Module 7 : Laser- I
Lecture   : Line Broadening in Lasers
  Example 1:
  A He-Ne laser has a gas discharge temperature of 400 K. The atomic mass of Ne (which is responsible for lasing) is $ 3.35\times 10^{-26}$kg. If the lasing wavelength is 630 nm, calculate the lineshape broadening due to Doppler effect.
  Solution:
 

The Doppler frequency broadening is given by

$\displaystyle \Delta\nu = 2\nu_0\sqrt{\frac{2kT\ln 2}{mc^2}}$

using $ \lambda = c/\nu$, the FWHM for wavelength is given by

                                                                                   $\displaystyle \Delta\lambda = \frac{c}{\nu^2}\Delta\nu \simeq \frac{c}{\nu_0^2}\Delta\nu$
Substituting the numerical values, $ \Delta\lambda = 0.002$nm.

   
2.6

Consequence of Line Broadening:

  We have seen that the atomic energy levels are broadened due to both homogeneous and inhomogeneous effects. As a result of this, the energy separation between the two laser levels itself is centred around some frequency $ \nu_0$with a spread $ \Delta\nu$. The line shape distribution corresponding to this transition will be denoted as $ g(\nu,\nu_0)$.
The laser is forced to operate at a signal frequency $ \nu_s$with a width $ d\nu$. In practice $ d\nu\ll\Delta\nu$. For instance for Ruby, the line width $ \Delta\nu\approx 0.5nm$while the laser output width is typically $ d\nu\approx .01$to .001 nm. Thus the signal may be
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