Calculating and fitting morphology-dependent resonances of a spherical particle with a concentric spherical shell

Determining the size and composition of core-shell particles using morphology-dependent resonances (MDRs) is a computationally intensive problem due to the large parameter space that needs to be searched during the fitting process. Very often, it is not even practical to consider a reasonable range of physical parameters due to time constraints, leading to restrictive assumptions concerning the system being studied. The lengthy computational time is so limiting that there has, to date, to the best of our knowledge, been no comprehensive study of fitting measured MDRs for core-shell particles. In this work, we address the issue of fitting speed by developing an algorithm that (i) reduces the multi-dimensional grid search to a one-dimensional search using a least squares method and (ii) implements a new method for calculating MDRs that is much faster than previous methods. With the program presented here, we analyze the best-fits for core-shell MDRs across a large range of physically relevant scenarios using noise levels typical for conventional spectroscopic experiments. For many cases, it has been found that excellent fits can be quickly determined. However, there are also some surprising situations where accurate best-fits are not possible (e.g., if only one mode order is present in the measured MDR set).