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markdown formatting fix in extraction-efficiency tutorial
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oskooi committed Apr 2, 2024
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Expand Up @@ -335,7 +335,7 @@ Note: because of a [bug](https://github.com/NanoComp/meep/issues/2704) for an $E

![](../images/dipole_extraction_eff_cyl.png#center)

The total emitted power obtained from the LDOS terms of the formula above must be multiplied by $\Delta V$, the volume of the voxel. In cylindrical coordinates, $\Delta V = \Delta r \times \Delta z \times 2 \pi r$. Meep implements an $r = 0$ source at $r = 0.5 \Delta r$, corresponding to the smallest-$r$ $E_r$ Yee grid point. This means that for a source at $r = 0$, $\Delta V = \pi / resolution^3$ since $\Delta r = \Delta z = 1 / resolution$. In 3D, $\Delta V = \Delta x \times \Delta y \times \Delta z = 1 / resolution^3$ for every voxel in the cell.
The total emitted power obtained from the LDOS terms of the formula above must be multiplied by $\Delta V$, the volume of the voxel. In cylindrical coordinates, $\Delta V = \Delta r \times \Delta z \times 2 \pi r$. Meep implements an $r = 0$ source at $r = 0.5 \Delta r$, corresponding to the smallest-$r$ $E_r$ Yee grid point. This means that for a source at $r = 0$, $\Delta V = \pi /$`resolution`$^3$ since $\Delta r = \Delta z = 1 /$`resolution`. In 3D, $\Delta V = \Delta x \times \Delta y \times \Delta z = 1 /$`resolution`$^3$ for every voxel in the cell.

As shown in the figure below, the results from the two coordinate systems have good agreement.

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