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

**3**

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).

## Comments

1,652Ansys EmployeeIt 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.

6MemberHello,

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).

1,652Ansys EmployeeIf 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.

6MemberThanks a lot, I'll try that and check the paper out as well.