Nonlinear Fiber Optics - 4 ed. Agrawal

454 Chapter 12. Novel Nonlinear Phenomena
12.1.1 Enhanced RIFS and Wavelength Tuning
In the 1986 experiment [1], 560-fs optical pulses were propagated as solitons in a 0.4-
km-long fiber and their spectrum was found to shift by up to 8 THz because of the
RIFS. It was found soon after that the fission of higher-order solitons generates such
frequency-shifted pulses [3], often called Raman solitons. Although the properties of
Raman solitons attracted attention during the 1990s [4]–[9], it was only after 1999
that the RIFS was used for producing femtosecond pulses whose wavelengths could be
tuned over a wide range by simply propagating them through microstructured or other
narrow-core fibers [10]–[21].
The theory of Section 5.5.4 can be used to study how the RIFS scales with the pulse
and fiber parameters. In general, one should employ Eq. (5.5.17) when an input pulse
with a power profile, P(t)=P 0 sech 2 (t/T 0 ), is launched into a fiber. Only in the case of
a fundamental soliton propagating inside a fiber with negligible losses, can we employ
Eq. (5.5.19). If we introduce Δν R = Ω p /(2π), the RIFS grows along the fiber length
linearly as
Δν R (z)=− 4T R|β 2 |z
15πT 4
0
= − 4T R(γP 0 ) 2 z
, (12.1.1)
15π|β 2 |
where we used the condition that N = γP 0 T0 2/|β
2| = 1 for a fundamental soliton. The
Raman parameter T R equals ≈3 fs and is defined in Eq. (2.3.42). The preceding equation
shows that the RIFS scales with the soliton width as T0 −4 , or quadratically with the
nonlinear parameter γ and the peak power P 0 . Such a quadratic dependence of Δν R on
the soliton peak power was seen in the original 1986 experiment [1].
It follows from Eq. (12.1.1) that RIFS can be made large by propagating shorter
pulses with higher peak powers inside highly nonlinear fibers. Using the definition of
the nonlinear length, L NL =(γP 0 ) −1 , the RIFS is found to scale as LNL −2 . As an example,
if we use a highly nonlinear fiber with β 2 = −30 ps 2 /km and γ = 100 W −1 /km,
L NL = 10 cm for 100-fs (FWHM) input pulses with P 0 = 100 W, and the spectral shift
increases inside the fiber at a rate of about 1 THz/m. Under such conditions, pulse
spectrum will shift by 50 THz over a 50-m-long fiber, provided that N = 1 can be
maintained over this distance.
Much larger values of RIFS were realized in a 2001 experiment in which 200-fs
pulses at an input wavelength of 1300 nm were launched into a 15-cm-long tapered
with a 3-μm core diameter [13]. Figure 12.1 shows the experimentally measured output
spectrum and the autocorrelation trace together with numerical predictions of the
generalized NLS equation (2.3.43). The parameters used for simulations corresponded
to the experiment and were L NL = 0.6 cm, L D = 20 cm, and T R = 3 fs. The effects of
third-order dispersion were included using L D ′ = 25 m. In this experiment, a spectral
shift of 45 THz occurs over a 15-cm length, resulting in a rate of 3 THz/cm, a value
much larger than that expected from Eq. (12.1.1). This discrepancy can be resolved by
noting that the soliton order N exceeds 1 under the experimental conditions, and the
input pulse propagates initially as a higher-order soliton inside the fiber.
The qualitative features of Figure 12.1 can be understood from the soliton-fission
scenario discussed in Section 5.5.4. For a non-integer value of N, the soliton order ¯N
is the integer closest to N. The fission of such a higher-order soliton creates ¯N fun-