Page 441 - Fiber Bragg Gratings

418 Chapter 9 Measurement and Characterization of Gratings

The agreement between measurement and theory is very good, with
the zeroes matching across almost the entire spectrum shown. Notice the
slight deviations, especially at the first side-lobe zero (RHS), and the third
side-lobe zero (LHS). These features are indicative of slight chirp and
nonuniformity in the writing process. Nevertheless, this grating has
~28,000 grating periods and shows a near-ideal response. One way to
measure such a narrow bandwidth is to use a high-quality tunable laser
source and a spectrum analyzer for reasons of resolution. It is difficult to
measure such gratings accurately in transmission with a broadband
source, since the bandwidth is almost the same as that of commercially
available optical spectrum analyzers (0.07 nm FWHZ). Although this
grating has a transmission dip of ~14 dB, the spectrum remains unre-
solved in transmission with a spectrum analyzer.
Gratings with such performance are particularly useful where the
phase response is required along with the reflection characteristics in
filtering applications, such as in pulse shaping and dark soliton generation
[4].

9.3 Phase and temporal response of Bragg
gratings

Figure 9.11 shows the computed reflection and accumulated phase-spec-
trum of a uniform-period unapodized Bragg grating. The measurement
of phase of a grating can only be made by the measurement of the grating's
complex amplitude reflectivity. A technique has been proposed for the
reconstruction of the phase of the grating using arguments based on
causality and minimum phase performed on the measured reflection spec-
trum of a grating, with reasonable success [5]. This may be done by
using interferometric techniques to characterize weak gratings (<20%
reflectivity) [6-9]. These measurements have at best limited spatial reso-
lution, or are difficult to implement, being interferometric. Other more
direct methods include the use of a network analyzer for the measurement
of dispersion [10,11]. The use of the network analyzer relies on the disper-
sion being constant over the frequency region of interest, and strictly it
is better suited to measuring apodized chirped gratings. This technique
has been applied to gratings to measure their dispersion [12,13]. Another
method for testing of a grating or phase mask uses a probe transverse to
the grating [14].