Page 415 - Fiber Optic Communications Fund

396 Fiber Optic Communications

[ co1 ]
A out,1
A co1 = . (9.33)
out
A co1
out,2
Optical fields in the upper and lower arms of the interferometer undergo phase shifts k(L +ΔL∕2) and k(L −
ΔL∕2), respectively, where k is the propagation constant and ΔL is the path-length difference between two
arms. Therefore, the inputs of the 3-dB coupler 2 can be written as

A 0
A co2 = √ exp [ik(L +ΔL∕2)], (9.34)
in,1
2
iA 0
co2
A = √ exp [ik(L −ΔL∕2)]. (9.35)
in,2
2
The outputs of the 3-dB coupler are
co2 co2
A = M A , (9.36)
out coupler in
A co2 = A exp (ikL)i sin (kΔL∕2), (9.37)
out,1 0
A co2 = A exp (ikL)i cos (kΔL∕2). (9.38)
out,2 0
The corresponding output powers are
2
2
2
P = |A co2 | = A sin (kΔL∕2), (9.39)
out,1 out,1 0
2
2
2
P out,2 = |A co2 | = A cos (kΔL∕2). (9.40)
0
out,2
Fig. 9.7 shows the power transmittances of ports 1 and 2. At a specific frequency, the power transmittance of
port 1 is maximum and at the same frequency, the power transmittance of port 2 is zero. This implies that if
the channel frequencies of a two-channel WDM system coincide with the frequencies corresponding to the
peak power transmittances of ports 1 and 2, they can be separated.

1 Port 1
Power transmittance (Arb. units)
Port 2

0 20 40 60 80 100 120 140 160 180 200
Relative frequency (GHz)

Figure 9.7 Power transmittance as a function of frequency deviation from the reference frequency of 194.8 THz.