MATLAB package for discrete dipole approximation by graphics processing unit: Fast Fourier Transform and Biconjugate Gradient

doi:10.1016/j.jqsrt.2020.107501

Journal of Quantitative Spectroscopy and Radiative Transfer

Volume 262, March 2021, 107501

https://doi.org/10.1016/j.jqsrt.2020.107501 Get rights and content

Highlights

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Introducing a MATLAB package for describing discrete dipole approximation technique.
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Including accelerative methods to reduce the computational time and memory.
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Providing a comprehensive explanation for all steps of the used accelerative methods.
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Accelerating computation procedure using graphics processing unit in MATLAB.
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For 1 million dipoles, graphics processing unit performance is ~10 times faster than CPU.
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Computing optical properties of the plasmonic nanoparticles using this package.

Abstract

A MATLAB package describing discrete dipole approximation (MPDDA) is introduced to calculate the optical properties of arbitrary shaped plasmonic nanoparticles (NPs). The polarizability function, induced dipoles, and dipole interaction matrix are discussed. To calculate the dipole moments, Fast Fourier Transform (FFT) and Biconjugate Gradient (BCG) were used to reduce the computational time and memory. To further accelerate the computational procedure, we used MATLAB functions and toolboxes supported by the graphics processing unit (GPU) and execute them on GPU by supplying a “gpuArray” argument. Using the GPU, the computation cost significantly decreased when compared to the CPU. We also simulated the optical properties of plasmonic NPs, such as extinction, absorption, and scattering efficiencies, electric field enhancement around monomeric and dimeric structures using this package. The accuracy and capabilities of the code have been confirmed by comparing with Mie theory (exact solution) and ADDA code (a DDA package developed in C).

Section snippets

Program summary section

Program title: MPDDA

Licensing provisions: GPL General Public License

Programming language: MATLAB R2016b

Program obtainable from: https://github.com/MasoudShabani/MPDDA-1.0

Nature of problem: Simulation of optical properties such as absorption, scattering, and extinction efficiencies, and field enhancement of monomeric and dimeric plasmonic nanostructures using the discrete dipole approximation. Accelerative methods (Fast Fourier Transform and Biconjugate Gradient) were used to reduce the

Discrete dipole approximation formalism

The DDA is a general and effective method to calculate optical properties such as absorption, scattering, and extinction cross-sections of the electromagnetic waves by particles with arbitrary shapes and compositions [1,22,42]. The DDA is a numerically exact method based on the volume-integral discretization derived directly from Maxwell's equations [42]. In this method, the target particle will be divided into N cubes [1]. Each cubical voxel represents a point dipole with polarizability of α_i

Biconjugate gradient

To obtain the polarization of each dipole, Eq. (7) can be solved using iterative methods. It has been shown that iterative methods are more efficient than direct methods [22,25,28]. In this subsection, we review the BCG method provided by Smith et al. [25] that uses more efficient modification for complex symmetric matrices. It is worth mentioning that this iterative technique also has been used in the well-known DDA codes, such as DDSCAT [22,27] and ADDA [28].

The BCG requires an initial guess

Absorption, scattering, and extinction efficiencies

By knowing the polarization vector of each dipole at different wavelengths, the absorption, extinction, and scattering cross-sections of a nanoparticle can be calculated as, (Fig. 10), [7] $C_{a b s} = \frac{4 π | k |}{{| E_{0} |}^{2}} \sum_{i = 1}^{N} [I m (\frac{P_{i} . P_{i}^{*}}{α_{i}^{*}}) - \frac{2}{3} {| k |}^{3} {| P_{i} |}^{2}]$ $C_{e x t} = \frac{4 π | k |}{{| E_{0} |}^{2}} \sum_{i = 1}^{N} [I m (E_{i n c, i}^{*}) . P_{i}]$ $C_{s c a t} = C_{e x t} - C_{a b s}$ where ‘Im’ and ‘*’ are representing the imaginary part and the complex conjugate, respectively. The absorption, extinction, and scattering efficiencies are expressed by dividing the corresponding optical

Conclusions

In this study, a package in MATLAB, named MPDDA, is introduced to calculate the optical properties of the monomeric and dimeric plasmonic nanostructures using the DDA. This study represents the application of BCG and FFT to accelerate the DDA in MATLAB software. All procedures of the DDA are discussed in detail, and their corresponding MATLAB functions are introduced. This package has the capability to run both in the CPU and GPU platforms. For running the simulation in the GPU, all of the

CRediT authorship contribution statement

M. Shabaninezhad: Conceptualization, Methodology, Software, Writing - original draft, Writing - review & editing, Investigation, Visualization, Validation. M.G. Awan: Writing - original draft, Validation, Resources. G. Ramakrishna: Supervision, Writing - review & editing.

Declaration of Competing Interest

No.

Acknowledgments

M. Shabaninezhad thanks the Physics Department of Western Michigan University for financial support and acknowledge Dr. Gupta and Dr. Saeed for providing access to Parallel Computing and Data Science Laboratory, Department of the Computer Science, Western Michigan University.

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Journal of Quantitative Spectroscopy and Radiative Transfer

MATLAB package for discrete dipole approximation by graphics processing unit: Fast Fourier Transform and Biconjugate Gradient

Highlights

Abstract

Section snippets

Program summary section

Discrete dipole approximation formalism

Biconjugate gradient

Absorption, scattering, and extinction efficiencies

Conclusions

CRediT authorship contribution statement

Declaration of Competing Interest

Acknowledgments

Comput Phys Commun

Comput Phys Commun

Chem Phys

J Comput Sci

J Quant Spectrosc Radiat Transf

J Quant Spectrosc Radiat Transf

J Quant Spectrosc Radiat Transf

J Quant Spectrosc Radiat Transf

Comput Phys Commun

Comput Phys Commun

J Quant Spectrosc Radiat Transf

J Quant Spectrosc Radiat Transf

Comput. Biol Med

Nanoscale Res Lett

Chem Phys Lett

Astrophys J

IEEE Trans Antennas Propag

J Microwaves Optoelectron

The finite element method in electromagnetics

Astrophys J

J Opt Soc Am A

Opt Lett

Acc Chem Res

J Phys Chem B

Absorption and scattering of light by small particles

J. Phys. Chem. B

J Phys Chem B

J Phys Chem B

Plasmonics

J Chem Phys

Nat Photonics

Nano Lett

J Chem Phys