Page 307 - Fiber Bragg Gratings

284 Chapter 6 Fiber Grating Band-pass Filters

gratings in each fiber. Fusing two fibers together creates a highly uniform
taper with excellent physical symmetry. A fused coupler with a grating
therefore has the potential of functioning as a device with the required
characteristics.
A variant on the fused taper device is shown in Fig. 6.41 (iv\ which
relies on the propagation constants of the two fibers being different [78].
However, the overlap of the modes and the grating becomes very large,
since the grating is in the entire waist region of the couple, and the fields
are bounded by air. A tilted grating will therefore act as a mode converter
when the Bragg matching condition is met,

where /^ and /3 2 are the propagation constants of the two odd and even
modes.
This device has been demonstrated by Kewitsch et al. [78] with two
identical fibers, one of which is pretapered as shown in Fig. 6.41 (iv) to
change the propagation constant. A grating written in the waist at 1547
nm "dropped" 98% of the light in a bandwidth of 0.7 nm with a reported
insertion loss of 0.1 dB. One problem with a fused taper device is the
coupling to radiation modes of the fiber on the short-wavelength side of
the Bragg wavelength, which can cause both cross-talk and loss.

6.7.2 Grating-frustrated coupler

The generic form of this device is shown in Fig. 6.41 (ii). The coupler
consists of two fibers, which are assumed to be parallel, and a single
Bragg grating is present in one waveguide alone. The grating-frustrated
coupler can be modeled in several ways. These methods include su-
permodes of the structure [80,76] or using the coupled-mode theory devel-
oped by Syms [81]. Syms's model applies to a grating in both regions of
the coupler and so has to be modified. In the following, the latter approach
has been taken to model this device.
The analysis is in two stages as in the analysis of Bragg gratings:
First, synchronous coupling is considered alone, i.e., at the Bragg-matched
wavelength, and then the detuned case is analyzed.
For synchronous operation, both fibers have identical effective mode
indexes at the Bragg wavelength: We ignore the perturbation introduced