relatively, of the laser modulator, the fiber optical system, the photodetector, the RF
filter, the RF amplifier, J 0 is the DC current of the laser pumping, ν 0L is the laser
optical frequency, m ¼ 1, 2, . . . .
The diagram for determination of the QWLD frequency of generation and RF
frequency of generation frequency is shown in Fig. 3.17a, b for OEO DM.
From Fig. 3.17a, b, we see that the increase of the pumping current leads to
appearance of the laser generation and radio-frequency generation at fulfillment of
amplitude and balance equations. These equations allow determination of frequency
and amplitude dependence for the laser and for OEO of the pumping current and
system parameters in the steady-state mode. APB equations cannot solve the issues
of dynamics, excitation and phase noises. Therefore, we must pass to formation of
differential equations (DE) on the base on the structural block model.
3.4.3 Differential Equations of OEO MZ with the Single
Optical Fiber
In this section, we pay the main attention to the effects of laser and MZ modulator
parameters on OEO operation. Therefore, we assume in this section that all RF
networks are wideband besides the RF narrowband filter (F in Fig. 3.2c) in order to
accent the OEO properties related to MZ modulator and the laser. We do not take
into consideration the photodetector and amplifier lags and suppose that the directional coupler C represents the ideal (“without electrical power reflection”) connector with the transfer function (from input to output connected with the electrical input
of MZ modulator) close to 1. The PD load and the internal resistance of the MZ
electrical input are supposed to be active (we assume that the reactive component of
the complex load impedance is equal to zero). In RF networks, the complete
matching occurs from PD to the MZ electric input (i.e., the standing-wave ratio in
networks is zero). To the optical PD input, the delayed laser emission (E 12L )
2 passes:
E
2
12L ¼ E
2
01L 1 þ γ
2
À
Á
þ γ 0:5 E
2
01L cos πU 0MZ =2U 0MZπ
ð
Þ ÀU 10MZ =U 0MZπ
ð
Þ cos 2πft þ φ 0L
ð
Þ
½
:
ð3:45Þ
Figure 3.17a–c shows the total amplitude-frequency characteristic, K OA Á K OF
(Fig. 3.17a) of the laser optical amplifier and the optical filter, as well as the phasefrequency characteristics of the optical amplifier φ OA and the optical filter φ OF
(Fig. 3.17b) for different values of the laser pumping current excess over its
threshold value A 0 ¼ J 0L /J 0Lth (curve 1 corresponds to A 0 ¼ 1.5, curve 2—A 0 ¼ 3,
curve 3—A 0 ¼ 5).
The graphical solutions for obtaining the laser steady-state frequency for the
pumping current A 0 ¼ 5 (curve 3) are shown in Fig. 3.17c. The point of the
116 3 Modulation Methods of Laser Emission in Optoelectronic oscillator (OEO) and OEO. . .
filter, the RF amplifier, J 0 is the DC current of the laser pumping, ν 0L is the laser
optical frequency, m ¼ 1, 2, . . . .
The diagram for determination of the QWLD frequency of generation and RF
frequency of generation frequency is shown in Fig. 3.17a, b for OEO DM.
From Fig. 3.17a, b, we see that the increase of the pumping current leads to
appearance of the laser generation and radio-frequency generation at fulfillment of
amplitude and balance equations. These equations allow determination of frequency
and amplitude dependence for the laser and for OEO of the pumping current and
system parameters in the steady-state mode. APB equations cannot solve the issues
of dynamics, excitation and phase noises. Therefore, we must pass to formation of
differential equations (DE) on the base on the structural block model.
3.4.3 Differential Equations of OEO MZ with the Single
Optical Fiber
In this section, we pay the main attention to the effects of laser and MZ modulator
parameters on OEO operation. Therefore, we assume in this section that all RF
networks are wideband besides the RF narrowband filter (F in Fig. 3.2c) in order to
accent the OEO properties related to MZ modulator and the laser. We do not take
into consideration the photodetector and amplifier lags and suppose that the directional coupler C represents the ideal (“without electrical power reflection”) connector with the transfer function (from input to output connected with the electrical input
of MZ modulator) close to 1. The PD load and the internal resistance of the MZ
electrical input are supposed to be active (we assume that the reactive component of
the complex load impedance is equal to zero). In RF networks, the complete
matching occurs from PD to the MZ electric input (i.e., the standing-wave ratio in
networks is zero). To the optical PD input, the delayed laser emission (E 12L )
2 passes:
E
2
12L ¼ E
2
01L 1 þ γ
2
À
Á
þ γ 0:5 E
2
01L cos πU 0MZ =2U 0MZπ
ð
Þ ÀU 10MZ =U 0MZπ
ð
Þ cos 2πft þ φ 0L
ð
Þ
½
:
ð3:45Þ
Figure 3.17a–c shows the total amplitude-frequency characteristic, K OA Á K OF
(Fig. 3.17a) of the laser optical amplifier and the optical filter, as well as the phasefrequency characteristics of the optical amplifier φ OA and the optical filter φ OF
(Fig. 3.17b) for different values of the laser pumping current excess over its
threshold value A 0 ¼ J 0L /J 0Lth (curve 1 corresponds to A 0 ¼ 1.5, curve 2—A 0 ¼ 3,
curve 3—A 0 ¼ 5).
The graphical solutions for obtaining the laser steady-state frequency for the
pumping current A 0 ¼ 5 (curve 3) are shown in Fig. 3.17c. The point of the
116 3 Modulation Methods of Laser Emission in Optoelectronic oscillator (OEO) and OEO. . .