Page 309 - Fiber Bragg Gratings

286 Chapter 6 Fiber Grating Band-pass Filters

3. We assume that there is no coupling between modes 1 and 4, 4
and 1, 2 and 3, and 3 and 2.
Taking the above considerations into account, the four coupled-mode equa-
tions which describe the coupling are

A similar procedure is followed as in the BRC coupler, and applying
the boundary conditions results in the outputs of the device [82]. The
grating-frustrated coupler works best when port 1 is excited (the fiber
without the grating) with the grating extending along the entire coupling
length and beyond, and with a coupler KL C = 77/2. With this value of
coupling, 100% of the power is transferred from one fiber to the other at
a wavelength far removed from the Bragg condition, i.e., the device func-
tions as a normal coupler. On-Bragg, the frustrated coupling depends on
the strength of the grating coupling constant. The dependence of the
transmission and reflection characteristics for port 1 excitation on the
grating coupling strength is shown in Fig. 6.42.
Figure 6.43 shows the theoretical performance of a device similar to
the one reported by Archambault et al. [83], with approximately 70% in
the dropped port. Note that with increasing xL c (over the coupling length),
the on-Bragg wavelength transmission approaches unity, and the reflected
power tends to zero. In practice, in-fiber gratings are limited to index
3
modulations of ~10~ , resulting in /cL c =* 10 for a coupling length of
~4 mm. Thus, the performance of this device is likely to remain limited,
however elegant the principle, since the return loss remains high and
dropped power will suffer a loss of ~1 dB, despite the insertion loss being
intrinsically low (0.2 dB).
Figure 6.44 shows the transmission characteristics of a GFC with a
3
K acL c = 9(Sn = 2.75 X 10~ , andL c - 1.57 mm). The FWHM bandwidth
is in excess of 4 nm, the pass-band transmission is >0.9, and the transmis-