Energy level jump in stimulated emision

[kunalghosh]

when some energy is suplied to an electron in a higher energy level E2 then how come it drops down to a lower energy level E1 but as per our knowlwdge of physics...it should jump to a higher energy level E3.

 

[JeffKoch]

You're not really supplying energy to the electron in E2, you're increasing it's probability to decay down to E1 by supplying a photon with an energy (E2-E1). You'll then wind up with two photons, each having energy (E2-E1) - if the first photon had been absorbed, you would wind up with no photons and an atom in an excited state E3.

 

[petr1243]

Yes you are absolutely correct. Originally there will be more atoms in the ground compared with the excited state. This will not produce "lasing". We will have a laser by using the process known as "optical pumping". Without this energy pump, population inversion will be nearly impossible, hence lasing isn't achieved. Due to this process, we will have population inversion which will give us "lasing". "Population Inversion" occurs when N_2-N_1>0 for a 3-level system. What happened to N_3? We disregard it since the decay rate from N_3 to N_2 is very rapid(wiki it). I recommend that you look at the rate equations for 3-level system in steady state: (N_T = N_1 + N_2 + N_3 = constant)

d/dt(N_T = N_1 + N_2 + N_3) = 0

Using the "steady state" concept, solve for N_2 and N_1 and you should apply this "population inversion" constraint for N_1 AND N_2. Good Luck!

 

[kunalghosh]

the last post left me totally clueless could you give some basic equations which i could solve to obtain the result ?

 

[petr1243]

dN3/dt = PN1 - Γ32N3

dN2/dt = Γ32N3 - Γ21N2

dN1/dt = -PN1 + Γ21N2

ΣdNi/dt = 0, i=1,2,3.

Where P:pumping rate and Γ:decay rate.

Goal: To get steady state values for Ni, i=1,2,3 and this is done by setting dNi/dt = 0 , i=1,2,3.

When we get each steady state value, we usually denote it as Nibar, i = 1,2,3.

A good exercise would be to obtain the steady state population inversion:

N2bar - N1bar > 0 , and from here we will get a constraint on the pumping rate.

You will see that that the greater P is w.r.t. the decay rate, the greater the population inversion, and hence the "gain", which will give us "lasing"

Also you can get all of the steady state values in terms of NTbar, using NTbar = ΣNibar; i=1,2,3.

If you need a schematic of this situation, here it is:(under the headline:3-level laser)

http://en.wikipedia.org/wiki/Population_inversion

p.s. I assumed that we have (photon flux)<<1, since it's not included in the 3-level population rate equations.