Polynomial Spectral Phase element

[soerenjalas]

Merge #261 first!

This PR adds an optical element that allows to add spectral phase parametrized through the Taylor series coefficients GDD, TOD, and FOD.

Description edited by @RemiLehe:

I added two automated test:

• When adding GDD to a Gaussian, the pulse broadens and acquires a chirp (which, in the envelope representation, corresponds to variations of the real and imaginary parts). This can be predicted analytically:

• When adding TOD>0 to a Gaussian, it creates post-pulses, for which the amplitude can be predicted analytically, using the stationary phase approximation:

[RemiLehe]

Closes #223

[RemiLehe]

Thanks for this PR.
Could you add automated tests? For instance,

• When applying GDD to a Gaussian pulse, the envelope should still be a Gaussian pulse, but with a longer duration. The increased duration can be calculated analytically (see e.g. the FBPIC Gaussian profile), which can then be tested in an automated test.
• When applying TOD to a pulse, I think that the scaling of the amplitude of the post-pulses can be roughly predicted analytically ; we could discuss this further.

[MaxThevenet]

Looks great, thanks for this PR! See comments below.

[RemiLehe]

Thanks for catching these typos @MaxThevenet!
I just updated the PR accordingly.