Discrete Dipole Approximation Model Research Articles

Atomistic polarization model for Raman scattering simulations of large metal tips with atomic-scale protrusions at the tip apex

Abstract Tip-enhanced Raman spectroscopy (TERS) has recently been developed to push the spatial resolution down to single-chemical-bond scale. The morphology of the scanning tip, especially the atomistic protrusion at the tip apex, plays an essential role in obtaining both high spatial resolution and large field enhancement at the Ångström level. Although it is very difficult to directly characterize the atomistic structures of the tip, the Raman scattering from the apex’s own vibrations of the metal tip can provide valuable information about the stacking of atoms at the tip apex. However, conventional quantum chemistry packages can only simulate the Raman scattering of small metal clusters with few atoms due to huge computational cost, which is not enough since the shaft of the tip behind the apex also makes significant contributions to the polarizabilities of the whole tip. Here we propose an atomistic polarization model to simulate the Raman spectra of large metal tips at subwavelength scales based on the combination of the atomistic discrete dipole approximation model and the density functional theory. The atomistic tip with different sizes and stacking structures is considered in its entirety during the calculation of polarizabilities, and only the vibrational contributions from the tip apex are taken into account to simulate the Raman spectra of the tip. The Raman spectral features are found to be very sensitive to the local constituent element at the tip apex, atomic stacking modes, and shape of the tip apex, which can thus be used as a fingerprint to identify different atomistic structures of the tip apex. Moreover, our approaches can be extended to the metal tips with sub-wavelength sizes, making it possible to consider both the large scale and the atomistic detail of the tip simultaneously. The method presented here can be used as a basic tool to simulate the Raman scattering process of the metal tips and other nanostructures in an economic way, which is beneficial for understanding the roles of atomistic structures in tip- and surface-enhanced spectroscopies.

Accurate and fast modeling of scattering from random arrays of nanoparticles using the discrete dipole approximation and angular spectrum method.

Lens-free microscopes can utilize holographic reconstruction techniques to recover the image of an object from the digitally recorded superposition of an unperturbed plane wave and a wave scattered by the object. Image reconstruction most commonly relies on the scalar angular spectrum method (ASM). While fast, the scalar ASM can be inaccurate for nanoscale objects, either because of the scalar approximation, or more generally, because it only models field propagation and not light-matter interaction, including inter-particle coupling. Here we evaluate the accuracy of the scalar ASM when combined with three different light-matter interaction models for computing the far-field light scattered by random arrays of gold and polystyrene nanoparticles. Among the three models-a dipole-matched transmission model, an optical path length model, and a binary amplitude model-we find that which model is most accurate depends on the nanoparticle material and packing density. For polystyrene particles at any packing density, there is always at least one model with error below 20%, while for gold nanoparticles with 40% or 50% surface coverage, there are no models that can provide errors better than 30%. The ASM error is determined in comparison to a discrete dipole approximation model, which is more computationally efficient than other full-wave modeling techniques. The knowledge of when and how the ASM fails can serve as a first step toward improved resolution in lens-free reconstruction and can also be applied to other random nanoparticle array applications such as lens-based super-resolution imaging, sub-diffraction beam focusing, and biomolecular sensing.

Au Nanobead Chains with Tunable Plasmon Resonance and Intense Optical Scattering: Scalable Green Synthesis, Monte Carlo Assembly Kinetics, Discrete Dipole Approximation Modeling, and Nano-Biophotonic Application

The development of optically tunable and intensely scattering materials is of wide interest in biophotonics and medicine, provided they are biocompatible. Highly linear, tunable, narrow-gap, and in...

