t + τ), which reflects the sense of statistical processes in OEO MZ and explains the
process of the laser phase noise transformation into the RF phase noise of OEO. The
autocorrelation function R MZ (u, t, t + τ) is determined by three components: the DC
component, which passes to the PD area after passage of MZ and the optical fiber
R MZ0 , and also by AC components R MZ1 and R MZ2 , which value depends on φ 0MZ or
the DC bias voltage in MZ.
The presented analysis of OEO as the correlator of random quantities allows the
conclusion that the distribution probability of the random quantity η depends not
only upon the ratio of the oscillation amplitude to the noise dispersion (or the SNR)
η
j j=σ
2
ξ in the correlator input, but upon the laser coherence time T c or the difference
[1 À exp (À2(ΔT M + T FOS )/T c )]. From the analysis of expressions (Eqs. 5.98–5.103)
and plots in Figs. 5.10, 5.11, and 5.13 depicted on these expressions, it follows that
at close ratio A 2 /A 1 to 1, the probability p 1 in the input is closer to 1, and the
probability p 1 is determined by the multiplier exp(À2τ/T c ). The probability distribution density of the correlator output process approaches to 1 at decrease of the
ratio 2(ΔT M + T FOS )/T c and at decrease of the laser phase noise dispersion σ
2
ξ . The
statistic process of fluctuation suppression in OEO can be defined as the process of
statistical adding of two optical harmonics, which pass to the PD area. As the result
of the statistical process and the process of photodetection, the laser phase noises are
suppressed. Thus, at closed feedback loop in OEO MZ, the spectrum in the photodetector output has the Lorentzian shape, and it is determined by the laser phase
noises, and its maximal value depends upon the ratio T FOS /T c .
References
1. I.V. Komarov, S.M. Smolskiy, Fundamentals of Short-Range FM Radar (Artech House, Norwood, 2003)
2. N. Yoshida, Oscillation Theory Of Partial Differential Equations (World Scientific Publishing,
Singapore, 2008)
3. Alexander A. Bortsov and Sergey M. Smolskiy, Opto-Electronic Oscillator with MachZender Modulator. Infocommunications Journal, Vol. XI, No 1, 45–53 (2019),DOI: 10.13140/
RG.2.2.20992.69126
4. J.W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts and Company
publishers, Englewood, 2006)
5. Alexander A. Bortsov, Yuri B. Il’in, Laser spectral line widening effect on RF phase and
amplitude noises of an optoelectronic oscillator OEO. J. Radio Eng. (2), 21–31 (2010),
DOI: 10.13140/RG.2.2.35665.07527
References
283
process of the laser phase noise transformation into the RF phase noise of OEO. The
autocorrelation function R MZ (u, t, t + τ) is determined by three components: the DC
component, which passes to the PD area after passage of MZ and the optical fiber
R MZ0 , and also by AC components R MZ1 and R MZ2 , which value depends on φ 0MZ or
the DC bias voltage in MZ.
The presented analysis of OEO as the correlator of random quantities allows the
conclusion that the distribution probability of the random quantity η depends not
only upon the ratio of the oscillation amplitude to the noise dispersion (or the SNR)
η
j j=σ
2
ξ in the correlator input, but upon the laser coherence time T c or the difference
[1 À exp (À2(ΔT M + T FOS )/T c )]. From the analysis of expressions (Eqs. 5.98–5.103)
and plots in Figs. 5.10, 5.11, and 5.13 depicted on these expressions, it follows that
at close ratio A 2 /A 1 to 1, the probability p 1 in the input is closer to 1, and the
probability p 1 is determined by the multiplier exp(À2τ/T c ). The probability distribution density of the correlator output process approaches to 1 at decrease of the
ratio 2(ΔT M + T FOS )/T c and at decrease of the laser phase noise dispersion σ
2
ξ . The
statistic process of fluctuation suppression in OEO can be defined as the process of
statistical adding of two optical harmonics, which pass to the PD area. As the result
of the statistical process and the process of photodetection, the laser phase noises are
suppressed. Thus, at closed feedback loop in OEO MZ, the spectrum in the photodetector output has the Lorentzian shape, and it is determined by the laser phase
noises, and its maximal value depends upon the ratio T FOS /T c .
References
1. I.V. Komarov, S.M. Smolskiy, Fundamentals of Short-Range FM Radar (Artech House, Norwood, 2003)
2. N. Yoshida, Oscillation Theory Of Partial Differential Equations (World Scientific Publishing,
Singapore, 2008)
3. Alexander A. Bortsov and Sergey M. Smolskiy, Opto-Electronic Oscillator with MachZender Modulator. Infocommunications Journal, Vol. XI, No 1, 45–53 (2019),DOI: 10.13140/
RG.2.2.20992.69126
4. J.W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts and Company
publishers, Englewood, 2006)
5. Alexander A. Bortsov, Yuri B. Il’in, Laser spectral line widening effect on RF phase and
amplitude noises of an optoelectronic oscillator OEO. J. Radio Eng. (2), 21–31 (2010),
DOI: 10.13140/RG.2.2.35665.07527
References
283