Why is two level laser impossible even with non-optical pump

In summary, while some exceptions exist, in general, a two-level laser is not possible due to the equal rates of stimulated emission and absorption in optically pumped systems. Other pumping methods, such as electron collision pumping, also cannot yield population inversion in a two-level system. Special conditions may allow for inversion for a short time, but this is not applicable to most real systems.
  • #1
misko
46
0
I think I understand why two level laser is not possible if we use optical pumping.

However, I don't understand why we can't create laser with two energy levels that are pumped by non optical pump? Why we can't create population inversion that way? For example, if we could somehow pump electrons from level 1 to level 2 with some collision processes then we could create population inversion on the level 2, right? Then electrons from level 2 would be able to go back to level 1 with stimulated emission. Why is this not possible?
 
Physics news on Phys.org
  • #2
I think the first MASER, the ammonia maser is based on a two-level system. The molecules in the higher energetic state are separated passing them through a quadrupole field, so that afterwards you have inversion of the occupation.
 
  • #3
Then why is the statement "2 level laser is not possible" is repeated over and over again?
 
  • #4
Folklore
 
  • #5
So if professor on the exam asks me "why can't we create lasers with only 2 energy levels?" and if I answer "oh actually we can, I know that every book on this topic says we can't but don't worry about that it's just folklore", what grade do you think I will get?

Anyone else want to contribute to the discussion?
I still don't understand it.
 
  • #6
Optically pumped two level system cannot give rise to population inversion because the the stimulated emission and absorption rate between both levels are equal. Denoting the upper population as ##N_2## and the lower one ##N_1##, the rate equation for ##N_2## is
$$
\frac{dN_2}{dt} = B_{12}I(\omega)N_1 - B_{21}I(\omega)N_2 - A_{21}N_2
$$
where ##B_{12}I(\omega)## the transition probability corresponding to the absorption from the lower to upper states (note that it is proportional to the intensity of the light at the resonant frequency between the two levels because we have assumed optical pumping), ##W_{21}N_2I(\omega)## the transition probability corresponding to the stimulated emission from the upper to lower states, and ##A_{21}## spontaneous emission probability. Now, we have ##B_{12}N_1 = B_{21}## and let's seek out the expression of ratio of the populations at the steady state
$$
\frac{dN_2}{dt} = 0 = B_{12}I(\omega)N_1 - B_{21}I(\omega)N_2 - A_{21}N_2
$$
which can be rearranged to give
$$
\frac{N_2}{N_1} = \frac{B_{12}I(\omega)}{B_{21}I(\omega) + A_{21}} < 1
$$
Thus, optical pumping cannot yield population inversion in a two level atom.
I acknowledge that this part of laser physics has also cast an enigmatic problem in my mind because the above steps was derived under optical pumping condition, this suggests that other pumping methods such as electron collision pumping may be able to lead to population inversion in two level systems. Other sources like http://spie.org/publications/optipedia-pages/press-content/fg12/fg12_p03_optical_pumping and http://physics.stackexchange.com/questions/72080/lasing-in-a-2-level-system always specified optical pumping to seemingly safe their argument in case that later two level population inversion can be achieved via non-optical pumping. However, I just found in page 292 in https://books.google.de/books?id=x3VB2iwSaxsC&pg=PA290&lpg=PA290&dq=population+inversion+with+two+level+system&source=bl&ots=21GKcwzCb9&sig=rBn8cKwKWz221pJEFTupKnW_FuI&hl=en&sa=X&ved=0ahUKEwin8tnv597KAhUMFiwKHQcMDfwQ6AEIUzAI#v=onepage&q=population inversion with two level system&f=false, that at least for electron collision pumping two level inversion is not possible either due to the Boltzmann distribution between the two populations,
$$
\frac{N_2}{N_1} = e^{-\Delta E/(kT_e)}
$$
which cannot even reach unity unless the electron temperature ##T_e## becomes infinity.
 
Last edited:
  • #7
blue_leaf77 said:
Thus, optical pumping cannot yield population inversion in a two level atom.

There are some special exceptions. Here is a quote from W. Demtröder, Atoms, Molecules and Photons:
Demtröder said:
Under special conditions it is also possible to achieve inversion for a short time in a two-level system, if the pumping time is short compared to all relaxation times of the system and even shorter than the Rabi oscillation time TR = π · h/(Mik · E(νik )), where Mik is the matrix element for the transition i → k and E is the electric field vector of the pump wave. These conditions, however, apply only to very few real systems that are specially designed.
 
  • #8
DrClaude said:
There are some special exceptions. Here is a quote from W. Demtröder, Atoms, Molecules and Photons:
I have heard that excimer laser effectively operates between only two levels, I think this laser falls into the category described by Demtroeder.
 

1. Why is it impossible to create a two-level laser with a non-optical pump?

The main reason for this is because a two-level laser requires a population inversion, meaning that the number of atoms in the excited state must be greater than the number of atoms in the ground state. However, non-optical pumps, such as electrical or chemical pumps, are not able to create this population inversion.

2. Can non-optical pumps still be used in the process of creating a two-level laser?

While non-optical pumps cannot create the necessary population inversion for a two-level laser, they can still be used in the process. For example, they can be used to excite atoms to the upper level, which can then undergo a radiative transition to the lower level, creating the necessary population inversion.

3. Why is a population inversion necessary for a two-level laser?

A population inversion is necessary because it creates the conditions for stimulated emission to occur. Stimulated emission is when an atom in an excited state is stimulated by a photon of the same energy to release a second photon, resulting in amplification of the light. Without this population inversion, stimulated emission cannot occur and there can be no laser.

4. Are there any alternative methods for creating a two-level laser?

Yes, there are alternative methods such as using a three-level or four-level laser. These types of lasers require a smaller population inversion and can therefore be achieved with non-optical pumps. However, they are less efficient and have other limitations compared to a two-level laser.

5. Can advances in technology make it possible to create a two-level laser with a non-optical pump?

It is unlikely that advances in technology will make it possible to create a two-level laser with a non-optical pump. The laws of physics dictate that a population inversion is necessary for a two-level laser, and it is unlikely that this principle will change. However, new technologies and materials may lead to more efficient methods for creating population inversions, making two-level lasers more viable in the future.

Similar threads

  • Atomic and Condensed Matter
Replies
6
Views
2K
  • Atomic and Condensed Matter
Replies
3
Views
1K
  • Atomic and Condensed Matter
Replies
1
Views
1K
  • Atomic and Condensed Matter
Replies
10
Views
1K
  • Atomic and Condensed Matter
Replies
1
Views
2K
  • Atomic and Condensed Matter
Replies
5
Views
2K
  • Atomic and Condensed Matter
Replies
3
Views
2K
  • Atomic and Condensed Matter
Replies
3
Views
6K
Replies
19
Views
4K
Back
Top