Inverse design of radiative thermal meta-sources via discrete dipole approximation model

The radiation from conventional thermal infrared sources is incoherent and unpolarized. It has been recently shown that patterning plasmonic materials into metasurfaces can enhance the coherence of thermal radiation through thermal excitation of localized resonant modes in meta-atoms, enabling realization of thermal emitting metasurfaces—metasources—with high directivity and spectral selectivity. Toward achieving flexible modulation of radiative heat using metasurfaces and realization of complex functionalities, the design rules and modeling tools should be modified to take into account the incoherent nature of thermal radiation. In this paper, we utilize a robust formulation based on discrete dipole approximation within the framework of fluctuation dissipation theorem, which can efficiently characterize the thermal emission from large-area finite thermal metasources consisting of nanostructured materials. We employ an evolutionary lattice approach for the inverse design of radiative thermal metasources through topology optimization without relying on the phase analysis based on the assumption of coherency. To this end, the interaction matrix of dipolar equations is initialized for a lattice of subwavelength blocks and the arrangement of the blocks is subsequently optimized via a genetic algorithm toward achieving a certain spatial emission pattern with minimal computational cost. This approach enables fast and efficient design of large-scale thermal metasources with arbitrary functionalities. In particular, we investigate steering, focusing, and arbitrary shaping of partially coherent thermal radiation via finite silicon carbide gratings supporting surface phonon polaritons. Moreover, we demonstrate that the use of electro-optical materials such as graphene enables active tuning of thermal emission and realization of geometrically fixed multifunctional thermal metasources.

Rapid quantitative protein detection by light transmission spectroscopy.

Rapid, sensitive, and quantitative protein detection is critical for many applications in medicine, environmental monitoring, and the food industry. Advancements in detection of proteins include the use of antigen-antibody binding; however, many current methods are time-consuming and have limiting factors such as low sensitivity and the inability to provide absolute values. We present a new high-throughput method for protein detection using light transmission spectroscopy (LTS), which can quantify and size nanoparticles in fluid suspension. LTS can quantify proteins directly and target specific proteins through antigen-antibody binding. This work shows that LTS can distinguish between and quantify bovine serum albumin, its antibody, and the BSA + Ab complex and determine BSA protein concentrations down to 5 μg/mL. We use both Mie and discrete dipole approximation models to provide geometric insight into the binding process.

Far Field Optical Properties of a Monolayer of SiO2 Spheres and Small Au Nanoparticles

ABSTRACTHere, we present a numerical study of the far field optical response of a monolayer composed by an hexagonal closed packed array of SiO2 spheres with a single Au NP at each interstitial position. The Optical Efficiencies, Reflection, Transmission and Absorption at normal incidence, were calculated using Discrete Dipole Approximation model extended to periodic targets. In order to consider different amounts of loads of Au NPs per unit of area in the monolayer, we have fixed the diameter of Au NPs (9 nm) and varied the diameter of the SiO2 spheres. The numerical calculations indicate that Au-SiO2 composite monolayers can absorb and scatter the incident electromagnetic wave, as the load of Au NPs increases the monolayer becomes less transparent to light and the spectra are red-shifted. The profile of the absorption spectrum of the Au-SiO2 composite monolayer is very similar to that of a Au NPs monolayer (composite monolayer without the Silica spheres) but less intense, presumably because the Silica spheres screen the coupling of the Localized Surface Plasmons of Au NPs.

Up-Conversion Luminescence Properties of Lanthanide-Gold Hybrid Nanoparticles as Analyzed with Discrete Dipole Approximation.

Up-conversion nanoparticles (UCNP) under near-infrared (NIR) light irradiation have been well investigated in the field of bio-imaging. However, the low up-conversion luminescence (UCL) intensity limits applications. Plasmonic modulation has been proposed as an effective tool to adjust the luminescence intensity and lifetime. In this study discrete dipole approximation (DDA) was explored concerning guiding the design of UCNP@mSiO2-Au structures with enhanced UCL intensity. The extinction effects of gold shells could be changed by adjusting the distance between the UCNPs and the Au NPs by synthesized tunable mesoporous silica (mSiO2) spacers. Enhanced UCL was obtained under 808 nm irradiation. The original theoretical predictions could not be demonstrated to full extend by experimental data, indicating that better models for simulation need to take into account in homogeneities in particle morphologies. Yet, one very certain conclusion resulting from the DDA calculations and experiments is that the absorbance can blue-shift with more Au NPs added and the absorbance can-red shift for samples with enhanced silica sizes in the UCNP@mSiO2-Au structures. Furthermore, when the DDA model is more consistent with the practical structure (dispersed Au NPs instead of Au shell), the theoretical absorbance occurs almost the same as the practical absorbance. All in all, the DDA could fit the extinction effect of Au perfectly and be suitable for guiding how to design the UCNP and Au.

