nonlinearity (nonlinear element) with detuned resonance circuits, there is a phenomenon of frequency pulling by the circuit with the higher Q-factor. Figure 4.6 shows
the typical fragmentation of the phase plane at Q 1 > Q 2 /2 (b) and at Q 2 > Q 1 /2 (c).
At Q 1 > Q 2 /2 the double-frequency mode with amplitudes U 10 , U 20 is established in
the system (b), while at Q 2 > Q 1 /2 the single-frequency mode with amplitudes U 20
and U 10 ¼ 0 (c) occurs. The feature of our investigation of the QWLD model is the
fact that we only consider the case of the single-frequency generation at equality of
fundamental frequency of both circuits.
4.2.5 Analog Laser DEs Model
The analog model (АМ) of the DE system (4.17) with utilization of operator transfer
functions (4.18)–(4.22) is presented in Fig. 4.7. The analog model contains of two
closed feedback loops: for strength E n and for population. There are three multipliers
in this model. In the moment t ¼ 0, the “stepped” pumping pulse passes in the input
of an adder. From this moment, the population increases to the threshold value and at
achievement of this threshold, the laser generation occurs. In the closed FB loop,
oscillations excite and then it passes to the output.
The analog model reflects the functional connection of the laser model parameters. This model gives us the understanding how the oscillation amplitude is settled
Fig. 4.5 Solutions of abbreviated equations for population N and for normalized slowly changing
amplitudes of the first harmonics of strength E 10n and polarization P 10n for pumping excess by
seven times than the threshold value. The time is normalized to the carrier lifetime on the upper
operating level T 1 . The frequency detuning ν 0n and ν 12 is 0.01, Q-factors are Q OF ¼ 50 and
Q 02 ¼ 33. The normalized time t/T 1 is on the abscissa axis
148
4 Semiclassical Theory and Laser Differential Equations for Optoelectronic. . .
the typical fragmentation of the phase plane at Q 1 > Q 2 /2 (b) and at Q 2 > Q 1 /2 (c).
At Q 1 > Q 2 /2 the double-frequency mode with amplitudes U 10 , U 20 is established in
the system (b), while at Q 2 > Q 1 /2 the single-frequency mode with amplitudes U 20
and U 10 ¼ 0 (c) occurs. The feature of our investigation of the QWLD model is the
fact that we only consider the case of the single-frequency generation at equality of
fundamental frequency of both circuits.
4.2.5 Analog Laser DEs Model
The analog model (АМ) of the DE system (4.17) with utilization of operator transfer
functions (4.18)–(4.22) is presented in Fig. 4.7. The analog model contains of two
closed feedback loops: for strength E n and for population. There are three multipliers
in this model. In the moment t ¼ 0, the “stepped” pumping pulse passes in the input
of an adder. From this moment, the population increases to the threshold value and at
achievement of this threshold, the laser generation occurs. In the closed FB loop,
oscillations excite and then it passes to the output.
The analog model reflects the functional connection of the laser model parameters. This model gives us the understanding how the oscillation amplitude is settled
Fig. 4.5 Solutions of abbreviated equations for population N and for normalized slowly changing
amplitudes of the first harmonics of strength E 10n and polarization P 10n for pumping excess by
seven times than the threshold value. The time is normalized to the carrier lifetime on the upper
operating level T 1 . The frequency detuning ν 0n and ν 12 is 0.01, Q-factors are Q OF ¼ 50 and
Q 02 ¼ 33. The normalized time t/T 1 is on the abscissa axis
148
4 Semiclassical Theory and Laser Differential Equations for Optoelectronic. . .