Far-Field Diffraction and Polarization Properties of a Three-Dimensional Hollow, Homogeneous, Isotropic Cone*†

Abstract

A brief description is given of a theory for computing the form of the far-field diffraction and polarization properties of a hollow, homogeneous, isotropic cone, when it is placed between arbitrarily oriented polarizer and analyzer. For this theory, the incident plane wavefront and circular aperture are normal to the axis of the cone. The solution is an “optical one” for which the circular aperture is large compared with the wavelength, the diffraction properties of the cone in the plane of circular aperture are negligible, and multiple reflections between the cone, circular aperture, and focusing system are neglected. All the multiple reflections which arise inside the cone walls and make contributions to the amplitude and phase in the circular aperture are, however, included. Within these limits, it is possible to compute the radiant flux and form of the farfield diffraction pattern for a cone of arbitrary angle, wall thickness, and optical properties, when it is placed between arbitrarily oriented polarizer and analyzer. In all cases, the symmetry properties of these far-field diffraction patterns can be predicted from the forms of the equations. Computations on the detailed forms of these far-field diffraction patterns have been carried out with an IBM 7090 computer, and three-dimensional models constructed and photographed to show their symmetry properties. It has not been possible experimentally to check these computations because of the problems arising in the making and testing of a cone of the required interferometer quality.