Discret dipole approximation method

Brioude A, Pileni MR Silver nanodisks optical properties study using the discrete dipole approximation method. J Phys Chem B 2005 109 23371-23377. 

Fiatau, P.). [1997] Improvements in the discrete-dipole approximation method of computing scattering and absorption. Opt. Lett, 22,1205-1207. 

Discrete dipole approximation. For particles with complex shape and/or complex composition, presently the only viable method for calculating optical properties is the discrete dipole approximation (DDA). This decomposes a grain in a very big number of cubes that are ascribed the polarizability a according to the dielectric function of the dust material at the mid-point of a cube. The mutual polarization of the cubes by the external field and the induced dipoles of all other dipoles is calculated from a linear equations system and the absorption and scattering efficiencies are derived from this. The method is computationally demanding. The theoretical background and the application of the method are described in Draine (1988) and Draine Flatau (1994). 

A direct experimental measurement of the surface plasmons bands of the gold nanoclusters was not straightforward, since the metallic patterns were quite small and stuck onto an opaque substrate (SiOz). Therefore, we performed theoretical calculations in order to infer the spectral features of the SPs used in our MEF experiments. The absor[ on spectra of gold triangular prisms and cylinders with thicknesses of 35 nm (according to the dimensions of the fabricated patterns) were calculated by using the Discrete dipole approximation (DDA). Further details on the method are ven in references [52-57]. 

Since enhanced electromagnetic fields in proximity to metal nanoparticles are the basis for the increased system absorption, various computational methods are available to predict the extent of the net system absorption and therefore potentially model the relative increase in singlet oxygen generation from photosensitizers. " In comparison to traditional Mie theory, more accurate computational methods, such as discrete dipole approximation (DDA/ or finite difference time domain (FDTD) methods, are often implemented to more accurately approximate field distributions for larger particles with quadruple plasmon resonances, plasmon frequencies of silver nanoparticles, or non-spherical nanoparticles in complex media or arrangements. ... 

The radiation characteristics of axisymmetric spheroidal microorganisms, such a C. reinhardtii (Fig. lA), with major and minor chameten a and b can be predicted numerically using (i) the T-matrix method (Waterman, 1965 Mackowski, 1994 Mishchenko et al., 2002, 1995), (ii) the discrete-dipole approximation (Draine, 1988), and (iii) the finite-difference time-domain method (Liou, 2002). Most often, however, they have been approximated as homogeneous spheres with some equivalent radius r and some effective complex index of refraction nix = n +ikx (Pettier et al., 2005 Berbero u et al., 2007 Dauchet et al., 2015), as discussed in Section 3.6.1. 

One of the important aspects is particle with comparable plasmon length shows similar LSPR. Numerical methods for plasmonic NPs include FDTD, discrete dipole approximation, and finite element method. An excellent introduction to these three methods can be found in the review by Zhao et al. [24]. 

In this chapter the problem of elastic light scattering, i.e. interaction of electromagnetic waves with finite objects, is discussed. A detailed overview of one of the widely used methods for plasmonics, the discrete dipole approximation (DDA), is presented. This includes the theory of the DDA, practical recommendations for using available computer codes, and discussion of the DDA accuracy. 

Gilev, K. V., Eremina, E., Yurkin, M. A., and Maltsev, V. P. (2010) Comparison of the discrete dipole approximation and the discrete source method for simulation of light scattering by red blood cells. Opt. Express, 18, 5681-5690. 

Yurkin, M. A., Hoekstra, A. G., Brock, R. S., and Lu,. Q. (2007) Systematic comparison of the discrete dipole approximation and the finite difference time domain method for large dielectric scatterers. Opt Express, 15,17902-17911. 

Yurkin, M. A. and Kahnert, M. (2013) Light scattering by a cube accuracy limits of the discrete dipole approximation and the T-matrix method, J. Quant Spectrosc. Radiat Transfer, http //dx.dol.Org/10.1016/j.jqsrt.2012.10.001. 

Figure 5.2 E-field enhancement contours external to monomers with different shapes, (a] and (b] are the E-field enhancement contours external to a triangular prism polarized along the two different primary symmetry axes, (c] and (d] are the E-fields enhancement contours for a rod and spheroid polarized along their long axes. The arrows show where is the maximum of E-filed. Results are obtained numerically via the discrete dipole approximation (DDA] method. Reprinted with permission from Ref. [64]. Cop5rright [2004], American Institute of Physics.

The inter-particle distance dependence of the near-field coupling would therefore reflect the distance decay of the near-field itself. In other words, each particle senses the near-field due to the other particle. By varying the distance of the other particle and monitoring the LSPR response, the spatial profile of the near-field can be deduced. The plot of the LSPR red-shift as a function of inter-particle gap (surface-to-surface separation) shows a much more rapid decay of the near-field than predicted by the dipolar model. This is because the dipolar model does not take into account the multipolar interactions between the particles, which become increasingly important at smaller and smaller inter-particle gaps. Plasmon coupling is therefore a multipolar interaction and its true distance-dependence can be quantitatively reproduced only by a complete treatment that includes all modes of interaction (dipolar, quadrupolar, octupolar). Computational electrodynamics methods such as discrete dipole approximation (DDA) (see Chapter 2) and finite-difference-time-domain (FDTD), which include a full multipolar treatment in addition to finite-size retardation effects, fit experimental trends well. 

Part 1, Theory and Computational Methods, opens with a chapter by M. A. Yurkin (Russia) who describes in detail the Discrete Dipole Approximation (DDA) approach, which is an efficient method to study the absorption and scattering of metal nanoparticles of arbitrary shapes. This chapter will serve as an important reference for theoreticians to model metal nanoparticles. Chapter 3 reports DDA results for nanoparticles of different sizes and shapes. This systematic analysis, inspired by recent literature, should represent an important reference for both experimentalists and theoreticians to verify and compare the absorption and scattering spectra of different nanoparticles. While these first two chapters are completely dedicated to metal nanoparticles. Chapter 4 introduces the discussion about the molecular counterpart. In this chapter E. Fabiano (Italy) sheds light on the optical and photophysical... 

The transition matrix relates the expansion coefficients of the incident and scattered fields. The existence of the transition matrix is postulated by the T-Matrix Ansatz and is a consequence of the series expansions of the incident and scattered fields and the linearity of the Maxwell equations. Historically, the transition matrix has been introduced within the null-field method formalism (see [253,256]), and for this reason, the null-field method has often been referred to as the T-matrix method. However, the null-field method is only one among many methods that can be used to compute the transition matrix. The transition matrix can also be derived in the framework of the method of moments [88], the separation of variables method [208], the discrete dipole approximation [151] and the point matching method [181]. Rother et al. [205] foimd a general relation between the surface Green function and the transition matrix for the exterior Maxwell problem, which in principle, allows to compute the transition matrix with the finite-difference technique. 

Whereas the volume integral equation method deals with the total field, the discrete dipole approximation exploits the concept of the exciting field, each volume element being explicitly modeled as an electric dipole moment. In this regard, we consider the field that excites the volume element Di rn... 

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