Page 113 - Fiber Bragg Gratings

92 Chapter 3 Fabrication of Bragg Gratings

where n av is the average index of the mode. It follows, therefore, from
Eqs. (3.1.20) and (3.1.21) that the new grating periods A~ and Ajr corres-
ponding to the superscripted Bragg wavelengths are

From Eqs. (3.1.4) and (3.1.22), it follows that the spacing AA between
the reflected wavelengths in any such superstructure is

Depending on the shape of the composite structure (and thus the magni-
tudes of the individual Fourier components), higher order components
can appear [87].
Superstructure gratings represent a number of types of gratings: the
DFB with a single phase step 4> < ZTT [85,86]; the grating Fabry-Perot
with (f> > 2 77 resulting in multiple high-finesse transmission peaks [89];
cascaded grating Fabry-Perots in which the phase steps (f> > 277- [87],
leading to replicated multi-band-pass transmission spectra; gratings with
multiple-flat-top reflection spectra, fabricated with unequal grating
lengths as well as phase steps [90]; and truly flat-top reflection gratings
fabricated by introducing regular 77/2 phase shifts (A/4) at equal intervals,
while altering the strength of the grating amplitude in each section to
mimic a sine function [91].
There are several methods of making these gratings. In order to
introduce a specific phase step, the simplest and most reliable is via the
replication of a phase mask with the appropriately prerecorded phase
steps [92]. Another method successfully used for introducing a 77/2 phase
step in a grating is by UV postprocessing [84]. After the grating has been
written, the small central section is illuminated with UV radiation to
introduce a phase shift. As the refractive index of the exposed region of
length SI increases by Sn, the transmission spectrum of the grating is
monitored to stop the exposure when SnSl = A/4. A disadvantage of post-
UV exposure is that it not only changes the phase between the two halves
of the grating, but also alters the local n eff of the fiber. This in turn
shifts the Bragg wavelength of the already-written grating exposed to UV