Nonlinear Fiber Optics - 4 ed. Agrawal

506 Chapter 12. Novel Nonlinear Phenomena
Figure 12.40: Measured THG spectra when 170-fs pulses at 1550 nm are launched along the (a)
slow or (b) fast axis of a 20-cm-long microstructured fiber. (After Ref. [202]; c○2003 OSA.)
two principal axes. Each peak appeared as a doublet whose relative heights varied with
the average power launched into the fiber. As in Figure 12.40, the longer-wavelength
THG peak results from the Raman soliton that separates from the main pump pulse
after a short distance into the fiber as a result of a large RIFS. The observed far-field
patterns associated with the THG peaks were complex with eight lobes around a central
dark spot and corresponded to a fiber mode whose order was relatively high (>20). A
theoretical model predicted the observed patterns quite well. For a fiber with 1.5-μm
core diameter, the mode order for which THG was phase-matched was as high as 48.
Problems
12.1 Explain why the spectrum of an ultrashort pulse propagating as a soliton shifts
toward longer wavelengths. Do you expect this shift to occur if the pulse were to
propagate in the normal-dispersion regime of the fiber? Discuss the logic behind
your answer.
12.2 A short pulse with 100 W peak power propagates as a fundamental soliton inside
a 10-m-long highly nonlinear fiber with γ = 100 W −1 /km and β 2 = −10 ps 2 /km.
Calculate the pulse width (FWHM) and the dispersion and nonlinear lengths.
Also estimate the Raman-induced spectral shift at the output of fiber assuming
T R = 3 fs.
12.3 A fourth-order soliton with 150-fs width (FWHM) undergoes fission inside a
10-m-long fiber with γ = 100 W −1 /km and β 2 = −10 ps 2 /km. Calculate the
widths, peak powers, and Raman-induced spectral shifts for the four fundamental
solitons created.
12.4 Explain the FROG technique and sketch a typical experimental setup used for it.
How would you extend this technique to make use of cross-correlation in place
of autocorrelation?
12.5 What is meant by the Cherenkov or nonsolitonic radiation? Under what conditions
is this radiation emitted by a soliton? Derive an expression for the radiation
frequency assuming that solitons are perturbed only by the third-order dispersion.