Lidar cross-sections of soot fractal aggregates: Assessment of equivalent-sphere models

This work assesses the ability of equivalent-sphere models to reproduce the optical properties of soot aggregates relevant for lidar remote sensing, i.e. the backscattering and extinction cross sections. Lidar cross-sections are computed with a spectral discrete dipole approximation model over the visible-to-infrared (400–5000 nm) spectrum and compared with equivalent-sphere approximations. It is shown that the equivalent-sphere approximation, applied to fractal aggregates, has a limited ability to calculate such cross-sections well. The approximation should thus be used with caution for the computation of broadband lidar cross-sections, especially backscattering, at small and intermediate wavelengths (e.g. UV to visible).

Modeling Microwave Backscattering From Parabolic Rice Leaves

Scattering from rice leaves contributes substantially to total vegetation canopy backscattering and detailed knowledge about it is necessary for developing a microwave scattering model. A parabolic curve is generally adopted to simulate the leaf shape but this is rarely incorporated into the calculation of the scattering. In this paper, two specific models, one based on physical optics (PO) approximation and the other on the discrete dipole approximation (DDA), are presented to involve the parabolic leaf curvature effects. Three typical leaves were chosen from 1433 parabolic leaves obtained during ground measurements. The PO and DDA models were used to calculate the leaf scattering. The generalized Rayleigh–Gans (GRG) approximation was also included in the simulation. The method of moments, a computational electromagnetic method, was utilized to evaluate the accuracy of each model. Validation of the models was conducted at incidence angles ranging from 10° to 60°, incidence azimuthal angles ranging from 0° to 360°, and incidence frequencies of 1.2 GHz (L-band), 5.4 GHz (C-band), and 9.65 GHz (X-band). Among the GRG approximation, the DDA model and the PO model, the latter gave the best accuracy −>65% in the cases tested, while the GRG model was the least accurate. The high accuracy of the PO model was maintained at both the low and high frequency bands. The PO model, therefore, has great potential for use to interpret radar measurements from rice fields and other types of vegetation canopy.

Perturbations of the optical properties of mineral dust particles by mixing with black carbon: a numerical simulation study

Abstract. Field observations show that individual aerosol particles are a complex mixture of a wide variety of species, reflecting different sources and physico-chemical transformations. The impacts of individual aerosol morphology and mixing characteristics on the Earth system are not yet fully understood. Here we present a sensitivity study on climate-relevant aerosols optical properties to various approximations. Based on aerosol samples collected in various geographical locations, we have observationally constrained size, morphology and mixing, and accordingly simulated, using the discrete dipole approximation model (DDSCAT), optical properties of three aerosols types: (1) bare black carbon (BC) aggregates, (2) bare mineral dust, and (3) an internal mixture of a BC aggregate laying on top of a mineral dust particle, also referred to as polluted dust. DDSCAT predicts optical properties and their spectral dependence consistently with observations for all the studied cases. Predicted values of mass absorption, scattering and extinction coefficients (MAC, MSC, MEC) for bare BC show a weak dependence on the BC aggregate size, while the asymmetry parameter (g) shows the opposite behavior. The simulated optical properties of bare mineral dust present a large variability depending on the modeled dust shape, confirming the limited range of applicability of spheroids over different types and size of mineral dust aerosols, in agreement with previous modeling studies. The polluted dust cases show a strong decrease in MAC values with the increase in dust particle size (for the same BC size) and an increase of the single scattering albedo (SSA). Furthermore, particles with a radius between 180 and 300 nm are characterized by a decrease in SSA values compared to bare dust, in agreement with field observations. This paper demonstrates that observationally constrained DDSCAT simulations allow one to better understand the variability of the measured aerosol optical properties in ambient air and to define benchmark biases due to different approximations in aerosol parametrization.

