Odit et al. stated that they had designed the meta-surface in such a way that Mie resonance can be accessed [1].
[1] Experimental demonstration of water based tunable metasurface,
Mikhail Odit, Polina Kapitanova, Andrei Andryieuski, Pavel Belov, and Andrei V. Lavrinenko
Are you looking to find the resonances of a known structure or to find out the structure that has a known resonance.
For the resonances of a known structure:
You can use the Mie theory itself (https://en.wikipedia.org/wiki/Mie_scattering) for spheres. For more complicated structures it's best to do a simulation for example using PlanOpSim, COMSOL or another program.
For findingind out the structure that has a known resonance:
You will have to use numerical fitting based on a forumula with parameters or with simulations as above. Note that fitting does not garantuee that you will find the real structure. Fitting only loks for a structure that best matches the behaviour you provide as input. There is no guarantuee that there is no better fit for a different structure.
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