2015
International Year of Light and Light-Based Technologies
From Stimulated Emission to Laser Beams
(2012-07-09) Stimulated Emission of Radiation (Einstein, 1916)
Stimulated emission is crucial to the equilibrium of blackbody radiation.
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 ).
A bound electron interacts stochastically
with photons in one of three ways :
Absorption
( Spontaneous ) Emission
Stimulated Emission
Rate = B12I (T)
Rate = A21 = A
Rate = B21I (T)
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 [ B12I (T) ] =
N2 [ A + B21I (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 ).
(2012-07-17) Bose-Einstein Statistics (1924)
The reason why lasers work...
Satyandra
N. Bose
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:
(2017-05-21) Optical Pumping
Using circularly polarized light to produce a population inversion.
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.)
