Module 8 : Laser- II
Lecture   : Rate equations for Lasers
 

Taking the beam profile to be gaussian, the intensity varies as $ I=I_0e^{-r^2}$, where $ r$is the distance from the centre of the beam where the intensity ( $ I_0$) is maximum. We define beam radius as the radial distance over which the intensity decreases by a factor $ e^2\simeq 7.389$from its maximum value at the centre. Thus nearly 94% of the energy is concentrated within the beam radius.

The angular divergence of the beam is given by

$\displaystyle \theta = \frac{\lambda}{\pi w_0}$

where $ w_0$is the radius of the beam at the point where the beam leaves the laser. The radius of the beam varies with the distance as

$\displaystyle w(z) = w_0\sqrt{1+\left(\frac{z}{z_0}\right)^2}$

where $ z_0 = \pi w_0^2/\lambda$.

   
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