COHERENT PATTERNS AND SELF-INDUCED DIFFRACTION OF ELECTRONS ON A THINNONLINEAR LAYER

Electron scattering on a thin layer where the potential depends self-c onsistently on the wave function has been studied. When the amplitude of the incident wave exceeds a certain threshold, a soliton-shaped bri ghtening (darkening) appears on the layer causing diffraction of the w ave. Thus the spontaneously formed transverse pattern can be viewed as a self-induced nonlinear quantum screen. Attractive or repulsive nonl inearities result in different phase shifts of the wave function on th e screen, which give rise to quite different diffraction patterns. Amo ng others, the nonlinearity can cause self-focusing of the incident wa ve into a ''beam,'' splitting in two ''beams,'' single or double trace s with suppressed reflection or transmission, etc.