# 2D magnetic dipole - discrepancy with Green function results (FDTD)

Member Posts: 3
edited January 13

Hello,

I'm intending to simulate the magnetic field distribution emanating from a 2D magnetic dipole (line source) over a lossy substrate at wavelengths between 500 and 1000 nms. As a preliminary work, I'm trying to compare the the results sampled from frequency-domain monitor with those from analytically known Green's function expression. While the general shape of the line (Hankel function) fits perfectly, there is a wavelength-dependent strong discrepancy in terms of complex magnitudes between the obtained results; this does not converge or change no matter how I decrease the mesh size. I'm also using cwnorm and normalizing the (current-density dependent) Green function results since Lumerical uses unit dipole moments.

Am I doing something wrong with the calculations, or is there some sort of amplitude normalization that I'm missing out Thanks for the responses.

I've also attached the formula that I'm using; since Lumerical uses unit dipole moments I'm normalizing this one with (-1i*w).

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• Posts: 1,692Ansys Employee

It is known that in lossy material the dipole power calculation in discrete grid suffers significantly. Please refer this article: dipolepower - Script command

If a very fine mesh is used, it can make it worse.

A alternative method is to use a small monitor box to remove the dipole power problem. However how large the box is a question: if it is too large, the loss from dipole to the monitors are large. If it is too small, then the spatial integration can lead to errors. So there is always a trade-off . I would suggest to use a smaller box, about 5 mesh cells. But you will need to try other values and see if it gives expected accuracy.

The box monitor can be found in the Object Library-analysis group. You can also refer the examples: Calculating the net power flow with a Power transmission box

Hope you can get reasonable result after tackling those issues.

• Posts: 6Member

Hello,

Thanks for your comment, I appreciate it. The problem is there even without the lossy substrate (just a 2D magnetic dipole radiating in free-space); I think I'm doing something wrong with the normalization (since Lumerical is using unit dipole moments while analytical formula uses unit current density).

• Posts: 1,692Ansys Employee

If it is due to dipole moment you can scale it to make sure the normalized spectrum is about the same.

For the field Hankel distribution, Taflove published a paper many years ago and found that such distribution matches well with theory except close to dipole, since it acts as a finite-sized radiation source.

• Posts: 6Member

Thanks a lot, I'll try that and check the paper out as well.