Boundary conditions for mode expansion monitors


Mode expansion monitors are very useful in FDTD simulations with waveguides because these monitors allow you to analyze how much power is coupled into any waveguide mode(s). The expansion monitor uses an eigenmode solver to calculate the waveguide modes. This calculation is independent of the FDTD calculation; in fact, you can look at the modes before running the calculation. Therefore, it is natural to ask: what boundary conditions are used by the eigenmode solver? are they influenced in any way by the boundary conditions selected for the FDTD simulation?

The answer is that the mode expansion monitor always uses metal boundary conditions, independently of your choice for the FDTD calculation. These boundary conditions are appropriate for guided modes as long as the modal fields are small enough at the edges of the simulation region for the eigenmode calculation (for more details check this KB page and this posting by @mbenes). Thus, it is important to make sure that the area of the mode expansion monitor is large enough so that the modal fields are small at the edges. Here, the FDTD simulation boundaries can have an impact because the area of the mode expansion monitor is limited by the FDTD region; in other words, if the mode expansion monitor is larger than the FDTD region, the monitor will be truncated.