How to calculate the aperture field strength distribution of corrugated horn antenna ?

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Miguel Ferrando-Rocher

Maybe this?

Clarricoats, P. J. B., & Olver, A. D. (1984). Corrugated horns for microwave antennas (No. 18). Iet.

ISO 690

Malcolm White

For a simple corrugated horn, if it is designed properly, the field distribution is mainly described by 2 modes of the circular aperture, which are given in the reference by Miguel Ferrando-Rocher . The modes and their fields can be calculated using Bessel functions and harmonic functions (sine and cos). The ratio of the two modes is given by the requirement that the radial electric fields of the two cancel each other at the top and bottom of the aperture. The corrugations are designed so that the radial electric fields are zero all the round the aperture, as well as the circumferential electric fields (which are zero for ordinary horns).