6 Operation Analysis of Optoelectronic oscillator (OEO)
with External Mach–Zehnder Modulator . . . . . . . . . . . . . . . . . . . . . 285
6.1
The General Statement of the OEO MZ Investigation
Task . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285
6.2
The Construction and Operation Principle of OEO MZ . . . . . . . . 286
6.2.1
Influence of the Phase Noise PSD on the Irregularity
of MZ Optical Channels and the Spatial Laser
Coherence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290
6.3
Mathematical Model of OEO MZ . . . . . . . . . . . . . . . . . . . . . . . 294
6.3.1
The Laser in OEO MZ . . . . . . . . . . . . . . . . . . . . . . . . . 294
6.4
Characteristics and the Transfer Function of the MZ
Modulator in OEO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299
6.4.1
The Total Transfer Function of the MZ Modulator . . . . . 304
6.4.2
The Total MZ Transfer Function with Account
of the Transfer Function of the Radio-Frequency
Electrodes of MZ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305
6.4.3
Abbreviated Equations of OEO MZ . . . . . . . . . . . . . . . 306
6.4.4
Fluctuations of the Photodetector Photo-Current
in OEO MZ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308
6.4.5
Power Spectral Density of the Detected Laser
Fluctuations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309
6.5
Differential Fluctuation Equations of OEO MZ . . . . . . . . . . . . . . 311
6.5.1
Symbolic Differential Equations of OEO MZ
with Fluctuations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312
6.5.2
Abbreviated Differential Equations of OEO
MZ with Fluctuations . . . . . . . . . . . . . . . . . . . . . . . . . . 313
6.5.3
Noise Currents in the NA Input and Output . . . . . . . . . . 314
6.5.4
Fluctuation Deviations of Amplitudes and Phase . . . . . . 316
6.5.5
The Coefficient of the Local Slope σ U . . . . . . . . . . . . . . 317
6.5.6
Symbolic Expressions for Fluctuations . . . . . . . . . . . . . 318
6.5.7
An Analysis of Formulas for PSD of Amplitude
and Phase Noises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319
6.5.8
The Function of the Suppression Coefficient
of PSD of the Phase Noise in OEO MZ Versus
the Laser Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324
6.5.9
The Formula for PSD of the Phase Noise
in OEO MZ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327
6.5.10 Utilization of Differential and Combined FOS
to Suppress the Resonance . . . . . . . . . . . . . . . . . . . . . . 329
6.5.11 PSD of the Phase Noise in OEO MZ with RF FODL
and MZ Modulator Taking into Account the laser,
PD and NA Noises . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330
6.5.12 Modulations of Two Channels in MZ . . . . . . . . . . . . . . 334
6.5.13 The Approximate Formula for the Coefficient K
2
ΓPN . . . . 340
xviii
Contents
with External Mach–Zehnder Modulator . . . . . . . . . . . . . . . . . . . . . 285
6.1
The General Statement of the OEO MZ Investigation
Task . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285
6.2
The Construction and Operation Principle of OEO MZ . . . . . . . . 286
6.2.1
Influence of the Phase Noise PSD on the Irregularity
of MZ Optical Channels and the Spatial Laser
Coherence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290
6.3
Mathematical Model of OEO MZ . . . . . . . . . . . . . . . . . . . . . . . 294
6.3.1
The Laser in OEO MZ . . . . . . . . . . . . . . . . . . . . . . . . . 294
6.4
Characteristics and the Transfer Function of the MZ
Modulator in OEO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299
6.4.1
The Total Transfer Function of the MZ Modulator . . . . . 304
6.4.2
The Total MZ Transfer Function with Account
of the Transfer Function of the Radio-Frequency
Electrodes of MZ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305
6.4.3
Abbreviated Equations of OEO MZ . . . . . . . . . . . . . . . 306
6.4.4
Fluctuations of the Photodetector Photo-Current
in OEO MZ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308
6.4.5
Power Spectral Density of the Detected Laser
Fluctuations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309
6.5
Differential Fluctuation Equations of OEO MZ . . . . . . . . . . . . . . 311
6.5.1
Symbolic Differential Equations of OEO MZ
with Fluctuations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312
6.5.2
Abbreviated Differential Equations of OEO
MZ with Fluctuations . . . . . . . . . . . . . . . . . . . . . . . . . . 313
6.5.3
Noise Currents in the NA Input and Output . . . . . . . . . . 314
6.5.4
Fluctuation Deviations of Amplitudes and Phase . . . . . . 316
6.5.5
The Coefficient of the Local Slope σ U . . . . . . . . . . . . . . 317
6.5.6
Symbolic Expressions for Fluctuations . . . . . . . . . . . . . 318
6.5.7
An Analysis of Formulas for PSD of Amplitude
and Phase Noises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319
6.5.8
The Function of the Suppression Coefficient
of PSD of the Phase Noise in OEO MZ Versus
the Laser Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324
6.5.9
The Formula for PSD of the Phase Noise
in OEO MZ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327
6.5.10 Utilization of Differential and Combined FOS
to Suppress the Resonance . . . . . . . . . . . . . . . . . . . . . . 329
6.5.11 PSD of the Phase Noise in OEO MZ with RF FODL
and MZ Modulator Taking into Account the laser,
PD and NA Noises . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330
6.5.12 Modulations of Two Channels in MZ . . . . . . . . . . . . . . 334
6.5.13 The Approximate Formula for the Coefficient K
2
ΓPN . . . . 340
xviii
Contents