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Metamaterials: imaginary part of permittivity being negative

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Hello dear friends, I'm working on a new metamaterial structure that have nonlinear properties with in a broad bandwidth. I have simulated the structure in cst and got the S11 and S21 of the structure. with the relations given in the articles calculated permittivity and permeability of the structure. but there is an amazing point in the result and that is the imaginary part of permittivity being negative. I don't know what is the meaning of it and googled that. what I found was an article named "On the signs of the imaginary parts of the effective permittivity and permeability in metamaterials" proving that negative imaginary part of the permittivity and permeability results from simulations errors! now I'm confused about my S-parameters results. Are they incorrect?
Please help me with your comments.
Thanks in advanced.
 

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