Page 174 - Fiber Bragg Gratings

4.5 Polarization couplers: Rocking filters 151

Remembering that <5Ae/Ae = 2n av(8kn')/(2n avhn\ with Skn' = &n x
- An y,

where B is the difference in the refractive index of the principle axes.
For the special case of 6 = 77/4, Eq. (4.5.6) simplifies to <f> = 6&n'/
(25). A rotation that changes sign over one beat length implies a change
in the rotation of 20 radians per beat length so that the coupling constant,
^ac>

and remembering that B = \IL b leads to

where A is the resonance wavelength. The coupler length L r is given by
the distance at which the input polarization is rotated by 77/2, from which
it follows that

Substituting Eq. (4.5.8) into Eq. (4.5.9), we get the rotation length
for 100% polarization conversion as

In order to calculate the bandwidth between the first zeroes of the
transmission spectrum, we note the argument of Eq. (4.4.12), aL r = ±TT,
which leads to

Using typical figures for the reported changes in the birefringence
[36,37,35,31], at a wavelength of 1550 nm, we find that the rocking filter
has a length of ~0.5 m. Note that the coupler length is only dependent
on the wavelength of operation and the induced birefringence, but not