Page 461 - High Power Laser Handbook

428 Fi b er L a s er s Intr oduction to Optical Fiber Lasers 429

Chirp Pulse
Amplitude (a.u.) phase delay

Nonlinear

Time (a.u.)
Figure 15.14 SPM and related chirp generated by an optical pulse.

new spectral components at the leading and trailing edge of an
optical pulse. Continuous generation of red-shifted components
happens at the leading edge of a pulse and blue-shifted compo-
nents at the trailing edge of a pulse, resulting in a positive chirp
17
(see Fig. 15.14 and Agrawal for more theoretical details). This
chirp is linear near the center of a gaussian pulse. The nonlinear
phase φ inside a fiber induced by an optical signal of power P
NL
0
can be expressed as
φ = PL (15.19)
γ
NL 0 eff
The nonlinear coefficient γ is defined as

2 πn
γ = 2 (15.20)
λA eff
where λ is the vacuum wavelength and n is a Kerr nonlinear coef-
2
2
ficient that is typically around 2.6 × 10 –20 m /W in silica fibers. The
nonlinear phase induced by SPM is sometimes referred to as the B
integral, which is particularly important in chirped pulse amplifica-
tion (CPA) systems where an optical pulse is first stretched in the
20
temporal domain to reduce its peak power, amplified, and then
compressed back to its original temporal shape. As a rule of thumb,
to prevent SPM-induced pulse breakup in a CPA scheme, the B inte-
gral needs to be less than π, unless special measures are imple-
mented to eliminate any small ripples in the temporal and spectral
pulse profiles.