Determining the size and refractive index of microspheres using the mode assignments from Mie resonances

A new method for determining the radius and refractive index of microspheres using Mie resonances is presented. Previous methods have relied on searching multidimensional space to find the radius and refractive index that minimize the difference between observed and calculated Mie resonances. For anything but simple refractive index functions, this process can be very time consuming. Here, we demonstrate that once the mode assignment for the observed Mie resonances is known, no search is necessary, and the radius and refractive index of best-fit can be found immediately. This superior and faster way to characterize microspheres using Mie resonances should supplant previous fitting algorithms. The derivation and implementation of the equations that give the parameters of best-fit are shown and discussed. Testing is performed on systems of physical interest, and the effect of noise on measured peak positions is investigated.