argE 12L ¼ arctg
k 01 sin φ 1 þ k 02 sin φ 2
k 01 cos φ 1 þ k 02 cos φ 2
&
'
¼ arctg
sin φ 1 þ γ sin φ 2
cos φ 1 þ γ cos φ 2
&
'
ð3:31Þ
Plots of the module and arguments of the transfer function of MZ modulator are
presented in Fig. 3.14.
We attract the reader’s attention that in the expression for |E 12L |
2 the phase
φ 0L1 (u g ) is modulated by the harmonic oscillation u g (t) ¼ U 1MZ cos
[2πf 0 t + ϕ 0e + φ em (t)]:
E 12L
j
j
2 ¼
E
2
0L
2
γ
1 þ γ
2
ð
Þ
2γ
À cos φ 0L1 u g
À Á À φ 0L2
Â
Ã
&
:
ð3:32Þ
If to assume that excitation of MZ optical channels is uniform, we may suppose
that
1þγ
2
ð
Þ
2γ
% 1 and using the trigonometric formula of the double angle, we can
write:
1.0
0.1;0.9
k 01 = 0
K
12 (j)
arg K
12L (j)
0.2;0.8
0.3;0.7
0.4;0.6
0.5
0.5
0
Phase (Radian)
π/2
2π
π
0
0
0.47
0.3
0.55
0.8
0.5j 00
1.5j 00
k 01 = 0
k 01 = 1
j 00
Phase (Radian)
π/2
2π
π
Fig. 3.14 The plot of
module and argument of the
transfer function of the MZ
modulator
104 3 Modulation Methods of Laser Emission in Optoelectronic oscillator (OEO) and OEO. . .