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Stimulated Emission

The document discusses the fundamentals of stimulated emission and laser operation. It describes how stimulated emission occurs when an excited atom decays to a lower energy state by emitting a photon when stimulated by another photon. It defines the rate of stimulated emission and explains the principle of detailed balance, where the total rate of absorption of photons must equal the total rate of emission. It also shows how the Einstein coefficients that describe absorption and emission probabilities can be used to calculate the photon density at equilibrium.

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Osborne Kachaje
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157 views5 pages

Stimulated Emission

The document discusses the fundamentals of stimulated emission and laser operation. It describes how stimulated emission occurs when an excited atom decays to a lower energy state by emitting a photon when stimulated by another photon. It defines the rate of stimulated emission and explains the principle of detailed balance, where the total rate of absorption of photons must equal the total rate of emission. It also shows how the Einstein coefficients that describe absorption and emission probabilities can be used to calculate the photon density at equilibrium.

Uploaded by

Osborne Kachaje
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© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Laser : Fundamentals and Applications

Stimulated Emission
• In 1917 Albert Einstein proposed another way of interaction of light
with matter which is called as stimulated emission. This process involves
decay of atom from excited state to ground state using a photon of light.
Laser : Fundamentals and Applications

Rate Of Stimulated Emission


• Rate of stimulated emission = dN2/dt
where N2 = population of the excited state

-dN2/dt ∝ N2ρ(hν12)

-dN2/dt = B21 N2ρ(hν12)

where B21 is called as rate constant of stimulated emission ,21 indicates


that transition is from level 2 to 1.
Laser : Fundamentals and Applications

Principle of Detail Balance


• According to principle of detail balance for a system rate of upward
transition is equal to the rate of downward transition at equilibrium.
Total rate of absorption = Total rate of emission
• Rate of absorption = B12N1ρ(hν12) --1
• Rate of spontaneous emission = A21N2
• Rate of stimulated emission = B21N2ρ(hν12)
• Total rate of emission = A21N2 + B21N2ρ(hν12) --2
From 1 & 2 -
B12N1ρ(hν12) = A21N2+ B21N2ρ(hν12)

B12, B21, A21 are collectively called as Einstein coefficients.


Laser : Fundamentals and Applications

Calculation of Einstein Coefficients


Laser : Fundamentals and Applications

• On solving the equation for ρ(hν12) we get:-


 
 
ρ(hν12)=
A21 N 2  1  -- 3
B12 N1   B21 N 2  
 1  B N  
 
  12 1  

Ratio of population of two state at equilibrium is given by Boltzmann distribution law:-


N2/N1 = e- (hν /kT)
12 -- 4
Here k is Boltzmann constant and T is temperature.
Using 4 & 3 :-
 
  h 12 / kT 
A21  e 
ρ(hν12) = B   B21  h12 / kT  
 1  B e
 
12

  12  

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