Improved recursive algorithm for light scattering by a multilayered sphere

Abstract

An improved recurrence algorithm to calculate the scattering field of a multilayered sphere is developed. The internal and external electromagnetic fields are expressed as a superposition of inward and outward waves. The alternative yet equivalent expansions of fields are proposed by use of the first kind of Bessel function and the first kind of Hankel function instead of the first and the second kinds of Bessel function. The final recursive expressions are similar in form to those of Mie theory for a homogeneous sphere and are proved to be more concise and convenient than earlier forms. The new algorithm avoids the numerical difficulties, which give rise to significant errors encountered in practice by previous methods, especially for large, highly absorbing thin shells. Various calculations and tests show that this algorithm is efficient, numerically stable, and accurate for a large range of size parameters andrefractive indices.

MieLab: A Software Tool to Perform Calculations on the Scattering of Electromagnetic Waves by Multilayered Spheres

“…Then, the incident and internal fields are expanded in wave functions which are regular inside the scatterer, whereas the external scattered field is expanded in wave functions that behave as outgoing waves at infinity. Finally, using the requirement of continuity of the tangential component of the electric and magnetic fields at the particle boundary, the unknown coefficients in the internal and scattered field expansions can be determined from the known expansion coefficients of the incident field [12].…”

“…A problem that occurs while performing electromagnetic calculations, even when exact solutions exist, is that they are usually quite complicated as infinite series composed of combinations of badly behaved Bessel functions [1,12] are involved. These difficulties make the integration of flexible and robust computational techniques (software applications) essential.…”

“…In this paper, we present MieLab, a software tool released as free software, which is based on the implementation [14] of Yang's algorithm for multilayered spheres [12] with several added features such as the possibility of calculating the optical response of an ensemble of independent (noninteracting) particles with a normal size distribution, a graphical user interface (GUI), an optimization algorithm (to fit the simulations to experimental results), and scripting capabilities.…”

Dispersion Diagram Analysis of Arrays of Multishell Multimaterial Nanospheres

“…A plane wave excitation with x-polarized electric field and y-polarized magnetic field is considered. The field in each region can be written using the M and N vector basis functions [16] as:…”

Size Characterisation Method and Detection Enhancement of Plasmonic Nanoparticles in a Pump–Probe System

“…This interest stems from their specific behaviour that depends on the particle size and shape and is very different from that of the bulk material. The optical scattering properties of nanoparticles have been well-known since the development of Mie theory [1] and, more recently, the stability of numerical solutions has allowed reliable calculations on spherical structures [2,3]. Additionally, the mechanical properties have been investigated, firstly by Raman scattering [4][5][6] and later by means of pump-probe techniques [7][8][9][10][11][12][13].…”