"Introduction". In: Fiber-Optic Communication Systems

296 CHAPTER 7. DISPERSION MANAGEMENT

Wavelength (nm)

Delay (ps)

Transmission

Figure 7.10: Transmittivity (dashed curve) and time delay (solid curve) as a function of wave-
length for a uniform-pitch grating for whichκ(z)varies linearly from 0 to 6 cm−^1 over the 11-cm
length. (After Ref. [61];©c1996 IEE; reprinted with permission.)

7.6.2 Chirped Fiber Gratings.....................

Chirped fiber gratings have a relatively broad stop band and were proposed for disper-
sion compensation as early as 1987 [65]. The optical period ̄nΛin a chirped grating is
not constant but changes over its length [51]. Since the Bragg wavelength (λB=2 ̄nΛ)
also varies along the grating length, different frequency components of an incident op-
tical pulse are reflected at different points, depending on where the Bragg condition is
satisfied locally. In essence, the stop band of a chirped fiber grating results from over-
lapping of many mini stop bands, each shifted as the Bragg wavelength shifts along the
grating. The resulting stop band can be as wide as a few nanometers.
It is easy to understand the operation of a chirped fiber grating from Fig. 7.11,
where the low-frequency components of a pulse are delayed more because of increasing
optical period (and the Bragg wavelength). This situation corresponds to anomalous
GVD. The same grating can provide normal GVD if it is flipped (or if the light is
incident from the right). Thus, the optical period ̄nΛof the grating should decrease for
it to provide normal GVD. From this simple picture, the dispersion parameterDgof
a chirped grating of lengthLgcan be determined by using the relationTR=DgLg∆λ,
whereTRis the round-trip time inside the grating and∆λis the difference in the Bragg
wavelengths at the two ends of the grating. SinceTR=2 ̄nLg/c, the grating dispersion
is given by a remarkably simple expression,

Dg=2 ̄n/c(∆λ). (7.6.6)

As an example,Dg≈ 5 × 107 ps/(km-nm) for a grating bandwidth∆λ= 0 .2 nm. Be-
cause of such large values ofDg, a 10-cm-long chirped grating can compensate for the
GVD acquired over 300 km of standard fiber.