Generalized Mie Theory Research Articles

Generalized Mie Theory for Full‐Wave Numerical Calculations of Scattering Near‐Field Optical Microscopy with Arbitrary Geometries

Scattering‐type scanning near‐field optical microscopy (s‐SNOM) is becoming a premier method for the nanoscale optical investigation of materials well beyond the diffraction limit. A number of popular numerical methods exist to predict the near‐field contrast for axisymmetric configurations of scatterers on a surface in the quasi‐electrostatic approximation. Here, a fully electrodynamic approach is given for the calculation of near‐field contrast of several scatterers in arbitrary configuration, based on the generalized Mie scattering method. Examples for the potential of this new approach are given by showing the coupling of hyperbolic phonon polaritons in hexagonal boron nitride (hBN) layers and showing enhanced scattering in core–shell systems. In general, this method enables the numerical calculation of the near‐field contrast in a variety of strongly resonant scatterers and is able to accurately recreate spatial near‐field maps.

Tightly focused linearly and radially polarized beam effect on the LSPR peak with varying particle size

Interactions of gold and silver spherical nanoparticles (NPs) of a wide range of radius size with tightly focused beams are investigated for a wide range of wavelengths. The scattering of tightly focused beams with a single NP of varying size is examined using a generalized Mie theory and average intensity enhancement in the near-field due to localized surface plasmons is examined for different tightly focused beams. A multipole expansion approach is used to observe the contribution of modes in shaping the scattered light intensity. Influence of particle size and tightly focused beam on intensity enhancement factor is investigated and a shift in localized surface plasmon resonance (LSPR) peak towards higher wavelength is observed with increasing particle size. Maximum intensity enhancement factor due to scattering of different incident beams by a metallic NP is theoretically examined and reported. Gold and silver NP having radius size ranging from 30–60 nm and 1–15 nm respectively showed a maximum intensity enhancement factor in different media. A significant enhancement for the tightly focused radially polarized beam is observed for gold and silver NPs of radius size between 50 nm and 100 nm. Variation towards higher wavelength in LSPR peak due to involvement of higher order of multipoles, and the surrounding medium are also examined in detail.

Models of light absorption enhancement in perovskite solar cells by plasmonic nanoparticles

AbstractNumerous experiments have demonstrated improvements on the efficiency of perovskite solar cells by introducing plasmonic nanoparticles, however, the underlying mechanisms are still not clear: the particles may enhance light absorption and scattering, as well as charge separation and transfer, or the perovskite's crystalline quality. Eventually, it can still be debated whether unambiguous plasmonic increase of light absorption has indeed been achieved. Here, various optical models are employed to provide a physical understanding of the relevant parameters in plasmonic perovskite cells and the conditions under which light absorption may be enhanced by plasmonic mechanisms. By applying the recent generalized Mie theory to gold nanospheres in perovskite, it is shown that their plasmon resonance is conveniently located in the 650–800 nm wavelength range, where absorption enhancement is most needed. It is evaluated for which active layer thickness and nanoparticle concentration a significant enhancement can be expected. Finally, the experimental literature on plasmonic perovskite solar cells is analyzed in light of this theoretical description. It is estimated that only a tiny portion of these reports can be associated with light absorption and point out the importance of reporting the perovskite thickness and nanoparticle concentration in order to assess the presence of plasmonic effects.

Simulation of Fe2O3/Au@MoS2 plasmonic core/shell@shell nanocomposites: Optical properties and photothermal application

The plasmonic and magneto-plasmonic nanocomposites are multi-functional structures that are applicable to medical applications such as tumor therapy, diagnosis, and biosensors. Here, the simulation of the optical and photothermal properties of plasmonic nanocomposites has been done. The spherical core@shell and core/shell@shell nanocomposites have been modeled using the generalized Mie theory. Au and Fe2O3 have been used as plasmonic and magnetic structures because of their bio-compatibility and then the role of MoS2 shell has been examined. The results show that these structures are very effective in photothermal therapy since their localized surfaced plasmon resonance is situated in the near-infrared region of electromagnetic waves. Among the simulated structures, Fe2O3@Au shows the best plasmonic behavior and absorption efficiency enhanced about 7 when the core radius is 20 nm, and the shell thickness and wavelength of incident light are between 5 and 10 nm and 700–800 nm, respectively. Maxwell-Garnett's effective medium theory has been used to calculate the effective permittivity of nanocomposites as well as the simulation of the temperature increase under laser radiation. The temperature enhancement of single nanocomposites shows very promising results. The single Fe2O3/Au@MoS2core/shell@shell nanocomposite illustrates the highest performance in temperature increase with 10−3K.

