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lead to fluorescence intermittency. Only recently, some near-infrared (NIR) lumi-
nescence with a lifetime of tens of microseconds was detected, which was attributed
to phosphorescence [ 14 ]. The experiments were originally designed to detect the
weak emission of singlet oxygen 1 O 2 upon photosensitization. When further spec-
troscopic characterization of the emitting species is provided, one could finally
improve its impact on photochemical reactions such as the mentioned photosensiti-
zation as manifested e.g., in the so-called Killer Red proteins [ 15 ]. On the basis of
the yet available data, we can neglect ISC as competitive process to fluorescence
and, consequently, restrict the further discussion to the transitions between the two
energetically lowest singlet states, i.e., S 1 and S 0 .
1.2 Einstein Factors: Absorption, Spontaneous
and Stimulated Emission
The kinetic formulation of Planck's law for the black-body radiation by Albert
Einstein provided three molecular photophysical parameters, A 21 , B 12 and B 21 .
These three parameters are deduced when the spectrum of a thermal light source,
such as the sun or a light bulb, is matched with the Boltzmann distribution. This
so-called two-level system (TLS) is met in an approximation in the pair S 0 and S 1 of
almost any good fluorophore. Therefore, the three Einstein factors A 21 for sponta-
neous emission, B 12 for absorption and B 21 for stimulated emission are of funda-
mental validity and significance in fluorescence spectroscopy. For details, the
interested reader is referred to more specialized articles, e.g., [ 16 ].
The complexity is reduced if two states of the same spin multiplicity, i.e., singlet
or triplet, are treated. Due to the same degeneracy of both aforementioned TLS
levels, the values of B 21 and B 12 become identical. The underlying processes are
still absorption and stimulated emission. The only reason that the latter process is
generally not observed in conventional fluorescence spectroscopy is the fact that the
excited state is, at room temperature, much less populated than the electronic
ground state. Stimulated emission, however, plays a role in pump-probe spectros-
copy [ 17 ], in stimulated emission microscopy [ 18 ] and, also, in STED-microscopy
[ 11 , 12 ]. Furthermore, strong pumping of the excited state of FPs can lead to laser
action which is, actually, a result of stimulated emission [ 19 ]. The importance of the
parameter B 21 ¼
B 12 is its connection to the Einstein-factor A 21 (1), where c is the
speed of light and h is Planck's constant.
8 p h
c 3
A 21 ¼
B 12 :
The unit of A 21 is that of a frequency. In fact, A 21 is the reciprocal value of the
radiative lifetime t rad of the upper state in the TLS which is, here, the excited state
S 1 . In other words, the knowledge of the absolute absorbance, i.e., B 12 , allows for
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