Page 184 - Fiber Bragg Gratings

4.7 Radiation mode couplers 161

sensitivity and strain. This allows the design of filters that depend only
on the properties of the guidance of the core.
The side-tap grating is modeled as a periodic collection of uniform
inclined planes of perturbed refractive index across the core. The mode
fields are defined by the wave-guiding parameters, but it is assumed for
the grating that the boundary of the cladding is absent; i.e., the grating
is written in an infinite medium, although it is itself confined to the core.
A consequence of this approximation is that refraction at the core-cladding
boundary may be ignored, but can be accounted for later, to form modes.
The assumption allows the design of filters in the same way in which the
Bragg grating can be modified. The physical phenomenon of scattering
is treated as Fraunhofer diffraction, with the amplitude of the scattering
obeying the laws of conservation of energy. Figure 4.17 shows the sche-
matic of the blazed grating. The mathematical description that follows
shows that this type of a grating is equivalent to an infinite sum of
small gratings written perpendicular to the axis of the fiber, but has an
azimuthal dependence that makes it possible to couple to a particular set
of radiation modes. In other words, the ^-dependence of the grating due
to the inclination of the planes is translated into a transverse variation
in refractive index modulation, with the result that it immediately con-
nects with the idea of the mode overlap integral, while separating the

Figure 4.17: Scattering of power from a blazed grating entirely embedded
in a cylinder.