Discrete Dipole Approximation Method Research Articles

Transfer learning for metamaterial design and simulation

Abstract We demonstrate transfer learning as a tool to improve the efficacy of training deep learning models based on residual neural networks (ResNets). Specifically, we examine its use for study of multi-scale electrically large metasurface arrays under open boundary conditions in electromagnetic metamaterials. Our aim is to assess the efficiency of transfer learning across a range of problem domains that vary in their resemblance to the original base problem for which the ResNet model was initially trained. We use a quasi-analytical discrete dipole approximation (DDA) method to simulate electrically large metasurface arrays to obtain ground truth data for training and testing of our deep neural network. Our approach can save significant time for examining novel metasurface designs by harnessing the power of transfer learning, as it effectively mitigates the pervasive data bottleneck issue commonly encountered in deep learning. We demonstrate that for the best case when the transfer task is sufficiently similar to the target task, a new task can be effectively trained using only a few data points yet still achieve a test mean absolute relative error of 3 % with a pre-trained neural network, realizing data reduction by a factor of 1000.

RDDA method for characterization of photonic nanojets.

This paper presents a reduced discrete dipole approximation (RDDA) method as a flexible and powerful tool for computing the field distribution of photonic nanojets (PNJs) based on superposition of the induced dipole radiation fields with a low number of lattice points at the surface of microparticles. Microparticles with spherical and ellipsoidal shapes have been studied using the RDDA method to produce PNJs. The incident beam polarization and filling factor effects in the PNJs' shape and confinement strength have been characterized by quality factor Q. The best confined PNJs have been found in microellipsoids with a specific range of the shape parameter and filling factor values.

Computational modeling of Chlamydomonas reinhardtii cellular radiation properties with synergistic consideration of complex structures and compositions.

The radiation characteristics of microalgae are of great significance for the design of photobioreactors and ocean optical remote sensing. Yet the complex structure of microalgae makes it difficult to theoretically predict its radiation characteristics based on traditional Mie theory. In this work, taking Chlamydomonas reinhardtii as an example, a multi-component cell model with a complex structure is proposed, which considers the organelles and shape of microalgae, and the volume change during the production of Chlamydomonas reinhardtii lipids. The theoretical calculation is carried out using the discrete dipole approximation method, and an improved transmission method is used for experimental measurement. The experimental data are compared and analyzed with the multi-component complex structure model, the homogeneous sphere model and the coated sphere model. The results show that the calculation accuracy of the multi-component complex structure model is higher, the error of the scattering cross-section is reduced by more than 8.6% compared with the homogeneous sphere model and coated sphere model, and the absorption cross-section and the scattering phase function are in good agreement with the experimental results. With the increase of lipids, the absorption cross-section and the scattering phase function vary slightly. However, the scattering cross-section has an observed change with increasing wavelength. In addition, the theoretical calculation error can be reduced when the influence of the culture medium is taken into account.

Theoretical and experimental study on the radiative properties of Parachlorella kessleri: considering the effect of internal microstructure.

A microalgal cell model with multiple organelles considering both the irregular overall shape and internal microstructure was proposed. The radiative properties of Parachlorella kessleri during the normal phase, starch-rich phase, and lipid-rich phase were calculated by the discrete dipole approximation method in the visible wavelengths. The accuracy of the model is verified with experimental measurements. The results showed that the theoretical calculation of the established microalgal cell model is more accurate than those of the equal volume spheres, such as the homogeneous sphere and the coated sphere, with the errors of the scattering cross-section reduced by more than 10.7%. The calculated scattering phase function of the multi-component model is basically in good agreement with the experimental results. Compared to the normal growth phase, the lipid enrichment during the lipid-rich phase leads to a sharp increase in the scattering cross-section by three to four times, while the absorption cross-section remains stable. Remarkably, in the starch-rich phase, the abundant production of starch results in a reduction of two to three times in the absorption cross-section compared to the normal growth phase, while the scattering cross-section varies little. The results can provide basic data and theoretical support for the design and optimization of photobioreactors.