Discrete-dipole approximation model for control and optimization of a holographic metamaterial antenna.

Since the discovery of materials with negative refractive index, widely known as metamaterials, it has been possible to develop new devices that utilize a metamaterial's ability to control the path of electromagnetic energy. Of particular promise, and already under intensive development for commercial applications, are metamaterial antennas for satellite communications. Using reconfigurable metamaterials in conjunction with the principles of holography, these new antennas can electronically steer the high gain antenna beam required for broadband communications while not having any moving parts, being thinner, lighter weight, and less expensive, and requiring less power to operate than conventional alternatives. Yet, the promise of these devices will not be realized without efficient and effective control and optimization. Toward this end, in this paper a discrete-dipole approximation (DDA) model of a waveguide-fed planar metamaterial antenna is derived. The proposed model is demonstrated to accurately predict the radiation of a two-dimensional metamaterial at a much reduced computational cost to full-wave simulation and at much greater fidelity than simpler models typically used in the field. The predictive capabilities of the derived DDA model opens possibilities for model-based control design for optimal beam steering.

Effects of internal mixing and aggregate morphology on optical properties of black carbon using a discrete dipole approximation model

Abstract. According to recent studies, internal mixing of black carbon (BC) with other aerosol materials in the atmosphere alters its aggregate shape, absorption of solar radiation, and radiative forcing. These mixing state effects are not yet fully understood. In this study, we characterize the morphology and mixing state of bare BC and BC internally mixed with sodium chloride (NaCl) using electron microscopy and examine the sensitivity of optical properties to BC mixing state and aggregate morphology using a discrete dipole approximation model (DDSCAT). DDSCAT is flexible in simulating the geometry and refractive index of particle aggregates. DDSCAT predicts a higher mass absorption coefficient (MAC), lower single scattering albedo (SSA), and higher absorption Angstrom exponent (AAE) for bare BC aggregates that are lacy rather than compact. Predicted values of SSA at 550 nm range between 0.16 and 0.27 for lacy and compact aggregates, respectively, in agreement with reported experimental values of 0.25 ± 0.05. The variation in absorption with wavelength does not adhere precisely to a power law relationship over the 200 to 1000 nm range. Consequently, AAE values depend on the wavelength region over which they are computed. The MAC of BC (averaged over the 200–1000 nm range) is amplified when internally mixed with NaCl (100–300 nm in radius) by factors ranging from 1.0 for lacy BC aggregates partially immersed in NaCl to 2.2 for compact BC aggregates fully immersed in NaCl. The SSA of BC internally mixed with NaCl is higher than for bare BC and increases with the embedding in the NaCl. Internally mixed BC SSA values decrease in the 200–400 nm wavelength range, a feature also common to the optical properties of dust and organics. Linear polarization features are also predicted in DDSCAT and are dependent on particle size and morphology. This study shows that DDSCAT predicts complex morphology and mixing state dependent aerosol optical properties that have been reported previously and are relevant to radiative transfer, climate modeling, and interpretation of remote sensing measurements.

Localized surface plasmon resonance in arrays of nano-gold cylinders: inverse problem and propagation of uncertainties

The plasmonic nanostructures are widely used to design sensors with improved capabilities. The position of the localized surface plasmon resonance (LSPR) is part of their characteristics and deserves to be specifically studied, according to its importance in sensor tuning, especially for spectroscopic applications. In the visible and near infra-red domain, the LSPR of an array of nano-gold-cylinders is considered as a function of the diameter, height of cylinders and the thickness of chromium adhesion layer and roughness. A numerical experience plan is used to calculate heuristic laws governing the inverse problem and the propagation of uncertainties. Simple linear formulae are deduced from fitting of discrete dipole approximation (DDA) calculations of spectra and a good agreement with various experimental results is found. The size of cylinders can be deduced from a target position of the LSPR and conversely, the approximate position of the LSPR can be simply deduced from the height and diameter of cylinders. The sensitivity coefficients and the propagation of uncertainties on these parameters are evaluated from the fitting of 15500 computations of the DDA model. The case of a grating of nanodisks and of homothetic cylinders is presented and expected trends in the improvement of the fabrication process are proposed.

