I am working on a meta surface absorber in visible to IR region. To explain the absorption mechanism i used electric field and magnetic field distribution, however i need to calculate or find any equation to find the resonance wavelength to support the simulation output.
Is there any equation to calculate or estimate the wavelengths?
Well, it really depends on your metasurface structure and nature of the resonance. You can divide resonances onto three groups - first one is related to resonances in the material itself (exciton peaks for example), the second one is related to the metasurface geometry (particle resonance, grating resonances) and the third option is a hybrid case, when you have combination of these two (plasmonic resonances, excotic states).
If your case is resonance from geometry then you need to understand its nature. If its from particles - you have one equation, if from grating - another equation, or is it Fano-resonance from a combination of modes.
So, the short answer is there is no general formula because it depends on the nature of absorption resonance in your structure. If you know this, then you can find an equation.
I hope it wiil help.
Best
You can try too look in the following books: M Born and E Wolf Principles of Optics (chapter about scattering on a metallic particles), Bohren And Huffman Absorption and Scattering of light by small particles, S Maier Plasmonics: Fundamentals and Applications, Novotny Principles of nanooptics.
Generally, grating resonances equations are easy to derive because they follow Bragg diffraction. Particle resonances are more complicated and depend on shape, however there are some valuable approximations that allow to get simple formulas under some assumptions, like diameter of a particle is much smaller then the wavelength.
Good luck with your research!
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