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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

1 Reply Last Post Jul 11, 2013, 6:00 PM EDT
COMSOL Moderator

Hello Tommy Cevi

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Josh Thomas Certified Consultant
Posted: 4 years ago Jul 11, 2013, 6:00 PM EDT
Tommy-

An answer to your question 1) if you still need it:

The eigenfrequency (predefined variable, freq) is the eigenvalue (predefined variable, lambda) times i divided by 2*pi.

freq=lambda*i/(2*pi)

The eigenfrequency and eigenvalue study types are functionally identical from what I can tell. Both of them use the eigenvalue solver. The solution data sets store the solutions a little differently (ie based on freq and lambda respectively), but that is the only difference that I've been able to notice. Maybe there are some other subtleties that I haven't noticed.

Best regards,
Josh Thomas
AltaSim Technologies

Tommy- An answer to your question 1) if you still need it: The eigenfrequency (predefined variable, freq) is the eigenvalue (predefined variable, lambda) times i divided by 2*pi. freq=lambda*i/(2*pi) The eigenfrequency and eigenvalue study types are functionally identical from what I can tell. Both of them use the eigenvalue solver. The solution data sets store the solutions a little differently (ie based on freq and lambda respectively), but that is the only difference that I've been able to notice. Maybe there are some other subtleties that I haven't noticed. Best regards, Josh Thomas AltaSim Technologies

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