Inverse design of functional photonic patches by adjoint optimization coupled to the generalized Mie theory

We propose a rigorous approach for the inverse design of functional photonic structures by coupling the adjoint optimization method and the 2D generalized Mie theory (2D-GMT) for the multiple scattering problem of finite-sized arrays of dielectric nanocylinders optimized to display desired functions. We refer to these functional scattering structures as “photonic patches.” We briefly introduce the formalism of 2D-GMT and the critical steps necessary to implement the adjoint optimization algorithm to photonic patches with designed radiation properties. In particular, we showcase several examples of periodic and aperiodic photonic patches with optimal nanocylinder radii and arrangements for radiation shaping, wavefront focusing in the Fresnel zone, and for the enhancement of the local density of states (LDOS) at multiple wavelengths over micron-sized areas. Moreover, we systematically compare the performances of periodic and aperiodic patches with different sizes and find that optimized aperiodic Vogel spiral geometries feature significant advantages in achromatic focusing compared to their periodic counterparts. Our results show that adjoint optimization coupled to 2D-GMT is a robust methodology for the inverse design of compact photonic devices that operate in the multiple scattering regime with optimal desired functionalities. Without the need for spatial meshing, our approach provides efficient solutions at a strongly reduced computational burden compared to standard numerical optimization techniques and suggests compact device geometries for on-chip photonics and metamaterials technologies.

Morphology-dependent resonance induced optical forces in a multiple-sphere system.

Optical fields and forces can be greatly enhanced for a microparticle when the whispering gallery modes (WGMs) are excited. In this paper, by solving the scattering problem using the generalized Mie theory, the morphology-dependent resonances (MDRs) and resonant optical forces derived from the coherent coupling of WGMs are investigated in multiple-sphere systems. When the spheres approach each other, the bonding and antibonding modes of MDRs emerge and correspond to the attractive and repulsive forces, respectively. More importantly, the antibonding mode is good at propagating light forward, while the optical fields decay rapidly for the bonding mode. Moreover, the bonding and antibonding modes of MDRs in the PT-symmetric system can persist only when the imaginary part of the refractive index is small enough. Interestingly, it is also shown that for a PT-symmetric structure, only a minor imaginary part of the refractive index is required to generate a significant pulling force at MDRs, making the whole structure move against the light propagation direction. Our work deepens the understanding of the collective resonance behavior of multiple spheres and paves the way for potential applications in particle transportation, non-Hermitian systems, integrated optical devices, etc.

Extinction by plasmonic nanoparticles in dispersive and dissipative media.

Extinction of small metallic spheres has been well understood through the classical Mie theory when the host medium is dispersive and transparent. However, the role of host dissipation on the particulate extinction remains a competition between the enhancing and reducing effects on the localized surface plasmonic resonance (LSPR). Here, using a generalized Mie theory, we elaborate on the specific influence mechanisms of host dissipation on the extinction efficiency factors of a plasmonic nanosphere. To this end, we isolate the dissipative effects by comparing the dispersive and dissipative host with its dissipationless counterpart. As a result, we identify the damping effects of host dissipation on the LSPR including the resonance widening and amplitude reducing. The resonance positions are shifted by host dissipation, which cannot be predicted by the classical Fröhlich condition. Finally, we demonstrate that a wideband extinction enhancement due to host dissipation can be realized away from the positions of the LSPR.

Controlling the polarization of chiral dipolar emission with a spherical dielectric nanoantenna.

