Page 281 - Fiber Bragg Gratings

258 Chapter 6 Fiber Grating Band-pass Filters

Figure 6.27: Band-pass and reflection spectra with two identically chirped
gratings (L g = 5 mm, chirp = 10 nm, and AL^ = 1.724 mm).

When the sign of the chirp of one of the gratings is reversed, the
band-pass transmission characteristics change from regular repeated pass
bands to a variable pass band. The path difference between the two grat-
ings is reduced to zero at some wavelength. A gap opens at this point and
the transmission is no longer uniform as in the previous cases. Ignoring
dispersion, the phase difference between the light reflected from these
two weakly reflecting, chirped gratings with a chirp of AA^ nm relative
to the wavelength A 0 in the center of the grating, is

where L g is the length of the grating. It is apparent from Eq. (6.3.11) that
the detuning 8 = 0 when

If AZy = 0, S — 0 at the wavelength A = A 0. For a fixed chirp bandwidth,
the detuning can be reduced to zero at any wavelength within the band-
width of the grating by tuning AL^. In Eq. (6.3.11) we have assumed that
the lengths of the two gratings are identical. This need not be the case;
it is enough that the bandwidth are identical, so that we have the extra
parameter that can be adjusted. This also applies to the previous cases
in which the sign of the chirp for both gratings was identical. The pass-