6 / 18
the electromagnetic field and
m
i
optical phonons, allowed by the selection
rules for CS, per one mode of the phonon field, then the full probability
W
(
s
)
n
s
+1;
m
i
+1
of the Stokes CS in this crystal (the speed of the process, 1/sec)
can be written as follows [22]:
W
(
s
)
n
s
+1
,m
i
+1
= (
n
s
+ 1)(
m
i
+ 1)
W
(
s
)
i
= (
n
s
+ 1)
W
(
s
)
sp
.
Here value
W
(
s
)
sp
= (
m
i
+1)
W
(
s
)
i
has been introduced that characterizes
the probability of a spontaneous CS. With the increase of pumping
intensity, one of the optical modes of the crystal, which are active for
CS (as a rule, corresponding to the most intensive line of the spontaneous
CS), can be characterized by the transition from the spontaneous CS
regime to the stimulated (forced) CS–SCS. The relationship between the
probabilities, 1/sec, for SCS
W
(
s
)
st
and spontaneous CS
W
(
s
)
sp
is, according
to (1), as follows:
W
(
s
)
st
=
n
s
W
(
s
)
sp
.
(6)
With regard to (6) for the intensity
I
(
s
)
st
SCS, we can write down:
I
(
s
)
st
=
n
s
I
s
sp
,
(7)
where
I
s
sp
is the intensity of the spontaneous Stokes CS process. With
the sufficiently high intensity of pumping exceeding the threshold of SCS
occurrence, the following relation is true for the SCS intensity:
I
(
s
)
st
=
I
(
s
)
sp
(0) exp(
αI
0
z
)
.
Characteristic values of the ratio
α
in SCS-crystals are around
0,01 сm/MW. On the crystal being one cm long and having the pumping
power density of
I
0
≈
10
8
W/cm
2
, the SCS intensity is equal to:
I
(
s
)
st
= (0
.
1
−
0
.
01)
I
0
.
Therefore, at the output of the crystal the SCS intensity increases
abnormally and becomes comparable with the intensity of pumping. At
the same time the value
n
s
becomes comparable with the value
n
0
≈
10
14
,
where
n
0
is the number of light quanta per one mode of the exciting
radiation field for ultrashort (
10
−
10
s.) intensive (
I
= 10
12
W/сm
2
) pulses
of a solid-state visible laser (0.5
μ
m).
Let us describe the photon-axion conversion in the physical vacuum. At
the first stage we will focus on the spontaneous processes. In accordance
with the theory [11–17] we assume the Lagrangian density of the system in
question as a sum of the density of the electromagnetic field Lagrangian,
8
ISSN 1812-3368. Herald of the BMSTU. Series “Natural Sciences”. 2014. No. 6