Module 7 : Laser- I
Lecture   : Introduction - Basics of stimulated emission
 

In the figure above, the excited state atoms are shown in red while those in the ground states are in green. However, the simple picture above does not work in practice because of the following :

  • The time for which an electron remains in an excited state is approximately $ 10^{-8}$seconds. Thus it is difficult to keep atoms in excited states till they are stimulated to radiate a photon. The excited atom is more likely to de-excite spontaneously . Photons released through spontaneous processes are emitted in random directions and are not coherent with the incident photon.
  • The photons that are incident and those which are generated may be absorbed by atoms in ground states, leading to depletion in the number of photons.
   
2.
 Interaction of Radiation with Matter:
 

In order to have an insight into the principle of laser, we need to understand the way radiation field interacts with matter. In the early 20th century, Planck formulated the theory of spectral distribution of thermal radiation. Einstein, by combining Planck's theory and the Boltzmann statistics gave a theory of stimulated emission which is the governing principle of lasers.

   
2.1 Blackbody Radiation :
 


Planck's formula gives the radiation of radiant intensity when electromagnetic radiation is confined to an isothermal cavity - known as the blackbody . In classical physics, radiation is considered as waves which form standing wave pattern in the cavity with nodes at the walls. The classical formula for the radiant energy density $ u(\nu)$at a frequency $ \nu$in the energy interval $ \nu$to $ \nu+d\nu$is obtained by counting the number of modes of the electromagnetic waves in this interval and multiplying it with the average energy per mode $ kT$. The resulting formula is known as Rayleigh- Jeans' Law , which is given by
                                     $\displaystyle u(\nu)d\nu = \frac{8\pi kT}{c^3}\nu^2 d\nu$
  Rayleigh-Jeans' formula leads to unphysical result in the short wavelength region (known as ultraviolet catastrophe ).
Planck suggested that the oscillating atoms could emit or absorb energy in tiny bursts called quanta , the energy of a quantum being proportional to its frequency.
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