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Theoritical Understanding Behind the LASERS

Image result for Lasers

LASER stands for Light Amplification through Stimulated Emission. The theoretical basis was given by Albert Einstein and the first laser was developed by T.H. Mainmann.

LASERs work on 3 main processes.
They are Stimulated Absorption, Spontaneous Emission and Stimulated Emission.

Stimulated Absorption:

When a photon with energy hf, is incident on an electron of an atom present in the ground state, the electron excites to higher energy levels by absorbing the photon. This process is directly proportional to the number of electrons in the ground state. 

Spontaneous Emission:

The excited electron stays for 100 nanoseconds in the excited state and then emits a photon i.e, releases energy which is equal to the difference between energies of the higher energy level and the minimum energy level, to get back to ground state. This process is directly proportional to the number of electrons in the excited state.

Stimulated Emission:

When the electron moves to a metastable state from the excited state by releasing no radiation but some ignorable amount of energy it stays for more than 100 nanoseconds. So then when we incident a photon towards the electron in the metastable state it emits a photon which has a similar phase with that of the electron incident. This creates coherent light waves with high directionality.
This process is directly proportional to the number of electrons in the excited state or in the metastable state.
Image result for stimulated absorption



The principle behind the working of the principle is population inversion.
 
POPULATION INVERSION: 

Image result for population inversion 

In general, an atom has more number of electrons in the ground state than in the higher energy levels. But after excitation of more number of electrons into the higher energy levels they settle down in the metastable for a longer time and that is known to be population inversion. In simple words, there will be more number of electrons in higher energy level than in lower energy levels.
As the Stimulated Emission is directly proportional to the number of electrons in the metastable state this process enhances and accelerates the process.
This population inversion can be achieved by pumping mechanisms or techniques. They are :
 1.Optical pumping
 2.Electrical discharge pumping 
 3.Chemical pumping
 4.Injection current pumping


Image result for pumping mechanism for population inversion


Einstein's coefficient (EC):

Let the number of electrons in the ground state is N1 and the excited state is N2.
Let energy density p(f)= nhf where n is the number of photons per unit volume at frequency f such that E2-E1=hf.
Absorption = B12*N1*p(f)
where B12 is EC of absorption.
Spontaneous Emission = A21*N2
where A21 is EC of spontaneous emission.
Stimulated emission = B21*N2*p(f)
where B21 is EC of stimulated emission.
Absorption is an upward transition and the other two are the downward transition processes of the electron.

Image result for einstein's coefficient in laser

In equilibrium both the transitions become equal i.e,
 B12*N1*p(f) = A21*N2 +  B21*N2*p(f)

 B12*N1*p(f) -  B21*N2*p(f) = A21*N2

 p(f) [ B12*N1 - B21*N2] = A21*N2

 p(f)*B21 [ N1 - N2] = A21*N2

 p(f) = (A21/B21)*(N2/N1-N2)

 p(f) = (A21/B21)*(1/(N1/N2)-1)
 
 From Maxwells Boltzmann distribution law :
N1/N2 = e^(E2-E1)/KT

p(f) = (A21/B21)*(1/(e^(E2-E1)/KT-1))

p(f) = (A21/B21)*(1/(e^(h(f))/KT-1))   ---------eqn1

By comparing  eqn1 with Plank's radiation formula we get :

Image result for einstein's coefficient in laser

The above relations are referred to as Einstein's relations.

This is the theoretical explanation behind the lasers.

For more interesting and easy explanations of physics comment in the comment section.





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