Editing Population inversion (section)

=== Stimulated emission ===
{{Main|Stimulated emission}}
If an atom is already in the excited state, it may be agitated by the passage of a photon that has a [[frequency]] ''ν''<sub>21</sub> corresponding to the energy gap Δ''E'' of the excited state to ground state transition. In this case, the excited atom relaxes to the ground state, and it produces a second photon of frequency ''ν''<sub>21</sub>. The original photon is not absorbed by the atom, and so the result is two photons of the same frequency. This process is known as ''stimulated emission''.

Specifically, an excited atom will act like a small electric dipole which will oscillate with the external field provided. One of the consequences of this oscillation is that it encourages electrons to decay to the lowest energy state. When this happens due to the presence of the electromagnetic field from a photon, a photon is released in the same phase and direction as the "stimulating" photon, and is called stimulated emission.

[[File:Stimulated Emission.svg|center|550px]]

The rate at which stimulated emission occurs is proportional to the number of atoms ''N''<sub>2</sub> in the excited state, and the radiation density of the light. The base probability of a photon causing stimulated emission in a single excited atom was shown by [[Albert Einstein]] to be exactly equal to the probability of a photon being absorbed by an atom in the ground state. Therefore, when the numbers of atoms in the ground and excited states are equal, the rate of stimulated emission is equal to the rate of absorption for a given radiation density.

The critical detail of stimulated emission is that the induced photon has the same [[frequency]] and [[phase (waves)|phase]] as the incident photon. In other words, the two photons are [[coherence (physics)|coherent]]. It is this property that allows [[optical amplifier|optical amplification]], and the production of a [[laser]] system. During the operation of a laser, all three light-matter interactions described above are taking place. Initially, atoms are energized from the ground state to the excited state by a process called ''[[laser pumping|pumping]]'', described below. Some of these atoms decay via spontaneous emission, releasing incoherent light as photons of frequency, ''ν''. These photons are fed back into the laser medium, usually by an [[optical cavity|optical resonator]]. Some of these photons are absorbed by the atoms in the ground state, and the photons are lost to the laser process. However, some photons cause stimulated emission in excited-state atoms, releasing another coherent photon. In effect, this results in ''optical amplification''.

If the number of photons being amplified per unit time is greater than the number of photons being absorbed, then the net result is a continuously increasing number of photons being produced; the laser medium is said to have a gain of greater than unity.

Recall from the descriptions of absorption and stimulated emission above that the rates of these two processes are proportional to the number of atoms in the ground and excited states, ''N''<sub>1</sub> and ''N''<sub>2</sub>, respectively. If the ground state has a higher population than the excited state (''N''<sub>1</sub> &gt; ''N''<sub>2</sub>), then the absorption process dominates, and there is a net attenuation of photons. If the populations of the two states are the same (''N''<sub>1</sub> = ''N''<sub>2</sub>), the rate of absorption of light exactly balances the rate of emission; the medium is then said to be ''optically transparent''.

If the higher energy state has a greater population than the lower energy state (''N''<sub>1</sub> &lt; ''N''<sub>2</sub>), then the emission process dominates, and light in the system undergoes a net increase in intensity. It is thus clear that to produce a faster rate of stimulated emissions than absorptions, it is required that the ratio of the populations of the two states is such that
''N''<sub>2</sub>/''N''<sub>1</sub> &gt; 1; In other words, a population inversion is required for laser operation.