Multi-pulse initialization in Laser Envelope

[omguptaup]

Hi,

I want to construct a pulse envelope which has multiple components. Primarily I want to do this to construct a large enough pulse without really compromising on the frequency bandwidth, which reduces with increasingly larger temporal profiles (but still satisfying the SVEA requirements). The namelist tutorial suggests that we can have pulse composed of two adjacent Gaussian functions. I have four questions listed below:

1. The envelope_profile term in the LaserEnvelope section takes in 3 spatial and 1 time component. What would an example look like?
2. If I don't want adjacent Gaussian functions, but in fact, overlapping Gaussian functions, is this method an appropriate way to do this? Eventually, I want to construct a single slowly-varying profile consisting of multiple Gaussian components. I have an additional doubt, which is, how would the code know whether the pulse has Gaussian sub-components nor not?
3. Do all Gaussian components (adjacent or overlapping) need to have the same width and height?
4. Can I do this only with LaserEnvelope or even with LaserEnvelopeGaussianXX, where XX is 2D, 3D or AM? Basically, what I want to know is if I can write time_envelope = tgaussian(center=center1, fwhm=laser_fwhm1) + tgaussian(center=center2, fwhm=laser_fwhm1)?

Best regards. Please let me know if any of the questions is not clear.

[NotAFlightRisk]

Checked on v5.1.

1. In 3D it's envelope_profile(x, y, z, t) returning the complex envelope ((x, y, t) in 2D, (x, r, t) in AM). It's only used to set up the field at the start, with t standing in for x, so your centres are x positions. Full example: tstAM_16_multiple_envelopes_wake.py sums three Gaussian beams into one profile.
2. Yes. The code doesnt know about sub-components - it evolves the total. The catch is it's a complex sum, so overlapping pulses interfere (relative phase matters). The slow-variation condition applies to that total too.
3. No. That benchmark varies a0 and waist, and different fwhm per component works the same way.
4. Not with + - tgaussian returns a plain function, so that's a TypeError. The helpers just call time_envelope(t) though, so a lambda works:

g1 = tgaussian(center=center1, fwhm=laser_fwhm1)
g2 = tgaussian(center=center2, fwhm=laser_fwhm1)

LaserEnvelopeGaussian3D(
    ...,
    time_envelope = lambda t: g1(t) + g2(t),
)

That's one waist and focus for both, and a0 scales the sum, so the peak can go above a0. For diferent waists use LaserEnvelope like the benchmark.

[Z10Frank]

Thank you @NotAFlightRisk , indeed that example tstAM_16_multiple_envelopes_wake.py was created to show how to combine different lasers, which do not have to be Gaussian, and do not have share the same a0, etc.

The only requirement is that they have the same carrier frequency and polarisation. This way the envelope of the superposition is just a sum, and phase differences in the overlapping parts are taken into account if the phases are defined in the laser envelopes (this is important for interference, e.g. if you want to reconstruct an experimentally measured laser through superposition of Laguerre-Gauss modes).

This combination of envelopes can be done in all geometries.

Recently we introduced the possibility to inject the laser envelope from x=0 through the box_side="xmin", as in the benchmark tstAM_18_Laguerre_Gauss_envelope_from_xmin.py. In that case you only need to define the a function of N arguments (N-1 transverse coordinates at x=0 and time). This makes easier to initialise more complex lasers, even without the SVEA at t=0, because the envelope is evolved through the envelope equation that does not neglect any derivative.

[omguptaup]

Thank you @NotAFlightRisk for the clear answers. I haven't gotten round to implementing it, but I'll comment here if anything goes wrong.