equations (complicated for analysis) to the single differential equation of the fourth
order. At that, the inertial nonlinear element was extracted and analyzed, its mathematical model is examined. We used for the QWLD analysis methods, which are
widely applied in the oscillations theory; we investigated the stability of the steadystate modes of QWLD. The special attention was attracted to the laser operation on
the boundary of the stable mode ultrahigh power density of the laser optical
resonator. Original results of the laser investigation described in this book are
relevant, because in many labs of the world, at present, the application ideas of
optical micro-tori or the micro-resonators have got the development in the laser
systems. We would like to note that first investigations of micro-tori application in
quantum systems were made by Soviet and Russian physicist V.B. Braginsky [3]
and they are seriously advanced by researches of his pupil M.L. Gorodetsky [4], as
well as the teams of A.B. Matsko, L. Maleki, V.S. Ilchenko [5], and by others.
The second, third, fourth, and fifth chapters of this book are devoted to the
methods to obtain of differential “abbreviated” equations on the base of Evtianov
approach [6] for OEO with external and direct modulation of the laser. In fourth, fifth
and sixth chapters, relying on the Evtianov–Kuleshov method [7] for the noise
analysis in traditional electronic oscillators, as well as on researches of Tikhonov
[8] and Goodmen [9] on the statistical analysis, relatively, RF and optical systems,
we developed the main methods for the amplitude and phase noise analysis in OEO
MZ and OEO DM. We could obtain the strict mathematically well-found formulas
for amplitude and phase noises in OEO depending on the spontaneous laser noise,
the delay time in the optical fiber, the laser coherence time, and its power. At that,
formation of the final phase RF noises of OEO is examined as the result of the
convolution operation of the laser optical spectrum and the RF spectrum of the
oscillation acting in the Mach–Zehnder modulator input. One of the results of our
analysis is that we could show how the PSD level of the “resonance peak,” which is
caused by the relaxation electron–photon resonance in the laser, influences on PSD
of the phase noise in OEO. The influence of the ratio of the laser coherence time to
the delay time in the optical fiber upon the OEO phase noise is another important
result, as well as the influence of the amplitude levels of optical harmonics in the
structure of the single-channel modulation in the MZ modulator. We noted that
equalization of the optical power in different optical channels allows the significant
suppression of the optical carrier, which leads also to reduction of the OEO phase
noise level.
In Chap. 6, we discuss the detailed description of the modulation methods and
constructions of the modern Mach–Zehnder modulators. This gives us a possibility
to show that utilization of the double-channel modulation (or RF modulation of two
“parallel-coupled” modulators, which are mounted on the single substrate) not only
increases the amplitude level of RF output oscillation in OEO MZ, but, at that,
phasenoises caused by the laser, the photoreceiver, the RF amplifier are significantly
suppressed. We note that in the double-channel structure, the essential role in
noisesuppression is played also by the “absolute” equalization of the optical power
passed in different MZmodulators.
Conclusion
509
order. At that, the inertial nonlinear element was extracted and analyzed, its mathematical model is examined. We used for the QWLD analysis methods, which are
widely applied in the oscillations theory; we investigated the stability of the steadystate modes of QWLD. The special attention was attracted to the laser operation on
the boundary of the stable mode ultrahigh power density of the laser optical
resonator. Original results of the laser investigation described in this book are
relevant, because in many labs of the world, at present, the application ideas of
optical micro-tori or the micro-resonators have got the development in the laser
systems. We would like to note that first investigations of micro-tori application in
quantum systems were made by Soviet and Russian physicist V.B. Braginsky [3]
and they are seriously advanced by researches of his pupil M.L. Gorodetsky [4], as
well as the teams of A.B. Matsko, L. Maleki, V.S. Ilchenko [5], and by others.
The second, third, fourth, and fifth chapters of this book are devoted to the
methods to obtain of differential “abbreviated” equations on the base of Evtianov
approach [6] for OEO with external and direct modulation of the laser. In fourth, fifth
and sixth chapters, relying on the Evtianov–Kuleshov method [7] for the noise
analysis in traditional electronic oscillators, as well as on researches of Tikhonov
[8] and Goodmen [9] on the statistical analysis, relatively, RF and optical systems,
we developed the main methods for the amplitude and phase noise analysis in OEO
MZ and OEO DM. We could obtain the strict mathematically well-found formulas
for amplitude and phase noises in OEO depending on the spontaneous laser noise,
the delay time in the optical fiber, the laser coherence time, and its power. At that,
formation of the final phase RF noises of OEO is examined as the result of the
convolution operation of the laser optical spectrum and the RF spectrum of the
oscillation acting in the Mach–Zehnder modulator input. One of the results of our
analysis is that we could show how the PSD level of the “resonance peak,” which is
caused by the relaxation electron–photon resonance in the laser, influences on PSD
of the phase noise in OEO. The influence of the ratio of the laser coherence time to
the delay time in the optical fiber upon the OEO phase noise is another important
result, as well as the influence of the amplitude levels of optical harmonics in the
structure of the single-channel modulation in the MZ modulator. We noted that
equalization of the optical power in different optical channels allows the significant
suppression of the optical carrier, which leads also to reduction of the OEO phase
noise level.
In Chap. 6, we discuss the detailed description of the modulation methods and
constructions of the modern Mach–Zehnder modulators. This gives us a possibility
to show that utilization of the double-channel modulation (or RF modulation of two
“parallel-coupled” modulators, which are mounted on the single substrate) not only
increases the amplitude level of RF output oscillation in OEO MZ, but, at that,
phasenoises caused by the laser, the photoreceiver, the RF amplifier are significantly
suppressed. We note that in the double-channel structure, the essential role in
noisesuppression is played also by the “absolute” equalization of the optical power
passed in different MZmodulators.
Conclusion
509