Module 8 : Laser- II
Lecture   : Rate equations for Lasers
  Exercise :
  A He-Ne laser operating at 630 nm has an emission width of $ \delta\lambda = 10^{-6}$nm. Calculate the temporal coherence length.(Ans. 400 m)
It may be noted that a laser beam is highly monochromatic with the spread of wavelength being very small.
  Exercise:
  An Argon laser operating in single mode has a linewidth of 7.5 MHz. Calculate its coherence length. (Ans. 40 m)
  Spatial Coherence:
  Spatial coherence describes the distance over which phase correlation exists between different points in the same wave in a direction perpendicular to the direction of observation. Spatial correlation arises because a source is never really a point source. Consider two point sources S $ _1$ and S $ _2$ at a distance $ d$from each other along the y-axis, as shown.

Suppose the waves arriving at the point P which is at a distance $ z$along the direction perpendicular to the line joining the sources are coherent. The phase difference between waves arriving at the point Q which is at a lateral distance $ x$is $ S_2Q-S_1Q$. Using straightforward geometry, we can see that the path difference is given by
$\displaystyle \delta l = x\frac{d}{z}$
  \includegraphics{spatial.eps}
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