342 CHAPTER 8. MULTICHANNEL SYSTEMS
filters can be tuned using thermo-optic tuning [38]. Micromechanical tuning has also
been used for InAlGaAs-based FP filters [39]. Such filters exhibited a tuning range of
40 nm with<0.35 nm bandwidth in the 1.55-μm region.
A chain of Mach–Zehnder (MZ) interferometers can also be used for making a
tunable optical filter. A MZ interferometer can be constructed simply by connecting
the two output ports of a 3-dB coupler to the two input ports of another 3-dB coupler
[see Fig. 8.8(b)]. The first coupler splits the input signal equally into two parts, which
acquire different phase shifts (if the arm lengths are made different) before they inter-
fere at the second coupler. Since the relative phase shift is wavelength dependent, the
transmittivityT(ν)is also wavelength dependent. In fact, we can use Eq. (7.5.5) to
find thatT(ν)=|H(ν)|^2 =cos^2 (πντ), whereν=ω/ 2 πis the frequency andτis the
relative delay in the two arms of the MZ interferometer [40]. A cascaded chain of such
MZ interferometers with relative delays adjusted suitably acts as an optical filter that
can be tuned by changing the arm lengths slightly. Mathematically, the transmittivity
of a chain ofMsuch interferometers is given by
T(ν)=M∏
m= 1cos^2 (πντm), (8.2.3)whereτmis the relative delay in themth member of the chain.
A commonly used method implements the relative delaysτmsuch that each MZ
stage blocks the alternate channels successively. This scheme requiresτm=( 2 m∆νch)−^1
for a channel spacing of∆νch. The resulting transmittivity of a 10-stage MZ chain has
channel selectivity as good as that offered by a FP filter having a finesse of 1600. More-
over, such a filter is capable of selecting closely spaced channels. The MZ chain can
be built by using fiber couplers or by using silica waveguides on a silicon substrate.
The silica-on-silicon technology was exploited extensively during the 1990s to make
many WDM components. Such devices are referred to asplanar lightwave circuitsbe-
cause they use planar optical waveguides formed on a silicon substrate [41]–[45]. The
underlying technology is sometimes called thesilicon optical-benchtechnology [44].
Tuning in MZ filters is realized through a chromium heater deposited on one arm of
each MZ interferometer (see Fig. 7.7). Since the tuning mechanism is thermal, it results
in a slow response with a switching time of about 1 ms.
A separate class of tunable optical filters makes use of the wavelength selectiv-
ity provided by a Bragg grating. Fiber Bragg gratings provide a simple example of
grating-based optical filters [46]; such filters have been discussed in Section 7.6. In its
simplest form, a fiber grating acts as a reflection filter whose central wavelength can
be controlled by changing the grating period, and whose bandwidth can be tailored by
changing the grating strength or by chirping the grating period slightly. The reflective
nature of fiber gratings is often a limitation in practice and requires the use of anop-
tical circulator. A phase shift in the middle of the grating can convert a fiber grating
into a narrowband transmission filter [47]. Many other schemes can be used to make
transmission filters based on fiber gratings. In one approach, fiber gratings are used
as mirrors of a FP filter, resulting in transmission filters whose free spectral range can
vary over a wide range 0.1–10 nm [48]. In another design, a grating is inserted in each
arm of a MZ interferometer to provide a transmission filter [46]. Other kinds of in-