Page 500 - High Power Laser Handbook

468 Fi b er L a s er s Pulsed Fiber Lasers 469

Based on Eq. (16.3), the SPM-induced spectral broadening depends
on the pulse shape and is more pronounced in pulses of steep leading
or trailing edges. This aspect is detrimental in pulse amplifiers that
operate in the saturated regime (i.e., pulse energy ~ saturation energy;
see Sec. 16.2.2), in which case the population inversion can be signifi-
cantly depleted by the pulse’s leading edge. As a result, the pulse
becomes distorted upon amplification and “steepens,” thus incurring
greater SPM for a given peak power.
Another case that can further exacerbate nonlinear phase modu-
lation effects is that of optical pulses exhibiting multiple frequencies
in their spectrum (e.g., corresponding to several longitudinal modes
of a laser cavity). In such cases, the nonlinear phase shifts of the dis-
tinct spectral components become coupled, which is referred to as
cross-phase modulation (XPM) and which may lead to overall greater
spectral broadening. 3
As is the general case with NLEs, nonlinear phase-shift detri-
ments are generally mitigated by reducing S NLE through the use of
large-core and short fibers. The choice of a seeding source that pres-
ents single-frequency spectral purity (for XPM avoidance) and a gen-
tly sloped temporal pulse profile is also instrumental for retaining
high spectral brightness through amplification.
Further SPM and XPM mitigation can be obtained by proper tem-
poral and spectral preconditioning of the input pulses, which may be
possible, for example, when the seeding source is a gain-switched
semiconductor laser or an externally modulated CW oscillator. For
example, the pulse steepening effect described earlier can be countered
by shaping the input pulse profile as a positive ramp, which results in
7,8
a symmetric near-Gaussian-like profile upon amplification.
Moreover, Eq. (16.3) shows that the SPM-induced ∆ν is opposite
in sign to the slope of the pulse and therefore always negative (posi-
tive) in the pulse leading (trailing) edge, which is referred to as posi-
tive chirp. Therefore, deliberately imparting a negative chirp on the
input pulse (e.g., by means of an electro-optical phase modulator)
can, in principle, compensate for such an effect and result in good
containment of SPM-induced spectral broadening upon propagation
or amplification through the fiber. 9

Four-Wave Mixing
In fibers, the four-wave mixing (FWM) process consists of an energy
conversion incurred by photon pairs in the main, high-irradiance
beam (usually called the FWM pump beam) upon scattering off the
host material (in this case, fused silica). The efficiency of this scatter-
ing event depends on the third-order term of the medium dielectric
susceptibility—hence, ultimately on n .
2
Because the process does not involve material resonances, a nec-
essary condition for significant FWM gain is that the total photon
energy be preserved, which means that the initial FWM spectral