such a filter is possible at variation of the refraction index on the boundary of
channels.
Retuning of parameters of the directional coupler of Х-type, we can change the
excitation coefficients of the different length light guides, which form the differential
RF FODL, and hence, to effectively control by the generation frequency of OEO
through the delay in FOS.
Figure 7.27a shows the OEO structure with the directional fiber-optical coupler of
X-type, while Fig. 7.27b shows the structure of the directional coupler of X-type.
This method of frequency control f ¼ f(ξ) versus the control parameter ξ in OEO
differs from the control method in OEO on the base of the directional coupler of
Y-type. Owing to the connection of optical powers Р 1 and Р 2 in FOS1 and FOS2,
relatively, in the fiber-optical directional X-coupler, the light flows with powers Р 1
and Р 2 are mutually related with each other. Owing to this, the function of generation
frequency in OEO f(ξ) due to the mechanism of mutual optical coupling
P 1, 2 $ cos
2 (ξ) becomes periodic on ξ, i.e., f $ cos
2 (ξ). At that, the power P in the
output of the directional coupler in FOS1 varies according the law P 1, 2 $ cos
2 (ξ),
and the frequency in OEO with differential RF FODL also varies according the law
f $ cos
2 (ξ). The control types examined in previous sections are quasi-linear
methods for frequency control: f ¼ f(ξ) % aξ + b, where a and b are constant
coefficients.
The generation frequency of OEO with RF FODL at small variations of arguments of the arctangent functions can be determined as
f gen ¼
m þ T gen
T 1FOS þT 2FOS
2
þ
T 1FOS ÀT 2FOS
2
cos 2C coupl Z
À
Á:
ð7:53Þ
AFC and PFC of differential RF FODL for different coefficients of the optical
coupling are presented in Fig. 7.27c. Functions of AFC are calculated for the
following values of the light-guiding parameters: L 1 ¼ 9.3 m, Т 1FOS ¼ 4.7 Â 10
À8 s,
A ¼ 0.5, B ¼ 1 À A, L 2 ¼ 13.3 m, Т 2FOS ¼ 6.7 Â 10
À8 s, T ¼ (Т 1FOS + Т 2FOS )/
2 ¼ 5.7 Â 10
À8 s. As shown in Fig. 7.27a, b AFC and PFC of the differential RF
FODL with the coupler of Х-type differ from the similar AFC and PFC with the
coupler of Y-type. Its main feature is the periodic dependence on the product of the
optical coupling coefficient by the length of the boundary segment (С coupl Z ) at the
fixed frequency of the module and the argument of the transfer function of the
differential RF FODL.
From derived functions for the generation frequency of OEO with the coupler of
Х-type, it follows that at linear law of variation of the optical coupling coefficients
C coupl in the coupler of Х-type, the law of generation frequency variation is periodic,
which period is determined by the product of С coupl Z.
The dependence of the optical coupling coefficient on the optical frequency v is
determined by the expression: C coupl ¼ C 0 (1 + C 1 v), in which С 0 and С 1 are real
coefficients depending on refraction indices of the light guide material, the boundary
medium and geometrical dimensions. This linear function is the approximation for
7.4 Frequency Control in OEO with RF FODL with Two Optical Fibers
425
channels.
Retuning of parameters of the directional coupler of Х-type, we can change the
excitation coefficients of the different length light guides, which form the differential
RF FODL, and hence, to effectively control by the generation frequency of OEO
through the delay in FOS.
Figure 7.27a shows the OEO structure with the directional fiber-optical coupler of
X-type, while Fig. 7.27b shows the structure of the directional coupler of X-type.
This method of frequency control f ¼ f(ξ) versus the control parameter ξ in OEO
differs from the control method in OEO on the base of the directional coupler of
Y-type. Owing to the connection of optical powers Р 1 and Р 2 in FOS1 and FOS2,
relatively, in the fiber-optical directional X-coupler, the light flows with powers Р 1
and Р 2 are mutually related with each other. Owing to this, the function of generation
frequency in OEO f(ξ) due to the mechanism of mutual optical coupling
P 1, 2 $ cos
2 (ξ) becomes periodic on ξ, i.e., f $ cos
2 (ξ). At that, the power P in the
output of the directional coupler in FOS1 varies according the law P 1, 2 $ cos
2 (ξ),
and the frequency in OEO with differential RF FODL also varies according the law
f $ cos
2 (ξ). The control types examined in previous sections are quasi-linear
methods for frequency control: f ¼ f(ξ) % aξ + b, where a and b are constant
coefficients.
The generation frequency of OEO with RF FODL at small variations of arguments of the arctangent functions can be determined as
f gen ¼
m þ T gen
T 1FOS þT 2FOS
2
þ
T 1FOS ÀT 2FOS
2
cos 2C coupl Z
À
Á:
ð7:53Þ
AFC and PFC of differential RF FODL for different coefficients of the optical
coupling are presented in Fig. 7.27c. Functions of AFC are calculated for the
following values of the light-guiding parameters: L 1 ¼ 9.3 m, Т 1FOS ¼ 4.7 Â 10
À8 s,
A ¼ 0.5, B ¼ 1 À A, L 2 ¼ 13.3 m, Т 2FOS ¼ 6.7 Â 10
À8 s, T ¼ (Т 1FOS + Т 2FOS )/
2 ¼ 5.7 Â 10
À8 s. As shown in Fig. 7.27a, b AFC and PFC of the differential RF
FODL with the coupler of Х-type differ from the similar AFC and PFC with the
coupler of Y-type. Its main feature is the periodic dependence on the product of the
optical coupling coefficient by the length of the boundary segment (С coupl Z ) at the
fixed frequency of the module and the argument of the transfer function of the
differential RF FODL.
From derived functions for the generation frequency of OEO with the coupler of
Х-type, it follows that at linear law of variation of the optical coupling coefficients
C coupl in the coupler of Х-type, the law of generation frequency variation is periodic,
which period is determined by the product of С coupl Z.
The dependence of the optical coupling coefficient on the optical frequency v is
determined by the expression: C coupl ¼ C 0 (1 + C 1 v), in which С 0 and С 1 are real
coefficients depending on refraction indices of the light guide material, the boundary
medium and geometrical dimensions. This linear function is the approximation for
7.4 Frequency Control in OEO with RF FODL with Two Optical Fibers
425