Page 192 - Fiber Bragg Gratings

4.7 Radiation mode couplers 169

Figure 4.21: Comparison of back reflection from two fibers: both have nomi-
nally the same u-values, but one has a photosensitive cladding only (after Ref.
[52]).

We note that the first back reflection minimum occurs at ~3° external
writing angle for the photosensitive cladding fiber, compared with 8° for
the standard fiber. This has an additional benefit of reducing the band-
width over which radiation loss occurs, as seen from the phase-matching
diagram in Section 4.2.5.
In Fig. 4.22 is shown the filter response for coupling to radiation
modes for the photosensitive cladding fiber. The benefit of making the
cladding photosensitive is clear, since it reduces the bandwidth at the
zero reflection writing angle (measured at 3° and calculated for the fiber
to be —3.6°). The core radius of this fiber is 3.4 /zm, and the photosensitive
cladding extends from a to 4a.
The agreement between the theoretical and experimentally observed
properties of tilted fiber Bragg gratings is extremely good [38] using the
complete theory presented by Erdogan [40,38]. In particular, the measured
peak visible at 1545 nm in Fig. 4.22 is shown to be due to leaky mode
coupling. The polarization dependence of tilted Bragg gratings in fibers
with a core radius of ~2.6 /mi and a core-to-cladding refractive index
3
difference of 5.5 X 10 ~ becomes obvious as the tilt angle exceeds 6.5°
[38]. Above this angle, thep-polarization scatters less efficiently than the
s-polarization. Below a tilt angle of 6.5°, the radiation loss is predomi-
nantly due to coupling to even-azimuthal order radiation modes, giving