5.3 Dynamics of Transients in ОЕО DM and the Oscillation
Amplitude
Let us determine the expression for the OEO oscillation amplitude in the smallsignal single-frequency mode with the help of abbreviated equation obtained in Sect.
5.1.3, and analyze the main features of transients’ dynamics in OEO DM.
We shall use deduced differential equations (Eq. 5.18) for the laser enclosed by
the positive feedback loop. For analysis convenience, we write once more the system
of differential equation (Eq. 5.18) with specified values of the slowly changing
functions of the normalized square strength E
2
0L , phase φ and the population
difference N(t), as well as the AC component of the laser pumping current J L :
A
B
A = (
+
)(1+β 0L )·
1
10
5
–0.6
–0.4
–0.2
0.2
0.4
0.6
–5
–10
1
Q 0EF Q 0L
A = (
+
) –1 · B
1
1
Q 0EF Q 0L
1
B
+ (
+
) –1 B
1
1
Q 0EF Q 0L
Im E L
Re E L
Re E L
_E L _
M
Im E L
G_E_
ψ m
(a)
(b)
(c)
Fig. 5.2 Plots of quantities A and B region of OEO DM oscillation stability for Q 0L ¼ 10,
Q 0EF ¼ 100 and β 0L ¼ 0.01 without account of the nonlinear inertia property of the OEO nonlinear
element (a). Representation of the laser field strength as the vector with the module |E L | and the
argument without account of fluctuation φ ¼ arg E L (E n ¼ E L ) (b). The same with account of
fluctuations (c)
5.3 Dynamics of Transients in ОЕО DM and the Oscillation Amplitude
223
Amplitude
Let us determine the expression for the OEO oscillation amplitude in the smallsignal single-frequency mode with the help of abbreviated equation obtained in Sect.
5.1.3, and analyze the main features of transients’ dynamics in OEO DM.
We shall use deduced differential equations (Eq. 5.18) for the laser enclosed by
the positive feedback loop. For analysis convenience, we write once more the system
of differential equation (Eq. 5.18) with specified values of the slowly changing
functions of the normalized square strength E
2
0L , phase φ and the population
difference N(t), as well as the AC component of the laser pumping current J L :
A
B
A = (
+
)(1+β 0L )·
1
10
5
–0.6
–0.4
–0.2
0.2
0.4
0.6
–5
–10
1
Q 0EF Q 0L
A = (
+
) –1 · B
1
1
Q 0EF Q 0L
1
B
+ (
+
) –1 B
1
1
Q 0EF Q 0L
Im E L
Re E L
Re E L
_E L _
M
Im E L
G_E_
ψ m
(a)
(b)
(c)
Fig. 5.2 Plots of quantities A and B region of OEO DM oscillation stability for Q 0L ¼ 10,
Q 0EF ¼ 100 and β 0L ¼ 0.01 without account of the nonlinear inertia property of the OEO nonlinear
element (a). Representation of the laser field strength as the vector with the module |E L | and the
argument without account of fluctuation φ ¼ arg E L (E n ¼ E L ) (b). The same with account of
fluctuations (c)
5.3 Dynamics of Transients in ОЕО DM and the Oscillation Amplitude
223