Hello.
For typical spherical lens, calculation of the focused intensity for the laser is simple: numerical number gives diffraction limited focused radius of the laser thus everything is straightforward in assuming perfect Gaussian beam.
I'm now confusing how to calculate the intensity of the 'focused line' from the axicon. Maybe I can take some ring over the axicon for calculating portion of the energy passing through that part (ring). The obtained energy, E, is divided by pulse duration to give power passing through the part then...what is next step to reach intensity?
Thickness of the ring may gives length of the focus contributed from only that ring but radius of focus? How to calculate this?
Even if I can get the radius thus eventual parameter to be obtained is the energy divided by focus volume only due to the ring and pulse duration (energy density per unit time).
And how I can convert this parameter to intensity?
I need this info for checking whether our laser is suitable to generate the axicon-based laser-produced plasma over long length. (~10 cm) (Please see the attached image without thinking mask.)
Theoretically, by using the generalized Huygens-Fresnel diffraction integral and the transfer matrix of the Axicon, you can find the electrical field in the output plan, and after that you can calculate the intensity of your laser.
Thanks Hamid and that means...the intensity profile is not simply obtained but required to do some sort of rigorous equation. Could you recommend article or paper to deal with this issue?
There is a large literature concerning the imaging through axicon, if the scalar diffraction theory is sufficient for you. See for example: Jarutis, Paskauskas, Stabnis, Focusing of Laguerre-Gaussian beams by axicon: Opt. Commun., 184 (2000) 105-112. You can also find a PhD dissertation by Anna Burvall, Axicon Imaging by scalar diffraction theory. I had no problem with finding and importing this dissertation. The lecture is long and full of mathematics but helpful for anywany trying to solve problems with axicon. If you need rigorous diffraction theory, things are much more complicated. I do not know any analytical solutions, but numerical methods still works.
Since an axicon creates a Bessel beam, you must follow its theory (using "self-reconstructing beams" as a keyword can also help you). One example of a reference that you can use is:
J. Ježek, et al., "Narrow polymer fibers obtained as a combination of photopolymerization and non-diffracting beams", Proc. of SPIE Vol. 6326, 63262H, (2006), doi: 10.1117/12.680575.
This paper resumes the theory, targeting an axicon application.
You can read this paper:High quality quasi-Bessel beam generated by round-tip axicon, published by Oto Brzobohatý et al. in Optics Express, Vol. 16, Issue 17, pp. 12688-12700 (2008). http://dx.doi.org/10.1364/OE.16.012688. They study theoretically and experimentally the spatial intensity distribution of the zero-order Bessel beam formed by the axicon which possess a rounded tip.
You can also read our papers for more calculations.
Thanks everyone! You're very helpful for me thus I've just finished intensity calculation. Among them, the paper suggested by Hamid Nebdi is extremely helpful as it has clear expression for intensity distribution behind the 'perfect' axicon. Thanks for everyone!
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