From 98c1fb9ed76ba77625952b5fda05bba523c6d776 Mon Sep 17 00:00:00 2001 From: Ardavan Oskooi Date: Tue, 2 Apr 2024 06:48:04 -0700 Subject: [PATCH] markdown formatting fix in extraction-efficiency tutorial --- doc/docs/Python_Tutorials/Local_Density_of_States.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/doc/docs/Python_Tutorials/Local_Density_of_States.md b/doc/docs/Python_Tutorials/Local_Density_of_States.md index d4d4478f6..ae2973959 100644 --- a/doc/docs/Python_Tutorials/Local_Density_of_States.md +++ b/doc/docs/Python_Tutorials/Local_Density_of_States.md @@ -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.