Extreme focus of a radially polarized beam

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Discussion Overview

The discussion revolves around the behavior of a radially polarized beam when it is extremely focused to a single point. Participants explore concepts related to interference, diffraction, and the resultant field patterns produced by such focusing.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions whether a radially polarized beam disappears upon extreme focusing due to the cancellation of electric fields in opposite directions.
  • Another participant suggests that the inquiry may relate to constructive and destructive interference, specifically asking if destructive interference occurs in this context.
  • A further response indicates that while focusing a beam to a single point may suggest cancellation, diffraction limits how small the focus can be, and the resultant field is a vector sum of all parts of the beam.
  • It is noted that there is no single point of total focus; rather, a pattern emerges around the nominal focus point, and off-axis points will not experience total cancellation.
  • A participant references a specific measurement related to the local field polarization vector mapping of a focused radially polarized beam, providing a source for further reading.

Areas of Agreement / Disagreement

Participants express differing views on the implications of focusing a radially polarized beam, particularly regarding cancellation and diffraction effects. The discussion remains unresolved, with multiple competing perspectives presented.

Contextual Notes

Participants mention the limitations of focusing optics and the inherent diffraction effects that influence the resultant beam pattern. The discussion also touches on the mathematical relationships involved, such as the 'sinx/x' pattern, without reaching a consensus on the implications.

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What happen if a radially polarized beam is extremely focused to a single spot?
Is it disappeared because E-fields in opposite direction subtract each other?

004965_10_fig1.jpg
 
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:welcome:
Are you asking about constructive / destructive interference?
 
anorlunda said:
:welcome:
Are you asking about constructive / destructive interference?
Yes, does destructive interference happen when focusing a radially polarized beam?
 
Could I re-word your idea a bit? You appear to be concerned that your image would appear to be focussed at a single point but that would involve the beam energy all being canceled out and it has to go somewhere so wtf?
Diffraction comes to your rescue. There is a limit to how small your 'single point' can be.
Addition of the field vectors depends on their direction and also on the exact point at which you are doing the calculation. The resultant of focussing all the parts of the beam will be the vector sum of all the elemental parts of the beam, at any point. But there is no single point where all the beam will focus; there is always a 'sinx/x' type pattern around the nominal focus point. If it's all symmetrical (for all three examples), I would expect to find a zero but, off axis, you will not get total cancellation and the energy would be diverted. However 'tight' you try to make the optics, there is always a finite beam width and the resulting image will have places where there is no cancellation
But the beam has a zero at its centre in any case, in your diagrams. Its image must also have zero value at the centre if it has circular symmetry. You will get a bright diffraction ring around the centre with a radius that's related to 1/d, where d is the aperture of your optics.
 
Thank you guys!
 

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