Tunable photonic crystals explained via Mie theory and discrete dipole approximation: a different light

A novel hybrid method based on Mie theory and the Discrete Dipole Approximation (DDA) was developed to study the microscopic parameters governing the optical response of tunable photonic crystals (PC). The method is based on a two-step process. An effective polarizability derived from Mie theory is determined by equating the extinction efficiency of an isolated nanoparticle (NP) to the extinction efficiency of an equivalent particle considering the dipolar limit. Then, this effective polarizability is used in the DDA framework to compute the optical response of an interacting particle array constituting the PC structure. As a particular example, the method was applied to a linear array of core-shell magnetite@silica NPs to study the dependence of extinction and absorption on system parameters such as core radius, shell thickness, total radius, interparticle separation, and size distribution. The results indicate that an increase in these parameters leads to a redshift of the extinction peak as well as an increase in its $FWHM$. Finally, the method is applied to fitting experimental results on reflection/transmission measurements of magnetite@silica NPs colloids subjected to different magnetic field strengths with very good agreement. The presented method reduces the computational cost and time for the NPs sizes considered, and can be applied to PCs responsive to different stimuli such as mechanical stress, electric field and temperature, \textit{inter alia}.