how to run this program?

[QJohn2017]

Hi, this is my first time to use Julia, I have installed the Julia 1.4 version on windows. And then I download this SFA program manually. But I don't konw how to run this program? Can you give me some guides? Thank you !

[jagot]

Hi!
Thanks for your interest in this package! I added some usage instructions to the README: https://github.com/jagot/StrongFieldApproximation.jl

Please note:

• I renamed the package to StrongFieldApproximation.jl to be clearer
• The package is not properly tested, i.e. I know "it works", but there are no real unit tests.
• The original paper, where the Lewenstein model for HHG was first described, actually derives the time-dependent dipole moment for positrons, not electrons, which I was not aware of when I wrote this package. This means that many of the phases have the wrong sign, but the magnitudes are correct (as correct as they can be within the SFA). This is something I mean to correct at some point, but I have not had the time yet.

If you have any more questions, please don't hesitate to ask.

[QJohn2017]

Hi, Thank you very much for your reply. I write a program of SFA by myself in Matlab. But When I use this program to plot the HHG and comparing the result to the following:

The result above comos from a theis https://portal.research.lu.se/portal/en/publications/subcycle-control-of-strongfield-processes-on-the-attosecond-timescale(3efc40a6-0524-459e-ade4-caa048df1307).html in page 117

and my result is as follows:

The simulation parameters are the same as that in the theis above. It can be seen that the harmonic spectrum in the this theis looks vergy beautiful, but the result of mine looks bad, I don't konw which result is right. there has another question, after a high pass filter, the |x(t)| figure in this two case is also different, the result in that thies looks very clearly, but in my result is in a mess, so I don't konw how to optimize my result and program.

[jagot]

That's my thesis you took the picture from :)

You can approximately reproduce the figure using this code

using DSP
using FFTW
import FFTW: fftfreq

# Library that provides simple specification of various electric
# fields.
using ElectricFields

# Unit arithmetic
using Unitful
using UnitfulAtomic

using StrongFieldApproximation
import StrongFieldApproximation: atomic_units

# Atom model, hydrogen-like argon with an ionization potential of 15.7596 eV
Ip,d = hydrogen_like(atomic_units(15.7596u"eV"))

# Definition of laser field, Gaussian pulse
@field(IR) do
    λ = 1030.0u"nm"
    I₀ = 1e14u"W/cm^2"
    env = :cw
    Tmax = 5
end

ndt = 200 # Time steps per laser cycle

@info "Solving SFA"
# Compute the time-dependent dipole moment x
tmin = -0.65
@time x,t = propagate(IR,Ip,d,ndt,tmin)

nt = length(t)
# We select only cycles 2–5 of the fundamental to avoid the transient
# behaviour in the beginning.
tsel = 2*ndt:nt
freq = fftshift(fftfreq(length(tsel),ndt))
# Multiply time-dependent signal by an apodizing Hann window and scale
# the result by the number of elements to achieve correct normalizing.
X = fftshift(fft(hanning(length(tsel)).*x[tsel]))/length(tsel)

# Design a Butterworth highpass filter
f = digitalfilter(Highpass(12,fs=ndt), Butterworth(20))
# Filter time-dependent dipole to reveal XUV bursts
fx = filtfilt(f,x)

I don't remember what I did to make the harmonic spectrum have such a low noise floor, but you can of course increase Tmax to include more cycles in the FFT, e.g. with Tmax=25, we get:

Note that there is not any extra information in this plot, since after the first two cycles, each laser cycle produces exactly the same time-dependent dipole moment x(t), because of the maximum excursion time is fixed to 0.65 cycles when tmin=-0.65 (only including the short trajectory, try tmin=-1.25 to also include the long trajectory). If instead we set Tmax=10 and tmin=0.0, we include all possible excursion times (i.e. the excursion time integral always start at t'=0, instead of t'=t-tmin) and hence also higher order trajectories:

Note that the plateau shows interference of the different trajectories, whereas the cut-off remains clean, since there is only one (purely non-classical) trajectory contributing.

When using tmin>=0, the computation scales as Tmax^2, whereas it scales as Tmax when tmin<0.

[QJohn2017]

Hi, thank you very much ! The julia code I could not run correctly yet, because I don't know the julia language at all, and I run the code one step by one according to your guides in https://github.com/jagot/StrongFieldApproximation.jl , errors occured. My main question is why the spectrum in your theis is so beautiful.

Another question is the plot of Filtered time-dependent dipole. My code in matlab is :

[b14 a14]=butter(20,12.0/100,'high'); fx = filtfilt(b14,a14,real(ele_dipole_x)); figure;plot(t/T,fx)
But the figure I plotted is not clearly like you, where it is

[jagot]

I cannot help you with your Matlab implementation, sorry (I don't have access to Matlab).

Looking at your filtered time-dependent plot

and your spectrum

they are very similar to my last plot, where I showed what happens if you include all trajectories

My earlier plots were calculated by limiting the maximum excursion times; instead of infinity, the maximum value of \tau is only 0.65T. See the connection in equations in the appendix of my thesis:

This will remove any possible interference due to the long trajectory (and even longer trajectories). If you find this unclear, you could read the chapters 3 and 4 in my thesis, and the references quoted therein.

[QJohn2017]

Thank you very much for your cleaar explanation. When I limited the excursion time tau to 0.65T, the filtered time-dependent plot looks like as your results:

but the spectrum looks wrong:

[jagot]

I believe you are seeing the effect of the transient behaviour during the first two cycles. Only perform the FFT from cycles 2–5, and don't forget to multiply the time-dependent signal by a window function, such as the Hann window, before transforming.

[QJohn2017]

Okay, Thank you very much ! I have changed my code that only perform the FFT from 2~5 cycles, and the result is ok:

Here I have another unreasonable request, your thesis made a very great job and you uses a lot of numerical methods, one of which is 3D TDSE code. I am a phD candidate of first year and do the HHG research just started. You know that, the comprehensive computation of HHG needs the 3D TDSE method, but it is so complicated for me. So, can you share a older 3D TDSE code version for me ? I know that my request is so unreasonable, but I have no resources to implement the TDSE code. But if inconvenient, I will appreciate you all the same. Thank you again!

[jagot]

No, that is not possible, I'm afraid, for two reasons: 1) one of my co-authors would not accept that (possibly in the future, but not now), and 2) it only runs on GPUs with support for double precision, which costs > €4000 (when I wrote the code, Nvidia sold gaming GPUs with decent double precision support, but not anymore).

Another very big problem with giving away research codes of this kind, is that they are very complex to run and there are so many mistakes you can make which makes the results completely nonsensical. You need to run the code under supervision for some months to understand all the details. The other approach is to write the code yourself (again under supervision) and discover all the mistakes yourself; that takes years.

I suggest you discuss with your supervisor what a suitable approach might be; if you really need the 3d TDSE (for HHG in elliptical/circular fields), then either you need to learn a lot of programming and numerical analysis and write the code yourself (don't use Matlab), or you might have luck with any of these freely available codes:

• Qprop by Dieter Bauer from Uni Rostock
• SCID-TDSE by Serguei Patchkovskii from MBI Berlin
• tRecX by Armin Scrinzi

All that being said, I hope to provide a new TDSE solver written in Julia, but that will take some years, because I have many things going on simultaneously.

[QJohn2017]

Okay, thank you very much ! I will search these code by your guides. Thanks again!