This PR proposes the following improvements, all meant to achieve #127:

• The option to output the normalized vector potential instead of the electric field is implemented. For the rationale, see Improvements of the laser envelope extension openPMD/openPMD-standard#281. This is certainly open for discussion. Converters from E to a0 and reverse are implemented in utils (it is a very vanilla version, definitely room for improvement there).
• The calculation of local and average frequency is in a separate function. This way, we can implement different methods to do this operation (e.g. FFT-based) easily.
• profile from_array and from_openPMD now also support RZ representation. Without this, operating on the 3D data was not practical. Again, very vanilla implementation, the implementation assumes axial symmetry for the envelope, the mode decomposition is not included in this PR.

With these changes, the output of an FBPIC simulation can be sent as the input of a HiPACE++ simulation. The figure below shows, for a laser pulse in a parabolic channel, the pulse width during propagation, when starting the HiPACE++ simulation from the output of the FBPIC simulation at different times. Significant differences can be observed, which could very much come from differences between the two codes: even without using LASY the two codes give slightly different results for this case. This is probably a matter of tuning the resolution, box size, time step etc., so I do not think it is necessarily a problem.

laser_width_hipace_fbpic.pdf

The scripts I used are posted below, so we can later work on the agreement. I had to add some .txt to upload the files.

inputs_fbpic.py.txt
inputs_hipace.txt
script_fbpic.sh.txt
script_hipace.sh.txt

The lasy handling was done using:

from lasy.profiles.from_openpmd_profile import FromOpenPMDProfile
from lasy.laser import Laser
import matplotlib.pyplot as plt
from openpmd_viewer.addons import LpaDiagnostics
import scipy.constants as scc

profile2 = FromOpenPMDProfile('./DATA', 26, (0,1), 'E', 'y', theta=0)

dim = 'xyt'
lo = (-100e-6, -100e-6, 0)
hi = (+100e-6, +100e-6, (m0.zmax-m0.zmin)/scc.c)
npoints=(128, 128, 500)
## Tested, also works with
# dim = 'rt'
# lo = (0, 0)
# hi = (+100e-6, (m0.zmax-m0.zmin)/scc.c)
# npoints=(300, 600)
laser = Laser(dim, lo, hi, npoints, profile2)
laser.write_to_file('./lasy_t3/laser3d', use_a0=True)