This example shows how to calculate power flow through a monitor by integrating the Poynting vector. It is also useful as an example of how to do other integrals involving monitor data. In particular, the script file shows a simple technique for integrating over an arbitrary area, such as a circle. The files in this section were created using FDTD Solutions, but a similar approach can be applied for MODE Solution’s propagator.
The script function
transmission can be used to calculate the total power transmitted through a power or profile monitor. However, to calculate the power transmitted through a portion of a monitor, you must integrate the Poynting vector over that region.
The following screenshot shows the layout of
usr_integrate_poynting.fsp. A plane wave source emits light in the positive z direction. There is a thin gold layer with a hole in it that reflects much of the light. Monitors are placed above and below the gold layer to measure transmission and reflection.
Run the simulation, then run the script
usr_integrate_poynting1.lsf. The script will first calculate the total transmission in two ways: using the built in transmission function, and manually integrating the Poynting vector. The two results should be exactly the same.
In the simulation, notice that the source polarization angle is 30 degrees, which means most of the beam is polarized in the X direction, with a smaller fraction polarized in the Y direction. This is consistent with the results shown below, where approximately 2/3 of the power is X polarized and 1/3 is polarized in Y.