directional coupler are included in the positive feedback network covering the
QWLD in OEO.
The transfer function of the feedback network K FBN can be defined as:
for OEO DM: K FBN ¼ i mod =E
2
L ,
for OEO MZ: K FBN ¼ u mod =E
2
Lin ,
where E
2
L is the normalized squared strength in the QWLD output, which is equal in
magnitude to the value in the FOS input, i mod is the AC current modulation
component in the QWLD in the OEO DM and u mod is the AC voltage modulation
component in the MZ input on the OEO MZ structure.
3.4 Equations of Amplitude and Phase Balance
for the Laser and for OEO
Before operations with OEO differential equations, let us analyze the OEO operation
on the base of the stationary (steady-state) algebraic equations, which are called in
the theory of nonlinear oscillations as the equations of amplitude and phase balance
(APB). Simplified structural (blocks) representation of the laser and complete OEO
structures, shown in Fig. 3.2, gives us a possibility to form the APB equations.
3.4.1 Equations of Amplitude and Phase Balance
for the Laser
The laser including in the OEO structure is formed by the closed in the loop of
optical nonlinear amplifier OA, the narrowband optical filter OF, and the fiber
optical delay line (RF FODL) in the form of lengthy (0.3 mm to 1 m) optical
channel. The optical oscillation frequency ν 0L , which is generated by the laser in
the free steady-state mode, can be obtained (of course, at satisfaction of the selfoscillation conditions) from the solution of the amplitude and phase balance equations for steady-state optical oscillations of the field strength in the optical resonator
and in the active laser element:
K OA ν
ð ÞK OF ν
ð ÞK FOS ν
ð Þ ¼ 1,
φ OA ν
ð Þ þ φ OF ν
ð Þ þ φ FOS ν
ð Þ ¼ À2πn
&
,
ð3:42Þ
where K OA (ν), φ OA (ν) are the module (AFC), and the argument (PFC) of the optical
amplifier; K OF (ν), φ OF (ν) are the module (AFC) and the argument (PFC) of the
optical filter with the natural frequency ν 0OF and with the time constant T OF ;
K FOS (ν), φ FOS (ν) are the module (AFC) and the argument (PFC) of the other laser
114 3 Modulation Methods of Laser Emission in Optoelectronic oscillator (OEO) and OEO. . .
QWLD in OEO.
The transfer function of the feedback network K FBN can be defined as:
for OEO DM: K FBN ¼ i mod =E
2
L ,
for OEO MZ: K FBN ¼ u mod =E
2
Lin ,
where E
2
L is the normalized squared strength in the QWLD output, which is equal in
magnitude to the value in the FOS input, i mod is the AC current modulation
component in the QWLD in the OEO DM and u mod is the AC voltage modulation
component in the MZ input on the OEO MZ structure.
3.4 Equations of Amplitude and Phase Balance
for the Laser and for OEO
Before operations with OEO differential equations, let us analyze the OEO operation
on the base of the stationary (steady-state) algebraic equations, which are called in
the theory of nonlinear oscillations as the equations of amplitude and phase balance
(APB). Simplified structural (blocks) representation of the laser and complete OEO
structures, shown in Fig. 3.2, gives us a possibility to form the APB equations.
3.4.1 Equations of Amplitude and Phase Balance
for the Laser
The laser including in the OEO structure is formed by the closed in the loop of
optical nonlinear amplifier OA, the narrowband optical filter OF, and the fiber
optical delay line (RF FODL) in the form of lengthy (0.3 mm to 1 m) optical
channel. The optical oscillation frequency ν 0L , which is generated by the laser in
the free steady-state mode, can be obtained (of course, at satisfaction of the selfoscillation conditions) from the solution of the amplitude and phase balance equations for steady-state optical oscillations of the field strength in the optical resonator
and in the active laser element:
K OA ν
ð ÞK OF ν
ð ÞK FOS ν
ð Þ ¼ 1,
φ OA ν
ð Þ þ φ OF ν
ð Þ þ φ FOS ν
ð Þ ¼ À2πn
&
,
ð3:42Þ
where K OA (ν), φ OA (ν) are the module (AFC), and the argument (PFC) of the optical
amplifier; K OF (ν), φ OF (ν) are the module (AFC) and the argument (PFC) of the
optical filter with the natural frequency ν 0OF and with the time constant T OF ;
K FOS (ν), φ FOS (ν) are the module (AFC) and the argument (PFC) of the other laser
114 3 Modulation Methods of Laser Emission in Optoelectronic oscillator (OEO) and OEO. . .