Pulsed plane-wave fields

[szabo137]

This PR adds an abstract interface for dealing with pulsed plane-wave fields in the context of pulsed-perturbative QED. As the root type of all background fields, to be used in the strong field part of QED.jl, we introduce the abstract base type AbstractBackgroundField. However, the interface is currently defined for pulsed plane-wave fields (see below).

Definition of the interface

The base type of the interface is AbstractPulsedPlaneWaveFields, where the following interface functions are mandatory

reference_momentum(::AbstractPulsedPlaneWaveFields) # return the reference momentum of the field
domain(::AbstractPulsedPlaneWaveFields) # return the interval, on which the BG field is non-zero
phase_duration(::AbstractPulsedPlaneWaveFields) # return the extent of the BG field in the phase variable phi
_pulse_envelope(::AbstractPulsedPlaneWaveFields, phi::Real) # return the value of the envelope function of the BG field in the phase variable phi, i.e. the phase profile 

The first three functions are just accessor functions for static properties of the background field. The last function _pulse_envelope defines the shape of the pulse, and it only needs to be implemented on one single value of $\phi$. With that, the following functions were implemented as well

pulse_envelope(::AbstractPulsedPlaneWaveFields,phi::Real) # return the value of the envelope function at phi if phi is in the domain, and zero otherwise
_amplitude(::AbstractPulsedPlaneWaveFields, pol::AbstactDefinitePolarization,phi::Real) # return envelope times oscillator for given polarisation direction
amplitude(::AbstractPulsedPlaneWaveFields, pol::AbstactDefinitePolarization,phi::Real) # same as _amplitude, but return zero if phi is not in the domain
generic_spectrum(::AbstractPulsedPlaneWaveFields,pnum::Real) # return the Fourier transform of the amplitude at a given pnum

For each function, which is defined for phi::Real or pnum::Real, the respective version for multiple values, i.e. phi::AbstractVector{<:Real} and pnum::AbstractVector{<:Real} is also implemented.

For the generic spectrum, the implementation is simply based on QuadGK and therefore worthy of improvement.

Todos

• remove temporary file src/QEDbase_polarisation_mock.jl before merging this. This needs Move particle definitions from QEDprocesses.jl to QEDbase.jl QEDbase.jl#25 to be merged in QEDbase.jl and the respective release.
• add integration tests for polarisation types from QEDbase
• write docstrings for the exported functions
• open issue on the enhancement of the default implementation of generic_spectrum.

[szabo137]

Currently in draft status, because it depends on QEDjl-project/QEDbase.jl#25

[szabo137]

@steindev This should be ready for final review now. I do not include elliptic polarization in this PR, because it is already fairly extensive. However, I opened #21 to include this in another PR.

[steindev]

Review interfaces. Rest is missing. But you do things at the moment.

[steindev]

Reviewed all files now. Overall very good. Minor questions and comments.

[steindev]

@szabo137 It seems you forgot a few comments. Apart from that, I am mostly fine with your revision.

[szabo137]

I addressed all open comments. Hopefully this time, no comment is hiding from me 😅