As multipolar analysis is a key to find out contribution of different dipole moments, quadrupole moments causing the resonance in a metamaterial. I want to know the method, software and calculation considerations multipolar analysis.
Attached image is for reference in which different polar moments are plotted wrt frequency for a metamaterial unit cell.
reference: DOI:10.1038/s41598-017-00708-5
Dear Angana Bhattacharya,
You can take the limits for the triple integration as it includes a unit cell of your structure. In other words, you can take a volume large enough to envelop your structure. Because the current density is calculated by 𝑱(𝒓)=−𝑖𝜔𝜀0(𝑛2−1)𝑬(𝒓), after all, the value becomes zero outside your structure.
The actual procedure can be found in our program paper.
Preprint MENP: An Open-Source MATLAB Implementation of Multipole Expa...
https://github.com/Hinamoooon/MENP
Hope this helps.
Hi Prateek, if your goal is to find the multipole decomposition of an isolated scatterer, there are many relevant publications, see for example Article The High‐Order Toroidal Moments and Anapole States in All‐Di...
and
Article An electromagnetic multipole expansion beyond the long-wavel...
The first one concerns the formulas for current multipoles explicitly taking into account the so-called toroidal contributions. The second presents exact formulas for the multipoles valid for any size of your structure.
As for the numerical implementation, I personally would recomment COMSOL Multiphysics, specifically the RF or Optics module, where you can directly calculate the multipoles through volume integrals over your meta-atom. There is also an available example showing how to do it https://www.comsol.com/model/multipole-analysis-of-electromagnetic-scattering-31901 , but the expressions for the multipoles that they use are a bit too involved for my taste (this is why I recommend that you use the formulas in the abovementioned publications instead).
On the other hand, if your intention is to perform the multipole decomposition of a periodic structure, then you can implement the method developed by my colleagues in Article Multipole analysis of dielectric metasurfaces composed of no...
,something that you can easily do in comsol too.
Good luck!
Thank you very much Sir Adrià for the detailed response! That was very helpful.
My structure is planer periodic terahertz metamaterial (a metal (gold) pattern deposited on quartz substrate) which shows electric dipole, magnetic dipole and toroidal dipole moments. As I don't have comsol license for now but i have calculated electromagnetic fields for unit cell of the periodic structure by FDTD method (Lumerical) and have time domain as well as frequency domain E and H fields data, transmittance, reflectance and also induced surface current density j in the metal pattern. Can i calculate individual moments with the help of MATLAB somehow by implementing volume integration formulas given in reference i mentioned. Will that be correct?
Hi prateek, could you please help me out with this. How did you do the volume integrals for your MM? How did you take the limits? I am having the same problem. I have all coordinate data and surface current data for my SRR. But I haven't understood how to take limits for the triple integration. Any help will be highly appreciated.
Dear Angana Bhattacharya,
You can take the limits for the triple integration as it includes a unit cell of your structure. In other words, you can take a volume large enough to envelop your structure. Because the current density is calculated by 𝑱(𝒓)=−𝑖𝜔𝜀0(𝑛2−1)𝑬(𝒓), after all, the value becomes zero outside your structure.
The actual procedure can be found in our program paper.
Preprint MENP: An Open-Source MATLAB Implementation of Multipole Expa...
https://github.com/Hinamoooon/MENP
Hope this helps.
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