## Abstract

The generalized multiparticle Mie-solution (GMM) is an extension of the well-known Mie-theory for single homogeneous spheres to the general case of an arbitrary ensemble of variously sized and shaped particles. The present work explores its specific application to periodic structures, starting from one- and two-dimensional regular arrays of identical particles. Emphasis is placed on particle arrays with a truncated periodic structure, i.e., periodic arrays (PAs) with finite overall dimensions. To predict radiative scattering characteristics of a PA with a large number of identical particles within the framework of the GMM, it is sufficient to solve interactive scattering for only one single component particle, unlike the general case where partial scattered fields must be solved for every individual constituent. The total scattering from an array as a whole is simply the convolution of the scattering from a single representative scattering center with the periodic spatial distribution of all replica constituent units, in the terminology of Fourier analysis. Implemented in practical calculations, both computing time and computer memory required by the special version of GMM formulation applicable to PAs are trivial for ordinary desktops and laptops. For illustration, the radiative scattering properties of several regular arrays of identical particles at a fixed spatial orientation are computed and analyzed. Numerical results obtained from the newly developed approach for PAs are compared with those calculated from the general GMM computer codes (that have been available online for about a decade). The two sets of numerical outputs show no significant relative deviations. However, the CPU time required by the specific approach for PAs could drop more than 10,000 times, in comparison with the general approach. In addition, an example PA is also presented, which consists of as large as ${10}^{8}$ particles and the general solution process is unable to handle.

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