Question

1) Find the complex conjugate refractive index n*,

corresponding to complex conjugate dielectric constant eps*

2) Plot n* and eps* versus frequency.

Assume eps*= eps_inf + delta_eps / (1+i.omega.tau)

Answer 1

=>

=>

=>

this is of the form:

complex refractive index will be:

and n* = x + iy

therefore,

(x+iy)² = a+ib

=> (x² - y²) + i [2xy] = a + ib

comparing both the sides gives:

2xy = b

=> x = b/(2y)

and x² - y² = a

=>

=> 4y⁴ + 2y² - b² = 0

substitute y² = p and b² = c

4p² + 2p - c = 0

solve this to get y which is the complex part of the refractive index.

use, x = b/(2y) to get the real part of the refractive index.

from the obtained relations, plot the real and imaginary parts separately versus frequency .