Light scattering by an arbitrary particle: the scattering-order formulation of the coupled-dipole method

Singham, Shermila Brito; Bohren, Craig F.

doi:10.1364/josaa.5.001867

Cited by 78 publications

(28 citation statements)

References 9 publications

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“…(83) can be used as an estimate. The range of size parameter and refractive index where SOF converges is limited [120]. Moreover, even when SOF converges, more advanced iterative methods converge faster (see Subsection 4.1).…”

Section: Scattering Order Formulationmentioning

confidence: 99%

The discrete dipole approximation: An overview and recent developments

Yurkin

Hoekstra

2007

Journal of Quantitative Spectroscopy and Radiative Transfer

781

458

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We present a review of the discrete dipole approximation (DDA), which is a general method to simulate light scattering by arbitrarily shaped particles. We put the method in historical context and discuss recent developments, taking the viewpoint of a general framework based on the integral equations for the electric field. We review both the theory of the DDA and its numerical aspects, the latter being of critical importance for any practical application of the method. Finally, the position of the DDA among other methods of light scattering simulation is shown and possible future developments are discussed.

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Section: Scattering Order Formulationmentioning

confidence: 99%

The discrete dipole approximation: An overview and recent developments

Yurkin

Hoekstra

2007

Journal of Quantitative Spectroscopy and Radiative Transfer

781

458

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“…2 The discrete-dipole approximation (DDA) This method, also known as the coupled-dipole method [5][6][7], was developed by Purcell and Pennypacker [8]. It is a very flexible and general technique for calculating the optical properties of particles of arbitrary shape [9].…”

Section: The Methods Of Fuchsmentioning

confidence: 99%

Plasmon frequencies of cube shaped metal clusters

Ruppin¹

1996

Z Phys D - Atoms, Molecules and Clusters

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Abstract. The plasmon frequencies of a cube shaped metal cluster are calculated by two different methods. Unlike the spherical cluster, which has a single plasmon frequency, cop/~, the cube has a series of optically active plasmon frequencies. The two dominant peaks appear at frequencies which are considerably lower than that of a spherical cluster. PACS: 36.40The plasma resonance absorption in metal clusters is usually interpreted in terms of the Mie resonance [1], which is characteristic of a spherical cluster. For a free electron like spherical cluster in air, the resonance occurs at the frequency co = cop/,~. In optical measurements on metal clusters, the spherical shape is indeed prevalent, but other geometrical shapes may occur [2]. We calculate here the optical absorption spectrum of a cube shaped metal cluster, having a frequency dependent dielectric constant of the formwhere cop is the plasma frequency and ? is a damping constant. Two different methods will be employed. The method of FuchsFuchs [3] discussed the case of ionic crystal cubes, and developed a method for calculating their infi'ared absorption spectrum. However, his approach is quite general, and is applicable to any material described by a frequency dependent dielectric constant e(co). The only assumption is that the cube is much smaller than the wavelength of light, so that retardation can be neglected. Fuchs has shown that the susceptibility of the cube can be written as a sum over normal modes in the formwhere eh is the dielectric constant of the surrounding medium. The depolarization factors nm determine the normal mode resonance frequencies, whereas C(m) gives the strength of the m-th peak. The C(m) satisfy the sum rulem For a sphere only the uniformly polarized mode contributes to the optical absorption, and its depolarization factor is n = 1/3, so that the susceptibility assumes the form 1 1 Z((]J) = 4T(, (,f,/,S h --This susceptibility yields the resonance at the frequency cop/V/3 (assuming that eh = 1). Assuming an external uniform field, the surface polarization at a discrete set of points on the surfaces of the cube was obtained by We have calculated the absorption cross section of a cube of edge a = 3 nm, in air, assuming a dielectric constant of the form (1), with cop = 8.65 x 1015, the sodium value. For the damping constant the value 7 = 0.02c% was used. In

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“…͑9͒, ͑15͒, ͑17͒, and ͑18͒ is called the order-of-scattering representation of the multiply scattered electric field. 15,16,25,26 In a particular p-order multiple-scattering sequence, denoted here by c p , light is scattered p times by suspended particles before arriving at the detector: First by particle n, then by particle m, and so on until it is scattered penultimately by particle ᐉ and lastly by particle j. Scattering by a given particle may occur a number of times within a scattering sequence. This situation is more likely for small particles for which single scattering is more nearly isotropic than for large particles for which single scattering is strongly forward peaked.…”

Section: Order Of the Scattering Solution Of The Multiple-scatterimentioning

confidence: 99%

Electric field autocorrelation functions for beginning multiple Rayleigh scattering

Lock

2001

Appl. Opt.

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Light scattering by an arbitrary particle: the scattering-order formulation of the coupled-dipole method

Cited by 78 publications

References 9 publications

The discrete dipole approximation: An overview and recent developments

The discrete dipole approximation: An overview and recent developments

Plasmon frequencies of cube shaped metal clusters

Electric field autocorrelation functions for beginning multiple Rayleigh scattering

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