Page 194 - Fiber Bragg Gratings

4.7 Radiation mode couplers 171

cladding. Two important parameters, the FWHM bandwidth and the tilt
angle for zero back reflection into the fundamental mode for step index
fibers for different u-values, are shown. The trend is as follows. Small core-
cladding index difference and large u-value give the smallest radiation loss
bandwidths, as well as the smallest tilt angles and accordingly the lowest
polarization sensitivity. The penalty is the increased bend loss sensitivity.

4.7.2 Copropagating radiation mode coupling: Long-
period gratings

These gratings couple light from forward-propagating guided modes to
the forward-propagating cladding modes (as with an LPG) and the radia-
tion field.
A schematic of the interaction and the phase-matching condition for
coupling to forward-propagating radiation modes is shown in Fig. 4.24.
The mode-coupling equations for forward coupling are given in Section
4.4 [Eqs. (4.4.11) and (4.4.12)]. The overlap integrals governing the inter-
action are shown in Eqs. (4.4.14M4.4.17) with the appropriate phase-
matching terms. This type of coupling is similar to counterpropagating
interactions, so far as the overlap of the modes is concerned. However,
the power is exchanged between the radiated and guided modes periodi-
cally, as shown in Fig. 4.9, so that the filter length governs the bandwidth

Figure 4.24: Schematic of co-propagating radiation field and bound cladding
mode coupling from a forward propagating guided mode with a blazed grating.