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Updating the dipole normalization FAQ
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momchil-flex committed Jul 8, 2024
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11 changes: 9 additions & 2 deletions _faqs/How-are-results-normalized.md
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Expand Up @@ -41,9 +41,16 @@ Source power normalization is applied depending on the source type. In the cases

The injected power values described below assume that the source spectrum normalization has also been applied.

- [PointDipole](https://docs.flexcompute.com/projects/tidy3d/en/latest/api/_autosummary/tidy3d.PointDipole.html#tidy3d.PointDipole){: .color-primary-hover}: Normalization is such that the power injected by the source in a homogeneous material of refractive index $n$ at frequency $\omega = 2\pi f$ is given by
- [PointDipole](https://docs.flexcompute.com/projects/tidy3d/en/latest/api/_autosummary/tidy3d.PointDipole.html#tidy3d.PointDipole){: .color-primary-hover}: The point dipole source represents an infinitesimal antenna with a fixed current density. The normalization is such that the power injected by the source in a homogeneous material of refractive index $n$ at frequency $\omega = 2\pi f$ is approximately given as follows

$$\frac{\omega^2}{12\pi}\frac{\mu_0 n}{c}.$$
* $\frac{\omega^2}{12\pi}\frac{\mu_0 n}{c}$, 3D simulation, electric current
* $\frac{\omega^2}{12\pi}\frac{\epsilon_0 n^3}{c}$, 3D simulation, magnetic current
* $\frac{\omega \mu_0}{16}$, 2D TE simulation, electric current
* $\frac{\omega \mu_0}{8}$, 2D TM simulation, electric current
* $\frac{\omega \epsilon_0 n^2}{8}$, 2D TE simulation, magnetic current
* $\frac{\omega \epsilon_0 n^2}{16}$, 2D TM simulation, magnetic current

There can be a small difference in the true power compared to the analytical values above due to the finite grid. Note that the current source definition used in Tidy3D is different from the definition of an electric dipole composed of two separated, oscillating electric charges, which is also common. The power normalization differs by a factor of $\omega^2$ for electric dipoles, and $\mu_0^2 \omega^2$ for magnetic dipoles.

- [UniformCurrentSource](https://docs.flexcompute.com/projects/tidy3d/en/latest/api/_autosummary/tidy3d.UniformCurrentSource.html#tidy3d.UniformCurrentSource){: .color-primary-hover}: No extra normalization applied.

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Expand Up @@ -24,8 +24,4 @@ _inputs:
text:
- key: category_name
---
The [tidy3d.PointDipole](https://docs.flexcompute.com/projects/tidy3d/en/latest/api/_autosummary/tidy3d.PointDipole.html){: target="_blank" rel="noopener"} source is normalized such that the power injected in a homogeneous material of refractive index $n$ at frequency $\omega = 2\pi f$ is given by

$\frac{\omega^2}{12\pi}\frac{\mu_0 n}{c}$.​​​​​

To calculate the radiated power of a dipole in the presence of dispersive, lossy, or non-homogeneous materials, you can use a [tidy3d.FluxMonitor](https://docs.flexcompute.com/projects/tidy3d/en/latest/api/_autosummary/tidy3d.FluxMonitor.html){: target="_blank" rel="noopener"} box. Refer to this [notebook](https://www.flexcompute.com/tidy3d/examples/notebooks/BullseyeCavityPSO/) for an example.
The [tidy3d.PointDipole](https://docs.flexcompute.com/projects/tidy3d/en/latest/api/_autosummary/tidy3d.PointDipole.html) source placed in a lossless homogeneous material injects power close to the [analytically expected](https://docs.flexcompute.com/projects/tidy3d/en/latest/faq/docs/faq/How-are-results-normalized.html#source-power-normalization) result for an infinitesimal antenna with oscillating current. There can be a small difference from the analytical result due to the finite grid, which disappears in the limit of high resolution. To calculate the radiated power of a dipole in the presence of dispersive, lossy, or non-homogeneous materials, you can use a [tidy3d.FluxMonitor](https://docs.flexcompute.com/projects/tidy3d/en/latest/api/_autosummary/tidy3d.FluxMonitor.html) box. Refer to this [notebook](https://www.flexcompute.com/tidy3d/examples/notebooks/BullseyeCavityPSO/) for an example.

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