Optics & Photonics News

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
Grating 2

OAP M4

Output
Target
plane
VRR
M1

M3 M2

Grating 1

Input
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.

Delay [ps]
C o m pressor
Stretcher

760 300 200 100

0 –100 –200 –300

840 760

500

400

300

200

100

0 –100 –200 –300

Residual delay [fs]
Parabolic
Spherical
Offner
(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.