Page 499 - High Power Laser Handbook

466 Fi b er L a s er s Pulsed Fiber Lasers 467

significant SRS suppression can occur only when the Stokes pulse
(which exhibits lower group velocity) accumulates a delay compara-
ble to the pulse duration over a sufficiently short portion of the fiber.
Such a walk-off effect becomes important in fused-silica fibers only for
pulse widths less than 10 ps and is nearly negligible for nanosecond
pulses. Moreover, the SRS gain bandwidth is much larger (~40 THz)
than SBS; therefore, the effect strength remains virtually unchanged,
even for very broad pulse spectra.
In light of the above characteristics, SRS is a dominant NLE for
the near-nanosecond regime, and its mitigation appears possible only
through a direct reduction of the S NLE value or by means of specialty
fiber designs, in which high propagation loss is selectively introduced
for the SRS-generated field. Recently proposed SRS-suppressing solu-
4
tions in the latter category include dual-hole, W-shaped-core, and
5
photonic stop-band fibers. 6
Nonlinear Phase Modulation
A direct manifestation of the optical Kerr effect is an intrapulse phase
shift φ , which, at each point z along the fiber and for spectrally nar-
NL
row pulses of interest here, is given by
7
2 πn z Pz′ τ)
(,
τ
φ NL (, ) λ 2 ∫ A dz′ (16.2)
z
0
where λ is the pulse carrier wavelength, n is the irradiance-dependent
2
refractive index coefficient, P is the pulse instantaneous power, and
τ denotes time in the reference frame that moves along the fiber at the
pulse group velocity. Incidentally, in the case of negligible changes in
the pulse temporal shape during in-fiber propagation, the time
dependence of P can be factored out of the integral in Eq. (16.2),
which, for z = L (whole fiber length), becomes equal to S NLE (Eq. (16.1).
As a result of the phase shift φ , which is referred to as self-phase
NL
modulation (SPM), the carrier frequency undergoes a corresponding
intrapulse shift (a chirp) ∆ν, given by

1 ∂φ n z 1 ∂P
ν
∆= - π NL - λ 2 ∫ ∂τ dz ′ (16.3)
∂τ 2 0 A
For typical laser pulses, the larger the magnitude of such a fre-
quency shift at the end of the fiber (z = L), the greater the pulse spec-
tral broadening—hence, the departure from high spectral brightness
conditions of interest for many applications. The nonlinear phase
shift also represents a limiting factor for the generation of ultrashort
pulses (see Chap. 17) and for the phase locking of multiple fiber-
based amplifiers and lasers in coherently beam-combined schemes.