Laser pumping
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Optical pumping
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Alfred Kastler (1902-1984; Nobel 1966)
Beam divergence
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Gaussian beam
In 1916, Albert Einstein turned his attention away from General Relativity to investigate the interaction of radiation with matter. Although he was certainly guided by Planck's law for blackbody radiation (which Planck had formulated in 1900) Einstein's most brillant discovery was that simple thermodynamical considerations imply the existence of what's called stimulated emission of radiation (and, incidentally, also impose the general form of Planck's law ).
Both absorption and stimulated emission are induced transitions, whose rates are proportional to the intensity I (T) of the surrounding radiation (a density of energy expressed in pascals (Pa) or joules per cubic meter). Being exact time-reversal of each other, they must occur at the same rate:
B12 = B21 = B
The coefficients A and B are properties of the atom and, thus, do not depend on the temperature T of the surrounding photon gas. When thermal equilibrium is achieved at a certain temperature T, the numbers of atoms in both states (which may depend on T) remain constant. So, the total transition rates from either energy level to the other are equal:
N1 [ B12 I (T) ] = N2 [ A + B21 I (T) ]
Solving for I, this yields: I (T) = ( A / B ) / [ N1 / N2 - 1 ]
On the other hand, the ratios of the populations of the two energy levels is an exponential function of the ratio of the energy difference to the thermal energy (kT) according to Boltzmann's statistics:
N2 / N1 = exp [ -( E2- E1 ) / kT ]
Einstein's equation:
A / B = 8p hn3 dn / c3
In this, dn stands for the width of the atomic transistion spectrum which is very narrow compared to the whole blackbody spectrum and is thus adequately represented by a delta distribution (instead of properly convoluting the blackbody spectrum with the so-called atomic lineshape function ).
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Absorption (electromagnetic radiation)
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Spontaneous emission
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Stimulated emission
Detailed balance
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Boltzmann distribution
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Planck's law
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Einstein coefficients
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Atomic spectral line
In a large enough cavity, the number of modes per unit of volume per unit of frequency interval is:
8p n2 / c3
Each electromagnetic mode of a cavity corresponds to a possible quantum state for a photon. At thermal equilibrium, the occupation number per quantum state is:
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Bose-Einstein statistics
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Satyendra Nath Bose (1894-1974)
Test of Bose-Einstein statistics for photons
(animation)
The technique known as optical pumping (French: pompage optique was invented by Alfred Kastler (1902-1984) in 1950. For this work, he was awarded the Nobel Prize for Physics in 1966.
The idea is to shine circularly-polarized light on atoms in a magnetic field for which a particular pair of quantum states exists: The least energetic one can absorbe a photon and go into the higher state without violating the conservation of angular momentum. On the other hand, the higher state is unable to absorbe photons from the circularly polarized beam because that would violate the conservation of angular momentum. (Atoms in the higher state thus become effectively transparent.)
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Optical pumping (animation)
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Population inversion (animation)
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Maser | Hydrogen Maser | Charles H. Townes (1915-2015; Nobel 1966)
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Videos :
How Lasers Work -- in theory (1:41)
by Henry Reich (Minute Physics, 2011年12月04日).
How Lasers Work -- in practice (3:53)
by Destin Sandlin (Smarter Every Day #33, 2011年12月04日).
zo = p n wo2 / l
½ q = l / ( p n wo )
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Propagation of Gaussian Beams: Part I Part II Part III (Oklahoma State University)
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Wikipedia : Tunable laser | Dye lasers (1966)
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Negative temperatures (1949)
|
Lars Onsager (1903-1976;
Nobel 1968).
Negative Temperatures are HOT (13:16)
by Philip Moriarty
(Sixty Symbols, 2013年03月12日).
Negative absolute temperatures in a distribution of vortices (9:51)
by Shaun Johnstone (2019年06月29日).
Focusing a 5W Laser with a magnifying glass
(8:25) by James J. Orgill
(The Action Lab, 2018年11月21日).
