5.5.4 The Equivalent Circuit of OEO MZ as a Random
Correlator
Let us consider in detail the analog models of OEO MZ, which are shown in
Figs. 5.10 and 5.11. Taking into account the mathematical calculations of Chap. 2,
we compose the equivalent circuit for OEO MZ. In Chap. 2 of this book, at
examination of the laser optical emission modulation in OEO MZ, we show that
for simplicity of mathematical computations at finding of ACF and PSD, we can
perform the approximation of the Bessel function and to transfer to the approximated
formulas to determine the “MZ nonlinearity” in the quadratic and non-quadratic
modes.
Figure 5.13 shows the structural diagrams of the equivalent circuit of OEO MZ as
a random correlator: the general structure of OEO MZ (a); OEO MZ operates in
quadrature mode with a phase difference in the MZ optical channels equal to “π/2”
(b); OEO MZ operates in the quadrature mode with a phase difference in the MZ
optical channels equal to “π” (c).
Thus, we transfer from the OEO model with the one multiplier (Fig. 5.13а) to the
model with two multipliers (Fig. 5.13b, c). This transfer function was substantiated
in Chap. 2 and is true not only for small (much lesser) voltage amplitudes, which
influence the electrical input, but also comparable in the magnitude with the DC
component of the bias voltage. Such representation of OEO MZ (with two multipliers) not only simplifies the mathematical analysis of the oscillating system, but
also facilitates understanding of the process of fluctuation suppression.
We note that for the structure in Fig. 5.13c, in which OEO MZ operates in the
“non-quadrature mode” with the phase difference in the MZ optical channels equal
to “π,” conditions of the soft self-excitation of the single-frequency generation of
OEO MZ on the fundamental are possible only at the specially selected nonlinear
Fig. 5.12 Calculated plots
of the autocorrelation
function K φ12 (Eq. 4.132) as
the function of the offset
F ¼ f À f 0 from the carrier
frequency f 0 at different
observation times
τ ¼ τ D ¼ ΔT M ¼ T 2M À T 1M
for the laser with the halfwidth spectral line
Δν L ¼ 1 kHz
5.5 Correlator’s Mathematical Model in OEO MZ
263
Correlator
Let us consider in detail the analog models of OEO MZ, which are shown in
Figs. 5.10 and 5.11. Taking into account the mathematical calculations of Chap. 2,
we compose the equivalent circuit for OEO MZ. In Chap. 2 of this book, at
examination of the laser optical emission modulation in OEO MZ, we show that
for simplicity of mathematical computations at finding of ACF and PSD, we can
perform the approximation of the Bessel function and to transfer to the approximated
formulas to determine the “MZ nonlinearity” in the quadratic and non-quadratic
modes.
Figure 5.13 shows the structural diagrams of the equivalent circuit of OEO MZ as
a random correlator: the general structure of OEO MZ (a); OEO MZ operates in
quadrature mode with a phase difference in the MZ optical channels equal to “π/2”
(b); OEO MZ operates in the quadrature mode with a phase difference in the MZ
optical channels equal to “π” (c).
Thus, we transfer from the OEO model with the one multiplier (Fig. 5.13а) to the
model with two multipliers (Fig. 5.13b, c). This transfer function was substantiated
in Chap. 2 and is true not only for small (much lesser) voltage amplitudes, which
influence the electrical input, but also comparable in the magnitude with the DC
component of the bias voltage. Such representation of OEO MZ (with two multipliers) not only simplifies the mathematical analysis of the oscillating system, but
also facilitates understanding of the process of fluctuation suppression.
We note that for the structure in Fig. 5.13c, in which OEO MZ operates in the
“non-quadrature mode” with the phase difference in the MZ optical channels equal
to “π,” conditions of the soft self-excitation of the single-frequency generation of
OEO MZ on the fundamental are possible only at the specially selected nonlinear
Fig. 5.12 Calculated plots
of the autocorrelation
function K φ12 (Eq. 4.132) as
the function of the offset
F ¼ f À f 0 from the carrier
frequency f 0 at different
observation times
τ ¼ τ D ¼ ΔT M ¼ T 2M À T 1M
for the laser with the halfwidth spectral line
Δν L ¼ 1 kHz
5.5 Correlator’s Mathematical Model in OEO MZ
263