Nonlinear Fiber Optics - 4 ed. Agrawal

426 Chapter 11. Highly Nonlinear Fibers
Table 11.1 Measured values of n 2 for different fibers
Method λ Fiber Measured n 2 Experimental
used (μm) type (10 −20 m 2 /W) conditions
SPM 1.319 silica core 2.36 110-ps pulses [13]
1.319 DSF 2.62 110-ps pulses [13]
1.548 DSF 2.31 34-ps pulses [14]
1.550 DSF 2.50 5-ps pulses [17]
1.550 standard 2.20 50-GHz modulation [18]
1.550 DSF 2.32 50-GHz modulation [18]
1.550 DCF 2.57 50-GHz modulation [18]
XPM 1.550 silica core 2.48 7.4-MHz modulation [15]
1.550 standard 2.63 7.4-MHz modulation [15]
1.550 DSF 2.98 7.4-MHz modulation [15]
1.550 DCF 3.95 7.4-MHz modulation [15]
1.548 standard 2.73 10-MHz modulation [19]
1.548 standard 2.23 2.3-GHz modulation [19]
FWM 1.555 DSF 2.25 two CW lasers [12]
1.553 DSF 2.35 10-ns pulses [16]
measurement errors associated with γ but also on how accurately one can estimate the
effective mode area A eff from the mode-field diameter. In the remainder of this section,
we discuss various measurement techniques and indicate why they may yield different
values of n 2 even at the same wavelength.
11.1.2 SPM-Based Techniques
The SPM technique makes use of broadening of the pulse spectrum (see Section 4.1)
and was first used in 1978 [9]. As seen from Eq. (4.1.17), this technique actually measures
the maximum value of the nonlinear phase shift, φ max , a dimensionless quantity
that is related to γ linearly through Eq. (4.1.7). Once γ has been determined, n 2 is estimated
from it using the relation n 2 = λA eff γ/(2π). The accuracy of such measurements
depends on how well one can characterize input pulses because SPM-induced spectral
broadening is quite sensitive to the shape of optical pulses used in the experiment.
In spite of the uncertainties involved, such a SPM technique is often used in practice
[20]. In a set of measurements performed in 1994, mode-locked pulses of 110-ps
duration were obtained from a Nd:YAG laser operating at 1.319 μm [13]. Pulses were
broadened spectrally inside the test fiber, and their spectrum measured using a scanning
Fabry–Perot interferometer. The input power was adjusted such that the measured
spectrum corresponds to one of the shapes shown in Figure 4.2 such that φ max is a
multiple of π/2. The effective mode area was calculated from the measured refractiveindex
profiles of the fiber and used to deduce the value of n 2 . For a silica-core fiber
(no dopants inside the core), the measured value of n 2 was 2.36 × 10 −20 m 2 /W with an
uncertainty of about 5%. The measured n 2 values were larger for DSFs (average value
2.62 × 10 −20 m 2 /W) because of the contribution of dopants. As discussed in Section
6.6.3, these values are lower by a factor of 8/9 compared with bulk measurements