Discrete Dipole Approximation DDA

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 problem of metallic particles like gold and silver particles is similar to the previous case except that the material is now highly polarizable. Hence, the polarization sheet is excited by the local field which cannot be taken as the incoming field only. It must be taken as the superposition of the incoming field and the polarization field. This problem is rather difficult in general and several theories have been proposed in the past [35-40]. For arbitrary shapes, one may directly use a numerical approach like the discrete dipole approximation (DDA) for instance. It has however been solved analytically for spherical particles by G. Mie and H. Chew et al. in... 

Absorption of and Emission fiom Nanoparticles, 541 What Is a Surface Plasmon 541 The Optical Extinction of Nanoparticles, 542 The Simple Drude Model Describes Metal Nanoparticles, 545 Semiconductor Nanoparticles (Quantum Dots), 549 Discrete Dipole Approximation (DDA), 550 Luminescence from Noble Metal Nanostructures, 550 Nonradiative Relaxation Dynamics of the Surface Plasmon Oscillation, 554 Nanoparticles Rule From Forster Energy Transfer to the Plasmon Ruler Equation, 558... 

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. 

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 simple dipole interaction model for polarizability has been extended later by many researchers [39-41] to form the basis of the so-called discrete dipole approximation (DDA) for calculating the optical properties of metal nanoclusters. To introduce simplification, in DDA, the nanocluster is divided into small cells (which may contain multiple number of atoms) and the response of each cell to the external field as well as the internal field of the induced dipoles at all the cells is evaluated to obtain the polarizability and optical absorption of metal nanoclusters. 

Fig. 3.18. Normalized differential scattering cross-sections of an oblate cylinder with ksb = 15 and 2ksa = 7.5. The cmves are computed with the TAXSYM routine, discrete somces method (DSM), multiple multipole method (MMP), discrete dipole approximation (DDA) and finite integration technique (CST)...

Fig. 3.19. Normalized differential scattering cross-sections of a dielectric cube computed with the TNONAXSYM routine and the discrete dipole approximation (DDA)...

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