Page 254 - Fiber Bragg Gratings

6.1 Distributed feedback, Fabry-Perot, superstructure, and moire gratings 231

From conservation of energy, we find that the reflectivity

Note that in general both grating sections need not be placed symmet-
rically around the phase step and that the gratings may have different
bandwidths and refractive index modulation amplitudes. However, the
simple band-pass filter has, in the center of a uniform grating, a 77/2
phase step, which has the effect of introducing a single pass-band in the
transmission spectrum. In this case, T\± = (Tf 2)*, and T\± = Tf lt Figure
6.2 shows the band-pass spectrum of two 3-mm-long gratings, each with
a quarter-wavelength step in the center. The amplitudes of the refractive
3
4
index modulation are 5 X 10~ and 10~ . Notice that although there is
a very narrow transmission band in the center of the grating spectrum
within a band stop of ~1 nm, there are strong side lobes on either side.
The band pass is a highly selective filter within a relatively narrow band
stop. A uniform grating of the same length but without the phase step
has a bandwidth approximately half that of the full band stop of the DFB
grating. The DFB grating may be viewed as being composed of two single
gratings, each half the length of a uniform one.
The phase mask allows the replication of phase-shifted DFB struc-
tures into fibers in a simple and controlled manner [6]. This has been
done successfully to produce a variety of band-pass DFB structures, and

Figure 6.2: The calculated transmission spectrum of 3-mm-long DFB grat-
4
ings, with a A/4 phase-step and refractive index modulation 5 X 10~ for the
3
dashed line and 10 ~ for the continuous line, respectively.