CONFOCOR
3
Carl Zeiss
Models
ConfoCor 3
58 M60-1-0025
e
02/2010
B. Anti-bunching Terms
Anti-bunching is the phenomenon that a molecule cannot produce emitted photons as long as it stays in
the excited state. Hence during the transition time required to drop back to the ground state, which
corresponds in most of the cases to the lifetime if no other photo-physical processes are involved, no
photon can be expected, which results in anti-correlation and hence a drop of the correlation function
below 1.
B.1
Independent to other terms
)
1
(
)
(
a
e
C
C
G
a
τ
τ
τ
−
⋅
−
−
=
not
normalized
(6a)
)
1
1
(
)
(
C
e
C
G
a
a
−
⋅
−
=
−
τ
τ
τ
normalized
(6b)
where C is the amplitude and
τ
a
the transition time, also referred to as the lifetime.
B.2 Dependent in combination with other terms
)
(
)
(
a
e
C
G
a
τ
τ
τ
−
⋅
−
=
(6c)
C in this case is either a fit parameter or a fixed value and often takes the value 9/5.
There are two cases to be distinguished: First, if the anti-bunching is independent with other processes,
than equations 6a and 6b in the non-normalized or normalized form must be used and the terms are
multiplied with other correlation terms. In case the anti-bunching is treated dependent to other
processes, than equation 6c is the correct one to use and the term is added to other correlation terms.
B.3 Stretched exponential – anti-bunching
This is a more general term adding frequency and stretched factors to the exponent.
1
1
1
)
(
1
1
1
)
(
κ
τ
τ
k
k
k
e
K
K
t
G
⋅
−
⋅
−
−
=
not
normalized
(6d)
1
)
(
1
1
1
)
(
1
1
1
K
e
K
t
G
k
k
k
−
⋅
−
=
⋅
−
κ
τ
τ
normalized
(6e)
where K
1
is the fraction of molecule, and
τ
k1
the exponential decay time, k
1
the frequency factor and
κ
1
the stretch factor.
