Page 259 - Fiber Bragg Gratings

236 Chapter 6 Fiber Grating Band-pass Filters

appears that the ratio for the sections C = 2 is an asymptotic value for
a flat-top band-pass filter. Increasing this ratio introduces a ripple in the
band pass as a result of the individual band-pass peaks separating, while
reducing it narrows the bandwidth of the pass band, also reducing the
transmission. The ripple in the pass band may be kept between 1% and
5% for a ratio of 1.8 < C < 2.6.
The bandwidth of the band pass is inversely dependent on the cou-
pling constant. In order to maintain a reasonable bandwidth of the filter,
coupling constants must remain low (/cL ~ 1), as should the grating section
(Li < 1 mm). For example, in the three-section grating, section lengths
of 0.5 and 1 mm with a /cL x = 1.4 will result in a bandwidth of —0.25
nm.
These results change with larger number of sections. For example,
Fig. 6.7A shows the transmission spectrum for a grating with a KL l —
1.4, but with a FWHM bandwidth of —0.1 nm. The bandwidth is exactly
the same as the single-phase-step DFB grating shown in Fig. 6.4B, but
the square top shows that the roll-off is steeper for the larger number of
sections [12]. A major concern is the trade-off between the bandwidth
and extinction. For many filter applications, an extinction of >30 dB is
necessary. This requirement immediately points to a r<L > 4.16. Therefore,
this filter may not be an ideal candidate, since both requirements may
be difficult to achieve.
Fiber Bragg gratings with multiple phase-shifted sections have been
realized for band-pass applications. Bhakti and Sansonetti [13] have mod-
eled the response of gratings with up to eight phase-shifted sections. The
design strategy was for an optimized band-pass filter with a — 0.8-nm
bandwidth, as well as negligible in-band ripple. Increasing the number
of sections was shown to make the pass band more rectangular, but re-
duced the stopped bandwidth. An asymptotic value for the band-stop
bandwidth is approached with greater than 5 phase shifts and is twice
the pass bandwidth. This is another severe limitation on the use of such
filters. Phase masks with the appropriate quarter-wavelength shifts [6]
were used to replicate a three-phase-shift grating. With careful UV illumi-
nation, the band pass was fully resolved and showed excellent agreement
with theory [13]. The band-pass/stop widths were 0.88 nm/2.77 nm with
a peak rejection of 13 dB. The optimized grating length were L v = L 4 =
0.22 mm and L 2 = L 3 = 0.502 mm, with a refractive index modulation
3
amplitude of 1.5 X 10~ .