Page 110 - Fiber Bragg Gratings

3.1 Methods for fiber Bragg grating fabrication 89

The shift in the wavelength of the gratings is dependent on the overall
change in the index of modulation, resulting in a change in the period
averaged n eff of the mode in the fiber. The shift A\ Bragg in the Bragg
wavelength, A Bragg as the UV induce index change 8n increases can be
shown to be

where 77 < 1, is the overlap of the guided mode and the distribution of
the refractive index modulation (see Chapter 4). Thus, when a grating is
superimposed on an already-written grating, both gratings move to longer
Bragg wavelengths.
By altering the angle of the interfering beams, several gratings may
be written at a single location using the prism interferometer or the
Lloyd mirror arrangement discussed in Section 3.1.6. These gratings show
interesting narrow band-pass features with uniform period [77] or chirped
gratings [78], and are discussed in Chapter 6.
If the temperature distribution along the length of a uniform grating
is a linear function of length, then the Bragg wavelength, too, will vary
linearly with length. The grating will demonstrate a linear chirp. This
means that the different wavelengths within the bandwidth of the grating
will not be reflected from the same physical location and the grating will
behave as a dispersive component. The temperature profile (or the strain
profile) may be altered to change the functional property of the grating
[79]. On the other hand, prestraining or imposing a temperature profile
along a fiber prior to writing a fiber grating will also result in a chirped
fiber grating once it is written and the stress/temperature profile is re-
moved [80,81]. However, the chirp in a grating fabricated in such a way
will have the opposite sign of a grating chirped by the application of a
temperature or strain profile after it has been manufactured.
During fabrication of the grating at an elevated temperature T w, the
Bragg wavelength will be defined by the period, A^ of the grating. After
fabrication, when the temperature is returned to a final temperature Tf,
the Bragg wavelength will be

where a is the thermal expansion coefficient of the fiber and dn eff/dT is
the temperature coefficient of the mode index; to the first approximation,