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GATE 2022 PH – Question 24

Electromagnetic theory · electromagnetic waves in free space, non-conducting and conducting media · 1 mark · Multiple select

For refractive index $n(\omega)=n_r(\omega)+in_{im}(\omega)$, which statements are correct?

  1. $n_r$ can be obtained from $n_{im}$ and vice versa
  2. $n_{im}$ could be zero
  3. $n$ is analytic in the upper half complex-frequency plane
  4. $n$ is independent of frequency for some materials

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Show answer and explanation

Correct answer: (A) $n_r$ can be obtained from $n_{im}$ and vice versa; (B) $n_{im}$ could be zero; (C) $n$ is analytic in the upper half complex-frequency plane

Explanation

Causality gives upper-half-plane analyticity and Kramers-Kronig relations connecting real and imaginary parts. Transparent frequency intervals can have zero imaginary part.