RP Photonics logo
RP Photonics
Encyclopedia
Technical consulting services on lasers, nonlinear optics, fiber optics etc.
Profit from the knowledge and experience of a top expert!
Powerful simulation and design software.
Make computer models in order to get a comprehensive understanding of your devices!
Success comes from understanding – be it in science or in industrial development.
The famous Encyclopedia of Laser Physics and Technology – available online for free!
The ideal place for finding suppliers for many photonics products.
Advertisers: Make sure to have your products displayed here!
… combined with a great Buyer's Guide!
VLib part of the
Virtual
Library

Forbidden Transitions

<<<  |  >>>  |  Feedback

Buyer's Guide

Use the RP Photonics Buyer's Guide to find suppliers for photonics products! You will hardly find a more convenient resource.

Definition: transitions between different energy levels of some atoms or ions for which dipole transitions are suppressed via symmetries

German: verbotene Übergänge

Categories: lasers, physical foundations

How to cite the article; suggest additional literature

Atoms or ions have different electronic energy levels, and transitions between such levels often involve the emission or absorption of light (photons). An absorbed photon can deliver the energy for an atom or ion to get into a higher-lying energy level, whereas spontaneous or stimulated emission releases energy which was previously stored in the atom or ion. Such transitions are used e.g. as laser transitions in laser gain media.

The likelihood of such transitions depends on the electronic levels involved. Strong transitions are those where certain selection rules are satisfied. For example, dipole transitions can occur only between energy levels with the angular momentum parameter l differing by one. Therefore, dipole transitions between energy levels with same parity are not allowed, i.e. they are forbidden. Some “less strongly forbidden” transitions are those which would be forbidden if the approximation of LS coupling were exact.

Dipole-forbidden transitions between energy levels may nevertheless occur based on other mechanisms such as quadrupole transitions. Also, for ions embedded in a crystal lattice or in a glass, internal electric and magnetic fields can break certain symmetries, so that e.g. originally dipole-forbidden transitions become possible by mixing of states with different parity. Such processes, however, are usually much less likely, i.e., they exhibit a small oscillator strength. The resulting transitions are sometimes called weakly allowed transitions rather than forbidden transitions, because there are mechanisms for such transitions, although not very strong ones. Whereas typical upper-state lifetimes are of the order of a few nanoseconds in the case of allowed transitions for spontaneous emission, forbidden transitions of isolated atoms or ions can have upper-state lifetimes of milliseconds or even many seconds, and for ions in crystals or glasses typically between microseconds and milliseconds. Such long-lived levels are called metastable states.

Essentially all the laser transitions in doped-insulator solid-state lasers (but not in semiconductor lasers and color center lasers) are weakly allowed transitions which are enabled by internal electric fields. The low transition rates lead to long upper-state lifetimes, allowing significant energy storage, which is the basis of pulse generation by Q switching. The combination of long upper-state lifetimes and low transition cross sections also causes a tendency for spiking phenomena and pronounced relaxation oscillations for such lasers.

Note that the achievable gain on forbidden transitions is not necessarily lower than for allowed transitions, because spontaneous emission is also weak. In other words, the στ product can be large despite the small emission cross section σ, because the weak transitions allow for a high upper-state lifetime τ.

Forbidden transitions of isolated atoms or ions are used for optical clocks (clock transitions). Here, the long upper-state lifetime is important because it leads to an extremely narrow linewidth of the transition, so that the transition frequency is very well defined.

See also: spontaneous emission, stimulated emission, upper-state lifetime, metastable states, optical frequency standards, optical clocks, Spotlight article 2011-03-13

How do you rate this article?

Your general impression: don't know poor satisfactory good excellent
Technical quality: don't know poor satisfactory good excellent
Usefulness: don't know poor satisfactory good excellent
Readability: don't know poor satisfactory good excellent
Comments:

Found any errors? Suggestions for improvements? Do you know a better web page on this topic?

Spam protection: (enter the value of 5 + 8 in this field!)

If you want a response, you may leave your e-mail address in the comments field, or directly send an e-mail.

If you like our website, you may also want to get our newsletters!

If you like this article, share it with your friends and colleagues, e.g. via social media:

arrow

Fiber Optics Software
with Further Improved
User Interface

In RP Fiber Power V6, one can use nice custom forms, which can be
tailored to specific applications.

custom form in RP Fiber Power

Users can make such forms themselves, or get them from RP Photonics within the technical support. The latter is like buying a custom software for every purpose – but without spending a lot of money every time!

Beginners can now get started very easily, even if they need quite special calculations!

– Show all banners –

– Get your own banner! –