Generation of Some Catastrophes in Optics by Binary Screens

Abstract

In this paper, the artificial generation of elementary catastrophe optics having odd codimensions K = 1, 3 and 5 such as the Fold, the Swallowtail and the Wigwam diffraction caustics is investigated theoretically. It is shown that the integral catastrophes with odd polynomials phase functions can be reduced to the well-known Airy-Hardy cosine integrals. In this connection, the caustic functions of the Fold, Swallowtail and Wigwam caustic beams are expressed in closed-form in terms of Airy-Hardy cosine functions. An optical method based on the Fourier transform similar to that described by Lohmann et al. [Optics Comm. 109 (1994) 361-367] is proposed for the generation of the Fold, Swallowtail and Wigwam caustic beams. The displaying of the catastrophe patterns with K = 1, 3 and 5 is optically implemented in the Fourier transform device by using simple binary screens with tailored polynomials transmission.