Einstein Coefficients of laser

Einstein Coefficients of laser:
Emission lines and absorption lines compared to a continuous spectrum.
Einstein coefficients are mathematical quantities which are a measure of the probability of absorption or emission of light by an atom or molecule.[1] The Einstein A coefficient is related to the rate of spontaneous emission of light and the Einstein B coefficients are related to the absorption and stimulated emission of light.

Contents [hide]
1 Spectral lines
2 Emission and absorption coefficients
2.1 Equilibrium conditions
3 Einstein coefficients
3.1 Various formulations
3.2 Spontaneous emission
3.3 Stimulated emission
3.4 Photon absorption
4 Detailed balancing
5 Oscillator strengths
6 See also
7 References
7.1 Cited bibliography
8 Other reading
9 External links
Spectral lines[edit]
In physics, one thinks of a spectral line from two viewpoints.

An emission line is formed when an atom or molecule makes a transition from a particular discrete energy level E2 of an atom, to a lower energy level E1, emitting a photon of a particular energy and wavelength. A spectrum of many such photons will show an emission spike at the wavelength associated with these photons.

An absorption line is formed when an atom or molecule makes a transition from a lower, E1, to a higher discrete energy state, E2, with a photon being absorbed in the process. These absorbed photons generally come from background continuum radiation (the full spectrum of electromagnetic radiation) and a spectrum will show a drop in the continuum radiation at the wavelength associated with the absorbed photons.

The two states must be bound states in which the electron is bound to the atom or molecule, so the transition is sometimes referred to as a "bound–bound" transition, as opposed to a transition in which the electron is ejected out of the atom completely ("bound–free" transition) into a continuum state, leaving an ionized atom, and generating continuum radiation.

A photon with an energy equal to the difference E2 - E1 between the energy levels is released or absorbed in the process. The frequency ν at which the spectral line occurs is related to the photon energy by Bohr's frequency condition E2 - E1 = hν where h denotes Planck's constant.[2][3][4][5][6][7]

Emission and absorption coefficients[edit]
An atomic spectral line refers to emission and absorption events in a gas in which {\displaystyle n_{2}} n_{2} is the density of atoms in the upper energy state for the line, and {\displaystyle n_{1}} n_{1} is the density of atoms in the lower energy state for the line.

The emission of atomic line radiation at frequency ν may be described by an emission coefficient {\displaystyle \epsilon } \epsilon with units of energy/time/volume/solid angle. ε dt dV dΩ is then the energy emitted by a volume element {\displaystyle dV} dV in time {\displaystyle dt} dt into solid angle {\displaystyle d\Omega } d\Omega . For atomic line radiation:

{\displaystyle \epsilon ={\frac {h\nu }{4\pi }}n_{2}A_{21}\,} \epsilon ={\frac {h\nu }{4\pi }}n_{2}A_{21}\,
where {\displaystyle A_{21}} A_{21} is the Einstein coefficient for spontaneous emission, which is fixed by the intrinsic properties of the relevant atom for the two relevant energy levels.


In the cases of thermodynamic equilibrium and of local thermodynamic equilibrium, the number densities of the atoms, both excited and unexcited, may be calculated from the Maxwell–Boltzmann distribution, but for other cases, (e.g. lasers) the calculation is more complicated.

Einstein coefficients[edit]
In 1916, Albert Einstein proposed that there are three processes occurring in the formation of an atomic spectral line. The three processes are referred to as spontaneous emission, stimulated emission, and absorption. With each is associated an Einstein coefficient, which is a measure of the probability of that particular

know more at:
http://www.astro.lu.se/Education/utb/...

https://www.physics.byu.edu/faculty/c...

http://winnerscience.com/2012/03/13/e...

http://electron6.phys.utk.edu/qm2/mod...

https://www.physicsforums.com/threads...

http://th.nao.ac.jp/MEMBER/tomisaka/L...

http://web.ift.uib.no/AMOS/nazila/las...

https://www.eng.fsu.edu/~dommelen/qua...

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