Energy level jump in stimulated emision

In summary, when energy is supplied to an electron in a higher energy level E2, it can drop down to a lower energy level E1 by emitting a photon with energy (E2-E1). This process can be used to achieve population inversion, where there are more atoms in the excited state E2 compared to the ground state E1. By using the process of "optical pumping", population inversion can be achieved and this leads to "lasing". The rate equations for a 3-level system in steady state can be used to solve for the steady state values of the population in each energy level. The goal is to obtain a population inversion constraint, which will determine the required pumping rate for lasing to occur. Additionally, the
  • #1
kunalghosh
2
0
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.
 
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  • #2
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.
 
  • #3
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!
 
  • #4
the last post left me totally clueless could you give some basic equations which i could solve to obtain the result ?
 
  • #5
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.
 

1. What is an energy level jump?

An energy level jump refers to the movement of an electron from one energy level to another within an atom or molecule. This can occur spontaneously or be induced by external energy sources.

2. What is stimulated emission?

Stimulated emission is a process in which an excited atom or molecule emits a photon of light upon interaction with another photon of the same energy. This occurs in lasers and other light-emitting devices.

3. How does stimulated emission lead to an energy level jump?

When an excited atom or molecule undergoes stimulated emission, it releases a photon and returns to a lower energy state. This can result in an energy level jump as the electron moves to a lower energy level.

4. What is the significance of energy level jumps in stimulated emission?

Energy level jumps in stimulated emission play a crucial role in the functioning of lasers and other light-emitting devices. They allow for the controlled release of photons, resulting in coherent and amplified light output.

5. How is stimulated emission different from spontaneous emission?

In spontaneous emission, an excited atom or molecule releases a photon of light without any external influence. In stimulated emission, the photon is released due to the interaction with another photon, resulting in a more controlled and amplified process.

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