This topic compares the analytical solutions and results simulated with MODE for a hollow metal waveguide:
- We first calculate the wavenumbers for 3 TE modes from 5GHz to 25GHz and compare the results to the analytical solutions.
- We also examine the error in the calculated wavenumbers as a function of the number of grid points.
This waveguide is created using a simulation box of dimensions 10nm x 20nm with METAL boundary conditions on all sides. The region is discretized such that the grid spacing is the same in both the x and y directions.
The analytical solutions for the TE modes are given by the following equation:
where a and b are the dimensions of the waveguide. This will be used to compare with the MODE results for modes TE10, TE01 and TE11.
The script hollow_metal_wg.lsf first performs a frequency sweep from 5GHz to 25GHz and selects the 3 modes that best overlap with the desired TE modes.
The following figure (generated using the Matlab interface) shows the propagation wavevector as a function of frequency for the 3 modes.
(Left) Propagation wavevector as a function of frequency for hollow metal waveguide. Dispersive characteristics of the first three modes are shown for frequencies ranging from 5 to 25 GHz. The solid lines show the analytic response, while the symbols (o) show the results calculated with MODE. (Right) The same figure generated using only built-in MODE functions (no Matlab interface).
Error amplitude as a function of grid points
The second part of hollow_metal_wg.lsf performs a systematic increase in the number of grid points and observes the rate of change of the error amplitude as a function of this decrease.
(Left) Error amplitude of MODE calculation for hollow metal waveguide modes at a frequency of 20 GHz compared to the analytic response. The x-axis shows the number of grid points along the long side of the hollow metal waveguide. (Right)The same figure generated using only built-in MODE functions.