Page 174 - Fiber Optic Communications Fund

Optical Modulators and Modulation Schemes 155

where V bias is a constant bias voltage. This driving condition is known as a balanced driving or push–pull
operation. Let V (t) be the message signal m(t). Using Eq. (4.54) in Eqs. (4.48) and (4.52) and ignoring
1
constant phase shift, we obtain
{[ ] }
V bias
A out = A cos m(t)− , (4.55)
0
2 V
{[ ] }
V bias
2
P = P cos m(t)− . (4.56)
out 0
2 V

Let us consider two cases: (i) V bias = V ∕2 and (ii) V bias = V .

Case (i) V bias = V ∕2. Let

[ ]
m(t)
A out = A cos −
0
V 4
[ ( ) ( )]
A 0 m(t) m(t)
= √ cos + sin . (4.57)
2 V V
When m(t) ≪ V ∕,

[ ] [ ]
m(t) m(t) m(t)
cos ≅ 1 and sin ≅ . (4.58)
V V V
Therefore, we have
[ ]
A 0 m(t)
1 + exp (−i2f t). (4.59)
out = √ V c
2
The above equation corresponds to an amplitude modulated (AM) wave used in commercial AM broadcasting.
Thus, in the small signal limit and with V bias = V ∕2, the MZ modulator acts as an AM modulator.

Case (ii) V bias = V . Now, Eq. (4.55) becomes

[ ]
m(t)
A out = A sin . (4.60)
0
V
When m(t)∕V ≪ 1,

( )
A
0
out = m(t) exp (−i2f t). (4.61)
c
V
Now, the MZM acts as a product modulator which multiplies the message signal and optical carrier. The above
equation also corresponds to a form of AM modulation known as double sideband with suppressed carrier
(DSB-SC). The output power in the small-signal limit is

2 2
A
0
2
P ≅ m (t). (4.62)
out 2
V