Page 180 - Fiber Bragg Gratings

4.7 Radiation mode couplers 157

Close to the edge of the band stop, strong dispersion can be seen with
increasing strength of the grating. However, this dispersion is limited to
a small bandwidth. At the center of the band, the group delay is a mini-
mum and is approximately l/(2/c acL^) for gratings with a reflectivity close
to 100%.

4.7 Radiation mode couplers

4.7.1 Counterpropagating radiation mode coupler:
The side-tap grating
These gratings couple from a forward-propagating guided mode to a back-
ward-propagating cladding mode, or a continuum of radiation modes. In
this section, a new and simple theory is presented to gain a physical
insight into the scattering of a guided mode into the counterpropagating
radiation modes. The theory for radiation mode coupling has been pre-
sented elsewhere by various authors: Marcuse [2], Erdogan and Sipe [38],
Mizrahi and Sipe [39], Erdogan [40], and Morey and Love [41], These
articles explain the phenomenon of radiation mode coupling using coupled
mode theory and have successfully described the short-wavelength radia-
tion loss from unblazed gratings [39], as well as the fine detailed spectrum
observed under cladding mode resonance in tilted gratings [38,40]. Sur-
prisingly little work has been reported on the application of these gratings.
The term "side-tap" is appropriate for such gratings since the radiation
is tapped from the side of the fiber, as happens when bending a fiber. A
particular difference from bending is the reduced bandwidth and wave-
length selectivity of the loss induced by such blazed gratings. Important
properties of blazed gratings are their stability and low intrinsic tempera-
ture sensitivity, which may be reduced even further by appropriate design
of fiber or coating [42,43]. Although the reflectivity into the counterpropa-
gating guided mode is not generally zero, for acceptable performance in
practical applications, it can be made very low by careful design of the
filter.
The intention of this section is to provide a physical insight into the
functioning of blazed gratings with the purpose of intentionally designing
filters, which predominantly exhibit only radiation loss. The potential
applications are numerous, e.g., in-fiber noninvasive taps, spectrum ana-
lyzers [44], and gain flattening of optical amplifiers using a single blazed
grating [45] and multiple blazed gratings [46] and mode converters [47].