self-phase modulation. Although not dangerous by itself,
self-phase modulation predicts the appearance of self-focusing,
which damages the laser optics. In order to increase the peak
power of today’s ultrafast lasers, it is essential that engineers
reduce or control self-phase modulation.
Computer-aided design and modeling, which has yet to
make its grand entrance into the field of ultrafast lasers, could
provide engineers with the tools to reduce self-phase modulation. This would greatly expand the utility of ultrafast lasers in
applications such as multiphoton imaging, laser micromachining of both absorptive and transparent media and the generation of attosecond pulses or nonlinear optics.
CPA: An early solution to self-focusing
Donna Strickland and Gerard Mourou demonstrated a simple
solution to self-focusing in their 1985 Optics Communications
paper. They started with a ps oscillator pulse that was purposely stretched in time within an optical fiber to reduce its
peak power. The 300-ps stretched pulse was further amplified
and then compressed in a standard two-grating compressor
to produce 2-ps pulses with 1 mJ of energy. The technique
was dubbed chirped-pulse amplification (CPA). Since then,
significant technological progress—such as the introduction of
the titanium-sapphire (Ti:S) material—has brought the pulse
duration down to less than 10 fs and the energy up to tens
or even hundreds of joules. Scientists at Lawrence Livermore
National Laboratory, U.S.A., achieved a record level of peak
power ( 1. 1 petawatt) in 1999, and researchers involved in several ongoing projects, including the Extreme Light Infrastructure project in Europe, are planning to generate a peak power
beyond 100 petawatt.
Dispersion management—how the pulse is being stretched,
amplified and compressed—is the key element in a CPA system.
In order to achieve high levels of amplification, one must stretch
seed oscillator pulses as much as possible. However, the more
they are stretched, the more difficult it is to compress the amplified pulses back to their original width or near their transform-limited duration. The fidelity of the stretch-compression scheme
becomes the quintessential part of all CPA systems.
Scientists have constructed a variety of schemes to stretch
and compress laser pulses. Very long optical fibers, due to
their dispersive capabilities, were initially used as stretchers.
Later, the use of spatially dispersive optical elements based
on diffraction gratings became widespread because they can
stretch optical pulses more than fibers. Researchers stretched
pulses quasi-linearly in time both in a positive (red colors first)
and a negative (blue colors first) dispersion way using lenses,
gratings, spherical mirrors, parabolic mirrors, etalons, etc. The
compressor designs have been very diverse, ranging from grating arrangements to bulk material and chirped mirrors.
With such a wide variety of dispersive elements and schemes
at their disposal, scientists began paying attention to the
stretching ratio and the residual phase of the compressed
pulses. The former is defined as the ratio between the duration
VRR M1 Input
770 nm 800 nm 830 nm
Optical 3-D layout and beam propagation for two optical stretch-
ers using Zemax. M1, M2 and FM are folding mirrors, SMCC
is a concave spherical (or parabolic) mirror, SMCX is a convex
spherical mirror and VRR is a vertical retro reflector. These lay-
outs are necessary for accurate dispersion calculations.
of the stretched pulse and the duration of the oscillator pulse.
More energy can be amplified if this factor is large. The latter
is used to show how good the compression process will be.
A residual phase near zero guarantees a good, compressed
pulse. The residual phase is also used in conjunction with the
time-bandwidth product to characterize the duration of the
Grating stretchers and compressors
The diffractive grating proved to be the most successful dispersive element used in CPA systems because it helped achieve
compressed pulses with good quality and large stretching
ratios. In 1969, Treacy showed how a two-grating assembly can
compress a positively chirped pulse. The grating stretcher was
developed much later by Martinez in 1987. Martinez realized
that a telescope placed among the gratings of a compressor will
effectively reverse the dispersion sign. The simple but ingenious
work by these scientists helped define the path for modern
ultrafast amplifier technology.
Today, almost any CPA system that produces more than
1 mJ/pulse uses diffraction gratings in its design, both in the
stretcher and the compressor. Initially, following Martinez’s
work, any stretcher design was regarded as the exact opposite
of a compressor, including those with lens telescopes. Later,
experimental studies pointed out the limitations of refractive
stretcher designs due to aberrations and additional dispersion
factors introduced by the glass. Reflective stretcher designs
were quickly developed after that.
The stretcher of a kHz repetition rate Ti:S CPA laser is
considered the industry standard. Its telescope is made of