Page 223 - Fiber Bragg Gratings

200 Chapter 5 Apodization of Fiber Gratings

gratings have an associated dispersion that may not be desirable for high-
speed applications, unless the grating length is much less than the length
of the pulse in the fiber, in which case the grating becomes a point reflector.

5.2.1 Self-apodization
Figure 5.3 shows the region of overlap of two monochromatic UV beams
with intensities I± and 7 2 with a mutual angle 6 m. The intensity I(z) at
any point z along the z-axis varies according to the phase-difference be-
tween the two beams and can be shown to be

where the term in brackets is the mutual phase difference between the
two beams, and L g is the length of the overlap, where a fiber grating can
form. The function is periodically modulated, and its visibility is

determined by the maximum and minimum intensities in the fringes.
The visibility is unity along the entire length L g only if the radiation is
monochromatic and the amplitudes of the two beams are identical.
If the UV radiation is composed of two monochromatic frequencies,
then the interference pattern is the sum of Eq. (5.2.1) for the frequencies

Figure 5.3: The overlap of two beams in the z direction.