Circularly polarized light (CPL) carrying spin angular momentum is crucial to many applications, such as quantum computing, optical communication, novel displays, and biosensing. Nonetheless, the emission from chiral molecules contains comparable CPL components with opposite handedness, resulting in low levels of CPL overall with a small dissymmetry factor and fixed handedness consistent with the handedness of the molecules. Nanoantennas have proved to be useful tools for controlling the emission properties of quantum emitters. In particular, dielectric resonators support electric and magnetic modes, which implies unparalleled opportunities to interact with chiral molecules whose emission originates from both electric and magnetic dipole transitions. In this work, we theoretically study the effects of a spherical dielectric nanoantenna on the directionality and polarization of emission from a chiral molecule. With exact analytical solutions based on generalized Mie theory, we show that directional chiral light emission and nontrivial polarization modulation, such as handedness reversal or chirality enhancement, can be achieved simultaneously for a chiral dipole tangentially coupled with a silicon nanosphere. The influence of the relative strength and orientation between the electric and magnetic dipole moments is also discussed. Our results suggest a new approach to controlling chiral dipolar emission and could benefit the development of chiral light sources.

Distributed silicon nanoparticles: an efficient light trapping platform toward ultrathin-film photovoltaics.

In this paper, a new architecture comprising silicon nanoparticles inside a hole transport layer laid on a thin silicon layer is proposed to develop ultrathin film solar cells. Using generalized Mie theory, a fast analytical approach is developed to evaluate the optical absorption of the proposed structure for various geometries, polarizations and angles of incidence. The analytical results are verified through comparison with full-wave simulations, illustrating a reasonable agreement. The electrical performance of a distributed silicon nanoparticle solar cell is determined for selected configurations. To be able to predict the light-trapping in a solar cell comprising randomly distributed nanospheres, a new technique based on probability theory is developed and validated through comparison with the simulation results. Both analytical and numerical results show that the excited Mie resonant modes in the proposed structure lead to a significant enhancement in both absorption and the photo-generated current, in comparison to a conventional silicon solar cell with an equivalent volume of the active layer. In the case of random distributions, other advantages, including the simple fabrication process, indicate that the cell is a promising structure for ultrathin photovoltaics.

Directional light emission by electric and magnetic dipoles near a nanosphere: an analytical approach based on the generalized Mie theory.

We present a theoretical study of directional light emission by dipole emitters near a spherical nanoparticle. Our analysis is extended from an exact electrodynamical approach for solving the coupling between a dipole and a sphere, providing a full picture of the directional emission for a complete set of combinations of variable emitters, particles, and their orientations. In particular, we show that the Mie resonances of a dielectric sphere are strongly influenced by the coupled dipole emitter, leading to the scattering properties that are different from the prediction by the standard Mie theory. Moreover, we demonstrate that the dielectric spheres have opposite effects on the emission direction and a decay rate of electric and magnetic dipoles. Our approach enriches the analytical toolbox for designing optical antennas and understanding dipole-sphere coupling.

Light–Matter Interactions in Films of Randomly Distributed Unidirectionally Scattering Dielectric Nanoparticles

We theoretically investigate the light scattering characteristics of monolayer films composed of randomly positioned unidirectionally scattering dielectric nanoparticles that support overlapping electric and magnetic dipole modes. We show using generalized Mie theory that the optical response of both sparse and dense nanoparticle films can be understood from the scattering properties of the individual dielectric nanoparticles, despite random particle-particle coupling effects, and validate these results with full wave electromagnetic simulations. The spectral, angular, and polarization dependent reflection and transmission scattering characteristics of these random particle films are also shown to be strikingly different from those of homogeneous dense solid thin films of equivalent dielectric permittivity.

Mode coupling in arrays of Al nanoparticles

The mechanisms of coupling between the lattice modes of a two-dimensional (2D) array consisting of Al nanoparticles and the localized modes of individual Al nanoparticles have been studied in detail. The results were obtained employing the finite-difference time-domain method (FDTD) and the generalized Mie theory. It was shown that interactions of single particles with 2D lattice modes significantly change the extinction spectra depending on the particle radius and the lattice period. The Rayleigh anomalies of higher orders contribute to formation of hybrid modes resulting in increase of the extinction efficiency in short wavelength range of the spectrum. It was shown that high intensity magnetic modes are excited in aluminum nanoparticles arrays. The patterns of spatial electromagnetic field distribution at the frequencies of hybrid modes have been studied. We note that comprehensive understanding the mode coupling mechanisms in arrays paves the way for engineering different types of modern photonic devices with controllable optical properties.

