Non-linear phenomena in catastrophe focusings

The main purpose of the present work is to research the influence of the weak non-linearity of the refraction index in the electromagnetic wave propagation in the vicinity of the catastrophe type focusing. The problem with a specially constructed phase screen, which creates in uniform media with linear refraction index focusing of the type under consideration, is investigated as a particular case for research. A flat electromagnetic wave falls on the phase screen and generates the focusing region behind the screen. The diffraction structure without any non-linearity is well known. It can be estimated, for example, by means Maslov's method of the canonical operator.