Multiple scattering effects in Doppler optical coherence tomography of flowing blood

We investigate the effect of multiple scattering on the optical coherence tomography (OCT) signal and the Doppler OCT signal of flowing blood. Doppler OCT measurements at 1300 nm are performed on flowing diluted porcine blood with hematocrit ranging between 0% and 15%. Measured blood hematocrit and mean red blood cell volume are used to calculate, using the discrete dipole approximation model, the (single) scattering coefficient and scattering anisotropy of blood. Monte Carlo simulations, based on the calculated scattering coefficients and scattering anisotropies, are compared to Doppler OCT measurements for hematocrit smaller than 10%. Good quantitative agreement between Doppler OCT measurements and Monte Carlo simulations is observed. Our measurements, calculations and simulations explain the relatively low attenuation coefficients and well preserved flow profiles measured with Doppler OCT for flowing blood. Monte Carlo simulations demonstrate the effect of the scattering anisotropy of the medium on the strength of multiple scattering effects in Doppler OCT signals. With increasing scattering anisotropy the OCT attenuation decreases; the distortion of the flow profile is strongest at intermediate scattering anisotropies (≈0.6).

Investigation of the presence of rod-shaped bacteria on food surface via elastic light scattering

We investigated the presence and related signal-to-noise ratio (SNR) of rod-shaped bacteria on a produce surface using elastic scattering. The theoretical noise was defined as a scattering signal from a rough produce surface while the signal was defined as a scattering signal from the increasing numbers of rod-shaped bacteria on the produce surface. In this research, we measured the surface topography of a tomato using BioAFM to provide the quantitative nature of the surface roughness which was, in turn, modeled with the discrete dipole approximation (DDA) for an accurate estimation of the background scattering signature. Then we included the DDA model of rod-shaped bacteria and calculated the combined elastic scattering signature in the upper hemispherical space with different polarizations, wavelengths, and incident angles. The total scattering cross-section (TSC) and partial scattering cross-section (PSC) were both computed on six predefined aperture locations. The results indicate that, upon proper selection of the wavelength and incident angle, it was possible to provide the minimum number of bacteria (~32) to provide a differentiable elastic scattering signal from the produce surface.

Extension of Discrete-Dipole Approximation Model to Compute Nonlinear Absorption in Gold Nanostructures

Discrete-dipole approximation (DDA) model has been widely used to provide quantitative predictions on the linear optical absorption of metallic nanostructures (MNS) irrespective of their geometry. Here, we demonstrate that it can be extended to the computations of MNS’ nonlinear light absorption. In the extended DDA (e-DDA) modeling, Drude’s dielectric function (or standard dielectric function) for given MNS in the dark is employed for the computation of linear absorption in an ensemble of the MNS. As excited by intense laser light, the dielectric function is altered in the presence of photoexcited electrons in the MNS. With the altered dielectric function and quasi-equilibrium approximation, the DDA model is reapplied to acquire the quantitative simulation on the nonlinear optical absorption. The results of e-DDA modeling are in good agreement with experimental data for gold nanorods and nanospheres.

