Laser profile for donut like Laguerre Gauss Beams

[VinithSamson11]

Hi,

I have a doubt regarding the generic laser profile function. The generic laser block for AM geometry is given by,

Laser(
box_side = "xmin",
space_time_profile_AM = [ Br_mode0, Bt_mode0, Br_mode1, Bt_mode1, ... ]
)

I have a scalar field of donut like Laguerre Gauss beam "B(x, r, theta, t)", how can I get the Br_mode0, Bt_mode0, Br_mode1, Bt_mode1....etc., from the provided scalar field "B(x, r, theta, t)" ?

[beck-llr]

Hi
please read https://smileipic.github.io/Smilei/Understand/azimuthal_modes_decomposition.html.
The answer to your question is found just below equation 42.
Let us know if that helped.

[VinithSamson11]

Yes, it helped. Thank You so much.

[VinithSamson11]

Hi @beck-llr ,

I also have some confusions regarding the space_time_profile in the Laser() block for "3Dcartesian" geometry.

The syntax is given by,
Laser( box_side = "xmin", space_time_profile = [ By_profile, Bz_profile ] )

The mathematical Bz profile function which I am using is a 4D function, that has dependencies on "x, y, z and t". But when I am defining a python function Bz(x, y, z, t) , I am getting the following warning & error:

[WARNING](0) src/Profiles/Profile.cpp:191 (Profile) Profile 'Laser[0].space_time_profile[1]' has 4 arguments but requires 3
On rank 0 [Python] TypeError: Bz() missing 1 required positional argument: 't'
[ERROR](0) src/Profiles/Profile.cpp:269 (Profile) Profile 'Laser[0].space_time_profile[1]': does not seem to return a correct value

Please let me know how can I define a 4D laser space_time_profile python function in 3Dcartesian geometry.

[Z10Frank]

Also, in the AMcylindrical geometry, the space_time_profile_AM you need to provide for each mode are functions of (r,t) and not x,r,theta,t. At the box_side = "xmin" the x is equal to 0, and the geometry will take care of the dependence on theta according to the mode number.

In 3D for a laser entering from box_side = "xmin" you would have a dependence on y,z,t. An example of Laguerre-Gauss laser injected in 3D is found in the namelist of this tutorial: https://smileipic.github.io/tutorials/advanced_vtk.html

You need to do some trigonometry to adapt the laser analytical expression to the mode definitions in this part of the documentation and pointed by @beck-llr .

[VinithSamson11]

Hi @Z10Frank,

Yes, I understood. At the box boundary, x=0 is fine, but when the profile propagates in x direction, the profile should have a dependence of x (according to the analytical LG profile expression in wikipedia ). So my question is whether SMILEI is taking care of this x dependence while running the simulation or its assigning a default value for x coordinate in the profile expression throughout the simulation?

I am currently using the namelist of the tutorial: https://smileipic.github.io/tutorials/export_VTK_namelist.py as a reference. Can I get the analytical expression of the Bz field used in the above namelist ? It would be better to know the analytic expression used, to understand it clearly.

Thank You.

[Z10Frank]

I agree that if a laser pulse was initialised entirely in the window from t=0 you should initialise also the x dependence according to the analytical expression, but for a Laser initialised from a border, the Maxwell's equations solver will ensure that this boundary condition will make these field enter the window following Maxwell's equations. The laser pulse, once inside the window, will respect the whole analytical expression (approximately) if your laser parameter are within the limits of the chosen approximation to derive the analytical expression (paraxial approximation and pulse much longer than the laser wavelength).

The python functions for the Laguerre-Gauss beam in 3D and the Gaussian beam in cylindrical coordinates in that namelist should follow the same analytical expressions in your page. The only differences are that they are computed at x=0, multiplied by the carrier wave at angular frequency omega and multiplied by a time envelope to have a pulse of finite length. The vector focus contains the coordinates of the focal point.

[VinithSamson11]

Thank You so much for the explanation :)