Simulation of wave propagation through an annulus

Here is a movie showing simulations of plane wave propagation through an annulus.

Wave propagation simulation

This simulation was performed by applying an annular aperture to a plane wave. The outer diameter of the aperture was 30 millimeters and the outer diameter was 6.15 millimeters. The wavefront dimensions were chosen as 1024x1024, but only the inner 512x512 region is pictured. The pixel scale was .117 millimeters, and the electromagnetic wavelength was 1 micron.

The movie shows the evolution of the plane wave amplitude as it propagates for 150 meters past the aperture. A near field propagator is used to perform wave propagation from 0 to 100 meters, and a far field propagator is used to perform wave propagation from 50 to 150 meters. For distances between 50 and 100 meters, both near and far field plane wave amplitudes are shown. The propagation distance is shown in the upper left corner of the movie.

The division between near and far field propagation is not as clear as the movie would seem to indicate. Papalexandris and Redding (2000, JOSA 17, 1764) performed a simulation of propagation from a rectangular aperture and concluded that switching between near and far field propagators at a Fresnel number of 30 minimized the average error in the simulated phase. (These authors clearly had interferometry in mind.) Here I've rather arbitrarily represented that there's a range over which both near and far field propagation are both valid - in this range the difference between near field and far field wavefronts is of order a few percent. Simulations requiring the highest precision would require specific studies to determine the level of error and the optimal propagation method.

Note that the plane wave doesn't reach the far field until the Fresnel number is much less than one. For the aperture size and electromagnetic wavelength chosen for this simulation, this far field propagation distance is much greater than 3 kilometers. Thus the movie terminates long before the plane wave amplitude arrives at its asymptotic far field form.