de l =dt ¼ G 0 e l n l À e l =T 0P ,
dn l =dt ¼ α N00 Á J 0L þ α N01 Á J 1L À
n l
T 1L
À G 0 n l e l ,
dφ L =dt ¼ 2πν 0P À 2πν 0 þ σ 0L þ ρ 0L e l ,
d
2 J 1L =dt
2
þ δ e dJ 1L =dt þ ð2π f 0e Þ
2 J 1L ¼ ðde L =dtÞδ e K 0DL de L ðt À T FOS Þ=dt:
8
> > > > <
> > > > :
ð5:36Þ
Taking into account the last transformations in DE (Eqs. 5.35 and 5.36), supposing that the nonlinear element slope is constant in the vicinity of small amplitude
deviations from the steady-state value, we obtain the following expression for
amplitude of AC component of QWLD emission intensity |e l1 | in the OEO closed
loop:
e l1
j j¼
K DL GS HY P L0
P L0 GK DL S HY
ð
Þ
2 cos 2 ωT FOS
ð
ÞþG
2 1þT
2
0P ωÀω 0L
ð
Þ
2
h
i
1þT
2
0e ωÀω 0e
ð
Þ
2
h
i
n
o 1=2 :
ð5:37Þ
The analysis of the last expression shows that the amplitude of AC component of
the square intensity of the laser optical emission |e l1 | (relatively, the amplitude of the
AC component of pumping current J 1L ¼ K DL e L ) in OEO depends not only on RF
circuit parameters, the time constant of the RF filter T 0e , the natural frequency of the
filter ω 0e , the average value of the nonlinear function slope S NF , but on the laser or
QWLD parameters. It depends also on the DC component of the QWLD output
power P L0 , the laser gain G, the natural frequency ω 0L of laser relaxation oscillations
(determined by the lifetime of active particles on the upper excited level, the
pumping excess over the threshold value and the gain), the photon lifetime in the
laser resonator T 0P . At that, at delay time T DL changing in the feedback circuit, the
phase incursion ωT DL changes of RF oscillations with ω, and the function |e l1 | is
periodic of the argument ωT DL . Expression (Eq. 5.37) well agrees with the expression for the amplitude of the oscillation square intensity (as well as for the expression
for gain) of QWLD presented in Chap. 3.
5.3.2 Simplified Estimation of the Setting Time of E
2
0L
intensity and the Pumping Current J L on the Base
of OEO Abbreviated Equations
In the primary analysis of dynamic features, we use abbreviated equations for the
laser enclosed by the positive feedback loop. The initial equation system for solution
of this problem is presented in this chapter under numbers (Eqs. 5.14, 5.15, and
5.18).
5.3 Dynamics of Transients in ОЕО DM and the Oscillation Amplitude
225
dn l =dt ¼ α N00 Á J 0L þ α N01 Á J 1L À
n l
T 1L
À G 0 n l e l ,
dφ L =dt ¼ 2πν 0P À 2πν 0 þ σ 0L þ ρ 0L e l ,
d
2 J 1L =dt
2
þ δ e dJ 1L =dt þ ð2π f 0e Þ
2 J 1L ¼ ðde L =dtÞδ e K 0DL de L ðt À T FOS Þ=dt:
8
> > > > <
> > > > :
ð5:36Þ
Taking into account the last transformations in DE (Eqs. 5.35 and 5.36), supposing that the nonlinear element slope is constant in the vicinity of small amplitude
deviations from the steady-state value, we obtain the following expression for
amplitude of AC component of QWLD emission intensity |e l1 | in the OEO closed
loop:
e l1
j j¼
K DL GS HY P L0
P L0 GK DL S HY
ð
Þ
2 cos 2 ωT FOS
ð
ÞþG
2 1þT
2
0P ωÀω 0L
ð
Þ
2
h
i
1þT
2
0e ωÀω 0e
ð
Þ
2
h
i
n
o 1=2 :
ð5:37Þ
The analysis of the last expression shows that the amplitude of AC component of
the square intensity of the laser optical emission |e l1 | (relatively, the amplitude of the
AC component of pumping current J 1L ¼ K DL e L ) in OEO depends not only on RF
circuit parameters, the time constant of the RF filter T 0e , the natural frequency of the
filter ω 0e , the average value of the nonlinear function slope S NF , but on the laser or
QWLD parameters. It depends also on the DC component of the QWLD output
power P L0 , the laser gain G, the natural frequency ω 0L of laser relaxation oscillations
(determined by the lifetime of active particles on the upper excited level, the
pumping excess over the threshold value and the gain), the photon lifetime in the
laser resonator T 0P . At that, at delay time T DL changing in the feedback circuit, the
phase incursion ωT DL changes of RF oscillations with ω, and the function |e l1 | is
periodic of the argument ωT DL . Expression (Eq. 5.37) well agrees with the expression for the amplitude of the oscillation square intensity (as well as for the expression
for gain) of QWLD presented in Chap. 3.
5.3.2 Simplified Estimation of the Setting Time of E
2
0L
intensity and the Pumping Current J L on the Base
of OEO Abbreviated Equations
In the primary analysis of dynamic features, we use abbreviated equations for the
laser enclosed by the positive feedback loop. The initial equation system for solution
of this problem is presented in this chapter under numbers (Eqs. 5.14, 5.15, and
5.18).
5.3 Dynamics of Transients in ОЕО DM and the Oscillation Amplitude
225