Module 7 : Laser- I
Lecture   : Line Broadening in Lasers
  $ g(\nu)$is a complicated function which depends on the transition involved and also on external factors. The broadening of spectral lines is classified into two major categories :
  Homogeneous Broadening :
  In homogeneous broadening all atoms interact identically with the radiation field so that each atom makes the same transition with identical lineshape and width. Two of the prominent causes of homogeneous broadening are natural line broadening and collision broadening. Other sources of homogeneous broadening are dipolar broadening arising out of interactions between electric and magnetic fields of neighbouring atoms and thermal broadening due to effects of lattice vibrations on atomic transitions.
  Inhomogeneous Broadening:
  In inhomogeneous broadening, different atoms interact differently with the radiation field. Doppler broadening due to thermal motion of atoms and broadening due to crystal inhomogeneities belong to this category.
2.5.1 Natural Linewidth :
 


Natural linewidth is an inherent width associated with any energy level due to quantum mechanical uncertainty principle. According to this principle, if $ \Delta t$is the minimum uncertainty in the lifetime of an atom in an energy level, the uncertainty in determining the energy level itself is given by

$\displaystyle \Delta E\Delta t \simeq h/2\pi$

Using $ E=h\nu$, the relation may be written as

$\displaystyle \Delta\nu\Delta t \simeq 1/2\pi$

Thus in a two level system, there is an width associated with both the upper and lower levels. This, in turn, implies that there is an inherent width in the frequency of photons emitted due to the transition. In a typical transition, the excited state lifetime is $ \sim 10^{-8}$seconds. The corresponding linewidth is about 16 MHz.

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