7.5. OPTICAL FILTERS 291
Figure 7.6: Dispersion management in a long-haul fiber link using optical filters after each
amplifier. Filters compensate for GVD and also reduce amplifier noise.
Optical filters can be made using an interferometer which, by its very nature, is
sensitive to the frequency of the input light and acts as an optical filter because of its
frequency-dependent transmission characteristics. A simple example is provided by the
Fabry–Perot (FP) interferometer encountered in Sections 3.3.2 and 6.2.1 in the context
of a laser cavity. In fact, the transmission spectrum|HFP|^2 of a FP interferometer
can be obtained from Eq. (6.2.1) by settingG=1 if losses per pass are negligible.
For dispersion compensation, we need the frequency dependence of the phase of the
transfer functionH(ω), which can be obtained by considering multiple round trips
between the two mirrors. A reflective FP interferometer, known as theGires–Tournois
interferometer, is designed with a back mirror that is 100% reflective. Its transfer
function is given by [52]
HFP(ω)=H 01 +rexp(−iωT)
1 +rexp(iωT), (7.5.3)
where the constantH 0 takes into account all losses,|r|^2 is the front-mirror reflectivity,
andTis the round-trip time within the FP cavity. Since|HFP(ω)|is frequency inde-
pendent, only the spectral phase is modified by the FP filter. However, the phaseφ(ω)
ofHFP(ω)is far from ideal. It is a periodic function that peaks at the FP resonances
(longitudinal-mode frequencies of Section 3.3.2). In the vicinity of each peak, a spec-
tral region exists in which the phase variation is nearly quadratic. By expandingφ(ω)
in a Taylor series,φ 2 is given by
φ 2 = 2 T^2 r( 1 −r)/( 1 +r)^3. (7.5.4)As an example, for a 2-cm-long FP cavity withr= 0 .8,φ 2 ≈2200 ps^2. Such a filter
can compensate the GVD acquired over 110 km of standard fiber. In a 1991 experi-
ment [53], such an all-fiber device was used to transmit a 8-Gb/s signal over 130 km
of standard fiber. The relatively high insertion loss of 8 dB was compensated by using
an optical amplifier. A loss of 6 dB was due to a 3-dB fiber coupler used to separate
the reflected signal from the incident signal. This amount can be reduced to about 1 dB
using an optical circulator, a three-port device that transfers power one port to another
in a circular fashion. Even then, relatively high losses and narrow bandwidths of FP
filters limit their use in practical lightwave systems.