Monitors at the inferace in the FDTD Solutions



Whose simulation result is recorded into a monitor (profile, power, index) between two adjacent materials when the monitor is located at the interface between two difference materials such as silicon and silver? I’m guessing it might be related to the mesh order or the order of the object in the object tree.



This is a good question and it turns out to be more complicated than just the mesh order. The data which is returned will depend on the monitor type (since the interpolation method used by default by each monitor is different), and the position of the monitor relative to the adjacent mesh cells.

E and H field data are collected at different positions within a mesh cell (or Yee cell):

The field calculations use the material data at the positions where the fields are calculated, so it’s possible that different field components are calculated using different materials if the material interface cuts through the mesh cell.

Frequency domain profile monitors will use “specified position” interpolation by default which interpolates the fields to the position of the monitor. Frequency domain power monitors will use “nearest mesh cell” interpolation by default which means that the fields returned will be interpolated to the origin of the mesh cell. Since the interpolated fields can contain components calculated in different materials, I would recommend placing the profile monitor half a mesh cell away from the material interface, especially if there is a discontinuity in the fields at the material interface.

Refractive index monitors use “specified position” interpolation by default and this returns the refractive index at the origin of the nearest Yee cell at the specified monitor position.

Hopefully this helps.



I appreciate your kind and detailed explanation.
If the mesh and the monitor are positioned at the same interface between Ag and Si without no numerical difference in y-direction as below, which material has the higher priority than another?



Assuming that the red grid shows the outline of the mesh cells in the image, I have added a couple of black dots on the image below to illustrate the location of the origin of the mesh cells on either side of the material interface:

In this case, the origin of the cell in the Ag material lands at the monitor location, so the fields returned by the monitor at the material interface will be the fields that are interpolated from the cell within the Ag material.