Nonlinear Fiber Optics - 4 ed. Agrawal

7.4. Spectral and Temporal Effects 243
Figure 7.4: XPM-induced wavelength shift of a 0.53-μm probe pulse as a function of the initial
time delay of the 1.06-μm pump pulse. Open circles show the experimental data and the solid
line shows the theoretical prediction. (After Ref. [54]; c○1988 AIP.)
the effective delay between the pulses was varied using time-dispersion tuning.
In a different experiment, a Nd:YAG laser was used to provide 33-ps pump pulses
at 1.06 μm and 25-ps probe pulses at 0.53 μm [54]. The delay between two pulses was
adjusted using a Mach–Zehnder interferometer. Because of a relatively large groupvelocity
mismatch (d ≈ 80 ps/m), the walk-off length was only about 25 cm. For a
1-m-long fiber used in the experiment, L/L W = 4. The probe spectra were recorded by
varying the delay T d and the peak power of the pump pulse. The spectra exhibited a
shift toward the red or the blue side with some broadening as the multiple peaks could
not be resolved. Such a XPM-induced shift is referred to as the induced frequency
shift [54].
Figure 7.4 shows the induced shift as a function of the time delay T d . The solid
line is the theoretical prediction of Eq. (7.4.14). The frequency shift for a given time
delay is obtained by maximizing Δν 1 (τ). The maximum occurs near τ = 0, and the
frequency shift is given by
Δν 1 = Δν max {exp(−τ 2 d ) − exp[−(τ d + δ) 2 ]}, (7.4.16)
where δ ≈−4 for the experimental values of the parameters and τ d = T d /T 0 with
T 0 ≈ 20 ps. Equation (7.4.16) shows that the maximum shift Δν max occurs for τ d = 0
and τ d = 4, but the shift vanishes for τ d = 2. These features are in agreement with
the experiment. According to Eq. (7.4.15) the maximum shift should increase linearly
with the peak power of the pump pulse. This behavior is indeed observed experimentally
as seen in Figure 7.5. The XPM-induced shift of the probe wavelength is about
0.1 nm/kW. It is limited by the walk-off length and can be increased by an order of
magnitude or more if the wavelength difference between the pump and probe is reduced