of physical quantities (temperature, pressure, electrical voltage, mechanical tensions)
are developed as well, and investigations of spatial directional patterns of light
sources (lasers, laser diodes, light-emitting diodes) are performed.
The phase-generator method can be used not only for measurement of differential
delays of different groups of light guide modes in multi-mode and small-modes
optical fibers, but also for studying of spatial, polarization, disperse, and nonlinear
characteristics of the single-mode optical fibers. With the help of this method, we can
examine the spatial and time coherence of optical emission sources, to study the
“speckle” interference picture in the output of optical fiber, to measure characteristics of spatial optical filters.
At development of this method, the analytical functions of parameters of the RF
oscillation phase difference Δφ ¼ φ 2 (R 2 ) À φ 1 (R 1 ) are determined versus parameters
of the fiber-optical section of OEO with RF FODL. At that, φ 2 (R 2 ) and φ 1 (R 1 ) are
phases of RF oscillations in the outputs of PD1 and PD2, relatively, and R 1 , R 2 are
generalized characteristic parameters of optical emission groups applied, relatively,
to the light-sensitive areas of PD1 and PD2.
For the optical selector OS, which extracts the light guide modes, the parameter
R is determined, for example, for the optical fiber, which has the step-like profile of
the refraction index as the ratio R ¼ (Θ/Θ 0 )
2 , where Θ 0 is the maximal angle
(numerical aperture) of the light emission propagation in the output of the optical
fiber FOS0 with respect to the optical fiber axis, Θ is the angle of the light emission
propagation of the degenerated group of modes in the FOS0 output with respect to
the optical fiber FOS0 axis.
At calculation of the phase difference Δφ ¼ φ 2 (R 2 ) À φ 1 (R 1 ), the values of R 1 ,
ΔR 1 and ΔR 2 are constants during the variation process of the R 2 quantity under
condition that R 2
1 À ΔR 2 . At increase of R 2 ! 1 À ΔR 2 value, the quantity
R 2 ¼ 1 À ΔR 2 , because the selecting area will come out of the aperture of the FOS0
light emission.
Figure 7.31 shows the experimental dependences of the generation frequency (а)
and the phase differences Δφ ¼ φ 2 (R 2 ) À φ 1 (R 1 ) (b) of OEO corresponding to the
structure in Fig. 7.30 at temperature variations of the optical fiber in the air
thermostat. At that, the multimode optical fiber has no the polymer envelope and
has the geometrical length of 100 m, the relative ratio of the refraction index of the
thread and the envelope is 0.01, the thread diameter is 50 μm.
On the base of presented experimental plots in Fig. 7.31, we can make the
following conclusions: the temperature frequency instability of OEO is the same
as quartz instability, i.e., it defines by the refraction index of the quartz light-guiding
thread, which for the optical fiber from the melted quartz (with doping) is 10
À5 1/
С.
Deviations from the linear law for the frequency function are connected with the
phenomenon of modes coupling and redistribution of optical emission between the
light-guiding thread and its quartz envelope. These periodic deviations from the
linear function are more noticeable in phase functions shown in Fig. 7.31b.
It is obtained from these functions that the slope of temperature variations of the
mode coupling coefficient of the single fiber with the length 100 m is 10
À3 to 10
À2 /
degree.
434
7 Optoelectronic oscillator (OEO) as the Time and Spatial Correlator of Random. . .
are developed as well, and investigations of spatial directional patterns of light
sources (lasers, laser diodes, light-emitting diodes) are performed.
The phase-generator method can be used not only for measurement of differential
delays of different groups of light guide modes in multi-mode and small-modes
optical fibers, but also for studying of spatial, polarization, disperse, and nonlinear
characteristics of the single-mode optical fibers. With the help of this method, we can
examine the spatial and time coherence of optical emission sources, to study the
“speckle” interference picture in the output of optical fiber, to measure characteristics of spatial optical filters.
At development of this method, the analytical functions of parameters of the RF
oscillation phase difference Δφ ¼ φ 2 (R 2 ) À φ 1 (R 1 ) are determined versus parameters
of the fiber-optical section of OEO with RF FODL. At that, φ 2 (R 2 ) and φ 1 (R 1 ) are
phases of RF oscillations in the outputs of PD1 and PD2, relatively, and R 1 , R 2 are
generalized characteristic parameters of optical emission groups applied, relatively,
to the light-sensitive areas of PD1 and PD2.
For the optical selector OS, which extracts the light guide modes, the parameter
R is determined, for example, for the optical fiber, which has the step-like profile of
the refraction index as the ratio R ¼ (Θ/Θ 0 )
2 , where Θ 0 is the maximal angle
(numerical aperture) of the light emission propagation in the output of the optical
fiber FOS0 with respect to the optical fiber axis, Θ is the angle of the light emission
propagation of the degenerated group of modes in the FOS0 output with respect to
the optical fiber FOS0 axis.
At calculation of the phase difference Δφ ¼ φ 2 (R 2 ) À φ 1 (R 1 ), the values of R 1 ,
ΔR 1 and ΔR 2 are constants during the variation process of the R 2 quantity under
condition that R 2
1 À ΔR 2 . At increase of R 2 ! 1 À ΔR 2 value, the quantity
R 2 ¼ 1 À ΔR 2 , because the selecting area will come out of the aperture of the FOS0
light emission.
Figure 7.31 shows the experimental dependences of the generation frequency (а)
and the phase differences Δφ ¼ φ 2 (R 2 ) À φ 1 (R 1 ) (b) of OEO corresponding to the
structure in Fig. 7.30 at temperature variations of the optical fiber in the air
thermostat. At that, the multimode optical fiber has no the polymer envelope and
has the geometrical length of 100 m, the relative ratio of the refraction index of the
thread and the envelope is 0.01, the thread diameter is 50 μm.
On the base of presented experimental plots in Fig. 7.31, we can make the
following conclusions: the temperature frequency instability of OEO is the same
as quartz instability, i.e., it defines by the refraction index of the quartz light-guiding
thread, which for the optical fiber from the melted quartz (with doping) is 10
À5 1/
С.
Deviations from the linear law for the frequency function are connected with the
phenomenon of modes coupling and redistribution of optical emission between the
light-guiding thread and its quartz envelope. These periodic deviations from the
linear function are more noticeable in phase functions shown in Fig. 7.31b.
It is obtained from these functions that the slope of temperature variations of the
mode coupling coefficient of the single fiber with the length 100 m is 10
À3 to 10
À2 /
degree.
434
7 Optoelectronic oscillator (OEO) as the Time and Spatial Correlator of Random. . .