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Stimulated Emission

Definition: a quantum effect, where photon emission is triggered by other photons

Opposite term: spontaneous emission

German: stimulierte Emission

Categories: article belongs to category laser devices and laser physics laser devices and laser physics, article belongs to category optical amplifiers optical amplifiers, article belongs to category physical foundations physical foundations


Cite the article using its DOI: https://doi.org/10.61835/nr2

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stimulated emission
Figure 1: Illustration of stimulated emission. An incoming photon stimulates an excited atom or ion to undergo a transition from the excited state to the ground state.

If a laser-active atom or ion is in an excited state (quantum-mechanical energy level) (e.g. by optical pumping), it may after some time spontaneously decay into a lower energy level, releasing energy in the form of a photon, emitted in a random spatial direction. That process is called spontaneous emission. It is also possible that the photon emission is stimulated (provoked) by incoming photons [1], if these have a suitable photon energy (or optical frequency); this is called stimulated emission (see Figure 1). In that case, a photon is emitted into the mode of the incoming photon. In effect, the power of the incoming radiation is amplified. This is the physical basis of light amplification in laser amplifiers and laser oscillators.

The physics of stimulated emission can be described in the context of quantum optics. There are also semiclassical descriptions (treating the interaction of an oscillating dipole or a higher-order multipole with an electromagnetic field), and the original idea of stimulated emission was published by Einstein [1] before quantum mechanics and quantum optics were fully developed.

Note that the amplification effect of stimulated emission can be reduced or entirely suppressed in a medium where too many laser-active atoms are in the lower state of the laser transition because these atoms absorb photons and thus attenuate light. In a simple two-level system, laser amplification requires a so-called population inversion.

In rate equation modeling, the rate of stimulated emission processes for an excited atom can be calculated as the product of the so-called emission cross-section and the photon flux density (number of photons per unit area and time). Such terms are regularly used in rate equation modeling. The photon flux density can be calculated as the optical intensity divided by the photon energy.

In a laser operated well above threshold, stimulated emission dominates over spontaneous emission, and the power efficiency can be high. For that condition to be fulfilled, the incident optical intensity must be higher than the saturation intensity.

More to Learn

Encyclopedia articles:


[1]A. Einstein, “Zur Quantentheorie der Strahlung”, Physikalische Zeitschrift XVIII, 121 (1917) (first prediction of stimulated emission)

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Questions and Comments from Users


How can a photon sent to an excited atom cause emission of another photon rather than causing the electron to get even further excited to the next energy state? And why are the two emitted photons coherent, have the same phase?

The author's answer:

If there is a suitable higher energy state, such excited state absorption can indeed happen. The relative probabilities are determined by transition cross-sections.

Coherence cannot be defined between just two photons, even if many talk as if it could, using naive models of photons. Also, the phase of one photon is undefined, therefore also the relative phase between two of them. I am afraid there is no simple answer to your question.


If the incident photon's energy is used to stimulate the emission, why is another photon of the same energy emitted again instead of having only one photon from the host being released?

The author's answer:

The stimulation of the mission does not cost energy. Note that an atom or ion is deexcited in the process, and that removed excitation energy must appear as an additional photon.


How can a photon cause stimulated emission? I mean, how does it interact with the electron? How can you theoretically show that the two photons emitted are coherent?

The author's answer:

Light interacts with atoms or ions, precisely speaking not only with single electrons within those. The interaction can be described in various different ways, e.g. with semiclassical or full quantum optics models. Unfortunately, those cannot be translated into a simple picture of how the interaction works.

I think the idea that the two photons are coherent is not a result of a clearly formulated theory, but rather a dubious claim within a kind of hand-waving arguments. It is not even so easy to clearly define what exactly that should mean.


Is the electric field of the incoming photon (em-wave) the cause of electrons in the atom to gain energy?

Also, if the photon emitted by de-excitation is the same as incoming photon, doesn't it violate the conservation of energy?

The author's answer:

The first question is somewhat philosophical. I would not say that the magnetic field does not play a role; it is a part of the incoming electromagnetic wave which cannot be separated from the electric field. However, you may view it as the aspect which most directly leads to the interaction with the electrons.

There is no problem concerning the conservation of energy. It may seem so because you can somewhat vary the photon energy while the original excitation energy is always the same. However, that excitation energy is actually not exactly defined for an excited level with a finite population lifetime: there is an uncertainty relation concerning energy and lifetime. Also, in practice we often deal with Stark level manifolds, where incoming photons can trigger transitions between different sub-levels.


Is the quantum state of the stimulated photon the same as that of the incident photon? If so, can stimulated emission be regarded as quantum cloning?

The author's answer:

An interesting question!

The new photon end ends up in the same radiation mode, and you may thus think it has the same quantum state. However, we should actually consider the quantum state of the light field (rather than that of every single photon), and that changes with the addition of a photon.

Quantum cloning is something different: for example, achieving that the light field in one resonator is exactly in the same quantum state as that in another resonator, without destroying that original quantum state.


How can we explain that stimulated photon emission occurs with the same direction, polarization and in phase of stimulating photon?

The author's answer:

Semiclassical descriptions make this obvious: the oscillating electromagnetic field interacts with the dipole moment of the atom such that energy is transferred from the atom to the field – without generating another field with different propagation direction, polarization etc.


Does stimulated emission cause an instantaneous transition of an electron to a lower level?

The author's answer:

In some simple models it does so, but keep in mind that simple intuitive models cannot fully describe quantum-mechanical processes. In a semi-classical model, it is a resonant effect needing some time. You may still say that this model only describes the probability of a stimulated emission event happening, which in that case happens instantly at a certain time; that view is supported by the fact that the stimulated photon may be detected at a certain instance of time.


Why does the atom get de-excited – couldn't the photon just pass by since it can't excite the atom further?

Is there any solid reason for the excited atoms to emit photons identical to triggering photons?

The author's answer:

It could just pass by, but there is some probability for stimulated emission to occur.

There are various theoretical frameworks to investigate this, for example semiclassical models. But you may seek for some simple argument, which I am afraid cannot be convincing.

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