Page 178 - Fiber Optic Communications Fund

Optical Modulators and Modulation Schemes 159

The desired Mach–Zehnder output power is

{
P 0 for bit ‘1’
P out = . (4.75)
0 for bit ‘0’
For bit ‘1’, substituting Eq. (4.74) in Eq. (4.73) and using Eq. (4.75), we obtain

[ ]
m(t) V bias
2
P cos − = P ,
0
0
V 2V
V V bias
− = j, j = 0, ±1, ±2, … (4.76)
V 2V
Similarly, for bit ‘0’,
[ ]
m(t) V
2 bias
P cos − = 0,
0
V 2V

−V V bias l
− = , l =±1, ±3, … (4.77)
V 2V 2

Subtracting Eq. (4.77) from Eq. (4.76), we find
( l ) V
V = j − . (4.78)
2 2
Addition of Eqs. (4.76) and (4.77) leads to

( l )
V =− j + V . (4.79)
bias
2
If we choose j = 0 and l =−1, we find

V
V = , (4.80)
4
V
V bias = . (4.81)
2
Thus, the polar NRZ in an electrical domain becomes a unipolar NRZ in an optical domain, as shown in
Fig. 4.19. The process of modulation can be visualized using Fig. 4.20. When V = V ∕4 corresponding to

bit ‘1’, constructive interference occurs and the MZM power transmission is at its peak. When V =−V ∕4,

destructive interference occurs and the MZM power output is zero. There are two approaches for the gen-
eration of RZ-ASK. The first approach is to apply the message signal, which is a polar RZ, as shown in
Fig. 4.21(a). The output of the MZ modulator will be a RZ-ASK signal. However, the achievable bit rate is
limited to 10 Gb/s using this approach [8]. The second approach is to introduce a RZ pulse carver in series
with a MZ modulator, as shown in Fig. 4.21(b). The pulse carvers can be realized by driving the MZ mod-
ulator with a sinusoidal electrical signal [8]. The advantage of the second approach is that higher bit rates
(≥40 Gb/s) can be realized.