Hi, I plan to calculate polarization sentivity of a metal nanowire by the equation
(TM/TE RATIO= ( ϵ /ϵ0+1)/2)2. ϵ is the relative permittivity of metal, which includes a real part and a imaginary part in the form of ϵ= ϵ' + i ϵ''. Do you think which part I should use to calculate? Or I just use the complex form and finally calculate the modulus of the whole item?
Thanks in advance.
Best Regards!
Just the real part, Especially if u are not looking at the reflection close to the plasmon resonance.
I always prefer to use just the real part. The notion of a complex-valued permittivity is only really valid in a CW regime, but even then is merely a calculational convenience rather than an accurate model of the physics. The underlying physics, of course, might be modelled as e.g. a Drude model or Lorentz oscillator, which is an explicitly time-dependent response.
An imaginary part of the permittivity (or similarly the permeability) follows from the EM fields driving microscopic currents or atomic states , and it is the loss in these currents (or states) that means that their back-action of on the EM fields is reduced. Thus the "imaginary part" notion is removed from even simple models of material response in two important respects: it is implicitly frequency domain rather than time domain, and it is unrelated to any actual microscopic physics.
See also (arxiv & PRA versions)
Article Refractive index and wave vector in passive or active media
Article Refractive index and wave vector in passive or active media
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