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Spontaneous Emission

Definition: a quantum effect, causing the spontaneous decay of excited states of atoms or ions

Opposite term: stimulated emission

German: spontane Emission

Categories: quantum optics, fluctuations and noise

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When an atom (or a laser ion in a gain medium) is excited into a higher-lying energy level, e.g. by absorption of a photon, it may after some time spontaneously return to its ground state, or to some intermediate energy level, by releasing the energy in the form of a photon, which carries the energy in some random direction. (More precisely, the photon can correspond to any propagation mode of the medium surrounding the atom or ion.) This process is called spontaneous emission.

Spontaneous emission is a quantum effect, which in a semiclassical picture can be described as an emission which is stimulated by vacuum noise, i.e. by the zero point fluctuations of the optical field. This view is supported by the fact that spontaneous emission can be suppressed or modified by placing an atom or ion in a microcavity structure, which modifies the mode structure of the optical field. Therefore, one should not see spontaneous emission as something “freely” done by atoms or ions, but as an effect which results from an interaction with the quantum-mechanical electromagnetic field, which is influenced by their environment.

The rate of spontaneous emission (and thus the lifetime of the excited level) is determined both by the properties of the atom and by the mode structure of the surrounding medium. For an atom in free space (or in a homogeneous medium), transition cross sections can be used for calculating the rate of spontaneous emission events (→ radiative lifetime). Typical upper-state lifetimes of atoms are a few nanoseconds if there are allowed transitions to lower levels; much longer values can occur for forbidden transitions.

Light produced by spontaneous emission is called luminescence. The luminescence emitted by a laser gain medium typically carries a total power which equals around one-tenths to one-third of the laser's output power. The optical spectrum of the luminescent light is essentially governed by transition cross sections.

Effect of Spontaneous Emission in Lasers

Spontaneous emission is important during the start-up phase of a laser, e.g. when generating pulses with Q switching. It provides the first “seed” for the build-up of laser radiation in the laser resonator.

After the start-up phase of a continuous-wave laser, spontaneous emission still has the important effect of causing a substantial power loss: a significant part of the applied pump power is needed just to replace the power lost by spontaneous emission. (An exception would be a Q-switched laser with pulsed pumping very shortly before the pulse generation.)

The direct influence of spontaneous emission on the generated laser radiation (after start-up) is quite weak in terms of optical power, but one can partly interpret the occurrence of laser noise as an effect of spontaneous emission.

Questions and Comments from Users

2020-05-27

Does the rate of spontaneous emission depend on the detuning parameter?

Answer from the author:

Yes, it does, if you put the emitting atom into a micro-resonator and consider the tuning between the natural emission frequency and the closest resonance frequency of the resonator.

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Bibliography

[1]D. Kleppner, “Inhibited spontaneous emission”, Phys. Rev. Lett. 47 (4), 233 (1981), doi:10.1103/PhysRevLett.47.233
[2]J. J. Sanchez-Mondragon and N. B. Narozhny, “Theory of spontaneous-emission line shape in an ideal cavity”, Phys. Rev. Lett. 51 (7), 550 (1983), doi:10.1103/PhysRevLett.51.550
[3]H. Summers et al., “Spontaneous emission control in quantum well laser diodes”, Opt. Express 2 (4), 151 (1998), doi:10.1364/OE.2.000151
[4]S. Noda et al., “Spontaneous emission control by photonic crystals and nanocavities”, Nature Photon. 1, 449 (2007), doi:10.1038/nphoton.2007.141

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See also: stimulated emission, quantum noise, radiative lifetime, upper-state lifetime, transition cross sections, fluorescence, laser threshold, parametric fluorescence, photonic crystals
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