optical rejection filter tuned on suppression of DC component. In OEO MZ the
relation of U 1MZ /U 0MZπ should be 2.4.
To form the equations of amplitude and phase balance separately for the laser and
for OEO, and also for formation and solution of symbolic and abbreviated differential equation of OEO, we considered the mathematical formulas for the complex
transfer functions of OEO elements (optical and RF parts). As the result of modulation method analysis of the complex transfer functions of OEO components, the
symbolic and abbreviated equations have been formed.
The special attention is attracted to formation and solution of abbreviated equations for OEO with the single optical fiber. Solutions allowed revealing of amplitude
and frequency functions versus the Q-factor of the RF filter, the delay time in the
optical fiber, the laser power, etc.
On the base of formed symbolic equations, the resonance curves are constructed
and discussed for OEO dependences of the amplitude-frequency at modulator
operation with the different DC bias voltage of OEO MZ. From the analysis of
symbolic equation solutions and from the analysis of resonance curves at different
OEO parameters, some interesting conclusions can be made. So, at sine nonlinearity
(or MZ operation in “quadrature”) the soft excitation OEO mode is possible, which
is caused by disturbance of OEO stability conditions in the initial state. On the
contrary, at cosine nonlinearity of the MZ modulator (or at MZ operation in the mode
“non-quadrature”), there is the rigid excitation mode only of the autonomous
oscillator. At modulation index grows and at the module of the transfer function
increases, there is the OEO rigid excitation only, and at that, zones of possible
steady-state values of amplitude are broadening and their transients depend on initial
conditions. Several examples of differential equation solutions with cosine and sine
nonlinearities are presented for different Q-factors of the RF filters (100 and higher)
at different DC bias voltages for MZ.
The problems of the laser parameters’ influence (the Q-factor of the optical filter,
the Q-factor of the spectral amplification line of the laser active medium, the
nonlinear function of the laser active medium, the lifetime of carriers on the upper
level, etc.) on the amplitude and the frequency of OEO. Some these problems will be
considered in future chapters.
References
1. V.V. Grigoriants, A.A. Dvornikov, Y.B. Il’in, et al, Oscillators of the radio-frequency range
with the optical carrier, in Proceeding of MPEI, Issue 607 (1983), pp. 76–79
2. A.A. Dvornikov, Y.B. Il’in, V.N. Konstantinov, About single-frequency modes of the oscillator
with the fiber-optical delay line in the feedback loop. Radio Eng. Electron. 29(11), 2234–2242
(1984)
3. V.V. Grigoriants, A.A. Dvornikov, Y.B. Il’in, et al., Radio signal generation in the system
«laser optical delay line». Quant. Electron. 11(4), 766–775 (1984)
130 3 Modulation Methods of Laser Emission in Optoelectronic oscillator (OEO) and OEO. . .
relation of U 1MZ /U 0MZπ should be 2.4.
To form the equations of amplitude and phase balance separately for the laser and
for OEO, and also for formation and solution of symbolic and abbreviated differential equation of OEO, we considered the mathematical formulas for the complex
transfer functions of OEO elements (optical and RF parts). As the result of modulation method analysis of the complex transfer functions of OEO components, the
symbolic and abbreviated equations have been formed.
The special attention is attracted to formation and solution of abbreviated equations for OEO with the single optical fiber. Solutions allowed revealing of amplitude
and frequency functions versus the Q-factor of the RF filter, the delay time in the
optical fiber, the laser power, etc.
On the base of formed symbolic equations, the resonance curves are constructed
and discussed for OEO dependences of the amplitude-frequency at modulator
operation with the different DC bias voltage of OEO MZ. From the analysis of
symbolic equation solutions and from the analysis of resonance curves at different
OEO parameters, some interesting conclusions can be made. So, at sine nonlinearity
(or MZ operation in “quadrature”) the soft excitation OEO mode is possible, which
is caused by disturbance of OEO stability conditions in the initial state. On the
contrary, at cosine nonlinearity of the MZ modulator (or at MZ operation in the mode
“non-quadrature”), there is the rigid excitation mode only of the autonomous
oscillator. At modulation index grows and at the module of the transfer function
increases, there is the OEO rigid excitation only, and at that, zones of possible
steady-state values of amplitude are broadening and their transients depend on initial
conditions. Several examples of differential equation solutions with cosine and sine
nonlinearities are presented for different Q-factors of the RF filters (100 and higher)
at different DC bias voltages for MZ.
The problems of the laser parameters’ influence (the Q-factor of the optical filter,
the Q-factor of the spectral amplification line of the laser active medium, the
nonlinear function of the laser active medium, the lifetime of carriers on the upper
level, etc.) on the amplitude and the frequency of OEO. Some these problems will be
considered in future chapters.
References
1. V.V. Grigoriants, A.A. Dvornikov, Y.B. Il’in, et al, Oscillators of the radio-frequency range
with the optical carrier, in Proceeding of MPEI, Issue 607 (1983), pp. 76–79
2. A.A. Dvornikov, Y.B. Il’in, V.N. Konstantinov, About single-frequency modes of the oscillator
with the fiber-optical delay line in the feedback loop. Radio Eng. Electron. 29(11), 2234–2242
(1984)
3. V.V. Grigoriants, A.A. Dvornikov, Y.B. Il’in, et al., Radio signal generation in the system
«laser optical delay line». Quant. Electron. 11(4), 766–775 (1984)
130 3 Modulation Methods of Laser Emission in Optoelectronic oscillator (OEO) and OEO. . .