5.3.3
Dynamics of Transients in OEO DM . . . . . . . . . . . . . . . 227
5.3.4
General Remarks About the Limit Cycle Realization
in the Closed OEO DM System of the Laser
Emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228
5.4
Fluctuation Differential Equations of OEO with the
Langevinian Noise Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
5.4.1
Main Regulations of the Fluctuation Laser
Model and Langevinian Noise Sources . . . . . . . . . . . . . 233
5.4.2
Symbolic Constitutive Differential Equations
of the Laser with Fluctuations . . . . . . . . . . . . . . . . . . . . 234
5.4.3
Symbolic DEs of the Laser with Fluctuations
in the Quasi-Stationary Small-Signal Mode . . . . . . . . . . 238
5.4.4
PSD of Amplitude and Phase Noise of the Laser . . . . . . 240
5.4.5
Abbreviated Equations for Amplitude and Phase
with Fluctuations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
5.4.6
Symbolic Fluctuation Equations of OEO . . . . . . . . . . . . 244
5.4.7
Differential Equations with Fluctuations
and the Analog Model of OEO MZ . . . . . . . . . . . . . . . . 249
5.5
Correlator’s Mathematical Model in OEO MZ . . . . . . . . . . . . . . 257
5.5.1
Description of Mathematical Models of the Laser
and the Mach–Zehnder Modulator at OEO Analysis
as the Correlator Enclosed by the Positive FB . . . . . . . . 258
5.5.2
The OEO Model as the Correlator with the Positive
Feedback . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260
5.5.3
The Mach–Zehnder Correlator-Interferometer . . . . . . . . 261
5.5.4
The Equivalent Circuit of OEO MZ as a Random
Correlator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263
5.5.5
The Autocorrelation Function of MZ at the Opened
Feedback Loop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266
5.5.6
The Autocorrelation Function of the Strength
Square of the MZ Field . . . . . . . . . . . . . . . . . . . . . . . . 267
5.5.7
The Autocorrelation Function of the PD Load
Voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269
5.5.8
The Convolution Operation of Strength Squares
of the Laser Field and the Radio-Frequency
Oscillation in OEO MZ . . . . . . . . . . . . . . . . . . . . . . . . 271
5.5.9
The Power Spectral Density S η in the Correlator
Output in OEO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273
5.5.10 The Oscillation Spectrum at Closed Feedback
Loop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278
5.6
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283
Contents
xvii
Dynamics of Transients in OEO DM . . . . . . . . . . . . . . . 227
5.3.4
General Remarks About the Limit Cycle Realization
in the Closed OEO DM System of the Laser
Emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228
5.4
Fluctuation Differential Equations of OEO with the
Langevinian Noise Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
5.4.1
Main Regulations of the Fluctuation Laser
Model and Langevinian Noise Sources . . . . . . . . . . . . . 233
5.4.2
Symbolic Constitutive Differential Equations
of the Laser with Fluctuations . . . . . . . . . . . . . . . . . . . . 234
5.4.3
Symbolic DEs of the Laser with Fluctuations
in the Quasi-Stationary Small-Signal Mode . . . . . . . . . . 238
5.4.4
PSD of Amplitude and Phase Noise of the Laser . . . . . . 240
5.4.5
Abbreviated Equations for Amplitude and Phase
with Fluctuations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
5.4.6
Symbolic Fluctuation Equations of OEO . . . . . . . . . . . . 244
5.4.7
Differential Equations with Fluctuations
and the Analog Model of OEO MZ . . . . . . . . . . . . . . . . 249
5.5
Correlator’s Mathematical Model in OEO MZ . . . . . . . . . . . . . . 257
5.5.1
Description of Mathematical Models of the Laser
and the Mach–Zehnder Modulator at OEO Analysis
as the Correlator Enclosed by the Positive FB . . . . . . . . 258
5.5.2
The OEO Model as the Correlator with the Positive
Feedback . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260
5.5.3
The Mach–Zehnder Correlator-Interferometer . . . . . . . . 261
5.5.4
The Equivalent Circuit of OEO MZ as a Random
Correlator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263
5.5.5
The Autocorrelation Function of MZ at the Opened
Feedback Loop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266
5.5.6
The Autocorrelation Function of the Strength
Square of the MZ Field . . . . . . . . . . . . . . . . . . . . . . . . 267
5.5.7
The Autocorrelation Function of the PD Load
Voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269
5.5.8
The Convolution Operation of Strength Squares
of the Laser Field and the Radio-Frequency
Oscillation in OEO MZ . . . . . . . . . . . . . . . . . . . . . . . . 271
5.5.9
The Power Spectral Density S η in the Correlator
Output in OEO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273
5.5.10 The Oscillation Spectrum at Closed Feedback
Loop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278
5.6
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283
Contents
xvii