of photocurrent versus the input voltage in the MZ electrical input is linear-cubic, the
slope of phase fluctuation is about 1, and at φ 0L2 (U 0M ) ¼ mπ this function is quadratic,
but at that, the transformation slope of phase fluctuations in MZ increases by several
times. Since at nonuniform excitation of MZ optical channels, for instance, k 02 % 0.55
and k 01 % 0.45, the phase-frequency MZ function (Eq. 3.31) has the local maximum at
φ 0MZ (U 0MZ ) ¼ 0.95mπ. Therefore, in this operating point, the MZ slope of phase
fluctuation transformation is minimal and, as it follows from the further analysis, the
transformation slope of MZ phase fluctuations is small. But at that, the second
harmonic level essentially exceeds the level of the first harmonic.
Thus, PD photocurrents in the open loops of OEO DM and OEO MZ at nodulation, relatively, of the QWLD pumping current (OEO DM) and of the MZ voltage
(in OEO MZ) are results of self-heterodyning, the level of harmonic components is
defined by the difference phase incursion of two optical harmonics Δϕ 0e , which pass
to PD area, and phase fluctuations of the laser φ em (t) define the spectrum of RF
oscillations in the PD load.
In OEO DM and in OEO MZ, the mode of radio-frequency doubling is possible
at DC component suppression, which significant level degrades of the OEO phase
noise. In this case, it is necessary to introduce the optical rejection filter tuned on the
suppression of DC component in OEO DM. And in OEO MZ, the ratio U 1MZ /U 0MZπ
should be x ¼ U 1MZ /U 0MZπ ¼ 2.4. The tasks of power spectral density determination
for the OEO phase noise, which are defined by laser phase fluctuations φ em (t), will
be solved in Chaps. 5–7. Further, in order to derive the amplitude and phase balance
equations and OEO differential equations, we present below the mathematical
description of transfer functions of various OEO components: the photodetector,
the RF amplifier and the RF filter, as well as the optical fiber and the optical
amplifier.
3.3 Mathematical Description of Transfer Functions
of OEO Components
3.3.1 The Optical Amplifier for the Laser
The expression for the transfer function of the optical amplifier for a laser represents
the ratio of the intensity amplitude (with the optical frequency ν) in the OA output
E Lout to its value in the input E Lin : K OA ¼ E Lout /E Lin .
For the double-level laser model (the point model in space without taking into
consideration the OA linear dimensions), TF of OA is obtained from the equation
solution of interaction of the plane monochromatic wave with the active medium.
The transfer function of the laser optical amplifier in the small-signal mode in linear
approximation can be written as:
108 3 Modulation Methods of Laser Emission in Optoelectronic oscillator (OEO) and OEO. . .
slope of phase fluctuation is about 1, and at φ 0L2 (U 0M ) ¼ mπ this function is quadratic,
but at that, the transformation slope of phase fluctuations in MZ increases by several
times. Since at nonuniform excitation of MZ optical channels, for instance, k 02 % 0.55
and k 01 % 0.45, the phase-frequency MZ function (Eq. 3.31) has the local maximum at
φ 0MZ (U 0MZ ) ¼ 0.95mπ. Therefore, in this operating point, the MZ slope of phase
fluctuation transformation is minimal and, as it follows from the further analysis, the
transformation slope of MZ phase fluctuations is small. But at that, the second
harmonic level essentially exceeds the level of the first harmonic.
Thus, PD photocurrents in the open loops of OEO DM and OEO MZ at nodulation, relatively, of the QWLD pumping current (OEO DM) and of the MZ voltage
(in OEO MZ) are results of self-heterodyning, the level of harmonic components is
defined by the difference phase incursion of two optical harmonics Δϕ 0e , which pass
to PD area, and phase fluctuations of the laser φ em (t) define the spectrum of RF
oscillations in the PD load.
In OEO DM and in OEO MZ, the mode of radio-frequency doubling is possible
at DC component suppression, which significant level degrades of the OEO phase
noise. In this case, it is necessary to introduce the optical rejection filter tuned on the
suppression of DC component in OEO DM. And in OEO MZ, the ratio U 1MZ /U 0MZπ
should be x ¼ U 1MZ /U 0MZπ ¼ 2.4. The tasks of power spectral density determination
for the OEO phase noise, which are defined by laser phase fluctuations φ em (t), will
be solved in Chaps. 5–7. Further, in order to derive the amplitude and phase balance
equations and OEO differential equations, we present below the mathematical
description of transfer functions of various OEO components: the photodetector,
the RF amplifier and the RF filter, as well as the optical fiber and the optical
amplifier.
3.3 Mathematical Description of Transfer Functions
of OEO Components
3.3.1 The Optical Amplifier for the Laser
The expression for the transfer function of the optical amplifier for a laser represents
the ratio of the intensity amplitude (with the optical frequency ν) in the OA output
E Lout to its value in the input E Lin : K OA ¼ E Lout /E Lin .
For the double-level laser model (the point model in space without taking into
consideration the OA linear dimensions), TF of OA is obtained from the equation
solution of interaction of the plane monochromatic wave with the active medium.
The transfer function of the laser optical amplifier in the small-signal mode in linear
approximation can be written as:
108 3 Modulation Methods of Laser Emission in Optoelectronic oscillator (OEO) and OEO. . .