A comprehensive study on the Rod-based plasmonic structures sensing using the modified discrete dipole approximation method

Using the previously introduced modified discrete dipole approximation (DDA) method by applying the full details of the nanoparticle and its surrounding environment, the detection sensitivity of molecules by plasmonic Rod-based nanosensors, including U-shaped and Rod-shaped structures, was investigated. In the calculations, the two factors of the magnitude of the wavelength shift and the ability to distinguish molecules with similar properties were of significant interest. The results indicated that the sensitivity of Rod-based nanostructures is significantly higher than that of spherical nanoparticles. Among the plasmonic Rod-based nanosensors, the silver U-shaped structure performs better than others. The wavelength shift of the absorption spectrum of different nanosensors for a given molecule was very different, making it possible to detect very similar molecules from each other by testing different sensors.

Fast and accurate electromagnetic field calculation for substrate-supported metasurfaces using the discrete dipole approximation

Abstract Metasurface design tends to be tedious and time-consuming based on sweeping geometric parameters. Common numerical simulation techniques are slow for large areas, ultra-fine grids, and/or three-dimensional simulations. Simulation time can be reduced by combining the principle of the discrete dipole approximation (DDA) with analytical solutions for light scattered by a dipole near a flat surface. The DDA has rarely been used in metasurface design, and comprehensive benchmarking comparisons are lacking. Here, we compare the accuracy and speed of three DDA methods—substrate discretization, two-dimensional Cartesian Green’s functions, and one-dimensional (1D) cylindrical Green’s functions—against the finite difference time domain (FDTD) method. We find that the 1D cylindrical approach performs best. For example, the s-polarized field scattered from a silica-substrate-supported 600 × 180 × 60 nm gold elliptic nanocylinder discretized into 642 dipoles is computed with 0.78 % pattern error and 6.54 % net power error within 294 s, which is 6 times faster than FDTD. Our 1D cylindrical approach takes advantage of parallel processing and also gives transmitted field solutions, which, to the best of our knowledge, is not found in existing tools. We also examine the differences among four polarizability models: Clausius–Mossotti, radiation reaction, lattice dispersion relation, and digitized Green’s function, finding that the radiation reaction dipole model performs best in terms of pattern error, while the digitized Green’s function has the lowest power error.

Sensitivity of Localized Surface Plasmon Resonance and Acoustic Vibrations to Edge Rounding in Silver Nanocubes.

Precise knowledge of the dependence of nano-object properties on their structural characteristics such as their size, shape, composition, or crystallinity, in turn, enables them to be finely characterized using appropriate techniques. Spectrophotometry and inelastic light scattering spectroscopy are noninvasive techniques that are proving highly robust and efficient for characterizing the optical response and vibrational properties of metal nano-objects. Here, we investigate the optical and vibrational properties of monodomain silver nanocubes synthesized by the chemical route, with edge length ranging from around 20 to 58 nm. The synthesized nanocrystals are not perfectly cubic and exhibit rounded edges and corners. This rounding was quantitatively taken into account by assimilating the shape of the nanocubes to superellipsoids. The effect of rounding on their optical response was clearly evidenced by localized surface plasmon resonance spectroscopy and supported by calculations based on the discrete dipole approximation method. The study of their acoustic vibrations by high-resolution low-frequency Raman scattering revealed a substructure of the T2g band, which was analyzed as a function of rounding. The measured frequencies are consistent with the existence of an anticrossing pattern of the two T2g branches. Such an avoided crossing in the T2g modes is clearly evidenced by calculating the vibrational frequencies of silver nanocubes using the Rayleigh-Ritz variational method that accounts for both their real size, shape, and cubic elasticity. These results show that it is possible to assess the rounding of nanocubes, including by means of ensemble spectroscopic measurements on well-calibrated particles.

