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Refractive Index and Absorption

  • Heinrich Hora

Abstract

As derived from the macroscopic theory of a plasma, the complex optical refractive index ñ is given by the dispersion relation of electromagnetic waves in a plasma, (Eq.:(5.12)), where the real part n, and the imaginary part κ, are evaluated algebraically
$$ \tilde{n}=n+i\kappa ={{(1-\frac{{{\omega }_{p}}^{2}}{\omega (1+i\nu /\omega )})}^{1/2}} $$
(6.1)
$$ n={{\left[ \frac{1}{2}\left\{ \left. {{\left[ {{\left( 1-\frac{{{\omega }_{p}}^{2}}{{{\omega }^{2}}+{{\nu }^{2}}} \right)}^{2}}+{{\left( \frac{\nu }{\omega }-\frac{{{\omega }_{p}}^{2}}{{{\omega }^{2}}+{{\nu }^{2}}} \right)}^{2}} \right]}^{1/2}}+\left( 1-\frac{{{\omega }_{p}}^{2}}{{{\omega }^{2}}+{{\nu }^{2}}} \right) \right\} \right. \right]}^{1/2}} $$
(6.2)
$$ \kappa ={{\left[ \frac{1}{2}\left\{ \left. {{\left[ {{\left( 1-\frac{{{\omega }_{p}}^{2}}{{{\omega }^{2}}+{{\nu }^{2}}} \right)}^{2}}+{{\left( \frac{\nu }{\omega }-\frac{{{\omega }_{p}}^{2}}{{{\omega }^{2}}+{{\nu }^{2}}} \right)}^{2}} \right]}^{1/2}}-\left( 1-\frac{{{\omega }_{p}}^{2}}{{{\omega }^{2}}+{{\nu }^{2}}} \right) \right\} \right. \right]}^{1/2}} $$
(6.3)
The real part n is sometimes called the refractive index. Here the sum with the complex refractive index is denoted by the circumflex ñ. For a collisionless plasma (υ = 0), both coefficients are clearly equivalent
$$ n=\tilde{n}={{(1-{{\omega }_{p}}^{2}/{{\omega }^{2}})}^{1/2}}\ (if\nu =0) $$
(6.4)
The imaginary part of ñ, κ, is called the absorption coefficient. Its meaning is seen immediately from its relation to the absorption constant K, which determines the attenuation of a laser intensity I at some depth x; if I0 is the intensity at x = 0
$$ \operatorname{I} = {I_0}{\text{exp}}( - \operatorname{Kx} $$
(6.5)
The absorption constant is then
$$ {\rm K} = \frac{{2\omega }}{c}\kappa $$
(6.6)

Keywords

Refractive Index Laser Intensity Collision Frequency Oscillation Energy Coulomb Collision 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Plenum Press, New York 1975

Authors and Affiliations

  • Heinrich Hora
    • 1
    • 2
  1. 1.University of New South WalesKensington-SidneyAustralia
  2. 2.Rensselaer Polytechnic InstituteHartfordUSA

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