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# Stimulated emission

In optics, stimulated emission refers to the process by which, when perturbed by a photon, matter may lose energy resulting in the creation of another photon. The perturbing photon is not destroyed in the process (cf. absorption), and the second photon is created with the same phase and frequency as the original. The process can be thought of as optical amplification, and it forms the basis of the laser and maser.

Stimulated emission can be modelled mathematically by considering an atom which may be in two electronic energy states, the ground state (1) and the excited state (2), with energies E1 and E2 respectively.

If the atom is in the excited state, it may decay into the ground state by the process of spontaneous emission, releasing the difference in energies between the two states as a photon. The photon will have frequency ν and energy hν, given by:

E2 - E1 = hν ,

where h is Planck's constant.

Alternatively, if the excited-state atom is perturbed by the electric field of a photon with frequency ν, it may release a second photon of the same frequency, in phase with the first photon. The atom will again decay into the ground state. This process is known as stimulated emission.

An energy level diagram illustrating the process is shown below:

In a group of such atoms, if the number of atoms in the excited state is given by N, the rate at which stimulated emission occurs is given by:

N / ∂t = - B21ρ(ν)N ,

where B21 is a proportionality constant for this particular transistion in this particular atom (referred to as an Einstein B co-efficient), and ρ(ν) is the radiation density of photons of frequency ν. The rate of emission is thus proportional to the number of atoms in the excited state, N, and the density of the perturbing photons.

The critical detail of stimulated emission is that the emitted photon is identical to the stimulating photon in that it has the same frequency, phase and polarisation (thus the two photons are totally coherent). It is this property that allows optical amplification to take place.

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