In 1916, Albert Einstein discovered the phenomenon called stimulated emission. It was not until 1960 that the first laser was constructed by T. H. Maiman. L.A.S.E.R is an acronym which describes the fundamental operation of a laser - Light Amplification by Stimulated Emission of Radiation. As I will demonstrate, there are various types of lasers, each with their own operation and output characteristics.
For lasing to occur, each type of laser must provide several key elements. Some sort of gain material, or collection of atoms which amplifies passing light must be present. A cavity must, of course, contain this material. The ends of the cavity should be constructed so the amplifying light can resonate, or repeatedly reflect off the ends of the cavity, thus constantly being amplified. A further necessity of the cavity is that it allow some of the amplified light to pass through one end, thus allowing output of this amplified light. A final characteristic of all lasers is the have some supply of power to replenish the amplifier and gain mechanism (as will be explored in the discussion of specific lasers, gain mechanisms - sometimes call the 'pump' - include such processes as collisions with particles, thermal energy and incident light), .
As you can see in the simple diagram below, the light is amplified while passing through the medium and reflecting between the mirrors. Mirror 2 is not totally reflective and allows some of the amplified light to pass through. This output is usually on the order of 1-5% of the intensity of the amplified light within the cavity.
The de-excitation of an atom can result in the production of a photon, whose frequency equals the change in the energy levels of the atom, divided by Plank's constant (see below).
If this photon passes near an excited atom in an energy state equal to the energy of the photon, stimulated emission may occur. This process, as can be seen below, results in the production of a photon that is coherent (in phase and in the same direction) with the incident photon.
These coherent photons are what produces the laser's output. Each time an atom de-excites, obviously, there is one less atom that can produce a photon. For this reason, there must be more atoms in a desired excited state, than in lower energy states into which the atom can de-excite.
Once we have the population inversion, photons can pass through the cavity, stimulating emission from this excess of excited atoms. Therefore, with a mirror on the ends of the cavity, as long as the population inversion is maintained, more photons will be produced with each time a photon passes through the cavity. At this point, some of the amplified light can escape to become output. As was previously described, one of the mirrors on the cavity reflects the majority of incident light, but allows some to pass.
For a good supplementary tutorial on lasers, check this out: http://members.aol.com/WSRNet/tut/ut1.htm
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Eastham, Derek. Atomic Physics of Lasers. Philadelphia: Taylor & Francis, 1986.
Milonni, Peter W. and Joseph H. Eberly. Lasers. New York: John Wiley & Sons, 1988.