# Diffraction: rectangular aperture and gaussian beam

1. Dec 3, 2009

### Enialis

Is the Fresnel-Kirchhoff formula (FKF) valid also for gaussian beams? I a book starting from the gaussian intensity:
$$U_0(x,y)=\sqrt{\frac{2}{\pi\omega_0^2}}\exp\left(-\frac{t^2+s^2}{\omega_0^2}\right)$$
it said that using the FKF in free space the gaussian beam spreads (in far-field assumption). It concludes that the field can be expressed with a standard Gaussian distribution but with complex exponential rather than real. How can be it proved?
Now my question is: what happen if there is a diffraction through rectangular aperture to this gaussian beam? What is the correct theory to use in far-field assumption?