Page 318 - Fiber Bragg Gratings

6.9 Polarization rocking band-pass filter 295

long fiber filters, since the bend-induced birefringence is small (beat length
—0.75 m at 1550 nm) even with the tightest tolerable bend in standard
telecommunications fibers [102]. The reported filter had a polarization
coupling efficiency of ~100% at a peak wavelength of 1540 nm, with a
FW bandwidth of 130 nm, in a filter that was only 17 beat lengths long
(L r = 10.89 m), with 27% of each beat length exposed to UV radiation
(duty cycle of 27%).
The bandwidth of these filters between the first zeroes of the trans-
mission spectrum follows from Eq. (4.4.12) as

so that the bandwidth, 2AA, from Eq. (4.5.11)

The fabrication of the rocking filter depends on the periodic exposure
to UV radiation of half of the beat length of the fiber. This induces a
refractive index modulation, which is only half of what it would be if the
second half of the beat length was modulated by a negative index change,
or if the rocking of the birefringence was truly ± $ per beat length. This
has the beneficial effect of halving the filter length L r This is particularly
useful, because the rocking angle <f> saturates at approximately 0.4°-0.5°
per beat length with exposure to many pulses [105]. In order to overcome
this problem, Psaila et al. [105] used a double pass scheme to double the
rocking angle per beat length. In the first pass, the fiber was exposed at
45° to the birefringent axes, half of each beat length of 14 mm. The
stationary fiber was exposed to a moving, pulsed UV beam through a 0.5-
mm slit, with the UV polarization orthogonal to the fiber propagation
axis. On the second scan, the fiber was rotated by 90° around the propaga-
tion axis, and the other half of the beat length was exposed in a similar
manner. The result is the doubling of the rocking angle per beat length,
leading to a rocking filter with —98% conversion efficiency, only 33 beat
lengths long, and with a FWFZ (full width to first zeroes) bandwidth of
20 nm.
It should be noted that the polarization coupler is a band-pass filter
in transmission and that it converts either input polarization to its orthog-
onal state. As a consequence of this, a concatenation of two such filters
results in a Mach-Zehnder type interferometer [106]. A schematic of this