Scattering of light with angular momentum from an array of particles

Understanding the scattering properties of various media is of critical importance in many applications, from secure, high-bandwidth communications to extracting information about biological and mineral particles dissolved in sea water. In this paper we demonstrate how beams carrying orbital angular momentum (OAM) can be used to detect the presence of symmetric or chiral subsets of particles in disordered media. Using a generalized Mie theory we calculate analytical expressions for quasi-monochromatic structured light scattered by dilute distributions of micro- and nanoparticles. These allow us to determine the angular momentum of the scattered field as a function of the angular momentum of the incident beam and of the spatial distributions of scattering particles. Our numerical results show that we can distinguish structured from random distributions of particles, even when the number density of ordered particles is a few percent of the total distribution. We also find that the signal-to-noise ratio, in the forward direction, is equivalent for all orders of the Laguerre-Gaussian modes in relatively dense (but still dilute) distributions, making them an ideal basis to encode and transmit multiplexed signals.

Practical Implementation of Accurate Finite-Element Calculations for Electromagnetic Scattering by Nanoparticles

The finite-element method (FEM) is increasingly used as a numerical tool to support experimental and theoretical studies of the optical properties of nanoparticles, in contexts such as surface-enhanced spectroscopy, molecular plasmonics, metamaterials, and optical trapping. Here, we investigate the validity of such calculations, focusing in particular on numerically challenging cases involving strong optical (plasmon) resonances and solutions with large electric field gradients and intensities. These are exemplified by elongated metallic nanoparticles and two closely spaced metallic spheres (dimer), where highly localized regions of intense electric field enhancements occur at the tip or in the gap, so-called electromagnetic hot-spots. We assess the accuracy of the FEM solutions by comparing the result to exact analytic solutions based on the T-matrix method for an elongated particle and generalized Mie theory for a dimer. Particular attention is given to the electromagnetic properties that have seldom been studied in this context, notably near-field properties such as surface-field enhancement factors and far-field radiation profiles. We also demonstrate explicitly how the accuracy of the FEM predictions can be inferred from the solution of two problems with different mesh and bounding box parameters. Such a numerical check is crucial in practice as no exact solutions are in general available to compare with. While we chose the commercial software COMSOL to illustrate our results, the methods and conclusions are equally applicable to other FEM implementations. We provide for convenience full details of how to set up these calculations in COMSOL, which we hope will allow readers to easily reproduce them and seamlessly adapt them to their modeling needs. We expect this work will cement the FEM as a reliable method for routine calculation of electromagnetic scattering by nanoparticles.

A Potential-Based Formalism for Modeling Local and Hydrodynamic Nonlocal Responses From Plasmonic Waveguides

In this paper, we propose a general boundary integral equation (BIE) approach for solving both exterior (e.g., scattering) and interior (e.g., guided wave propagation) problems involving general plasmonic waveguiding structures with arbitrary cross-sectional geometries and with a continuous translational symmetry in the direction of wave propagation. Contrary to the field-based approach which deals with the electric and magnetic fields, we employ a potential-based formalism instead, involving vector and scalar potentials, and match them at the media interfaces. The proposed approach can handle not only conventional plasmonic waveguides on the order of a few hundred nanometers but also those whose critical sizes are a few nanometers and in which the nonlocal hydrodynamic effects need to be accounted for. The BIEs describing the interaction of light with the plasmonic waveguide are solved by the method of moments (MoM) algorithm. Two illustrative examples, the first one of which deals with the scattering problem, while the second computes the dispersion diagram of a plasmonic cylinder, are considered for both local and nonlocal cases. An excellent agreement is observed between the numerical and theoretical results, with the latter being derived from the generalized Mie theory.

Virtual Plasmonic Dimers for Ultrasensitive Inspection of Cluster–Surface Coupling

Plasmonic sensors owe their sensitivity to the susceptibility of collective electron modes to tiny changes of the local environment. Simple sensors are based on metal nanoparticles where spectral shifts of the resonance are frequently treated in view of an “effective” dielectric medium surrounding each particle. Using single-object spectroscopy probing a large number of silver particles on Si(111)-(7 × 7) in a photoemission electron microscope (PEEM), we show that this picture breaks down because of the formation of image dipoles in the substrate. Even at particle sizes as small as 10 nm, that is, small compared to the excitation wavelength, the dipole approximation is no longer valid because the system inherently creates higher order multipole modes. To validate this scenario, we compare plasmon energies, lifetimes, and their variability to the case of a surface with lower permittivity. Model calculations based on generalized Mie theory reveal that the formation of multipole modes is extremely sensitive ...