Simulating the sensing properties of silver nanoparticles for identifying molecular structures using modified discrete dipole approximation method ‎

Simulating the sensing properties of silver nanoparticles for identifying molecular structures using modified discrete dipole approximation method ‎

Numerical study on optimization of quantitative treatment conditions for skin cancer photothermal therapy considering multiple blood vessels

BackgroundIn recent years, lasers have gained considerable attention as a potential treatment option in the medical field. Photothermal therapy, in particular, has been investigated as a technique to remove tumor tissue by leveraging photothermal effects. The method involves raising the temperature of the tumor tissue to destroy it and has primarily been studied for skin cancer treatment. ObjectiveThis study aimed to simulate a skin layer with squamous cell carcinoma by using numerical modeling and investigate the effect of different numbers of blood vessels on the temperature distribution in the medium under conditions such as varied laser intensity and gold nanoparticle volume fraction. MethodsOptical properties of the light absorption enhancer were calculated using the discrete dipole approximation method, and the temperature and velocity distribution were computed using continuity, momentum, and energy equations. ResultsQuantitative determination of the apoptotic variable was performed to evaluate the treatment effect for each case, and the treatment condition with the maximum treatment effect was identified. Laser intensity with optimal therapeutic effect was confirmed to be 0.13 W, 0.15 W, 0.18 W, and 0.24 W, depending on the number of vessels, respectively, and the volume fraction of injected GNRs was confirmed to be 10−6 for all vessel numbers. ConclusionThe results of this study can serve as a guide for selecting appropriate treatment conditions when conducting photothermal therapy in the future

Spectral analysis of oxidation on localized surface plasmon resonance of copper nanoparticles thin film

Copper nanoparticles (CuNPs) possess localized surface plasmon resonance (LSPR) effect. Cu thin films composed of individual CuNPs exhibit stronger LSPR than the individual CuNPs due to the LSPR coupling among CuNPs. However, CuNPs are easy to be oxidized, which results in the rapid LSPR damping of the CuNPs thin films. Simulation of the variations of the coupled LSPR of two adjacent CuNPs with the thickness of oxide shells formed during oxidation is of great importance for understanding the mechanisms of the strong LSPR of CuNPs thin films and its rapid attenuation. In this paper, Discrete-dipole approximation method is used to simulate the extinction spectra of two adjacent spherical CuNPs as a function of the shell thickness (t), the ambient refractive index (n), the diameter (D) of the CuNPs, and the inter-nanoparticle spacing (L). The calculation is validated by experimental results. According to our model, for a definite CuNPs thin films, the oxide shell thickness of CuNPs can be calculated only if the extinction spectra and the morphology are provided. Further, it is found when the oxide shell thickness is small (t/R< 0.3), increasing n and decreasing L/D have an obvious synergistic effect on enhancing the coupled LSPR, but this synergistic effect weakens with the deepening of oxidation, and disappeared when t/R > 0.5. This study provides a calculation method for coupled core-shell nanoparticles and throws light on the role of oxidation on the rapid damped LSPR of CuNPs thin films.

Effects of microstructure and moisture content on the radiative properties of porous films for radiative cooling

Global warming is a major concern, and active cooling technology, which consumes substantial energy, contributes to global warming. Radiative cooling (RC) is a form of passive cooling. An optically selective porous film can provide cost-effective and efficient radiative cooling. This study aims to investigate the theoretical effects of the structural parameters on the cooling performance of porous films. An improved diffusion-limited cluster aggregation (DLCA) algorithm is established to reproduce porous structures with moisture content. A combination of discrete dipole approximation and Monte Carlo method was employed to predict the structure-related solar reflectance and “sky window” emissivity. An optimal design of a porous RC film was developed. The results demonstrate that the BaSO4 porous film can achieve high solar reflectance (∼ 97%), high “sky window” emissivity (∼ 99%), and a net cooling power of 102 W/m2 during the day. In particular, the effect of moisture content on the cooling performance of the porous RC film was analyzed. Moisture content enhances the cooling performance at night but decreases it during the daytime. The results provide guidance for designing optically selective porous films for radiative cooling.

