## Abstract

The discrete-dipole approximation (DDA) is a powerful method for calculating absorption and scattering by targets that have sizes smaller than or comparable with the wavelength of the incident radiation. We present a new prescription—the surface-corrected-lattice-dispersion relation (SCLDR)—for assigning the dipole polarizabilities while taking into account both target geometry and finite wavelength. We test the SCLDR in DDA calculations for spherical and ellipsoidal targets and show that for a fixed number of dipoles, the SCLDR prescription results in increased accuracy in the calculated cross sections for absorption and scattering. We discuss extension of the SCLDR prescription to irregular targets.

© 2004 Optical Society of America

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### Equations (13)

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(1)
$${\alpha}_{\mathrm{CMR}}=\frac{3{d}^{3}}{4\pi}\left(\frac{{m}^{2}-1}{{m}^{2}+2}\right).$$
(2)
$$\alpha =\frac{{\alpha}^{(\mathrm{nr})}}{1-(2/3)i({\alpha}^{(\mathrm{nr})}/{d}^{3})(\mathit{kd}{)}^{3}},$$
(3)
$${\alpha}_{\mathrm{LDR}}=\frac{{\alpha}^{(0)}}{1+({\alpha}^{(0)}/{d}^{3})[({b}_{1}+{m}^{2}{b}_{2}+{m}^{2}{b}_{3}S)(\mathit{kd}{)}^{2}-(2/3)i(\mathit{kd}{)}^{3}]},$$
(4)
$$S=\sum _{j}({a}_{j}{e}_{j}{)}^{2},$$
(5)
$${\mathbf{E}}_{j}^{\mathrm{mac}}={\mathbf{C}}_{j}^{-1}{\mathbf{E}}^{0},$$
(6)
$${\mathbf{P}}_{j}={d}^{3}\left(\frac{{{m}_{j}}^{2}-1}{4\pi}\right){\mathbf{E}}_{j}^{\mathrm{mac}}={d}^{3}\left(\frac{{{m}_{j}}^{2}-1}{4\pi}\right){\mathbf{C}}_{j}^{-1}{\mathbf{E}}^{0},$$
(7)
$${\mathbf{P}}_{j}={\mathit{\alpha}}_{j}\left[{\mathbf{E}}^{0}-\sum _{k\ne j}{\mathbf{A}}_{\mathit{jk}}{\mathbf{P}}_{k}\right],$$
(8)
$${\mathit{\alpha}}_{\mathrm{RCB},j}={d}^{3}\left(\frac{{{m}_{j}}^{2}-1}{4\pi}\right){\mathbf{\Lambda}}_{j}^{-1},$$
(9)
$${\mathbf{\Lambda}}_{j}\equiv {\mathbf{C}}_{j}-\sum _{k\ne j}{\mathbf{A}}_{\mathit{jk}}\left(\frac{{{m}_{k}}^{2}-1}{4\pi}\right){d}^{3}{\mathbf{C}}_{k}^{-1}{\mathbf{C}}_{j}$$
(10)
$${\mathbf{C}}_{j}=1+\left(\frac{{m}^{2}-1}{4\pi}\right)\mathbf{L},$$
(11)
$${\mathit{\alpha}}_{\mathrm{SCLDR},j}={\mathit{\alpha}}_{\mathrm{RCB},j}[1+({\mathit{\alpha}}_{\mathrm{RCB},j}/{d}^{3})\mathbf{B}{]}^{-1},$$
(12)
$${B}_{\mathit{ij}}=({b}_{1}+{m}^{2}{b}_{2}+{m}^{2}{b}_{3}{{a}_{i}}^{2}{\delta}_{\mathit{ij}})(\mathit{kd}{)}^{2}-(2/3)i(\mathit{kd}{)}^{3},$$
(13)
$$\mathrm{Frac}.\mathrm{Err}.\equiv \frac{Q(\mathrm{DDA})-Q(\mathrm{Mie})}{Q(\mathrm{Mie})}.$$