satisfied and the laser generation can be excited only in the “rigid” manner, which is
initiated by the pulse from external source.
When the А point is unstable, the process of oscillation growth is developed in the
oscillating system, which are restricted by the nonlinearity of the RF amplifier and
there are conditions for the limit cycle existence for RF oscillations. The stability of
this cycle is determined by the sign of the partial derivatives of right parts over the
one variable at analysis of the characteristic equation obtained in Chap. 4. The limit
cycle is stable if the appropriate expressions for coefficients are more than zero.
The phase plane of the oscillator with rigid excitation having the stable limit cycle
is more complicate, at that, the number of singular points (interception point of
isoclinic lines F 1 (N L ) and F 2 (E L )) is even and existence of lengthy generation of
Fig. 5.4 Phase portraits in the “soft” mode of oscillation setting in OEO DM (a). The phase portrait
of the normalized square strength (E)
2 ¼ (E 0L )
2 and the population difference N (a, b). Y-axis—the
normalized square strength (or the intensity), Х-axis—the population. The scale on the Y-axis is
1.0 ¼ 1 (V/m)
2
. The scale on the Х-axis is 1.0 ¼ 1 mW. N (1.0 point on the scale is 10
18 1/cm
3
). (с)
The enlarged image of the phase portrait is shown and the transient development with the exit to the
limit cycle on the time diagram E 0L , N 0 . The scale on the time axis t is 5 points ¼ 0.1 ns
230
5 Optoelectronic oscillator (OEO) Differential Equations as the Laser System with. . .
initiated by the pulse from external source.
When the А point is unstable, the process of oscillation growth is developed in the
oscillating system, which are restricted by the nonlinearity of the RF amplifier and
there are conditions for the limit cycle existence for RF oscillations. The stability of
this cycle is determined by the sign of the partial derivatives of right parts over the
one variable at analysis of the characteristic equation obtained in Chap. 4. The limit
cycle is stable if the appropriate expressions for coefficients are more than zero.
The phase plane of the oscillator with rigid excitation having the stable limit cycle
is more complicate, at that, the number of singular points (interception point of
isoclinic lines F 1 (N L ) and F 2 (E L )) is even and existence of lengthy generation of
Fig. 5.4 Phase portraits in the “soft” mode of oscillation setting in OEO DM (a). The phase portrait
of the normalized square strength (E)
2 ¼ (E 0L )
2 and the population difference N (a, b). Y-axis—the
normalized square strength (or the intensity), Х-axis—the population. The scale on the Y-axis is
1.0 ¼ 1 (V/m)
2
. The scale on the Х-axis is 1.0 ¼ 1 mW. N (1.0 point on the scale is 10
18 1/cm
3
). (с)
The enlarged image of the phase portrait is shown and the transient development with the exit to the
limit cycle on the time diagram E 0L , N 0 . The scale on the time axis t is 5 points ¼ 0.1 ns
230
5 Optoelectronic oscillator (OEO) Differential Equations as the Laser System with. . .