Abstract

Our space marching algorithm is of the split-step Fourier transform type. In this method, space is divided in thin slices Δz. The first step involves the propagation of the angular plane wave spectrum of the incident light field through a slice as if the latter were homogeneous. At the exit of the slice the propagated plane waves are reassembled into an intermediate field. In the second step the intermediate field is multiplied by the x,y dependent transmission function of the slice as if the latter were a thin phase filter, induced by the sound. A similar technique (that does not necessarily involve the plane wave spectrum) is often called the beam propagation method, and has been used for the analysis of gratings before. In our case, however, we are interested in soundfields of arbitrary shape and–this feature ultimately constitutes the novelty of our method–in avoiding the processing of the sound carrier. The latter is not of intrinsic interest to us and merely uses up computer time in dealing with the fine inhomogeneous detail it induces. What the sound carrier does we know already: It splits each incident order of light up into three other ones when traversing a small distance Δz. In our algorithm we make use of this a priori knowledge to involve only the envelope or profile of the sound field in the simulation.

© 1990 Optical Society of America