# Discussion Forum

## Relation Eigenvalue/Eigenfrequency problem

 Topics: 4.2, RF Module, eigenfrequency
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Tommy Cevi

October 4, 2012 12:07pm UTC

Relation Eigenvalue/Eigenfrequency problem

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

Josh Thomas
Certified Consultant
AltaSim Technologies, LLC

July 11, 2013 10:00pm UTC in response to Tommy Cevi

Re: Relation Eigenvalue/Eigenfrequency problem

Tommy-