Polarized radiative transfer in heterogeneous black carbon aerosol particles

Research on the polarized radiative transfer of black carbon (BC) aerosol particles in the atmosphere is of great help for real-time monitoring of climate change. Existing studies generally have not considered the effects of complex morphology and heterogeneity of BC aerosol particles on the polarized radiative transfer. BC aggregates with different coating shapes are established in accordance with the heterogeneous particle superposition model. The vector Monte Carlo method (VMCM) combined with Discrete dipole approximation (DDA) method proposed in this work offers a general method for calculating the polarized radiative transfer of heterogeneous BC aerosol particles with arbitrary coating shapes. The effects of sulfate coating volumes and shapes, and wavelengths on the Stokes parameters, the degree of polarization P, transmissivity T, and reflectivity R of atmosphere containing heterogeneous BC aerosol particles are discussed. The results show that the simplification of coating shape underestimates the Stokes parameter I and the degree of polarization P of the top of atmosphere and overestimates the I of the bottom of atmosphere. The simplification models of coating shape result in a maximum underestimation of the peak I by ∼26% at the bottom of atmosphere and a maximum overestimation of the peak I by ∼8% at the top of atmosphere, relative to that of the irregular coating models. Moreover, coating volumes and wavelengths also significantly affect the polarized radiative transfer characteristics. Thus, the influence of these factors should be considered for the calculation of polarized radiative transfer of heterogeneous BC aerosol particles in the atmosphere.

Near-Field Single-Scattering Calculations of Aerosols: Sensitivity Studies

We model the effects of the photosensitive parameters of aerosols on their optical properties to provide a solid framework for further experimental and theoretical studies. A spherical dust particle is used to study the effects of the ambient medium, size, surface roughness, wavelength, and imaginary part of the complex refractive index. Five Gaussian random spheres with different aspect ratios are simulated to study the dependence of aerosol light scattering properties on particle shape distribution. To investigate the influence of composition, we model two typical kaolinite-like particles (pure and composite) collected from Southwest Sahara, with 0 and 2% hematite at different mixing states. Using the method of discrete-dipole approximation in DDSCAT, a comparative study is performed with the Mueller matrix elements, scattering, absorption, extinction efficiencies, single scattering albedo, and linear depolarization ratio as indicators. For single, microscopic dust particles, near-field calculations are carried out. The results show that the intensity of backscattering and the scattering efficiency decreases in water compared to dry air. Light in the visible range is more efficient for aerosol scattering experiments. A small number of impurities in the sample will increase its absorbing properties, but, in general, the scattering efficiencies strongly depend on the single-particle mixing state. Smaller particles with a diameter comparable to the wavelength of incident light show higher scattering efficiencies but lower backscattering intensities than larger particles, while surface roughness is shown to strongly alter the polarizability of the particle but has a negligible effect on its single-scattering albedo. Moreover, different shapes have a strong effect on the degree of linear polarization, but, in general, using the spherical over elliptic shape model can underestimate the scattering efficiencies by up to 4%. Finally, variation in the imaginary part of the complex RI can underestimate the single scattering albedo by up to 35.8%.

Effect of necking and polydispersity in aggregate and primary particle size on the scattering matrix of soot aggregates

Morphology of soot aggregates includes complex structures such as necking and polydispersity in aggregate and primary particle size, which have considerable influences on their optical behavior. In this study, a comprehensive analysis of the impact of necking and polydispersity in aggregate and primary particle size is conducted to identify their effects on scattering matrix elements. Typical morphological parameters associated with flame-soot are used to generate aggregate representations via a tunable algorithm based on cluster-cluster aggregation. Necking is implemented via a modified cylindrical connector model and the level-set function model with different coefficients, whereas polydispersity in aggregate and monomer size is introduced assuming log-normal distributions. Scattering properties are calculated via discrete dipole approximation and multi-sphere T-matrix method. Individual impacts of these morphological features on the scattering matrix elements are presented, and the aggregate volume based approach is evaluated for representing the impact of necking. According to the results, the impacts of necking and primary particle polydispersity are similar and dominated by the resultant volume change, whereas that of aggregate polydispersity is more complicated. Accordingly, the aggregate volume based approach performs well in representing the effect of necking on the scattering matrix for the specified cases. The deficiency of the aggregate volume based approach is discussed and a potential way to improve it is proposed.

