Page 504 - High Power Laser Handbook

472 Fi b er L a s er s Pulsed Fiber Lasers 473

successful suppression of all external feedback, in-fiber Rayleigh
scattering still provides an intrinsic source of distributed feedback,
especially in long fibers. In some cases, parasitic lasing may result in
forward- or backward-propagating pulses that are energetic enough
to cause damage.
16.2.3 Optical Damage
Pulse power scaling within fibers is ultimately limited by optical dam-
age, which is primarily ascribed to dielectric breakdown triggered by
photoionization. According to recent measurements in Yb-doped fibers,
13
failure occurs at constant irradiance I in excess of ~450 GW/cm for
2
f
pulses longer than ~50 ps. This value is consistent with irradiance values
2
(~400 GW/cm ) inferred from some recent megawatt peak power
demonstrations. Correspondingly, the maximum damage-free peak
power scales as I × A, with A being the mode field area, until a critical
f
value P is attained. Beyond P , the in-fiber guided beam is expected
c
c
to undergo self-focusing (SF), which is the spatial manifestation of
the irradiance-proportional increase in the medium refractive index.
Ultimately, SF results in spatial beam collapse and ensuing runaway
irradiance divergence, which leads to damage. Recent analyses 14,15
suggest that P for the fundamental mode (LP ) of silica fibers is
c
01
independent of mode field area and can be approximated with that of
a Gaussian beam in bulk silica. This is given by
λ 2
P c (16.8)
2 π nn
02
Here λ is the wavelength, n is the refractive index, and n is the second-
0
2
-20
order nonlinear refractive index coefficient, which is ~2.6 × 10 m /W
2
2
for pulses greater than 1 ns (and as low as 2.2 × 10 -20 m /W in shorter
pulses, for which electrostrictive contributions to n vanish). At λ =
2
~1.06 μm, which is a common wavelength for Yb-doped fibers, P for
c
fused silica is in the ~5 MW range, which is actually higher than for
many optical materials. For example, solid-state laser crystals of
widespread use for high-power pulsed lasers, such as Nd:YAG and
Ti:sapphire, exhibit greater values for n —namely, ~3 × 10 -19 and ~3 ×
2
2
10 -20 m /W, respectively. This corresponds to P = ~330 kW (Nd:YAG
16
c
at 1.06 μm) and ~2 MW (Ti:sapphire at 0.8 μm). However, bulk lasers
and amplifiers based on these and other crystals can be designed for
damage-free operation in the SF regime, which is usually accom-
plished by ensuring that the crystal’s physical length does not exceed
the SF collapse length L , which for a Gaussian beam is given by 17
c
A
L (16.9)
e P
λ - 1
P c