On the base of OEO differential equations (Eq. 5.35), the analog model of OEO
was constructed presented in Figs. 2.2 and 5.1a.
On the base of Eq. (5.35) and the mentioned analog model, the dependences of
the population, the square of strength of optical emission and the AC component of
the QWLD pumping current in transient at impact of stepwise pumping at the closed
positive feedback loop in OEO. The time-functions of the square strength, the
population, the pumping current, and phase portraits in the soft mode of RF
oscillation setting in OEO with the direct modulation of the laser pumping current
are presented in Fig. 5.3.
The one of difficulties at solution of Eq. (5.35) finding at the analog modeling is
the determination of the nonlinearity of the RF nonlinear amplifier (A) in order to
“compensate of the multiplicative QWLD nonlinearity.”
At modeling of laser differential equations (Eq. 5.35), we use the following
values of parameters (the same as in Chap. 3) for the mesa-strip laser with the
thickness of the dielectric film d ¼ 1.2 μm: g 0 ¼ 10
3 , τ D ¼ 7.2 Á 10
À12 s, I thr ¼ 12 mA,
ε sh ¼ 0. The values of parameters of QWLD are: the lifetime of carriers
T 1 ¼ τ n1 ¼ 0.5 Á 10
À9 s, the threshold level population difference is 10
18 1/cm
3 ,
the lifetime of photons or the time constant of the optical resonator
T 0F ¼ τ ph ¼ 1.2 Á 10
À12 s, the volume of the QWLD active zone is 10
À11 cm
À3 .
We investigated transient processes of oscillation setting in OEO without and
with delay (Fig. 5.4) in the loop of positive feedback.
As the result of computer modeling, it is stated that the transient process of the
exit to the OEO generation mode is accompanied by ripples. Plots are presented in
Fig. 5.6. At large oscillation amplitude of the square strength, the strong nonlinear
distortions are arisen, which are caused by the laser multiplicative nonlinearity.
The level of nonlinear distortions depends upon a choice the DC pumping
current. The setting time of laser oscillations is 0.8 ns (or from 0 to 40 point in
Fig. 5.3a–c). The setting time of OEO RF oscillations is on the time axis t of 40 ns
(or from 50 to 100 points in Fig. 5.3e). The period of laser ripples in the transients
equaled about 0.4 ns depends upon the pumping current level and is determined by
the lifetime of carriers. The frequency of RF oscillation in the steady-state mode is
close to the natural frequency RF filter (F) and was 4–10 GHz (the oscillation period
is 0.25–0.1 ns) and depended on a choice of the natural frequency of the RF filter.
5.3.4 General Remarks About the Limit Cycle Realization
in the Closed OEO DM System of the Laser Emission
The transient is realized in the case if the singular point is the stable knot, i.e.,
characteristic roots р 1 and р 2 are real and negative. In order to the singular point А
(the focus) becomes unstable (i.e., characteristic roots р 1 and р 2 must be positive), it
is necessary to intensify the positive feedback. At that, the unstable point А in
enclosed by the stable limit cycle, which is shown in Fig. 5.4. This means that during
228
5 Optoelectronic oscillator (OEO) Differential Equations as the Laser System with. . .
was constructed presented in Figs. 2.2 and 5.1a.
On the base of Eq. (5.35) and the mentioned analog model, the dependences of
the population, the square of strength of optical emission and the AC component of
the QWLD pumping current in transient at impact of stepwise pumping at the closed
positive feedback loop in OEO. The time-functions of the square strength, the
population, the pumping current, and phase portraits in the soft mode of RF
oscillation setting in OEO with the direct modulation of the laser pumping current
are presented in Fig. 5.3.
The one of difficulties at solution of Eq. (5.35) finding at the analog modeling is
the determination of the nonlinearity of the RF nonlinear amplifier (A) in order to
“compensate of the multiplicative QWLD nonlinearity.”
At modeling of laser differential equations (Eq. 5.35), we use the following
values of parameters (the same as in Chap. 3) for the mesa-strip laser with the
thickness of the dielectric film d ¼ 1.2 μm: g 0 ¼ 10
3 , τ D ¼ 7.2 Á 10
À12 s, I thr ¼ 12 mA,
ε sh ¼ 0. The values of parameters of QWLD are: the lifetime of carriers
T 1 ¼ τ n1 ¼ 0.5 Á 10
À9 s, the threshold level population difference is 10
18 1/cm
3 ,
the lifetime of photons or the time constant of the optical resonator
T 0F ¼ τ ph ¼ 1.2 Á 10
À12 s, the volume of the QWLD active zone is 10
À11 cm
À3 .
We investigated transient processes of oscillation setting in OEO without and
with delay (Fig. 5.4) in the loop of positive feedback.
As the result of computer modeling, it is stated that the transient process of the
exit to the OEO generation mode is accompanied by ripples. Plots are presented in
Fig. 5.6. At large oscillation amplitude of the square strength, the strong nonlinear
distortions are arisen, which are caused by the laser multiplicative nonlinearity.
The level of nonlinear distortions depends upon a choice the DC pumping
current. The setting time of laser oscillations is 0.8 ns (or from 0 to 40 point in
Fig. 5.3a–c). The setting time of OEO RF oscillations is on the time axis t of 40 ns
(or from 50 to 100 points in Fig. 5.3e). The period of laser ripples in the transients
equaled about 0.4 ns depends upon the pumping current level and is determined by
the lifetime of carriers. The frequency of RF oscillation in the steady-state mode is
close to the natural frequency RF filter (F) and was 4–10 GHz (the oscillation period
is 0.25–0.1 ns) and depended on a choice of the natural frequency of the RF filter.
5.3.4 General Remarks About the Limit Cycle Realization
in the Closed OEO DM System of the Laser Emission
The transient is realized in the case if the singular point is the stable knot, i.e.,
characteristic roots р 1 and р 2 are real and negative. In order to the singular point А
(the focus) becomes unstable (i.e., characteristic roots р 1 and р 2 must be positive), it
is necessary to intensify the positive feedback. At that, the unstable point А in
enclosed by the stable limit cycle, which is shown in Fig. 5.4. This means that during
228
5 Optoelectronic oscillator (OEO) Differential Equations as the Laser System with. . .