292 CHAPTER 7. DISPERSION MANAGEMENT
Figure 7.7: (a) A planar lightwave circuit made using of a chain of Mach–Zehnder interferome-
ters; (b) unfolded view of the device. (After Ref. [56];©c1996 IEEE; reprinted with permission.)
A Mach–Zehnder (MZ) interferometer can also act as an optical filter. An all-fiber
MZ interferometer can be constructed by connecting two 3-dB directional couplers in
series, as shown schematically in Fig. 7.7(b). The first coupler splits the input signal
into two equal parts, which acquire different phase shifts if arm lengths are different,
before they interfere at the second coupler. The signal may exit from either of the two
output ports depending on its frequency and the arm lengths. It is easy to show that the
transfer function for the bar port is given by [54]
HMZ(ω)=^12 [ 1 +exp(iωτ)], (7.5.5)whereτis the extra delay in the longer arm of the MZ interferometer.
A single MZ interferometer does not act as an optical equalizer but a cascaded chain
of several MZ interferometers forms an excellent equalizing filter [55]. Such filters
have been fabricated in the form of aplanar lightwave circuitby using silica wave-
guides [56]. Figure 7.7(a) shows the device schematically. The device is 52×71 mm^2
in size and exhibits a chip loss of 8 dB. It consists of 12 couplers with asymmetric
arm lengths that are cascaded in series. A chromium heater is deposited on one arm
of each MZ interferometer to provide thermo-optic control of the optical phase. The
main advantage of such a device is that its dispersion-equalization characteristics can
be controlled by changing the arm lengths and the number of MZ interferometers.
The operation of the MZ filter can be understood from the unfolded view shown in
Fig. 7.7(b). The device is designed such that the higher-frequency components prop-
agate in the longer arm of the MZ interferometers. As a result, they experience more
delay than the lower-frequency components taking the shorter route. The relative delay
introduced by such a device is just the opposite of that introduced by an optical fiber
in the anomalous-dispersion regime. The transfer functionH(ω)can be obtained an-