# FDE Solver - Modal Analysis - Power Integration over a Triangle

#1

Hello,

I am using FDE solver for a modal analysis. The cross section of the waveguide has a triangle-shaped region. I need to calculated the power/intensity over a specific region of the cross section. In the “Modal analysis” tab of the “Eigensolver Analysis,” the “Power and Integration density” can calculate the same thing; however, it only integrates over a rectangular or circle. Is there any way to do the same thing over a triangle (or generally a specific shape) in the cross section.

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#2

There are only rectangular and circular shapes in the GUI, by default. If you would like to do something similar with your custom shape, you would probably need to define a “filter” and manually integrate the fields.

## Defining a filter based on the material

This is very similar to the idea of this KB article (Pabs) making use of the material information to define a filter. Now the filter will be defined based on its shape and index. It can involve multiple material too eg, fraction of light in the core, cladding, etc. I have made a very simple example that calculates the light confined in a triangular waveguide using a filter. fraction_integrated_filter.lms (237.7 KB)

The data group contains the material and mode information. The “ratio” is the calculated “fraction integrated”

The script for integration is in the Analysis Script tab of the Edit anlaysis group window.

If the filter is different from the shape of the waveguide, you could maybe first “record” the filter with the shape for integration before the simulation is run. You may need to use the Script File Editor, but the idea is very similar. You could also define your filter mathematically.

#3

As @kchow has mentioned, the spatial filter can be also defined based on its geometry.

When you press the ‘Calculate Modes’ button in the Eigensolver Analsys window, a set of monitors are automatically generated corresponding to the order of modes.

To calculate the integration of |E(x,y)|^2 over a triangular region, you need to take the following steps:

1. Get the |E(x,y)|^2 data from the ‘modeXXX’ monitor (‘XXX’ corresponds to the mode order)
2. Create a spatial filter, Filter(x,y), (‘1’ for the inside of the triangular region and ‘0’ for the outside)
3. Multiply |E(x,y)|^2 and Filter(x,y), and then do the integration.

I have attached a simple simulation file containing a triangular waveguide [ FDE_tri_sf.lms (235.4 KB) ]

The definition of the triangle and the spatial filter are as follows:

After running the simulation, execute the script file [FDE_tri_sf.lsf (669 Bytes) ]

The script will generate two plots for the spatial filter and the |E|^2 filtered:

Finally, it will calculate the integration of |E|^2 over the triangular region.

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