Better conversion from electric field to vector potential?

[MaxThevenet]

The conversion between (scalar) electric field $E$ and vector potential $A$ should be

$E = - \frac{\partial A}{\partial t}$.

Assuming

$E = \Re[\mathcal{E}e^{-i\omega_0t}]$ and $A = \Re[\mathcal{A}e^{-i\omega_0t}]$

that should read

$\frac{\partial \mathcal{A}}{\partial t} -i\omega_0\mathcal{A} = \mathcal{E}$.

In the current implementation at

lasy/lasy/utils/laser_utils.py

Line 494 in 0529779

def field_to_vector_potential(grid, omega0):

we neglect the time derivative (first LHS term), which may be too rough in some cases. A more accurate option, e.g., solving in $\omega$ space, could be useful in some cases.