Nonlinear Fiber Optics - 4 ed. Agrawal

434 Chapter 11. Highly Nonlinear Fibers
Section 2.3, and n 2 may become as small as 1.8 × 10 −20 m 2 /W. The n 2 value is higher
for fibers whose cores are doped with GeO 2 and increases by an amount ≈0.5 Δ, where
Δ is the relative core–cladding index difference (in percent). For standard fibers with
Δ = 0.3%, the n 2 value is expected to increase by 0.15 and is thus close to 2.9 × 10 −20
m 2 /W under quasi-CW conditions.
A natural question one may ask is how the nonlinear effects can be enhanced inside
an optical fiber. One can increase n 2 by doping the core but this increase is limited
in practice to a factor of 2 or so. A much more dramatic enhancement is possible by
controlling the effective mode area. This parameter is used to enhance the value of the
nonlinear parameter in highly nonlinear fibers. We turn to the design of such fibers in
the following sections.
11.2 Fibers with Silica Cladding
A simple way to enhance the value of the nonlinear parameter γ ≡ 2πn 2 /(λA eff ) consists
of reducing the core diameter of a silica fiber, while also controlling its refractiveindex
profile, because A eff depends on both the core size and the doping levels that
determine how tightly the mode is confined to the core [39]. For example, dispersionshifted
fibers, with a core diameter of 6 μmorso,haveA eff close to 50 μm 2 compared
with the standard fibers for which A eff ≈ 75 μm 2 . The situation is even more favorable
in dispersion-compensating fibers in which A eff is close to 20 μm 2 ,andγ is enhanced
by a factor of 4 compared with its value for standard fibers. Even though such fibers
were originally developed for controlling fiber dispersion, they were used during the
1990s for generating supercontinuum and making Raman amplifiers because of the
enhanced nonlinear effects inside them [40]–[43].
The same approach has been used to develop new kinds of highly nonlinear fibers
with controlled dispersive properties [44]–[47]. Included among such fibers are the
dispersion-decreasing fibers, in which the magnitude of dispersion parameter D decreases
along the length of fiber [44], and the dispersion-flattened fibers in which the
slope of the dispersion parameter D is reduced to values as small as 0.0002 ps/km-nm 2
[45]. As early as 1999, dispersion-shifted fibers with γ close to 20 W −1 /km were fabricated
[39] by controlling the doping levels within the core and the cladding such that
the optical mode was confined so tightly to the core that A eff was only 10.7 μm 2 . Moreover,
the dispersion could be flattened over a wavelength range >100 nm by adopting
the depressed-cladding design shown in Figure 11.6(a). In this design, the refractive
index is reduced to below that of silica within an inner-cladding region surrounding the
core by doping it with fluorine. The diameter of inner cladding plays an important role
and it can be used to control the dispersive properties of the fiber. Figure 11.6(b) shows
the calculated dispersion spectrum D(λ) for several dispersion-flattened fibers with
different values of the inner-cladding radius b while maintaining a/b = 0.58, where
a is the core radius. Even though γ at a wavelength of 1.55 μm was only near 3.2
W −1 /km for such fibers, their low losses (0.22 dB/km), relatively flat dispersion, and
long lengths (1 km or more) still made them suitable for nonlinear applications.
The values of the nonlinear parameter γ for most highly nonlinear fibers with silicabased
core and cladding are in the range of 10 to 20 W −1 /km [45]. It is difficult to