Page 181 - Fiber Bragg Gratings

158 Chapter 4 Theory of Fiber Bragg Gratings

Figure 4.14 shows a schematic of the blazed "side-tap" grating written
in the core of an optical fiber. The guided mode shown on the LHS of the
figure can couple to the radiation field or to a "supermode" of a composite
waveguide formed by the cladding and air interface. These are shown as
a field distribution leaving the core at an angle and as a mode of the
waveguide formed by the cladding, respectively. While the radiated fields
form a continuum if unbounded [see Eq. (4.2.5)], they evolve into the bound
supermodes of the composite waveguide in the presence of a cladding.
The power in the radiated field and the radiated bound mode may grow
provided the overlap of the interacting fields and the transverse distribu-
tion of the "source" (refractive index perturbation) is nonzero (see Section
4.2.3). The exchange of energy between the core mode and the radiated
bound supermode is determined by the prevailing phase-matching condi-
tions discussed in Section 4.2.5 and is solely a coherent interaction; the
coupling to the unbound continuum of the radiation field is, however, only
partly governed by this requirement. Physically, the radiated field exiting
from the fiber core at a nonzero angle is spread away so that the distance
over which it is coupled to the driving field is limited. This may be under-
stood by the following: The driving mode field amplitude, which is assumed
to be spatially constant, overlaps with a radiation field that is spreading

Figure 4.14: Schematic of counter-propagating radiation field and bound
cladding mode coupling from a forward propagating guided mode with a blazed
grating.