Effect of Finite Terms on the Truncation Error of Mie Series for Modeling Light Scattering

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The finite sum of the squares of the Mie coefficients is very useful for addressing problems of classical light scattering. An approximate formula available in the literature, and still in use today, has been developed to determine a priori the number of the most significant terms needed to evaluate the scattering cross section. Here we obtain an improved formula, which includes the number of terms needed, for the scattering cross section to be determined with an error smaller than the prescribed accuracy. This approximation can be a promising and valuable approach for modeling light scattering phenomena. © 2012 Optical Society of America

Light scattering today is still an important and active field, whose application largely outgrows the field of atmospheric optics, affecting several issues in optical trapping, spherical cloaking, plasmonics and realistic physical based rendering.[Ref] For instance, recent examples exploiting various light scattering phenomena include optical trapping of free-standing nanostructures, such as polymer nanofibers and other nanoparticles.[Ref1, Ref2] In particular, the phenomenon of scattering of plane waves by a spherical body is described exactly by the Mie theory in terms of an infinite series.[Ref] For the purpose of numerical computation, only a finite number of terms are retained, based on the size of the scatterers in relation to the wavelength. The number of terms conserved is commonly determined by Wiscombe’s criterion.[1] This method has been initially proposed to compute the spherical functions by downward recursion, and to utilize the new vector processing technology of the time, which requires a number of terms established a priori. Nowadays, with the increased computational power and c...

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