Gaussian beam passing through a circular aperture

Gaussian beam passing through a circular aperture. The distribution is determined by the size of the aperture relative to the size of the beam. If the beam is much larger than the aperture, the far-field pattern will be similar to an Airy function. If the beam is much smaller than the aperture, the far-field pattern will be close to a Gaussian. For intermediate cases, the resulting distribution will be a combination of the two. This can be expressed mathematically as the convolution of a circular function and a Gaussian function.
  • #1
yoni3468
5
0
Hi all,

when I have a Gaussian beam passing through a circular aperture:
What should be the far field (Fraunhoffer's) distribution?

Thanks in advance,
Yoni
 
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  • #2
The far-field diffraction pattern is the Fourier transform of the field at the aperture. So, it depends on how over- or under-filled the aperture is by the beam. If the beam size is much larger than the aperture, the far-field pattern is close to an Airy function. If the beam severely underfills the aperture, the far-field pattern is nearly a Gaussian. Intermediate cases will present intermediate results- the transform of circ(r/D)*Gaus(ar) = Somb(D*u) # Gaus(u/a), where '#' is the convolution operator, etc.
 
  • #3
Thank you!

Yoni
 

Related to Gaussian beam passing through a circular aperture

1. What is a Gaussian beam?

A Gaussian beam is a type of laser beam that has a bell-shaped intensity distribution, with the highest intensity at the center and gradually decreasing towards the edges.

2. What is a circular aperture?

A circular aperture is a circular opening through which light can pass. It can be found in various optical devices such as lenses, telescopes, and cameras.

3. How does a Gaussian beam pass through a circular aperture?

When a Gaussian beam passes through a circular aperture, the beam is diffracted and the resulting intensity distribution is a combination of the Gaussian beam profile and the diffraction pattern of the aperture.

4. What is the effect of the size of the circular aperture on the Gaussian beam?

The size of the circular aperture affects the diffraction pattern of the Gaussian beam passing through it. A smaller aperture will result in a larger diffraction pattern, while a larger aperture will result in a smaller diffraction pattern.

5. Why is the Gaussian beam passing through a circular aperture important in optics?

The Gaussian beam passing through a circular aperture is important in optics because it allows us to control the shape and intensity of the laser beam. This is essential in various applications such as laser cutting, laser printing, and laser microscopy.

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