Discrete dipol approximation

Figure 7.4 Influence of nanorod shape on its optical extinction properties, as simulated using the discrete dipole approximation, (a) different aspect ratios, fixed volume, (b) fixed aspect ratio, variable volume, (c) aspect ratio and volume fixed, variable end cap geometry, (d) convexity of...

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). 

W. H. Yang, G. C. Schatz, and R. P. Vanduyne. Discrete Dipole Approximation for Calculating Extinction and Raman Intensities for Small Particles with Arbitrary Shapes Journal of Chemical Physics, 1995, 103, 869-875. 

Application of fast-Fourier transform techniques to the discrete-dipole approximation. Optics Letters 16(15) 1198-1200. 

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]. 

Yang, W. -H., Schatz, G. C., and Van Duyne, R. P. (1995). Discrete dipole approximation for calculating extinction and Raman intensities for small particles with arbitrary shapes. J. Chem. Phys. 103 869-875. 

Draine, B.T., and Goodman, J.J. (1993) Beyond clausius-mossotti wave propagation on a polarizable point lattice and the discrete dipole approximation, Astrophysical J., 405 685-697. 

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. ... 

Fig. 10.5 Experimental (symbols) and calculated (dashed lines) SERS intensity as a function of segment length for smooth and rough rods produced using on-wire lithography. Theoretical values were calculated using the discrete dipole approximation and scaled to maximum experimental value (Figure reproduced from Ref. [66])...

User Guide for the Discrete Dipole Approximation Code DDSCAT 6.1. 

Draine, B.T. and Flatau, P.J. (1994) Discrete-dipole approximation for scattering calculations. Journal of the Optical Society of America A, 11, 1491-1499. 

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... 

B. T. Draine, The Discrete-Dipole Approximation and its Application to Interstellar Graphite Grains, The Astrophysical Journal, 333, pp. 848-872,1988. 

B. T. Draine and P. J. Flatau, The Discrete-Dipole Approximation for Scattering Calculations, Journal of Optical Society of America A, 11,1491-1499,1994. 

Z. Ivezic and M. P. Mengii , An Investigation of Dependent/Independent Scattering Regimes for Soot Particles Using Discrete Dipole Approximation, International Journal of Heat Mass Transfer, 39, pp. 811-822,1996. 

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... 

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