Testing numerical implementations of strong-field electrodynamics

We test current numerical implementations of laser-matter interactions by comparison with exact analytical results. Focusing on photon emission processes, it is found that the numerics accurately reproduce analytical emission spectra in all considered regimes, except for the harmonic structures often singled out as the most significant high-intensity (multiphoton) effects. We find that this discrepancy originates in the use of the locally constant field approximation.

Figure 1

Comparison of the electric field strength (normalized to peak field strength) in one of the polarization directions for an infinite plane wave (dashed blue line) and a degree-8 super-Gaussian wave of 100 fs in duration (solid red line) ($\lambda =0.8$ $\mu \mathrm{m}$).

Figure 2

Comparison of analytical and numerical frequency emission spectra in the supercritical regime. The parameters are $a_0=80$ and $\gamma =10$. The black line shows the analytical calculation, and the blue (gray) line shows the statistical photon distribution from several thousand numerical runs.

Figure 3

Comparison of analytical and numerical angular emission spectra in the supercritical regime. The parameters are $a_0=80$ and $\gamma =10$. The black line shows the analytical calculation, and the blue (gray) line shows the statistical photon distribution from several thousand numerical runs.

Figure 4

Comparison of the analytical (black) and numerical (blue or gray) frequency spectra for the case of subcritical $a_0$. The parameters are $a_0=20$ and $\gamma =9000$.

Figure 5

Comparison of the analytical (black) and numerical (blue or gray) angular emission rates for the case of subcritical $a_0$. The parameters are $a_0=20$ and $\gamma =9000$.

Figure 6

Comparison of the analytical (black) and numerical (blue or gray) frequency spectra for the case of critical $a_0$. The parameters are $a_0=30$ and $\gamma =15.078$.

Figure 7

A zoom-in of the collapsed part of the spectrum in Fig. 6 ($a_0=30,\gamma =15.078$). The inset shows a further zoom into an individual harmonic.

Figure 8

Comparison of the analytical (black) and numerical (blue/gray) angular emission rates for the case of critical $a_0$. The parameters are $a_0=30,\gamma =15.078$.

Figure 9

Comparison of the analytical (black) and numerical (blue or gray) angular emission rates for the case of near-critical $a_0$. The parameters are $a_0=30$ and $\gamma =16$.

Figure 10

The full spectrum for a monochromatic field (blue solid line) and the LCF approximation to it (red dashed line, marked ‘LCFA’). $a_0=20$ to illustrate. The vertical black line marks the boundary of the first harmonic.