7.6. FIBER BRAGG GRATINGS 297
Figure 7.11: Dispersion compensation by a linearly chirped fiber grating: (a) index profilen(z)
along the grating length; (b) reflection of low and high frequencies at different locations within
the grating because of variations in the Bragg wavelength.
Chirped fiber gratings have been fabricated by using several different methods [51].
It is important to note that it is the optical period ̄nΛthat needs to be varied along
the grating (zaxis), and thus chirping can be induced either by varying the physical
grating periodΛor by changing the effective mode index ̄nalongz. In the commonly
useddual-beam holographic technique, the fringe spacing of the interference pattern
is made nonuniform by using dissimilar curvatures for the interfering wavefronts [66],
resulting inΛvariations. In practice, cylindrical lenses are used in one or both arms
of the interferometer. In adouble-exposure technique[67], a moving mask is used to
vary ̄nalongzduring the first exposure. A uniform-period grating is then written over
the same section of the fiber by using thephase-mask technique. Many other variations
are possible. For example, chirped fiber gratings have been fabricated by tilting or
stretching the fiber, by using strain or temperature gradients, and by stitching together
multiple uniform sections.
The potential of chirped fiber gratings for dispersion compensation was demon-
strated during the 1990s in several transmission experiments [68]–[73]. In 1994, GVD
compensation over 160 km of standard fiber at 10 and 20 Gb/s was realized [69]. In
1995, a 12-cm-long chirped grating was used to compensate GVD over 270 km of fiber
at 10 Gb/s [70]. Later, the transmission distance was increased to 400 km using a 10-
cm-long apodized chirped fiber grating [71]. This is a remarkable performance by an
optical filter that is only 10 cm long. Note also from Eq. (7.1.2) that the transmission
distance is limited to only 20 km in the absence of dispersion compensation.
Figure 7.12 shows the measured reflectivity and the group delay (related to the
phase derivativedφ/dω) as a function of the wavelength for the 10-cm-long grating
with a bandwidth∆λ= 0 .12 nm chosen to ensure that the 10-Gb/s signal fits within
the stop band of the grating. For such a grating, the periodΛchanges by only 0.008%
over its entire length. Perfect dispersion compensation occurs in the spectral range