Page 279 - Fiber Bragg Gratings

256 Chapter 6 Fiber Grating Band-pass Filters

Figure 6.24: The apodized reflection (dashed line) and band pass (continuous
line) of the asymmetric Michelson interferometer, with a path difference of 2.67
mm. The output is sinusoidal as in the case of a low-finesse FP interferometer.

two beam as a function of phase difference, hence the sinusoidal variation,
also the case with the low-finesse FP interferometer. The wavelength
difference <5A between the peaks of the band pass is

where A$A) is the differential phase of the two gratings, which becomes
important when the gratings are dissimilar, for example, chirped. Using
Eq. (6.3.10) one can calculate the exact number of pass bands within the
bandwidth of the gratings. Note that with Bragg-wavelength detuned
gratings, the resultant bandwidth for the pass bands is the difference
between the individual bandwidths of the gratings. The measured re-
sponse of such a filter is shown in Fig. 6.25. The extinction is 28 dB.
There are three possible combinations for arranging chirped gratings
in the Michelson interferometer: both gratings with the same sign of the
chirp, either both positive or both negative, or with opposite chirp. In Fig.
6.26, the first two arrangements are shown (A and B). The difference
between A and B is that the dispersion of the gratings has been reversed,
and that a pair of such filters may be used to compensate for most of the
dispersion in each filter.
The transmission band pass of the identical-sign, linearly chirped
grating Michelson interferometer with AL^- = 1.724 mm is shown in Fig.
6.27. The gratings are 5 mm long with a chirped bandwidth of 10 nm.