About monopole, dipole, quadrupole, hexapole, octupole etc


Lumerical’s FDTD Solutions is the first commercial tool providing dipole sources (electrical and magnetic), which is the physical “point” source.

However, in the literature, there are more similar names, such as monopole, dipole, quadrupole, hexapole, octupole. In particular, some papers discussed their scattering. How did they get them? This paper
Analysis of symmetry breaking configurations in metal nanocavities: Identification of
resonances for generating high-order magnetic modes and multiple tunable magneticelectric
Fano resonances
Liancheng Wang, Zhiqiang Liu, Xiaoyan Yi, Yiyun Zhang, Hongjian Li, Jinmin Li, and Guohong Wang

has some detailed analysis:

I reviewed this paper before it was published, and from their results, you can see they have done a lot of analysis.

Basically, it is the near field mode profile that is similar to one of those “poles” (or charges). Those poles are corresponding to resonance peaks. Thus, users only need to monitor the resonate wavelength from profile monitors. This is one reason our Profile Monitor has 5 frequency points by default You do not need monitor the profiles for other wavelengths, since they do not provide any further useful information.

More information about those “poles” can be found in the Multipole Expansion theory.

BTW: different from the textbooks about dipole where the dipole is formed by positive and negative charges, in my understanding, you cannot use two dipole sources to form a quadrupole point source in FDTD:

because higher order poles will need tensors for their moment. The moment is the fundamental physical quantity for those poles.

There are some discussion in this Chinese post: 偶极子四极子六极子八极子十极子等的散射仿真. Please note it is in Chinese .