Saturn’s F ring grains: Aggregates made of crystalline water ice

We present models of the near-infrared (1–5 μm) spectra of Saturn’s F ring obtained by Cassini’s Visual and Infrared Mapping Spectrometer (VIMS) at ultra-high phase angles (177.4–178.5°). Modeling this spectrum constrains the size distribution, composition, and structure of F ring particles in the 0.1–100 μm size range. These spectra are very different from those obtained at lower phase angles; they lack the familiar 1.5 and 2 μm absorption bands, and the expected 3 μm water ice primary absorption appears as an unusually narrow dip at 2.87 μm. We have modeled these data using multiple approaches. First, we use a simple Mie scattering model to constrain the size distribution and composition of the particles. The Mie model allows us to understand the overall shapes of the spectra in terms of dominance by diffraction at these ultra-high phase angles, and also to demonstrate that the 2.87 μm dip is associated with the Christiansen frequency of water ice (where the real refractive index passes unity). Second, we use a combination of Mie scattering with Effective Medium Theory to probe the effect of porous (but structureless) particles on the overall shape of the spectrum and depth of the 2.87 μm band. Such simple models are not able to capture the shape of this absorption feature well. Finally, we model each particle as an aggregate of discrete monomers, using the Discrete Dipole Approximation (DDA) model, and find a better fit for the depth of the 2.87 μm feature. The DDA models imply a slightly different overall size distribution. We present a simple heuristic model which explains the differences between the Mie and DDA model results. We conclude that the F ring contains aggregate particles with a size distribution that is distinctly narrower than a typical power law, and that the particles are predominantly crystalline water ice.

Discrete dipole approximation simulations on GPUs using OpenCL—Application on cloud ice particles

The global distribution and climatology of ice clouds are among the main uncertainties in climate modeling and prediction. In order to retrieve ice cloud properties from remote sensing measurements, the scattering properties of all cloud ice particle types must be known. The discrete dipole approximation (DDA) simulates scattering of radiation by arbitrarily shaped particles and is thus suitable for cloud ice crystals. The DDA models the particle as a collection of equal dipoles on a lattice, and is computationally much more expensive than approximations restricted to more regularly shaped particles. On a single computer the calculation for an ice particle of a specific size, for a given scattering plane at one specific wavelength can take several days. We have ported the core routines of the scattering suite “ADDA” to the open computing language (OpenCL), a framework for programming parallel devices like PC graphics cards (graphics processing units, GPUs) or multi-core CPUs. In a typical case we can achieve a speed-up on a GPU as compared to a CPU by a factor of 5 in double precision and a factor of 15 in single precision. Spreading the work load over multiple GPUs will allow calculating the scattering properties even of large cloud ice particles.

Localized surface plasmon resonance of single silver nanoparticles studied by dark-field optical microscopy and spectroscopy.

Localized surface plasmon resonance (LSPR) of Ag nanoparticles (NPs) with different shapes and disk-shaped Ag NP pairs with varying interparticle distance is studied using dark-field optical microscopy and spectroscopy (DFOMS). Disk-, square-, and triangular-shaped Ag NPs were fabricated on indium tin oxide-coated glass substrates by electron beam lithography. The LSPR spectra collected from single Ag NPs within 5×5 arrays using DFOMS exhibited pronounced redshifts as the NP shape changed from disk to square and to triangular. The shape-dependent experimental LSPR spectra are in good agreement with simulations using the discrete dipole approximation model, although there are small deviations in the peak wavelengths for square- and triangular-shaped NPs. The LSPR spectra of disk-shaped Ag NP pairs with varying interparticle distances were acquired from five different locations across the pair axis. It was clearly observed that the LSPR wavelength redshifts as the interparticle distance decreases, indicating a strong interaction when two Ag NPs are close to each other.

Surface Plasmon Enhanced Third-Order Nonlinear Optical Effects in Ag−Fe3O4 Nanocomposites

We report an approach to enhance the third-order nonlinear optical properties of a nanocrystal through the attachment of another metallic nanoparticle. Both two-photon absorption (TPA) cross section and nonlinear refractive (NR) cross section of a Fe3O4 nanocube with and without the attachment of an Ag nanoparticle are characterized by using the Z-scan technique. As compared to pristine Fe3O4 nanocube, the TPA and NR cross section of Ag-particle-attached Fe3O4 nanocube is increased by several folds at light frequencies far below the surface plasmon resonance of Ag particle, with precise values depending on the size of the Ag particle. These enhanced values are in agreement with the theoretically calculated enhancement by discrete dipole approximation modeling, which reveals that the local electric field induced by the metal nanoparticle should play an essential role in the enhancement.