Refractive Index and Absorption

  • Heinrich Hora


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
$$ \tilde{n}=n+i\kappa ={{(1-\frac{{{\omega }_{p}}^{2}}{\omega (1+i\nu /\omega )})}^{1/2}} $$
$$ n={{\left[ \frac{1}{2}\left\{ \left. {{\left[ {{\left( 1-\frac{{{\omega }_{p}}^{2}}{{{\omega }^{2}}+{{\nu }^{2}}} \right)}^{2}}+{{\left( \frac{\nu }{\omega }-\frac{{{\omega }_{p}}^{2}}{{{\omega }^{2}}+{{\nu }^{2}}} \right)}^{2}} \right]}^{1/2}}+\left( 1-\frac{{{\omega }_{p}}^{2}}{{{\omega }^{2}}+{{\nu }^{2}}} \right) \right\} \right. \right]}^{1/2}} $$
$$ \kappa ={{\left[ \frac{1}{2}\left\{ \left. {{\left[ {{\left( 1-\frac{{{\omega }_{p}}^{2}}{{{\omega }^{2}}+{{\nu }^{2}}} \right)}^{2}}+{{\left( \frac{\nu }{\omega }-\frac{{{\omega }_{p}}^{2}}{{{\omega }^{2}}+{{\nu }^{2}}} \right)}^{2}} \right]}^{1/2}}-\left( 1-\frac{{{\omega }_{p}}^{2}}{{{\omega }^{2}}+{{\nu }^{2}}} \right) \right\} \right. \right]}^{1/2}} $$
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
$$ n=\tilde{n}={{(1-{{\omega }_{p}}^{2}/{{\omega }^{2}})}^{1/2}}\ (if\nu =0) $$
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
$$ \operatorname{I} = {I_0}{\text{exp}}( - \operatorname{Kx} $$
The absorption constant is then
$$ {\rm K} = \frac{{2\omega }}{c}\kappa $$


Refractive Index Laser Intensity Collision Frequency Oscillation Energy Coulomb Collision 
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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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