Index of Refraction and Sellmeier’s Equation

Now that we know how the classical dipole behave, we can solve the equation of motion for the macroscopic polarization density, given as:

\begin{equation} \frac{d^2P}{dt^2}+(\gamma + \frac{2}{T_2′})\frac{dP}{dt}+\omega_0^2P = \frac{Ne^2}{m}E \end{equation}

which we found using our heuristic model of the polarization.

Table of Contents:

  1. Steady-State Solution to Equation of Motion for Macroscopic Polarization
  2. Wave Equation with Polarization Source
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