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Three-level lasers

A three-level laser energy diagram.

To achieve non-equilibrium conditions, an indirect method of populating the excited state must be used. To understand how this is done, we may use a slightly more realistic model, that of a three-level laser . Again consider a group of N atoms, this time with each atom able to exist in any of three energy states, levels 1, 2 and 3, with energies E

1 , E

2 and E

3 , and populations N

1 , N

2 and N

3 , respectively.

Note that E

1 < E

2 < E

3 ; that is, the energy of level 2 lies between that of the ground state and level 3.

Initially, the system of atoms is at thermal equilibrium, and the majority of the atoms will be in the ground state; i.e., N

1 ≈ N , N

2 ≈

N

3 ≈ 0. If we now subject the atoms to light of a frequency , the process of optical absorption will excite the atoms from the ground state to level 3. This process is called pumping , and does not necessarily always directly involve light absorption; other methods of exciting the laser medium, such as electrical discharge or chemical reactions may be used. The level 3 is sometimes referred to as the pump level or pump band , and the energy transition E

1 → E

3 as the pump transition , which is shown as the arrow marked P in the diagram above.

If we continue pumping the atoms, we will excite an appreciable number of them into level 3, such that N

3 > 0. In a medium suitable

for laser operation, we require these excited atoms to quickly decay to level 2. The energy released in this transition may be emitted as a photon (spontaneous emission), however in practice the 3→2 transition (labeled R in the diagram) is usually radiationless , with the energy being transferred to vibrational motion (heat) of the host material surrounding the atoms, without the generation of a photon.

An atom in level 2 may decay by spontaneous emission to the ground state, releasing a photon of frequency ν

12 (given by E

2 – E

1 =

hν

12 ), which is shown as the transition L , called the laser transition in the diagram. If the lifetime of this transition, τ

21 is much longer than the lifetime of the radiationless 3 → 2 transition τ

32 (if τ

21 τ

32 , known as a

favourable lifetime ratio ), the population of the E

3 will be essentially zero ( N

3 ≈ 0) and a population of excited state atoms will accumulate in level 2 ( N

2 > 0). If over half the

N atoms can be accumulated in this state, this will exceed the population of the ground state

N

1 . A population inversion ( N

2 > N

1 ) has thus been achieved between level 1 and 2, and optical amplification at the frequency ν

21 can be obtained.

Because at least half the population of atoms must be excited from the ground state to obtain a population inversion, the laser medium must be very strongly pumped. This makes three-level lasers rather inefficient, despite being the first type of laser to be discovered (based on a ruby laser medium, by Theodore Maiman in 1960). A three-level system could also have a radiative transition between level 3 and 2, and a non-radiative transition between 2 and 1. In this case, the pumping requirements are weaker. In practice, most lasers are four-level lasers , described below.