For simplicity sake, we consider OEO as the generator with the single nonlinear
element, i.e., in our oscillator structure, the only one nonlinear is present. We analyze
two variants of modes. In the first mode, we consider that the OEO nonlinearity is
present only in the RF amplifier, and “small amplitude oscillations” pass at the
electrical input of the MZ modulator and the MZ modulator operates “in quadrature.” In the second mode, the RF amplifier A operates in the linear mode with
amplification, and the nonlinear MZ characteristic i PD ¼ f(u MZ ) is used as the OEO
nonlinearity.
3.4.3.1 The Nonlinear Element Is the RF Amplifier A
The instantaneous value of the output current of the amplifying stage is equal to
i A ¼ α e u PD À β e u
3
PD
À
Á
, where u PD is the instantaneous values of the input voltage,
which coincides with the voltage on the PD output. Then the nonlinear dependence
of the i A current and differential equation (Eq. 3.50) in time domain are written as:
i A ¼ α e u PD À β e u
3
PD
À
Á
.
3.4.3.2 The Nonlinear Element Is the Mach–Zehnder Modulator
The instantaneous output PD voltage is equal u PD ¼ R PD i PD , where i PD is the
instantaneous “output” photocurrent of PD, R PD is the active load resistance of
PD. The nonlinear function i PD ¼ f(u MZ ) takes a form:
i PD ¼ 0:5γ E 0L
ð Þ
2 K 0FOS:MZ cos πU 0MZ =2U 0MZπ
ð
Þ À u MZ
½
ð 3:51Þ
and Eq. (3.50) in the time domain is written as: i A ¼ α e R PD i PD À β e (R PD i PD )
3 .
Equation (2.50) is a nonlinear differential equation of the second order. For
arbitrary nonlinearities they cannot be solved in general case, for the specific cases
(for instance, the high Q-factors) these equation can be simplified or “abbreviated”
till the one order less.
3.4.3.3 Abbreviated Equations of OEO MZ with the Single Optical
Fiber
In order to obtain the abbreviated equations of OEO MZ with the single optical fiber,
we write differential equations for OEO in operator form:
120 3 Modulation Methods of Laser Emission in Optoelectronic oscillator (OEO) and OEO. . .
element, i.e., in our oscillator structure, the only one nonlinear is present. We analyze
two variants of modes. In the first mode, we consider that the OEO nonlinearity is
present only in the RF amplifier, and “small amplitude oscillations” pass at the
electrical input of the MZ modulator and the MZ modulator operates “in quadrature.” In the second mode, the RF amplifier A operates in the linear mode with
amplification, and the nonlinear MZ characteristic i PD ¼ f(u MZ ) is used as the OEO
nonlinearity.
3.4.3.1 The Nonlinear Element Is the RF Amplifier A
The instantaneous value of the output current of the amplifying stage is equal to
i A ¼ α e u PD À β e u
3
PD
À
Á
, where u PD is the instantaneous values of the input voltage,
which coincides with the voltage on the PD output. Then the nonlinear dependence
of the i A current and differential equation (Eq. 3.50) in time domain are written as:
i A ¼ α e u PD À β e u
3
PD
À
Á
.
3.4.3.2 The Nonlinear Element Is the Mach–Zehnder Modulator
The instantaneous output PD voltage is equal u PD ¼ R PD i PD , where i PD is the
instantaneous “output” photocurrent of PD, R PD is the active load resistance of
PD. The nonlinear function i PD ¼ f(u MZ ) takes a form:
i PD ¼ 0:5γ E 0L
ð Þ
2 K 0FOS:MZ cos πU 0MZ =2U 0MZπ
ð
Þ À u MZ
½
ð 3:51Þ
and Eq. (3.50) in the time domain is written as: i A ¼ α e R PD i PD À β e (R PD i PD )
3 .
Equation (2.50) is a nonlinear differential equation of the second order. For
arbitrary nonlinearities they cannot be solved in general case, for the specific cases
(for instance, the high Q-factors) these equation can be simplified or “abbreviated”
till the one order less.
3.4.3.3 Abbreviated Equations of OEO MZ with the Single Optical
Fiber
In order to obtain the abbreviated equations of OEO MZ with the single optical fiber,
we write differential equations for OEO in operator form:
120 3 Modulation Methods of Laser Emission in Optoelectronic oscillator (OEO) and OEO. . .