How to measure power radiated by a dipole in a dispersive, lossy medium?



Measuring the power radiated by a dipole source requires special considerations. While [this related topic][1] describes the need to use [dipolepower][2] in non-homogeneous media, additional challenge arises when the dipole is placed in a dispersive material with [non-zero imaginary part of the refractive index][3].

The issue about using dipoles in a dispersive material is a theoretical issue, rather than a numerical issue. In dispersive materials, the imaginary part of the greens function begins to diverge, leading to infinite amounts of power. Here are two possible ways to deal with this issue in FDTD:

  1. Create a small volume of dielectric material right near the dipole location (maybe 5 mesh cells in size). This avoids the entire problem, since the dipole is not located in a dispersive material. You can then use the dipole power function or monitor box to measure the radiated power. When using the dielectric material, set the real part of the refractive index to be matched with the surrounding lossy material. Obviously, this works better with single frequency or narrow band simulations due to the dispersive nature of the surrounding material. Also, make sure to set correct [mesh order][4] for the dielectric.

  2. Place the dipole within the dispersive material as you want and use the transmission box to measure the power (don’t use the dipole power). The box should have some finite size (minimum ~5 mesh cells). You will be able to measure the amount of power radiated out of that box, but you will not have information about power absorbed within this box, which might make this approach less suitable for highly lossy materials.
    [1]: When I try to measure the transmission of a dipole source, it is sometimes greater than 1?

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Would there be a screenshot or a simple simulation file that shows the first idea?

I am guessing that matching the real part of the refractive index is to avoid reflection from the interface. But it should still have some reflection and interference that potentially affect the power the dipole radiates, like this example. Is this a flip-side of this approach?