Gaussian beam passing through a circular aperture

[yoni3468]

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

[Andy Resnick]

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.

[yoni3468]

Thank you!

Yoni