Site-selective growth and plasmonic spectral properties of L-shaped Janus Au-Ag gold nanodumbbells for surface-enhanced Raman scattering

Ligand-mediated interface control has been broadly applied as a powerful tool in constructing asymmetric multicomponent nanoparticles (AMNP), and induces the anisotropic growth with fine-tuning morphology, composition, plasmonic property and functionality. As a new kind of AMNP, the synthesis of Janus Au-Ag nanoparticles with tunable negative surface curvature is still a challenge. Here, we demonstrate that the synergistic surface energy effects between gold nanodumbbells (Au NDs) with a negative surface curvature and 4-mercaptobenzoic acid (4-MBA) can direct the site-selective growth of anisotropic silver domains on gold nanodumbbells (Au NDs@Ag NPs). By adjusting the 4-MBA concentration-dependent interfacial energy, the Au NDs@Ag NPs could be continuously tuned from dumbbell-like core–shell structures, to L-shaped Janus, and then rod-like core–shell structures with directional and asymmetric spatial distributions of resizable Ag domains by site-selective growth. Based on the calculation results of discrete dipole approximation (DDA) method, it has been found that the Au NDs@Ag L-shaped Janus NPs with Ag island domains created polarization orientation-dependent plasmonic extinction spectra and hot spots around the negatively curved waist and Ag domains. The L-shaped Janus Au NDs@Ag NPs exhibited significantly plasmonic spectrum properties with four apparent LSPR peaks that cover from visible to near-infrared range and higher surface-enhanced Raman scattering (SERS) activity compared with the original Au NDs. The best SERS enhancement factor of 1.41 × 107 was achieved. This synergistic surface energy effect-based method involving the asymmetric growth of silver coating on gold nanoparticles with negatively curved surface presents a new method to design and fabricate nanometer optical devices based on asymmetric multicomponent nanoparticles.

An Accelerated Method for Investigating Spectral Properties of Dynamically Evolving Nanostructures

The discrete-dipole approximation (DDA) is widely applied to study the spectral properties of plasmonic nanostructures. However, the high computational cost limits the application of DDA in static geometries, making it impractical for investigating spectral properties during structural transformations. Here we developed an efficient method to simulate spectra of dynamically evolving structures by formulating an iterative calculation process based on the rank-one decomposition of matrices and DDA. By representing structural transformation as the change of dipoles and their properties, the updated polarizations can be computed efficiently. The improvement in computational efficiency was benchmarked, demonstrating up to several hundred times acceleration for a system comprising ca. 4000 dipoles. The rank-one decomposition accelerated DDA method (RD-DDA) can be used directly to investigate the optical properties of nanostructural transformations defined by atomic- or continuum-scale processes, which is essential for understanding the growth mechanisms of nanoparticles and algorithm-driven structural optimization toward enhanced optical properties.

Effective index model as a reliable tool for the design of nanostructured thin-film solar cells

Nanostructured anti-reflection coatings (ARC) are used to reduce the reflectivity of the front surface of solar cells. Computational electromagnetism helps to evaluate the spectral reflectivity of of this type of ARC using several approaches. They typically require large computational resources both in time and hardware elements (memory allocation, speed of processors, etc.). Long computational times may jeopardize optimization processes based on the iterative evaluation of a given merit function that depends on several parameters. Then, simplified analytic methods can speed up this evaluation with moderate computational resources. In this contribution we adapt an Effective Index Model (EIM) to the case of the design of an ARC made with nanoparticles (NP) embedded in a medium at the front surface of a thin-film silicon solar cell. Our approach modifies the discrete dipole approximation method to adapt it to the geometric and material properties of the NPs. The results obtained from the analytic method are compared with those evaluated through a Finite Element Method (FEM) for several cases involving variations in the size and geometry of the NP arrangement, obtaining reflectances that differ less than 10% for the worst case analyzed but bieng about 100 times faster than the FEM.

