Page 109 - Fiber Bragg Gratings

88 Chapter 3 Fabrication of Bragg Gratings

maximum change in the period is a single period over the length of the
UV writing spot, as

where w is the radius of the spot used for writing the short section of
grating. Combining Eqs. (3.1.11) and (3.1.12) gives the following interest-
ing relationship:

Equation (3.1.13) suggests the use of a minimum spot size related to the
relative velocities. Further, it should be noted that at any one time, an
entire grating of spot size 2,w is written with a constant amplitude and
period. In the limit, this method trades in some of the refractive index
modulation for chirp, but can at best imprint a quasi-stepped function
instead of a continuous one, especially when the grating is being apodized.

3.1.13 Timing of the Bragg wavelength, moire,
Fabry-Perot, and superstructure gratings

The effective index of a propagating mode in a fiber is both temperature
and strain sensitive. The functional dependence of the mode index is given
by the relationship

where dn/dT is the temperature coefficient of refractive index, AT" is the
change in temperature, dn/dcr is the longitudinal stress optic coefficient,
and A<r is the applied longitudinal stress. Since the Bragg wavelength is
a function of n eff [see Eq. (3.1.4)], the simplest method of altering the
transfer characteristics of a fiber grating is to impose a temperature or
strain profile along the length of the grating. However, prestraining a
fiber during grating fabrication alters the Bragg grating wavelength in
the relaxed state [7]. It is also possible to multiplex several gratings at
the same location to form moire type gratings [7,77]. It should be noted
that the Bragg wavelengths of all multiplexed gratings written at the
same location shift to longer wavelengths as each grating is superimposed.