7.5.1 The Heating Process of Optical Fiber, Which Is
in Non-tensioned State for Free Thread Setting
Let us consider the temperature impact on the single optical fiber with the free thread
setting in the coil or winding in the reel. The heating process of the optical fiber,
which is in the non-tensioned state with the free thread setting, is described by
thermodynamic system equations at examination of the nonuniform cylindrical body
with the geometrical length L. Figure 7.29 shows the transverse (a) and longitudinal
(b) sections of the optical fiber segment in the free state. We see in Fig. 7.29 of the
quartz light-guiding thread, the quartz reflecting envelope and the polymer protective envelope, relatively, with diameters a thr , a prot, env , a polym . For further analysis,
we introduce the weight coefficients a q. thr and a q. env , which are defined by the ratio
of volumes, which are occupied by the quartz thread plus the quartz envelope, to the
volume occupies by the polymer envelope of the optical fiber. At that, the weight
coefficients are determined by equations: a q.thr ¼ (a q.thr0 )
2 /(a pol )
2 and
a q. env ¼ (a pol À a q. thr0 )
2 /(a pol ).
At the quasi-static variation of the optical fiber, we assume that the temperature
distribution over its volume is uniform and we neglect by the influence of microbends arising in the optical fiber surface at temperature impact. Then, increments of
refraction indices of the thread n thr and the envelope n env and of the geometrical
length L of the optical fiber as the response on the temperature impact can be written
as: n thr ¼ n thr0 1 þ
dn thr
dT OF
T OF , n env0 1 þ
dn env
dT
0
OF
T
0
OF , L ¼ L 0 1 þ
dL
dT
0
OF
T
0
OF ,
dL
dT
0
OF
¼
a thr
1
L 0
dL pol
dT
0
OF
, where L 0 , n thr0 , n env0 are initial values of the optical fiber lengths, the
thread refraction and envelope indices, relatively, at zero temperature, T
0
OF is
temperature of the optical fiber in degrees centigrade,
1
L 0
dL
dT
0
OF
is the temperature
constant or relative linear variations of the optical fiber,
dn thr
dT
0
OF
and
dn env
dT
0
OF
are temperature
constants (or slopes) of refraction indices of the thread and envelope, relatively. For
the quartz optical fiber without the special boron and germanium dopes, its relative
values are
1
n thr
dn thr
dT
0
OF
¼ 10
À5 ,
1
n env
dn env
dT
0
OF
¼ 10
À5 . We note that for the optical fiber from
the fused quartz, which is produced without special dopes, temperature constants of
the refraction indices of the thread and the envelope are less by an order than the
crystalline quartz. By means of an introduction of special dopes from germanium
Fig. 7.29 Transverse and longitudinal sections of the optical fiber
428
7 Optoelectronic oscillator (OEO) as the Time and Spatial Correlator of Random. . .
in Non-tensioned State for Free Thread Setting
Let us consider the temperature impact on the single optical fiber with the free thread
setting in the coil or winding in the reel. The heating process of the optical fiber,
which is in the non-tensioned state with the free thread setting, is described by
thermodynamic system equations at examination of the nonuniform cylindrical body
with the geometrical length L. Figure 7.29 shows the transverse (a) and longitudinal
(b) sections of the optical fiber segment in the free state. We see in Fig. 7.29 of the
quartz light-guiding thread, the quartz reflecting envelope and the polymer protective envelope, relatively, with diameters a thr , a prot, env , a polym . For further analysis,
we introduce the weight coefficients a q. thr and a q. env , which are defined by the ratio
of volumes, which are occupied by the quartz thread plus the quartz envelope, to the
volume occupies by the polymer envelope of the optical fiber. At that, the weight
coefficients are determined by equations: a q.thr ¼ (a q.thr0 )
2 /(a pol )
2 and
a q. env ¼ (a pol À a q. thr0 )
2 /(a pol ).
At the quasi-static variation of the optical fiber, we assume that the temperature
distribution over its volume is uniform and we neglect by the influence of microbends arising in the optical fiber surface at temperature impact. Then, increments of
refraction indices of the thread n thr and the envelope n env and of the geometrical
length L of the optical fiber as the response on the temperature impact can be written
as: n thr ¼ n thr0 1 þ
dn thr
dT OF
T OF , n env0 1 þ
dn env
dT
0
OF
T
0
OF , L ¼ L 0 1 þ
dL
dT
0
OF
T
0
OF ,
dL
dT
0
OF
¼
a thr
1
L 0
dL pol
dT
0
OF
, where L 0 , n thr0 , n env0 are initial values of the optical fiber lengths, the
thread refraction and envelope indices, relatively, at zero temperature, T
0
OF is
temperature of the optical fiber in degrees centigrade,
1
L 0
dL
dT
0
OF
is the temperature
constant or relative linear variations of the optical fiber,
dn thr
dT
0
OF
and
dn env
dT
0
OF
are temperature
constants (or slopes) of refraction indices of the thread and envelope, relatively. For
the quartz optical fiber without the special boron and germanium dopes, its relative
values are
1
n thr
dn thr
dT
0
OF
¼ 10
À5 ,
1
n env
dn env
dT
0
OF
¼ 10
À5 . We note that for the optical fiber from
the fused quartz, which is produced without special dopes, temperature constants of
the refraction indices of the thread and the envelope are less by an order than the
crystalline quartz. By means of an introduction of special dopes from germanium
Fig. 7.29 Transverse and longitudinal sections of the optical fiber
428
7 Optoelectronic oscillator (OEO) as the Time and Spatial Correlator of Random. . .