Nonlinear Fiber Optics - 4 ed. Agrawal

11.1. Nonlinear Parameter 427
Figure 11.1: Experimental setup for measuring n 2 using SPM-induced spectral broadening.
(After Ref. [20]; c○1998 IEEE.)
because the fiber used did not maintain the linear state of polarization of launched
pulses during their transmission.
The same technique was used in 1998 to measure n 2 of relatively long dispersionshifted
fibers near 1.55 μm [20]. Figure 11.1 shows the experimental setup schematically.
A mode-locked fiber laser provided 51.7 ps pulses that were first amplified
and filtered and then launched into a 20-km-long test fiber. It was necessary to account
for changes in the width and peak power of pulses along the fiber because of its
long length. The dispersive and modal characteristics of the test fiber were quantified
through separate measurements to ensure the accuracy. The NLS equation was then
solved to fit the measured spectra and to deduce the values of γ and n 2 . The measured
value n 2 = 2.45 × 10 −20 m 2 /W is smaller in the 1.55-μm wavelength region compared
with its values measured near 1.3-μm. A reduction by about 2% is expected from
the frequency dependence of n 2 . The remaining change may be related to different
amounts of dopants or measurement errors.
In place of deducing the SPM-induced phase shift from spectral broadening, a related
technique deduces it from spectral changes occurring when light from two lasers
operating at slightly different wavelengths is transmitted through the fiber. Such an approach
does not require short optical pulses, and measurements can be performed with
CW lasers. In a 1996 experiment [18], two CW semiconductor lasers (both DFB type)
were used and their wavelength difference (0.3–0.5 nm) was stabilized by controlling
the laser temperature. The optical signal entering the fiber oscillates sinusoidally at
the beat frequency (∼ 50 GHz) because of the optical interference and its amplitude is
given by
E in (t)=Re[A 1 exp(−iω 1 t)+A 2 exp(−iω 2 t)] = Re[A 1 cos(Δωt)exp(−iω av t)],
(11.1.3)
where Δω = ω 1 −ω 2 is the beat frequency, ω av =
2 1(ω 1 +ω 2 ) is the average frequency,
and the two fields are assumed to have the same power (|A 1 | = |A 2 |).
When such a signal propagates inside the fiber, the SPM-induced phase shift is also
time-dependent. Similar to the discussion in Section 4.1.1, if we neglect the effects of