Page 237 - Fiber Bragg Gratings

214 Chapters Apodization of Fiber Gratings

This is especially useful, since apodization and chirp can be programmed
in at the same time. A parameter that needs to be attended to while
fabricating a chirped grating is the loss in the amplitude of the refractive
index modulation. This must be compensated for, since otherwise the
grating will have a varying reflectivity as a function of wavelength. There
are two possibilities. The first one is to slow down both ly and v sc while
maintaining the ratio so that a stronger grating results as the grating is
chirped. Alternatively, the intensity of the writing beam may be increased
to take account of the reduction in the amplitude of the modulation index.
There is no published data available on the choice of either approach [20].
It is useful to consider the application of this technique in the fabrica-
tion of longer, chirped apodized gratings. Very much in the spirit of the
sine profile TH reflection grating and the superstructure grating, another
approach to the production of long chirped gratings uses a simple analogy
in Fourier transforms. A grating with a uniform period, modulated by a
low spatial frequency, pure sinusoidal envelope of period A e, will produce
two side bands only. This grating has the following refractive index ampli-
tude modulation profile:

where N and M are integers indicating the orders of the periods involved,
and 2/zA^o is the UV induced index change. Simplifying Eq. (5.2.11) di-
rectly leads to the resultant spatial frequencies,

There are only two spatial frequencies present, at the sum and differ-
ence frequencies. Note that in Eq. (5.2.12) the amplitude of the index
modulation for each spatial frequency has been halved and that two Bragg
reflections will occur. Note also that there can be higher order terms
according to the ratio of N and M. The next reflection will occur at roughly
half the fundamental Bragg wavelength, for N = M = 2, and at shorter
wavelengths for other orders, predicted here but not as yet reported in
the literature. The new reflections occur at a wavelength separation of