Abstract
We investigate bright and dark diffractive focusing emerging in the free propagation of specific wave profiles. These general wave phenomena manifest themselves in matter, water, and classical waves. In this article, we lay the foundations for these effects and illustrate their origin in Wigner phase space. Our theoretical studies are supported by experimental demonstrations of dark focusing in water waves. Moreover, by using different phase slits we analyze several aspects of bright and dark focusing for classical and matter waves.
Highlights
In a previous article [5], we have addressed the diffractive focusing of a rectangular wave packet for matter waves and the classical analogy arising in the diffraction from a slit
We call the later phenomenon dark focusing by analogy and in contrast to the bright focusing familiar from the diffractive focusing of rectangular wave packets or a slit with constant phase
We introduce the phenomena of bright and dark focusing which manifest themselves in the free propagation of particular wave packets
Summary
Focusing is usually associated with an increase of intensity. The other extreme is zero intensity. There are other waves which preserve their shape (nondiffracting) in the propagation direction, as the Bessel light beams [8], or that accelerate in the direction of the transverse coordinate: the Airy wave packets, which were firstly predicted in the context of quantum physics [9] and later experimentally demonstrated with the help of classical waves [10, 11] Their properties are beyond the scope of this article. We investigate matter, water, and classical wave packets of constant amplitude with an initial phase dependence on the transverse coordinate This feature results in unexpected focusing effects: an increase of the degree of focusing in some cases, or the emergence of temporary darkness in the middle of the wave packet, corresponding to localized minima in the intensity pattern. We establish the necessary conditions to describe these bright and dark focusing effects and investigate the properties of this new type of focusing from different perspectives
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