I have developed a code for simulating three-dimensional ultrashort pulse propagation. It solves the unidirectional coupled-mode equations using an efficient pre-conditioned Runge-Kutta method, which permits adaptive step sizing. It supports an arbitrary set of linear modes, each with an arbitrary dispersion/loss profile curve. It incorporates the complete spatio-temporal ionization rate , calculated using one of several models; ADK [1], PPT [2] and Yudin-Ivanov [3] – can be chosen.

## Example: ionization-induced defocusing in an HHG gas jet target

In this example, a 70 fs pulse is focused into a 3 mm thick stream of 200 mbar Argon. Whilst the peak intensity at the focus in the absence of gas is 3.7 x 10^{14} W/cm^{2}, ionization-induced defocusing which, occurs in the middle and at the trailing edge of the pulse clamps the peak intensity to 1.6 x 10^{14} W/cm^{2}. The following animation shows the evolution of the spatio-temporal intensity, represented in shades of red, and the free-electron plasma density, represented in shades of blue.

## References

[Bibtex]

```
@Article{Ammosov-1986-Tunnel,
Title = {Tunnel ionization of complex atoms and of atomic ions in an alternating electric field},
Author = {Ammosov, M.V and Delone, N.B and Krainov, V.},
Journal = {Sov. Phys. JETP},
Year = {1986},
Pages = {1191},
Volume = {64},
Annote = {Zh. Eksp. Teor. Fiz 91 4 2008},
Date-modified = {2007-08-26 15:29:45 +0100},
File = {Ammosov-1986-Tunnel.pdf:A/Ammosov-1986-Tunnel.pdf:PDF},
Owner = {dane_austin},
Timestamp = {2012.08.10}
}
```

[Bibtex]

```
@Article{Perelomov-1966-Ionization,
Title = {Ionization of atoms in an alternating electric field},
Author = {Perelomov, AM and Popov, VS and Terent'ev, MV},
Journal = {Soviet Journal of Experimental and Theoretical Physics},
Year = {1966},
Pages = {924},
Volume = {23},
File = {Perelomov-1966-Ionization.pdf:P/Perelomov-1966-Ionization.pdf:PDF},
Owner = {dane_austin},
Timestamp = {2011.10.10}
}
```

[Bibtex]

```
@Article{Yudin-2001-Nonadiabatic,
Title = {Nonadiabatic tunnel ionization: Looking inside a laser cycle},
Author = {Yudin, Gennady L. and Ivanov, Misha Yu.},
Journal = {Phys. Rev. A},
Year = {2001},
Month = {Jun},
Pages = {013409},
Volume = {64},
Abstract = {We obtain a simple closed-form analytical expression for ionization rate as a function of instantaneous laser phase ?(t), for arbitrary values of the Keldysh parameter ?, within the usual strong-field approximation. Our analysis allows us to explicitly distinguish multiphoton and tunneling contributions to the total ionization probability. The range of intermediate ??1, which is typical for most current intense field experiments, is the regime of nonadiabatic tunneling. In this regime, the instantaneous laser phase dependence differs dramatically from both quasistatic tunneling and multiphoton limits. For cycle-averaged rates, our results reproduce standard Keldysh-like expressions.},
Doi = {10.1103/PhysRevA.64.013409},
File = {Yudin-2001-Nonadiabatic.pdf:Y/Yudin-2001-Nonadiabatic.pdf:PDF},
Issue = {1},
Numpages = {4},
Owner = {dane_austin},
Publisher = {American Physical Society},
Timestamp = {2012.08.10},
Url = {http://link.aps.org/doi/10.1103/PhysRevA.64.013409}
}
```