Plasmoelectronic properties of self-assembled gold nanoparticles: impedance spectroscopy experiments combined with numerical simulations

Plasmoelectronics is a fast developing field driven by the combination of charge transport and surface plasmons in metal nanostructures. In this paper, we report on theoretical and experimental investigations of the plasmoelectronic properties of self-assembled monolayers of colloidal gold nanoparticles (NPs). A local plasmonic-electronic nanojunction is introduced, as the fundamental building block of a mesoscale electrical network, and serves as the beginning point for the development of a multiscale modeling strategy. The interparticle charge tunneling and accumulation account for the dynamical charge transport; the plasmoelectronic properties are implemented at the nanoscale using electrodynamic calculations based on the discrete dipole approximation (DDA) method. The electric characteristics of the macroscopic NP network are calculated using a numerical resolution of the current-bias equations based on Kirchhoff's laws. Disorder effects due to size and position fluctuations of the NPs within the network as well as dislocations and point defects in their spatial arrangement are taken into account. The effects of light excitation intensity and wavelength on the nanojunction photoconductance and on the macroscopic photoresistance of the NP network are addressed. In particular, plasmoelectronic conduction paths are extracted from the coupled DDA-Kirchhoff numerical simulations, and their statistical distribution is investigated as well as their dependence on path length. The theoretical results are compared with impedance spectroscopy measurements performed under optical excitation. We found a good agreement between the predicted impedance Nyquist plots and resonance properties, and the measurements. In particular, we were able to estimate the surface plasmon-assisted photoelectric conversion efficiency involving first neighbor NPs. We found that the photoconductance of a single nanojunction formed by a dimer of nearly touching NPs is around 18 nS/W/cm2 under resonant plasmonic excitation. The presented work provides insight into the photoinduced charge transport in self-assembled NP networks and opens the route to novel applications in the field of plasmoelectronics.

Quantitative Analysis of Photothermal Therapy of Tumor Tissue Using Various Gold Nanoparticle Injection Schemes.

Photothermal therapy is a new chemotherapy technique using photothermal effects, a phenomenon in which light energy is converted into thermal energy. Since the treatment technique is performed without surgical incision, it does not cause bleeding and patients are expected to make rapid recoveries, which are significant advantages. In this study, photothermal therapy with direct injection of gold nanoparticles into tumor tissue was simulated through numerical modeling. The treatment effect resulting from changing the intensity of the irradiated laser, volume fraction of the injected gold nanoparticles, and number of gold nanoparticle injections was quantitatively evaluated. The discrete dipole approximation method was applied to calculate the optical properties of the entire medium, and the Monte Carlo method was applied to identify the absorption and scattering behavior of lasers in tissue. In addition, by confirming the temperature distribution of the entire medium through the calculated light absorption distribution, the treatment effect of photothermal therapy was evaluated, and the optimal treatment conditions were suggested. This is expected to accelerate the popularization of photothermal therapy in the future.

Ballistic cluster–cluster aggregation model optimization

In this paper, an optimized model based on the ballistic cluster–cluster aggregation model is proposed to study the optical properties of aggregated particle structures. The critical improvement of the optimized model is the ability to arbitrarily select the original number of particles in the simulation and set different sizes of particles, whereas the original model is limited to 2n particles. Herein, the discrete dipole approximation method was used to calculate the optical extinction properties of the aggregation structure. First, the effect of porosity, which is a significant parameter, is explored, and acceptable error values are calculated. Second, simulations are performed using the optimized model for conditions applicable to the original model (N = 2n), and the difference between the two model calculations is assessed. Finally, the extinction performance of the aggregate with an arbitrary number of particles (N ≠ 2n) simulated by the optimized model is calculated and compared with the results obtained by the interpolation method. The numerical results verify the generalizability and accuracy of the optimized model.