Nonlinear Fiber Optics - 4 ed. Agrawal

432 Chapter 11. Highly Nonlinear Fibers
Figure 11.5: Values of n 2 as a function of the relative index difference Δ when fiber core is doped
with GeO 2 (filled circles) or cladding is doped with fluorine (empty circles). Straight lines show
a linear fit to the data (After Ref. [27]; c○2002 IEEE.)
beyond 1.6 μm. Indeed, the measured values of n 2 are close to 4×10 −20 m 2 /W for the
DCFs [25].
The dopant dependence of n 2 does not explain fully the spread in n 2 seen in Table
11.1. It turns out that the length of the fiber used in the experiment also affects the
measurements. The reason is related to the fact that most optical fibers do not maintain
the state of polarization during propagation of light. If the polarization state changes
randomly along the fiber length, one measures an average value of γ that is reduced by
a factor of 8/9 (see Section 6.6.3), compared with the value expected for bulk samples
that maintain the linear polarization of the incident light [29]. If the standard relation
γ = 2πn 2 /(λA eff ) is used to deduce n 2 , the resulting value would be smaller by a factor
of 8/9. Of course, one can account for the polarization effects by simply multiplying
this value by 9/8.
The measured value of n 2 is also affected by the width of optical pulses used during
the experiment. It turns out that the n 2 value is considerably larger under CW or quasi-
CW conditions in which pulse width exceeds 10 ns. The reason is that two other
mechanisms, related to molecular motion (Raman scattering) and excitation of acoustic
waves through electrostriction (Brillouin scattering), also contribute to n 2 . However,
their relative contributions depend on whether the pulse width is longer or shorter than
the response time associated with the corresponding process. For this reason, one
should be careful when comparing measurements made using different pulse widths.
The Raman contribution to the nonlinear susceptibility has been discussed in Section
2.3.2. The first and second terms in Eq. (2.3.38) represent the electronic (Kerr)
and the nuclear (Raman) contributions, respectively. When pulse width is much larger
than the duration of the Raman response function h R (t), we can treat h R (t) as a delta
function, and the electrons and nuclei contribute to n 2 fully. This is the case in practice
for pulses with widths >1 ps. In contrast, the Raman contribution nearly vanishes