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Enable to initialize spatial/temporal/angular chirped laser #1196

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@huixingjian huixingjian commented Jan 19, 2025

This PR adds three optional parameters: temporal chirp <laser name>.phi2, spatial chirp <laser name>.zeta, angular chirp <laser name>.beta, to initialise spatio-temporal coupling based on Gaussian lasers (see docstring in this PR). All of them are set to be conform to the definition in [Akturk, 2004].

The parameters could be tested through the following formula, with the laser envelope expressed as $a=a_0e^{i\theta}$:
$\Phi^{(2)} = \frac{4\phi^{(2)}}{4(\phi^{(2)})^2+\tau^4}$
Here $\tau$ is duration in s, and laser.phi2 refers to group-delay dispersion $\phi^{(2)} $, and $\Phi^{(2)}$ can be calculated by $\frac{\partial^2 \theta }{\partial t ^2}$.

Similarly, the spatial chirp is tested through:
$\nu = \frac{4\zeta c}{w_0^2L_0^2(1+4\zeta^2L_0^2)}$
Here $L_0$ and $w_0$ are the laser duration and laser waist respectively. $\zeta$ is laser.zeta, and $\nu = \frac{\partial^2 \theta }{\partial z \partial y} $

Finally, the angular chirp term is tested through:

$\beta = \frac{p}{ k_0} |_{\phi^{(2)} = 0, \zeta = 0}$

Here $k_0$ is laser wavenumber and $p$ is the pulse front tilt.

This PR also added on one CI test to check the correctness of these initial parameters

@huixingjian huixingjian changed the title upadte STCs Enable to initialize spatial/temporal/angular chirped laser Jan 19, 2025
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