8.2. WDM COMPONENTS 341
whereNis the number of channels,ηsis the spectral efficiency, andBis the bit rate.
At the same time, the filter bandwidth∆νFP(the width of the transmission peak in
Fig. 8.7) should be large enough to pass the entire frequency contents of the selected
channel. Typically,∆νFP∼B. The number of channels is thus limited by
N<ηs(∆νL/∆νFP)=ηsF, (8.2.2)whereF=∆νL/∆νFPis thefinesseof the FP filter. The concept of finesse is well
known in the theory of FP interferometers [32]. If internal losses are neglected, the
finesse is given byF=π
√
R/( 1 −R)and is determined solely by the mirror reflectivity
R, assumed to be the same for both mirrors [32].
Equation (8.2.2) provides a remarkably simple condition for the number of chan-
nels that a FP filter can resolve. As an example, ifηs=^13 , a FP filter with 99% reflecting
mirrors can select up to 104 channels. Channel selection is made by changing the fil-
ter lengthLelectronically. The length needs to be changed by only a fraction of the
wavelength to tune the filter. The filter lengthLitself is determined from Eq. (8.2.1)
together with the condition∆νL>∆νsig. As an example, for a 10-channel WDM signal
with 0.8-nm channel spacing,∆νsig≈1 THz. Ifng= 1 .5 is used for the group index,
Lshould be smaller than 100μm. Such a short length together with the requirement
of high mirror reflectivities underscores the complexity of the design of FP filters for
WDM applications.
A practical all-fiber design of FP filters uses the air gap between two optical fibers
(see Fig. 8.8). The two fiber ends forming the gap are coated to act as high-reflectivity
mirrors [33]. The entire structure is enclosed in a piezoelectric chamber so that the gap
length can be changed electronically for tuning and selecting a specific channel. The
advantage of fiber FP filters is that they can be integrated within the system without
incurring coupling losses. Such filters were used in commercial WDM fiber links start-
ing in 1996. The number of channels is typically limited to below 100 (F≈155 for the
98% mirror reflectivity) but can be increased using two FP filters in tandem. Although
tuning is relatively slow because of the mechanical nature of the tuning mechanism, it
suffices for some applications.
Tunable FP filters can also be made using several other materials such as liquid
crystals and semiconductor waveguides [34]–[39]. Liquid-crystal-based filters make
use of the anisotropic nature of liquid crystals that makes it possible to change the
refractive index electronically. A FP cavity is still formed by enclosing the liquid-
crystal material within two high-reflectivity mirrors, but the tuning is done by changing
the refractive index rather than the cavity length. Such FP filters can provide high
finesse (F∼300) with a bandwidth of about 0.2 nm [34]. They can be tuned electrically
over 50 nm, but switching time is typically∼1 ms or more when nematic liquid crystals
are used. It can be reduced to below 10μs by using smectic liquid crystals [35].
Thin dielectric films are commonly used for making narrow-band interference fil-
ters [36]. The basic idea is quite simple. A stack of suitably designed thin films acts
as a high-reflectivity mirror. If two such mirrors are separated by a spacer dielectric
layer, a FP cavity is formed that acts as an optical filter. The bandpass response can
be tailored for a multicavity filter formed by using multiple thin-film mirrors separated
by several spacer layers. Tuning can be realized in several different ways. In one ap-
proach, an InGaAsP/InP waveguide permits electronic tuning [37]. Silicon-based FP