So the first thing is, let's approximate that we could take the sum not to some finite level, which would be the case if there's a finite number of elements in the chain.

The transformation of Gaussian beams is taken as an example, an approximate analytical propagation expression in terms of a sum of elementary functions is derived.

With the rectangular function expanded into a finite sum of complex Gaussian functions, an approximate analytical propagation equation of HChG beams is derived.