the appropriate codes. Figure 3.20a shows the example of solution (Eq. 3.64) with
values of K 0FODL /Q EF ¼ 3, 1/Q EF ¼ 0.05, m 00 π/2 ¼ 0, β 00 ¼ 5.1. The example of
(Eq. 3.64) solution for K 0FODL /Q EF ¼ À2.5, 1/Q EF ¼ 0.05, m 00 π/2 ¼ π/2,
β 00 ¼ À10.5 is presented in Fig. 3.20b.
The example of (Eq. 3.64) solution is shown in Fig. 3.21a for values: K 0FODL /
Q EF ¼ 5, 1/Q EF ¼ 0.05, m 00 π/2 ¼ 0, β 00 ¼ 10.1. From solution analysis we can make
a conclusion that at sine nonlinearity or at MZ “quadrature” mode, the “soft” selfexcitation mode of OEO is possible, which is caused by the disturbance of OEO
stability conditions. We can also conclude that at cosine nonlinearity, there is the
“rigid” self-excitation mode only or at MZ operation in the “non-quadrature” mode.
At large modulation indices (Fig. 3.21b, c), β 00 ¼ 10.5, and at the gain K 0FODL /
Q EF ¼ 2.5, the nonlinearity cos[m 00 π/2 + β 00 x], m 00 π/2 ¼ π/4, for 1/Q EF ¼ 0.01,
there is the rigid OEO self-excitation only. At that, zones of possible steady-state
values broaden, and their transients depend on initial conditions.
Plots of the resonance characteristics of OEO MZ i.e., functions of the oscillation
amplitude U 10MZ of OEO MZ versus the generation frequency s ¼ j( f/f 0e ) are
presented in Figs. 3.20 and 3.21. Figure 3.15 shows functions of the DC component
of the optical emission and the AC component of fundamental harmonic in the MZ
output. Numbers “1” and “2” designate the values of constant relative DC bias
voltage in the “quadrature” and “non-quadrature” modes. They are equal, relatively,
0.5 and 1.0 and correspond in Fig. 3.15 to phases φ 0MZ ¼
πU 0MZ
U 0MZπ
¼ π=2 and π,
relatively. At that, we should note that at OEO MZ excitation in the quadrature
mode, when the excitation conditions are fulfilled, OEO MZ begins to generate at the
cosine nonlinearity. We may speak about the soft mode of excitation. In this case, in
Fig. 3.19 The graphical
method for frequency and
amplitude determination in
the OEO steady-state mode
3.4 Equations of Amplitude and Phase Balance for the Laser and for OEO
125
values of K 0FODL /Q EF ¼ 3, 1/Q EF ¼ 0.05, m 00 π/2 ¼ 0, β 00 ¼ 5.1. The example of
(Eq. 3.64) solution for K 0FODL /Q EF ¼ À2.5, 1/Q EF ¼ 0.05, m 00 π/2 ¼ π/2,
β 00 ¼ À10.5 is presented in Fig. 3.20b.
The example of (Eq. 3.64) solution is shown in Fig. 3.21a for values: K 0FODL /
Q EF ¼ 5, 1/Q EF ¼ 0.05, m 00 π/2 ¼ 0, β 00 ¼ 10.1. From solution analysis we can make
a conclusion that at sine nonlinearity or at MZ “quadrature” mode, the “soft” selfexcitation mode of OEO is possible, which is caused by the disturbance of OEO
stability conditions. We can also conclude that at cosine nonlinearity, there is the
“rigid” self-excitation mode only or at MZ operation in the “non-quadrature” mode.
At large modulation indices (Fig. 3.21b, c), β 00 ¼ 10.5, and at the gain K 0FODL /
Q EF ¼ 2.5, the nonlinearity cos[m 00 π/2 + β 00 x], m 00 π/2 ¼ π/4, for 1/Q EF ¼ 0.01,
there is the rigid OEO self-excitation only. At that, zones of possible steady-state
values broaden, and their transients depend on initial conditions.
Plots of the resonance characteristics of OEO MZ i.e., functions of the oscillation
amplitude U 10MZ of OEO MZ versus the generation frequency s ¼ j( f/f 0e ) are
presented in Figs. 3.20 and 3.21. Figure 3.15 shows functions of the DC component
of the optical emission and the AC component of fundamental harmonic in the MZ
output. Numbers “1” and “2” designate the values of constant relative DC bias
voltage in the “quadrature” and “non-quadrature” modes. They are equal, relatively,
0.5 and 1.0 and correspond in Fig. 3.15 to phases φ 0MZ ¼
πU 0MZ
U 0MZπ
¼ π=2 and π,
relatively. At that, we should note that at OEO MZ excitation in the quadrature
mode, when the excitation conditions are fulfilled, OEO MZ begins to generate at the
cosine nonlinearity. We may speak about the soft mode of excitation. In this case, in
Fig. 3.19 The graphical
method for frequency and
amplitude determination in
the OEO steady-state mode
3.4 Equations of Amplitude and Phase Balance for the Laser and for OEO
125