Nonlinear Fiber Optics - 4 ed. Agrawal

Chapter 11
Highly Nonlinear Fibers
As seen in the preceding chapters of this book, three major nonlinear effects occurring
inside optical fibers—self-phase modulation (SPM), cross-phase modulation (XPM),
four-wave mixing (FWM)—are governed by a single nonlinear parameter γ, defined
in Eq. (2.3.29). For most optical fibers γ has a value of ∼1 W −1 /km. It was realized
during the 1990s that this value is too small for optical fibers to be useful as a nonlinear
medium for practical applications. To solve this problem, several new kinds of fibers
with γ > 10 W −1 /km have been developed, and they are collectively referred to as
highly nonlinear fibers. This chapter deals with the properties of such fibers. The
techniques used to measure the nonlinear parameter are described first in Section 11.1.
Sections 11.2 to 11.5 then focus on four kinds of fibers that have been developed to
enhance the nonlinear effects. In each case, dispersive properties of the fibers are also
described because they play an important role whenever highly nonlinear fibers are
used for practical applications. It will be seen in Chapter 12 that the combination of
unusual dispersive properties and a high value of γ leads to a variety of novel nonlinear
effects.
11.1 Nonlinear Parameter
The nonlinear parameter γ, defined in Eq. (2.3.29), can be written as γ = 2πn 2 /(λA eff ),
where λ is the wavelength of light and A eff is the effective mode area given in Eq.
(2.3.30). This area depends on the fiber design, and it can be reduced with a proper
design to enhance γ. On the other hand, the nonlinear-index coefficient n 2 is a material
parameter related to the third-order susceptibility, as indicated in Eq. (2.3.13). This
parameter is fixed for each glass material. Thus, the only practical approach for enhancing
γ for silica-based optical fibers is to reduce the effective mode area A eff . The
use of non-silica glasses provides an alternative approach to designing highly nonlinear
fibers. Before focusing on the design of such fibers, it is important to discuss the
techniques used to determine n 2 experimentally. Accurate measurements of both γ and
A eff are necessary for this purpose.
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