Take the 2-minute tour ×  I am currently experimenting with
Huygens-Fresnel principle. I am trying to simulate the
propagation of a beam, emerging from an aperture slot of width
w. I assume the slot to be long and therefore work in two
dimension.  My elementary wave is given by $$
A_E(x,x_0)=\frac{\exp\left(2\pi i/\lambda 2\sqrt{(x-x_0)^2+a^2}
\right)}{\left(2\pi\sqrt{(x-x_0)^2+a^2}\right)^{(1/2)}} $$ where
a is the distance to the screen, x is the position on the screen
and {x0,0} is the center of the elementary wave. This wave
should carry an intensity of 1.  According to the Huygens-
Fresnel principle, I should be able to calculate the amplitude
in any place {x,a} behind the slot via $$ A(x)=\int_{-w/2}^{w/2}
A(x,x_0)\text{d}x_0 $$ $$ \approx\sum_{n=0}^{w/\Delta w}
A(x,n*\Delta w) \Delta w $$ This seems to work quite well
(result does not change notably for smaller step width) for
$\Delta w<\lambda/5$.  I am using in Mathematica in 2
dimensions. This should numerically calculate the image on a
180° screen i