frequency. To this moment, the problems of OEO oscillation stability and selfexcitation, the research of the laser parameters’ influence on the OEO oscillations.
In the future, for solution of mentioned problems, we shall address to OEO differential equations examination taking into account the laser presence at its consideration in quasi-classical approximation on the base of the double-level model in the
dipole assumption.
3.5 Conclusions
This chapter is devoted to investigation of modulation methods of laser emission, to
formation of the mathematical model of the autonomous OEO on the base of
differential equations. We describe some methods, which allow obtaining of the
extremely low phase noise level in OEO or to “transform” it into the ultralow-noise
Plots of sample individual solutions:
y
y
y(0) = 1
y′(0) = 0
t
y′
y
y
y(0) = 0
y′(0) = 1
a)
b)
c)
d)
t
y′
Plots of sample individual solutions:
y
y
y(0) = 1
y′(0) = 0
t
y′
y
y
y(0) = 0
y′(0) = 1
t
y′
Plots of sample individual solutions:
y
y
y(0) = 1
y′(0) = 0
t
y′
y
y
y(0) = 0
y′(0) = 1
t
y′
Plots of sample individual solutions:
y
y
y(0) = 1
y′(0) = 0
t
y′
y
y
y(0) = 0
y′(0) = 1
t
y′
y′′(t) + 0.01y′(t) + y(t) + 0 = 0 –2.5cos
–2 y(t)
π
4
y′′(t) + 0.01y′(t) + y(t) + 0 = 0 –2.5cos
–10.5 y(t)
π
4
y′′(t) + 0.01y′(t) + y(t) + 0 = 2.5 cos(10.5 y(t) + 6.9115) + 0
y′′(t) + 0.01y′(t) + y(t) + 0 = 5 cos(10.1 y(t)) + 0.0005
Fig. 3.22 Examples of OEO MZ differential equations solution with the cosine nonlinearity at
Q EF ¼ 100 at different values of MX bias DC voltage for various gains. Above figures, there are the
solvable equations for K 0FOLD /Q EF ¼ 5, nonlinearity Àcos[π/4 À β 00 x], β 00 ¼ 2.0 (a), K 0FOLD /
Q EF ¼ 2.5, nonlinearity cos[β 00 x + 6.91], β 00 ¼ 10.5 (b), K 0FOLD /Q EF ¼ 5, nonlinearity cos[β 00 x],
β 00 ¼ 10.1 (c), K 0FOLD /Q EF ¼ 5, nonlinearity Àcos[π/4 À β 00 x], β 00 ¼ 10.5 (d)
128 3 Modulation Methods of Laser Emission in Optoelectronic oscillator (OEO) and OEO. . .