Nonlinear Fiber Optics - 4 ed. Agrawal

220 Chapter 6. Polarization Effects
Figure 6.16: PMD-induced pulse-width fluctuations as a function of DGD in the (a) linear and
(b) nonlinear propagation regimes. The dotted curves show the range of fluctuations in the linear
case. (After Ref. [161]; c○2001 IEEE.)
collective-variable approach has been used to find an analytic expression for the probability
density function of width fluctuations [163]. It shows that the XPM-induced
coupling between the orthogonally polarized components of a soliton narrows down
the width distribution considerably.
Problems
6.1 Derive an expression for the nonlinear part of the refractive index when an optical
beams propagates inside a high-birefringence optical fiber.
6.2 Prove that Eqs. (6.1.15) and (6.1.16) indeed follow from Eqs. (6.1.11) and (6.1.12).
6.3 Prove that a high-birefringence fiber of length L introduces a relative phase
shift of Δφ NL =(γP 0 L/3)cos(2θ) between the two linearly polarized components
when a CW beam with peak power P 0 and polarization angle θ propagates
through it. Neglect fiber losses.
6.4 Explain the operation of a Kerr shutter. What factors limit the response time of
such a shutter when optical fibers are used as the Kerr medium?
6.5 How can fiber birefringence be used to remove the low-intensity pedestal associated
with an optical pulse?
6.6 Solve Eqs. (6.3.1) and (6.3.2) in terms of the elliptic functions. You can consult
Reference [45].
6.7 Prove that Eqs. (6.3.14) and (6.3.15) can be written in the form of Eq. (6.3.19)
after introducing the Stokes parameters through Eq. (6.3.16).
6.8 What is meant by polarization instability in birefringent optical fibers? Explain
the origin of this instability.