A Boundary Integral Equation Scheme for Simulating the Nonlocal Hydrodynamic Response of Metallic Antennas at Deep-Nanometer Scales

Modeling the interaction between light and a plasmonic nanoantenna, whose critical dimension is of a few nanometers, is complex owing to the “hydrodynamic” motion of free electrons in a metal. Such a hydrodynamic effect inevitably leads to a nonlocal material response, which enables the propagation of longitudinal electromagnetic waves in the material. In this paper, within the framework of a boundary integral equation and a method of moments algorithm, a computational scheme is developed for predicting the interaction of light with 3-D nonlocal hydrodynamic metallic nanoparticles of arbitrary shape. The numerical implementation is first demonstrated for the test example of a canonical spherical structure. The calculated results are shown to be in the excellent agreement with the theoretical results obtained with the generalized Mie theory. In addition, the capability of treating 3-D structures of general shapes is demonstrated by ellipsoids and dimers.

Plasmon heating of one-dimensional gold nanoparticle chains

Metallic nanoparticle chains exhibit strong plasmon coupling in periodic arrays that provides numerous opportunities for manipulating heating at nanoscale. The energy transport in a chain is sensitive to the interparticle plasmon coupling. A better understanding of optical and heating properties of the chain would provide useful guidance for future design of the novel devices. In this work, we use the organization of gold nanoparticles as linear assemblies and perform a detailed analysis of the heating features as a function of the number of particle, interparticle spacing and particle size in the chains using General Mie Theory. The results show that the heat generation of particle presents an exponential decay with increasing of the interparticle spacing. As the number of particle increases, the particle spacing increases and radius decreases, the boundary effect is gradually diminished to the center particle. When the particle spacing is 1 nm, the number of particle is seven and the radius is 10 nm, the heat production of center particle is 1.65 times than that of a single particle. The large particle size effectively increases the cross-section of absorption as well as the range of electromagnetic radiation, and thus more light energy can be absorbed and converted into heat as the radius increases. This study provides an original understanding on the plasmon heating behavior of one-dimensional nanoparticle chains and may be generalized to other types of aggregates formed by large numbers of interacting particles.

Cluster Assemblies Produced by Aggregation of Preformed Ag Clusters in Ionic Liquids.

Room-temperature ionic liquids (RTILs) can be used as electrosterical stabilizers for nanoparticles without adding stabilizing agents. However, the nanoparticle stability and its mechanisms are still in discussion. We deposited preformed 2 nm ±0.6 nm silver clusters into the ionic liquid C4MIM PF6 using in situ UV/vis absorption to monitor the deposition process. The time- and temperature-dependent cluster aggregation process was studied with ex situ UV/vis absorption spectroscopy analyzed with electrodynamic calculations using generalized Mie theory. On an atomistic level, the sample structure was investigated using EXAFS and a neural network based analysis of XANES. The combination of all methods shows that an aggregation of the original 2 nm clusters without coalescence takes place, which can be controlled or stopped by choosing an appropriate sample temperature. This approach allows the controlled production of chainlike cluster aggregates in RTIL, promising for a number of applications.

Influences of dipole–quadrupole strong interactions on optical properties of plasmonic nanodimers

An extended analytical method based on the dipole-quadrupole electromagnetic interaction is proposed to investigate the optical properties of strongly interacting plasmonic nanoparticles for which the known coupled dipoles approximation (CDA) is inaccurate. The introduced simple and novel method used here, namely coupled dipole-quadrupole approximation (CDQA), is used to elaborate on the optical interactions of individual modes including dipole-dipole, dipole-quadrupole and quadrupole-quadrupole. A simple and versatile formula is presented for the modified dipole-polarizability by considering an adjacent quadrupole effect, leading to accurate prediction of remarkable features in the optical properties of nanoparticle clusters in simple or complex forms. Interestingly, in a nanodimer configuration, it is shown that the quadrupole strongly affects the dipolar resonance energy, though the dipole impact on quadrupole properties are negligible. The findings are verified by the approximated methods, numerical computations and generalized Mie theory.