How to simulate super-gauss laser?

[Hatisa]

I want to simulate a continuous super-gauss laser. My input settings are as follows.

I just use supergauss(y, 0, 6 * micron, 10) to simulate the laser.(2D PIC)

However, to simulate the laser, we also need to know the phase. Gauss laser phase are as follows:

And Super-Gauss Laser phase:

and

I'm having a hard time programming the phase shift described above.
I'm seeking guidance from experts on whether my simulation approach is sound and how to simulate super-Gaussian beams effectively.
Thanks!

[Status-Mirror]

Hey @Hatisa,

You may have already come across our Gaussian beam demo. To achieve this, we take the equation you label "Gauss laser phase", and evaluate all the $z$ terms at the simulation boundary. You can probably do something similar with your $\phi(r_2,z)$.

I'm less familiar with your particular profile, but I think EPOCH might struggle to evaluate some of your terms in the input deck. Instead, you might find it better to calculate the numerical values of $\phi(r,z)$ at the simulation boundary in a separate program, to obtain a table of $r$ and $\phi$ value pairs. Then, you can set the laser terms in a similar way to how they're done in the Gaussian beam demo using the interpolate function in the maths parser.

The net effect is that for each $r_2$, (or $y$ in EPOCH), the cell position will be substituted into your interpolate function, and the phase will be returned. Each cell will know what the phase should be, and you can hopefully use this to inject your pulse.

Hope this helps,
Stuart