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simulating e&m wave propagation..

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Hello everyone.

I'm really struggling to simulate a cavity problem.

My goal is to be able to know what's going to happen if i introduce spatially dependent phase inbetween mirrors of a cavity that supports certain transverse modes.

Well, i believe solving for eigenmodes of a cavity is near impossible.

If you guys know something about this sort of challenge or know any good e&m simulators, could you direct me to it?

Thank you

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