High School Limit of Focal Spot Size for Lensing EM Radiation Across Frequencies

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SUMMARY

The discussion centers on the limitations of focusing electromagnetic (EM) radiation, particularly in relation to the minimum spot size achievable by lenses as a function of frequency. Key concepts include the "beam waist" and the "Airy Disk," which define the narrowest point of a converging beam and the diffraction limit, respectively. The Abbe diffraction limit is noted as r = λ/2.8, indicating that the spot size is influenced by both the wavelength and the aperture size. The conversation highlights that while lenses can focus RF waves, there remains a fundamental limit to the size of the focused spot due to diffraction effects.

PREREQUISITES
  • Understanding of electromagnetic radiation and its properties
  • Familiarity with the concepts of beam waist and Airy Disk
  • Knowledge of diffraction limits in optical systems
  • Basic grasp of lens design and functionality
NEXT STEPS
  • Study the mathematical derivation of the Airy Disk from diffraction theory
  • Explore the implications of the Abbe diffraction limit in microscopy
  • Investigate the design and application of metamaterial lenses for RF waves
  • Learn about the relationship between aperture size and diffraction effects in optical systems
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Researchers, optical engineers, and physicists interested in the behavior of EM radiation, particularly in applications involving lensing and diffraction limits.

houlahound
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Did not know how to word this properly.

Looking for an equation to show the behaviour of how EM can be "lensed" as a function of wavelength/frequency.

ie RF waves can not be lensed/focussed to a spot.

what equation determines the minimum spot size a lens can focus EM radiation as a function of frequency?
 
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houlahound said:
what equation determines the minimum spot size a lens can focus EM radiation as a function of frequency?

I believe you're asking about the Airy Disk. Try the math in this article: https://en.wikipedia.org/wiki/Airy_disk
 
thanks guys. this is precisely the physics I was looking for.

haven't read through it all in detail but am I right in thinking the spot size is purely a function of the hardware transforming the light?

in the airy pattern, which is what is caused by diffraction from a circular aperture, would that increase the beam diameter after the aperture ie in general the smaller the aperture will cause greater spreading ie more diffraction. so therefore, if I am thinking right, a smaller beam will be achieved by a transparent lens than an aperture via diffraction.

I am going to try link the beam waist formula to the airy disc radius, but not sure if I am messing up the wrong two concepts.
 
houlahound said:
in the airy pattern, which is what is caused by diffraction from a circular aperture, would that increase the beam diameter after the aperture ie in general the smaller the aperture will cause greater spreading ie more diffraction. so therefore, if I am thinking right, a smaller beam will be achieved by a transparent lens than an aperture via diffraction.

You're right in that a lens will make a smaller airy disk than an open aperture, but there's still a fundamental limit to how small the airy disk can be which is based on the size of the aperture and the wavelength of the incoming light/radiation. A larger aperture and/or smaller wavelength gives a smaller airy disk.
 

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