Nonlinear Fiber Optics - 4 ed. Agrawal

11.1. Nonlinear Parameter 429
Figure 11.2: Experimental setup for measuring n 2 using a Sagnac interferometer and a CW laser.
(After Ref. [22]; c○1998 OSA.)
11.1.3 XPM-Based Technique
The XPM-induced phase shift was used as early as 1987 to measure n 2 [11]. A 1995
experiment employed a pump-probe configuration in which the pump and probe signals
were obtained from CW sources [15]. Figure 11.3 shows the experimental setup
schematically. When the pump light was modulated at a low frequency (< 10 MHz),
the probe spectrum developed FM sidebands because of the XPM-induced phase shift.
The theory behind the formation of the FM sidebands is similar to that discussed
earlier in the SPM case when two CW lasers were used. The main difference is that one
of the lasers acts as the pump and its intensity is changed in a periodic fashion using
a modulator. As a result, the phase shift induced on the probe through XPM beam
becomes time dependent. If we again neglect the dispersive effects, the probe field at
the fiber output can be written as
E 2 (t)=Re{A 2 exp(−iω 2 t)exp[ibφ max cos 2 (2π f m t)]}, (11.1.6)
where φ max = 2γP 0 L eff , f m is the modulation frequency, P 0 is the peak power of the
pump beam, and the parameter b is defined in Eq. (6.2.11). If we calculate the probe
spectrum by taking the Fourier transform of Eq. (11.1.6), the spectrum is found to
exhibit peaks at multiples of f m because of the XPM-induced phase shift. As before,
the power ratio of two neighboring peaks depends on φ max and can be used to deduce
the value of n 2 .
As discussed in Section 6.2.2, the XPM-induced phase shift depends on the relative
states of polarizations associated with the pump and probe beams through the parameter
b. If the state of polarization is not maintained inside the test fiber for the two
beams, one must make sure that the measured value is not affected by such polarization
effects. In practice, pump light is depolarized before it enters the fiber [15]. Under
such conditions, the relative polarization between the pump and probe varies randomly,
and the measured value of nonlinear phase shift corresponds to b = 2/3. In the experimental
setup shown in Figure 11.2, two CW beams differing in their wavelengths by
about 10 nm acted as the probe and the pump. The pump intensity was modulated at a
relatively low frequency of 7.36 MHz. XPM inside the fiber converted pump-intensity
modulations into phase modulations for the probe. A self-delayed heterodyne technique
was used to measure the nonlinear phase shift as a function of pump power. A