Editing Population inversion (section)

=== Four-level laser ===
[[File:Population-inversion-4level.png|frame|right|A four-level laser energy diagram.]]
Here, there are four energy levels, energies ''E''<sub>1</sub>, ''E''<sub>2</sub>, ''E''<sub>3</sub>, ''E''<sub>4</sub>, and populations ''N''<sub>1</sub>, ''N''<sub>2</sub>, ''N''<sub>3</sub>, ''N''<sub>4</sub>, respectively. The energies of each level are such that ''E''<sub>1</sub> &lt; ''E''<sub>2</sub> &lt; ''E''<sub>3</sub> &lt; ''E''<sub>4</sub>.

In this system, the pumping transition '''P''' excites the atoms in the ground state (level 1) into the pump band (level 4). From level 4, the atoms again decay by a fast, non-radiative transition '''Ra''' into the level 3. Since the lifetime of the laser transition '''L''' is long compared to that of '''Ra''' ({{nowrap|''τ''<sub>32</sub> ≫ ''τ''<sub>43</sub>}}), a population accumulates in level 3 (the ''upper laser level''), which may relax by spontaneous or stimulated emission into level 2 (the ''lower laser level''). This level likewise has a fast, non-radiative decay '''Rb''' into the ground state.

As before, the presence of a fast, radiationless decay transition results in the population of the pump band being quickly depleted (''N''<sub>4</sub> ≈ 0). In a four-level system, any atom in the lower laser level ''E''<sub>2</sub> is also quickly de-excited, leading to a negligible population in that state (''N''<sub>2</sub> ≈ 0). This is important, since any appreciable population accumulating in level 3, the upper laser level, will form a population inversion with respect to level 2. That is, as long as ''N''<sub>3</sub> &gt; 0, then ''N''<sub>3</sub> &gt; ''N''<sub>2</sub>, and a population inversion is achieved. Thus optical amplification, and laser operation, can take place at a frequency of ''ν''<sub>32</sub> (''E''<sub>3</sub> − ''E''<sub>2</sub> = ''hν''<sub>32</sub>).

Since only a few atoms must be excited into the upper laser level to form a population inversion, a four-level laser is much more efficient than a three-level one, and most practical lasers are of this type. In reality, many more than four energy levels may be involved in the laser process, with complex excitation and relaxation processes involved between these levels. In particular, the pump band may consist of several distinct energy levels, or a continuum of levels, which allow optical pumping of the medium over a wide range of wavelengths.

Note that in both three- and four-level lasers, the energy of the pumping transition is greater than that of the laser transition. This means that, if the laser is optically pumped, the frequency of the pumping light must be greater than that of the resulting laser light. In other words, the pump wavelength is shorter than the laser wavelength. It is possible in some media to use multiple photon absorptions between multiple lower-energy transitions to reach the pump level; such lasers are called ''up-conversion'' lasers.

While in many lasers the laser process involves the transition of atoms between different [[electron]]ic energy states, as described in the model above, this is not the only mechanism that can result in laser action. For example, there are many common lasers (e.g., [[dye lasers]], [[carbon dioxide laser]]s) where the laser medium consists of complete molecules, and energy states correspond to vibrational and [[rotational modes]] of oscillation of the molecules. This is the case with [[maser#Astrophysical masers|water masers]], [[Astrophysical maser|that occur in nature]].

In some media it is possible, by imposing an additional optical or microwave field, to use [[quantum coherence]] effects to reduce the likelihood of a ground-state to excited-state transition. This technique, known as [[lasing without inversion]], allows optical amplification to take place without producing a population inversion between the two states.