Posts for the month of March 2012

Notes on Light Propogation using the Eikonal

I want to try and figure out whether it is possible to solve the eikonal equation for a complex function of the wave fronts to simulate absorption of light. Here, we will recap assuming the wave front function is real. The wave equation for the electric field is given by,

$ \nabla^2 \vec{E} + \frac{n^2 \omega^2}{c^2} \vec{E} = 0 $

where we will assume an electric field intensity of

$ \vec{E} = \vec{E}_0 e^{i\left(k R - \omega t \right)} $

where

$k = \frac{\omega}{c} = \frac{2 \pi}{\lambda} $

If we assume a short wavelength than the wave equation reduces to

$ \left[\nabla R\right]\cdot \left[\nabla R\right] = n^2 $

The time averaged Poynting vector is given by,

$\vec{S} = \frac{|\vec{E}|^2}{4 c^2 \mu_0} \nabla R$

and the intensity is $|S|$ given by,

$I = \frac{n^2}{4 c^2 \mu_0} |\vec{E}|^2 $

  • Posted: 2012-03-07 09:34
  • Author: wd15
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