A theory is developed for the optical properties of particles of arbitrary shape, composed of a homogeneous isotropic material with a dielectric constant $\epsilon \left(\omega \right)$. The particles are so small that retardation can be neglected. An expression is obtained for the average dielectric constant of a medium containing a small fractional volume of particles. Calculations for a cube show that six resonances contribute to the optical absorption. They span a frequency range such that ${\epsilon }^{\prime }\left(\omega \right)$, the real part of the dielectric constant, lies between -3.68 and -0.42, as contrasted with the single resonance for a sphere at ${\epsilon }^{\prime }\left(\omega \right)=-2\mathrm{}$. A comparison of the theory with experiments on the optical absorption of NaCl and MgO cubes shows that the width of the absorption peak can be explained by the frequency range of the cube resonances. Previous theories which assumed spherical particles required an unphysically high damping in $\epsilon \left(\omega \right)$ to account for the width.

• Received 11 March 1974

DOI:https://doi.org/10.1103/PhysRevB.11.1732