I am currently investigating two-dimensional dielectric cavities and their electromagnetic TM/TE eigenmodes. For these studies I use the "Electromagnetic Waves" module while only considering the out-of-plane vector (corresponding to TM modes) and a perfectly matched layer in order to restrict myself to outgoing boundary conditions (Sommerfeld radiation condition). I have a few questions regarding such simulations in COMSOL:
1) How are the eigenvalue and the eigenfrequency studies related to each other?
Typically, in two dimensions the three dimensional EM equations without any sources boil down to
(∇² + ε_r(x,y) k²) E(x,y) = 0
such that one would assume that the eigenvalue λ should be related to the eigenfrequency k simply by λ = k². However, when I simply switch from an eigenvalue study to an eigenfrequency study. I get completely different solutions. The solutions from the eigenfrequency study are not found in the eigenvalue study and vice versa.
2) Comparing the eigenfrequencies from the calculations for a simple circular dielectric cavity to the actual analytic results (which can easily be obtained for such a system), the calculated eigenfrequencies don't match, although convergence regarding the mesh discretization has been reached. Although the real parts of the eigenfrequencies roughly match, the imaginary parts are off by 5 orders of magnitude.
I would be happy for any suggestions!
Best regards,
Tommy
1) How are the eigenvalue and the eigenfrequency studies related to each other?
Typically, in two dimensions the three dimensional EM equations without any sources boil down to
(∇² + ε_r(x,y) k²) E(x,y) = 0
such that one would assume that the eigenvalue λ should be related to the eigenfrequency k simply by λ = k². However, when I simply switch from an eigenvalue study to an eigenfrequency study. I get completely different solutions. The solutions from the eigenfrequency study are not found in the eigenvalue study and vice versa.
2) Comparing the eigenfrequencies from the calculations for a simple circular dielectric cavity to the actual analytic results (which can easily be obtained for such a system), the calculated eigenfrequencies don't match, although convergence regarding the mesh discretization has been reached. Although the real parts of the eigenfrequencies roughly match, the imaginary parts are off by 5 orders of magnitude.
I would be happy for any suggestions!
Best regards,
Tommy