Since stretcher designs are diverse, 3-D computer
modeling is needed to pinpoint which one is the most
appropriate for the task.
one spherical (or parabolic) mirror and a flat mirror. The
stretching ratio is as high as 10,000 and its footprint is
roughly 1 × 4 square feet. This stretcher works better than a
lens-telescope stretcher and is used to amplify 40-fs pulses.
Below 40 fs, the dispersion characteristics of the stretcher
need to be calculated very precisely because even its smallest
aberrations become important.
Computer programs calculate dispersion
How do we accurately calculate the dispersion of a relatively
complex 3-D optical system where the rays bounce back and
forth many times between components? The most accurate way
is with the help of a commercial, well-tested 3-D ray tracing
computer program such as Zemax, CodeV, Oslo or Fred. This
method is more precise when compared to previously used
analytical calculations and 2-D ray tracing computations.
The exact optical path can be calculated for any wavelength
within the interval of interest, for any of the three modules
that form a CPA laser: the stretcher, the amplifier material
and the compressor. The stretcher is the hardest to calculate
because of the multiple passes between its components. The
dispersion of the amplifier material is easy to compute because
the laser is usually made of well-characterized glasses, sapphires
and/or other crystals. The compressor is also straightforward
to study because exact analytical formulas for their measurement already exist. A perfectly aligned compressor is, in fact,
a fantastic resource for anyone who wants to benchmark a ray
tracing program in order to avoid potential errors. Once the
optical path is known anywhere in the CPA system, the laser
designer can calculate the stretching ratio, residual phase and
shape of the compressed pulse.
Accurate dispersion calculations are priceless
Let’s have a closer look at a special CPA system, the optical parametric CPA (OPCPA). An OPCPA’s laser pulse is amplified in a
nonlinear crystal by as much as 10,000 to 100,000 times. Two
or more crystals can be used sequentially to further increase the
amplification. Since these crystals are usually thin, they don’t
introduce significant dispersion. Therefore, the designer of the
OPCPA just needs to make sure the compressor is compensated
by the stretcher exactly. In other words, the stretcher is an exact
opposite of the compressor. Since stretcher designs are diverse,
3-D computer modeling is needed to pinpoint which one is the
most appropriate for the task. For OPCPAs, studies show that an
Offner-type stretcher made of a concave and a convex spherical
mirror is the best match for the compressor.
Other CPA designs introduce significant dispersion by
amplifying material such as a regenerative amplifier with
770 nm 800 nm 830 nm
Optical 3-D layout of a compressor with the off-axis parabola
(OAP) used to focus the beam. M1 to M4 are folding mirrors
and VRR is the vertical retro reflector.
C o m pressor
Residual delay [fs]
(Left) The delay introduced by one compressor and three
stretchers. The stretcher delay curves appear as one because
there are extremely small differences between them. (Right)
The residual delay from summing the compressor and the
stretcher delay curves. The Offner stretcher is almost exactly
opposite of the compressor because the residual delay is
almost zero from 760 nm to 840 nm.
intracavity polarizers, Pockels cells and gain media. The total
length of the material could add up to 1 to 2 m, and in this
case, a complete analysis including the stretcher, compressor
and the amplifier is necessary. Any combination of grating
groove densities, curvatures, distances and incidence angles—
both in the stretcher and the compressor—could result in the
best dispersion compensation case. The most important thing
to know is the dispersion characteristics of all the CPA laser
system components. This can only be achieved by using a computerized 3-D ray tracing model.
Misalignment in CPA lasers
Computerized 3-D optical simulations can also study laser
misalignment. The typical causes for misalignment are