Nonlinear Fiber Optics - 4 ed. Agrawal

6.3. Evolution of Polarization State 195
Figure 6.7: Effective beat length as a function of input power for beams polarized along the fast
(solid line) and slow (dashed line) axes. (After Ref. [34]; c○1986 OSA.)
Figure 6.7 shows how LB
eff varies with p for θ = 0◦ and θ = 90 ◦ . The effective beat
length becomes infinite when P 0 = P cr and θ = 90 ◦ because of complete cancellation
between the linear and nonlinear birefringences [35]. This is the origin of polarization
instability. The critical power level P cr at which LB
eff becomes infinite is the same at
which the number of fixed points on the Poincaré sphere changes from 2 to 4. Thus,
polarization instability can be interpreted in terms of the emergence of elliptically polarized
fixed points on the Poincaré sphere. The two viewpoints are identical.
As a result of large changes in LB eff , the output polarization state can change drastically
when P 0 is close to P cr and the input beam is polarized close to the fast axis.
Figure 6.8 shows the transmittivity T p as a function of the input power for several values
of θ after assuming that a crossed polarizer at the fiber output blocks the light at
low intensities (see Figure 6.1). When θ = 0 ◦ or 90 ◦ , T p remains zero at all power
levels. Small changes in θ near the slow axis still keep T p near zero. However, T p
changes dramatically when θ is changed slightly near the fast axis. Note the extreme
sensitivity of T p to the input polarization angle as θ is varied from 89 ◦ to 90 ◦ . Figure
6.8 is drawn for the case (Δβ)L = 2π or L = L B . However, the qualitative behavior
remains the same for other fiber lengths as well.
Polarization instability was first observed in 1986 by transmitting 80-ps pulses
(at 532 nm) through a 53-cm-long fiber with a measured intrinsic beat length L B ≈
50 cm [37]. The input pulses were right-circularly polarized and passed through a circular
analyzer at the fiber output that transmitted only left-circularly polarized light.
The shape of output pulses was found to change dramatically when the peak power
exceeded a critical value. The measured critical power and the output pulse shapes
were in agreement with the theoretical predictions. In a later experiment, polarization
instability led to significant enhancement of weak intensity modulations when the input
signal was polarized near the fast axis of a low-birefringence fiber [44]. The 200-ns input
pulses were obtained from a Q-switched Nd:YAG laser operating at 1.06 μm. The