= Stimulated emission
{wiki}
Stimulated emission is emission induced by incident <light>, in contrast with the unprompted decay in <spontaneous emission>. It supplies the amplification mechanism of a <laser>. https://openstax.org/books/university-physics-volume-3/pages/8-6-lasers[OpenStax, §8.6: stimulated emission]{ref}.
For an emitter with upper and lower <energy> values $E_2>E_1$, the resonant <photon> has <frequency> $\nu$ satisfying
$$
\Delta E=E_2-E_1=h\nu,
$$
where $h$ is the <Planck constant>. In the elementary <photon> picture, an incident <photon> stimulates an emitter in the upper <quantum state> to emit an additional <photon> into the same optical <normal mode>, with the same <frequency>, propagation direction and <photon polarization>. The emitter supplies the extra <energy>; the stimulating <photon> is not consumed. This builds the existing field and its <optical coherence>. An emitter in the lower <quantum state> can instead undergo <photon absorption>, so <stimulated emission> alone does not establish net <optical gain>.
For example, a $2.0\,\mathrm{eV}$ gap corresponds to $\nu\approx4.8360\times10^{14}\,\mathrm{Hz}$ and a <vacuum> <wavelength> of about $620\,\mathrm{nm}$. One ideal <stimulated emission> event converts one incoming <photon> into two outgoing <photons> in the selected optical <normal mode>, adding $2.0\,\mathrm{eV}$ of <light> <energy> while lowering the emitter's <energy> by that amount.
\Image[/laser-stimulated-emission-cycle.png]
{title=<Stimulated emission> and one illustrative four-level <laser> pumping cycle}
{description=Left: one incoming <photon> induces an additional <photon> while the emitter falls from $E_2$ to $E_1$. Right: pumping supplies <energy>, rapid relaxation feeds the upper lasing state, <stimulated emission> supplies <light>, and rapid lower-state relaxation completes a four-level cycle. These paths are schematic, not universal to all <lasers>; line spacing is not to scale.}
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