Filling factor

[optoliv]

Is there a predefined filling factor (ratio between beam waist and aperture radius)? I couldn't find a method to change either the aperture size or the beam waist so I assume there must be one. However, in one of the additional papers to this toolbox (Multipole expansion of strongly focussed laser beams) I've read that one can define the truncation of the beam by the aperture. Could someone explain to me what I am missing?

[ilent2]

Hi,

How are you creating your beam and which version of the toolbox are you using? If you are using BscPmGauss from OTTv1.5, there is a truncation_angle parameter that can be passed in when you construct the beam. I've just updated the documentation to describe this (it should be live soon at https://ott.readthedocs.io/en/latest/Conceptual-Notes.html)

If you are using far-field point-matching or paraxial point-matching, you will need to add the aperture yourself by masking the input field. Let me know if you need more information.

Cheers, Isaac

[optoliv]

Hi, thank you very much for your fast reply! I’m using BscPmGauss from the current version to visualize a gaussian beam in the focal plane. I wanted to compare the intensity of the beam in the paraxial limit to an analytic formula and it turned out that the intensity doesn't have the same shape, that’s why I thought it might have to do something with the filling factor. However, sadly it turns out that this didn’t solve my problem. I used "reshape(sum(abs(E).^2,1),[nx,ny])“ and then plotted the intensity values for y=0 against the xrange. Would you happen to know what I’ve done wrong?

Thanks again and all the best! Livia

Am 30.06.2020 um 17:03 schrieb Isaac Lenton notifications@github.com:

Hi,

How are you creating your beam and which version of the toolbox are you using? If you are using BscPmGauss from OTTv1.5, there is a truncation_angle parameter that can be passed in when you construct the beam. I've just updated the documentation to describe this (it should be live soon at https://ott.readthedocs.io/en/latest/Conceptual-Notes.html https://ott.readthedocs.io/en/latest/Conceptual-Notes.html)

If you are using far-field point-matching or paraxial point-matching, you will need to add the aperture yourself by masking the input field. Let me know if you need more information.

Cheers, Isaac

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[ilent2]

Hi Livia,

The results from BscPmGauss will be slightly different from paraxial Gaussian beams but you should be able to get something that looks somewhat similar for low numerical apertures (or large beam waists), for example:

figure();
beam = ott.BscPmGauss('NA', 0.1, 'index_medium', 1.0);
x = linspace(-10, 10, 100);
im = beam.visualise('range', {x, 0});  % y = 0
plot(x, im ./ max(abs(im)));   % Normalise intensity for comparison
hold on;
w0 = 1./(asin(0.1).*pi);  % paraxial beam waist for NA, (Wikipedia)
plot(x, exp(-x.^2./w0.^2))
hold off;

If you use higher NA (smaller beam waist) then the results will be much less similar.

Hope this helps, good luck!

[optoliv]

Hi Isaac,

thank you so much, you helped me a lot! I didn’t use the visualise function because in the comments in the class Bsc.m it says: % Supported types include: % - 'irradiance' -- :math:\sqrt{Ex^2 + Ey^2 + Ez^2} % - 'E2' -- :math:Ex^2 + Ey^2 + Ez^2 and I was looking for the absolute value squared, so I thought it would be easier to just adjust the code written in the example program „beam_visualisation.m". By looking deeper into the Bsc.m class I found out that the irradiance and E2 are in fact defined as the absolute value (squared) of the E-field. I just thought you might want to change that.

I would have one more question that is regarding the function "beam.power“. By changing the beam power I can see that the intensity maxima change accordingly, however, the integral over the whole curve is several orders of magnitude smaller than the power I set for the beam. It would be great if you could explain what happens there to me since I have spent quite some time now looking through the different papers of this toolbox but I couldn’t find an explanation.

All the best, Livia

Am 01.07.2020 um 04:55 schrieb Isaac Lenton notifications@github.com:

Hi Livia,

The results from BscPmGauss will be slightly different from paraxial Gaussian beams but you should be able to get something that looks somewhat similar for low numerical apertures (or large beam waists), for example:

figure(); beam = ott.BscPmGauss('NA', 0.1, 'index_medium', 1.0); x = linspace(-10, 10, 100); im = beam.visualise('range', {x, 0}); % y = 0 plot(x, im ./ max(abs(im))); % Normalise intensity for comparison hold on; w0 = 1./(asin(0.1).*pi); % paraxial beam waist for NA, (Wikipedia) plot(x, exp(-x.^2./w0.^2)) hold off; If you use higher NA (smaller beam waist) then the results will be much less similar.

Hope this helps, good luck!

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[ilent2]

Hi Livia,

Thanks for pointing out the mistake in the documentation for 'irradiance' and 'E2', I've just updated it now.

For the beam power: someone else sent me an email a couple of days ago with a similar question, they had noticed the units for the fields seemed inconsistent with the beam power. Turns out the beam power was not in SI units. When looking into this further I also found that the calculation accuracy and run-time also depends on the beam power (there is not much difference for powers between 1e3 and 1e-3, but its something to be aware of), I've added a warning about this when the power is set and I should hopefully be able to fix this in the next release of the toolbox.

For now, here are some notes about the units:

• To convert the beam power into SI units you will need to multiply by 1./(2Zk.^2) where Z is the medium impedance and k is the medium wavenumber.
• To convert the output from farfield to SI units, you will need to divide H by the impedance and divide both H and E by the medium wavenumber. Integrating over the far-field should give the correct beam power.
• To convert the output from emFieldRtp/Xyz to SI units, you will need to divide H by the impedance only. However, I’ve found that trying to calculate the beam power by integrating over the near-field gives incorrect results. After talking to my supervisors, we think this is probably related to how quickly the integral converges (you might get better results by transforming the coordinates).

Cheers, Isaac