I'm trying to understand that why gain mediums have negative electrical permittivity. Imaginary part of the electrical permittivity is positive for loss mediums in sign convention where time harmonics are taken as exp(-iwt).
In short, consider electrical permittivity is e = e'+ie''. Then, for lossy medium e">0, whereas for gain medium e"
I hope this excerpt taken from Preprint Wave optics in Infrared Spectroscopy
helps...
In my opinion, It is best to treat most uses of the sign of permittivity/ permeability/ (and especially of refractive index) as gain or loss as handy rules-of-thumb rather than as some absolute physical truth. The uses typically rely on a collection of sign conventions and approximations that might not always be obvious or clearly explained.
I suggest starting with a time-dependent, dynamical model of some permittivity response (either a Drude or Lorentz model with loss will suffice), and (Fourier) transforming it into the frequency domain. You will then see how the loss parameter appears in the imaginary part of the model's spectral response.
Thanks everyone for your suggestions.
I have found the derivation on the above mentioned topic in a book Lasers by Ajoy Ghatak and Thyagarajan.
Hi Paul,
In sign convention that I'm working with, the imaginary part of permittivity shouldn't be negative except for the gain medium (lasers/masers) that show negative imaginary permittivity. Anyway, problem is sorted out.
Thanks for taking out time to give your input on the topic.
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