Transfer Matrix Algorithm For Light Scattered By Multilayered Spheres And Its Applications

Scattering properties of electromagnetic waves on particles have always been an important topic in the theory of electromagnetic wave propagation and scattering. When the size of a parti-cle size comparable or larger than the wavelength of incident light or electromagnetic wave, the Rayleigh scattering theory is no longer applicable. Simulating the electromagnetic wave scattered by a particle by using the analytic solution for a plane electromagnetic wave scattered by a spher-ical particle, obtained by G. Mie before a century, has been a very practical method. The method, usually called Mie scattering, is suitable to simulate electromagnetic waves scattered by materials where particles distribute sparsely, such as the atmosphere with water drops or dusts, solutions with suspending particles. Scattered waves can be known when expansion coefficients for all scat-tered modes are calculated. Mie's solution was extended to the case when the sphere was coated with a film by A.L. Aden and M. Kerker 60 years ago, which can actually be extended to mul-tilayered cases. However, solutions for multilayered spheres are very complicated, which were usually implicitly expressed in recurrence of a fractional expression, from the core to the outside of the sphere. Zeros in these denominators may cause great error or even overflow in calculations. With hard works of many researchers in more than half a century, algorithms for Mie scattering on multilayered spheres have been greatly improved and the ranges of applicable parameters have been broadened. Nevertheless, any algorithm with such a recurrence of fractional expressions can never get rid off the possibility of singularities.In this thesis, we obtain explicit solutions for the scattering expansion coefficients with trans-fer matrices between layers. All singular can be eliminated from the explicit solution. The problem was thus completely solved in theory. Implemented in Matlab language, the transfer matrix algo-rithm was demonstrated to be valid and, at least, not worse than any existing algorithm. We use this algorithm to calculate the optical properties of nanoparticles with two different combinations of gold and silver layers, taking into account the coupling between the incident light and the surface plasmon. It was found that with a decrease in the outermost shell thickness or the middle layer thickness, positions of the peaks of the localized surface plasmon resonance (LSPR) for SiO2-Au-Ag (SiO2-Ag-Au) nanoshells demonstrate distinct redshifts. The calculated results indicate that the LSPR of the two-layered gold-silver nanoshells can be controlled to the near-infrared region by changing the geometry, which has practical biomedical applications.