem to be most suitable as alternative plasmonic materials because their optical properties are dominated by conduction electrons near the plasmon frequency. There is the flame spray pyrolysis process, which is currently developed to produce such kind of nanoparticles. In this paper, based on an extension of the discrete sources method, the effect of the hydrodynamic Drude model of the quantum nonlocal effect on the optical characteristics of semiconductor nanoparticles is analyzed. The influence of accounting for the nonlocal effect (NLE) on the optical properties under spherical particles deformation has been investigated. It has been shown that accounting for the NLE leads to a plasmon resonance blue shift and a damping similar to noble metals. It was found that smaller particles demonstrate larger NLE influence than larger ones. Besides, the influence of polarization on the local and nonlocal responses of 3D nonspherical semiconductor particles has been investigated as well. Using simulation accounting for the nonlocal effect, it is shown that the extinction of a nonspherical ZrN particles exceeds that of a gold particle.

Discrete Source Method for the Study of Influence Nonlocality on Characteristics of the Plasmonic Nanolaser Resonators

The discrete source method is generalized so as to investigate the nonlocal effects in multilayered particles on a substrate. The scheme for constructing an approximate solution and the corresponding numerical algorithm are described in detail. The developed approach is used to study the optical characteristics of 3D cavities of plasmonic nanolasers. It is shown that the amplitude of surface plasmon resonance and the amplification factor of the near-field intensity are reduced significantly when the nonlocal effects are taken into account. It is also shown that the amplification factor can be increased by more than twice by varying the material and thickness of the cavity shell and the direction of the incident wave.

Effect of Spatial Dispersion on Plasmon Resonance in Silver Nanoparticles

Using the modified discrete sources method, the problem of calculating plasmon spectra of the characteristic energy loss of electrons during the interaction with silver nanoparticles from 2 to 8 nm in size is solved. The calculated spectra are compared with the experimental data confirming the significant spatial dispersion effect. The importance of the consideration of this factor when analyzing the properties of plasmonic nanoparticles for applications in biosensorics and biomedicine is discussed.

Transition matrix of a nonspherical particle in the non-local optical response theory

In this paper, we present two methods for deriving the transition matrix of a nonspherical particle in the non-local optical response theory, which is important for particles of size below about 10 nm. The key point in our analysis is the separation of the internal field into a transverse and a longitudinal component. The first method for T-matrix calculation relies on the null-field equation for the total field inside the particle, the null-field equation for the longitudinal field outside the particle, and the integral representation of the scattered field. The second method uses a projection scheme for the additional boundary condition instead of the null-field equation for the longitudinal field. When the non-local effects are neglected, the transition matrix becomes the transition matrix in the local optical response theory, while for spherical particles, the transition matrix is analytically equivalent to the transition matrix derived by the extended Mie scattering theory that considers non-local optical response. The numerical results obtained by the T-matrix method are in good agreement with the results delivered by the discrete sources method which also considers non-local optical response.

An Analysis of the Quantum Effect of Nonlocality in Plasmonics Using the Discrete Sources Method

We consider the mathematical problem of electromagnetic wave scattering by a plasmonic dimer composed of noble metal nanoparticles with sizes less than tens of nanometers. To develop mathematical models, the efficient discrete sources method is used, which makes it possible to take all peculiar features of such systems into account, including the shapes of particles and the effects of spatial dispersion, which are also known as nonlocal effects. It is shown that in the case of external fields that are independent of the azimuthal harmonics, it is possible to approximate the problem solution using the system of vertical dipoles on the axis of symmetry of the particle. Based on the hybrid scheme of the discrete sources method, the problem of excitation of a dimer by the field of a point charge in uniform straight motion in a homogeneous space is first solved.

Extension of the discrete sources method to investigate the non-local effect influence on non-spherical core-shell particles

The Discrete Sources Method (DSM) has been extended to model non-spherical, axisymmetric core-shell particles by taking into account the Non-local Effect (NLE). For this purpose, the Generalized Non-local Optical Response (GNOR) model of the NLE has been employed. By using the extended DSM numerical scheme, prolate and oblate core-shell spheroidal particles have been examined. The simulation results show that the influence of the NLE on both the far and the near field properties of plasmonic core-shell particles is essential. In particular it has been found that the plasmon resonance amplitude is decreased by about 40%, the near field intensity is reduced up to one order of a magnitude, and the blue shift of the plasmon resonance can reach value of 15 nm. Besides, it has been demonstrated that a larger shell refractive index leads to a higher value of the plasmon resonance.