Page 312 - Fiber Bragg Gratings

6.8 Side-tap and long-period grating band-pass filters 289

and the guided mode over the long grating length (centimeters), with a
bounded cladding. With an unbounded cladding, the loss spectrum of the
LPG becomes extremely wide (>100 nm) [87], since the dispersion in (rc eff
verv
~ ^cladding) is weak. Figures 6.45a and b show light exiting from the
side of a fiber by an STG and an LPG. The cladding mode has a better
chance of interacting with the LPG. A ray exiting the core at an angle of
10° to the fiber axis will travel —0.4 mm before being reflected back toward
the grating in a 125-yum diameter fiber. Shallower angle rays may miss
the STG altogether after the first reflection at the cladding-air interface.
This is less likely in the LPG, which may be 2-10 times longer than a
typical STG. Therefore, there may be continual exchange of energy be-
tween the radiated mode and the guided mode with the LPG, unless the
cladding is made "infinite" by applying index-matching oil to the cladding.
Instead of coupling to discrete radiation modes (approximately the same
as the cladding modes), light is coupled to a continuum of the radiation
field, so that a broadband loss spectrum is seen in transmission rather
than a narrow bandwidth of the cladding mode [87].
Note that the angular distribution of the radiation for the LPG as a
function of wavelength is reversed compared to the STG; i.e., the longest
wavelengths exit at the largest angle (see Chapter 4).
The basic principle of the coupling relies on the phase-matching condi-
tions, and the overlap integrals determine the strength and the wave-

Figure 6.45: Light radiated from the STG and (b) from the LPG.