Single-slit focusing and its representations

Abstract

theory of light. Three years later he participated with his Mémoire sur la Diffraction de la Lumière in the Grand Prix of the French Academy of Sciences [2]. It was on this occasion that Siméon Poisson predicted that an opaque disc illuminated by parallel light would create a bright spot in the center of a shadow. This phenomenon was experimentally confirmed by Francois Arago and led to the victory of the wave over the particle theory. In the present article we discuss an effect related to the Poisson spot which is the onedimensional analogue of the camera obscura [3,4].Indeed, we have recently found [5] that a rectangular matter wave packet which undergoes free time evolution according to the Schrödinger equation focuses before it spreads. This phenomenon has been confirmed for light [6], water and surface plasmon waves [7]. In the present article we illustrate this effect in Wigner phase space and verify it using classical light in real space.Our article is organized as follows: in Sect. 2 we first give a brief history of the diffraction of waves, and then review several focusing effects especially those associated with the phenomenon of diffraction in time introduced in Moshinsky [8].We dedicate Sect. 3 to the discussion of the focusing of a rectangular wave packet from the point of view of the timedependent wave function. In particular, we show this effect Abstract We illustrate the phenomenon of the focusing of a freely propagating rectangular wave packet using three different tools: (1) the time-dependent wave function in position space, (2) the Wigner phase-space approach, and (3) an experiment using laser light.

Equivalence between quantum backflow and classically forbidden probability flow in a diffraction-in-time problem

“…[16] for a review and Refs. [17][18][19][20][21][22][23] for some more recent results). The question of finding the maximal reentry probability, addressed in this paper, is essentially Moshinsky's DIT problem in a variational context: for ℓ ≥ 0, one looks for a normalized initial wave function of the form θ(−x)ψ(x) that maximizes the probability transfer from the spatial region x > ℓ to the region x < ℓ during a time interval τ 1 < t < τ 2 .…”

Quantum Mechanical and Optical Analogies in Surface Gravity Water Waves

“…According to intuition we gain from classical physics, a wave that has passed through a slit will expand. However, this picture is incomplete; it was predicted [44] that a rectangular one-dimensional quantum wave packet created from a plane wave by a one-dimensional slit first focuses and only then expands. This phenomenon can be described by applying the Schrödinger equation.…”

Diffraction of particles in free fall

“…Regarding δx, the main preoccupation should be a proper definition of width that eliminates the ever-growing contributions of wave packet standard deviations (due to the uncertainty principle). This was carefully explained in [28] in connection with the focusing effect of light, including experimental results in [50] as a happy outcome.…”