3.3.4
The Transfer Function of the Fiber Optical System . . . . . 112
3.3.5
The Radio-Frequency Filter . . . . . . . . . . . . . . . . . . . . . 112
3.3.6
The Nonlinear RF Amplifier in OEO . . . . . . . . . . . . . . . 112
3.3.7
The Feedback Network in OEO . . . . . . . . . . . . . . . . . . 114
3.4
Equations of Amplitude and Phase Balance for the Laser
and for OEO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
3.4.1
Equations of Amplitude and Phase Balance
for the Laser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
3.4.2
Equations of Amplitude and Phase Balance
for the RF Part of OEO DM and OEO MZ . . . . . . . . . . 115
3.4.3
Differential Equations of OEO MZ with the Single
Optical Fiber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
3.5
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
4 Semiclassical Theory and Laser Differential Equations
for Optoelectronic oscillator (OEO) Analysis . . . . . . . . . . . . . . . . . . 133
4.1
Semiclassical Laser Equations and OEO Differential
Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
4.1.1
OEO as the Laser Spanned by the Feedback Loop . . . . . 136
4.1.2
Quasi-Classical Laser Theory . . . . . . . . . . . . . . . . . . . . 137
4.1.3
Wave Differential Equation of the Laser . . . . . . . . . . . . 140
4.1.4
Differential Equations of QWLD . . . . . . . . . . . . . . . . . . 141
4.2
Constitutive Equations of a Laser . . . . . . . . . . . . . . . . . . . . . . . . 143
4.2.1
DE for the Single-Frequency Single-Mode Regime . . . . . 143
4.2.2
Nonlinear Symbolic Differential Equations
for QWLD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
4.2.3
Q-Factors of Spectral Lines of Amplification
of Quantum-Well Laser Diodes . . . . . . . . . . . . . . . . . . . 146
4.2.4
Abbreviated Equations of QWLD . . . . . . . . . . . . . . . . . 147
4.2.5
Analog Laser DEs Model . . . . . . . . . . . . . . . . . . . . . . . 148
4.2.6
Kinetic Equations of a Laser . . . . . . . . . . . . . . . . . . . . . 150
4.3
Laser Kinetic Equations and the Pumping System . . . . . . . . . . . . 150
4.3.1
Laser Pumping System . . . . . . . . . . . . . . . . . . . . . . . . . 151
4.3.2
Nonlinear Symbolic DEs for QWLD . . . . . . . . . . . . . . . 154
4.3.3
Population and the Laser Analog Model
in the Quasi-Stationary Mode . . . . . . . . . . . . . . . . . . . . 158
4.3.4
Normalized Differential Equations of the Laser . . . . . . . 159
4.4
Abbreviated DE for the Laser in Quasi-Stationary Mode . . . . . . . 161
4.4.1
Approximation of the Complex Nonlinearity
E n  N n by Cubic Polynomial . . . . . . . . . . . . . . . . . . . 161
4.4.2
Abbreviated DEs for the Laser in the Quasi-Stationary
Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
4.4.3
Steady-State Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 166
Contents
xv