Page 259 - Fiber Optic Communications Fund

240 Fiber Optic Communications

where is the common phase of both polarizations. Owing to fluctuations in ambient properties, the matrix
c
M changes with time. Typically, the rate of change of the matrix elements of M is much slower than the
transmission data rate. Therefore, the matrix elements can be estimated using digital signal processing, which
is discussed in Chapter 11.
Let the output of the local oscillator be
[ ]
q LO,x
q = , (5.151)
LO q LO,y
A LO
q LO,j = √ exp [−i( LO t + LO )], j = x or y. (5.152)
2

Fig. 5.39 shows a schematic of the receiver. The x- and y-components of the received field and LO output are
separated using polarization beam splitters PBS1 and PBS2, respectively. The x-components of the received
∘
field and the LO output are combined using a 2 × 490 optical hybrid and pass through the four photodetectors
as discussed in Section 5.6.4. With =Δ = 0, the outputs I and I are given by
IF I,x Q,x
RA A
T LO
I = Re [M s + M s ], (5.153)
I,x xx x xy y
2

I I+,x
PBS1
q r q r,x + I I,x
Σ
I ‒
q r,y I*,x
2 × 4 90 o
optical hybrid I Q+,x
PBS2
q LO + I Q,x
Σ
q LO,x
‒
q LO,y I Q*,x

I I+,y
+ I
Σ I,y
‒
I I*,y
2 × 4 90 o
optical hybrid I Q+,y
+ I Q,y
Σ
‒
I Q*,y

Figure 5.39 Block diagram of a dual polarization IQ receiver PBS = polarization beam splitter, LO = local oscillator.