Abstract
We present the theoretical models and review the most recent results of a class of experiments in the field of surface gravity waves. These experiments serve as demonstration of an analogy to a broad variety of phenomena in optics and quantum mechanics. In particular, experiments involving Airy water-wave packets were carried out. The Airy wave packets have attracted tremendous attention in optics and quantum mechanics owing to their unique properties, spanning from an ability to propagate along parabolic trajectories without spreading, and to accumulating a phase that scales with the cubic power of time. Non-dispersive Cosine-Gauss wave packets and self-similar Hermite-Gauss wave packets, also well known in the field of optics and quantum mechanics, were recently studied using surface gravity waves as well. These wave packets demonstrated self-healing properties in water wave pulses as well, preserving their width despite being dispersive. Finally, this new approach also allows to observe diffractive focusing from a temporal slit with finite width.
Highlights
Propagation of waves of different nature is at the heart of most physical processes we are familiar with
It was demonstrated that for vanishingly narrow spectrum, water-waves are governed by the Nonlinear Schrödinger equation (NLSE) that describes the evolution of the scaled complex wave packet envelope A = aã0 in the physical space:
Numerous examples presented here demonstrate essential features that are common to propagation of hydrodynamics surface water gravity wave trains and quantum mechanical wavefunctions and electromagnetic pulses and optical beams
Summary
Propagation of waves of different nature is at the heart of most physical processes we are familiar with. Quantum mechanical wave functions are essential for understanding of every subatomic physical process [4,5]. These diverse phenomena and processes, that are illustrated, are governed by different physical laws or forces. Quite often the propagation of those waves is described by the same set of mathematical equations resulting in shared physical behavior in different systems [6,7,8]. We highlight the essential advantages of studying classical gravity water-wave packets over a quantum mechanical or optical system. Paraxial Helmholtz equation describing wave propagation dynamics of an optical beam. Helmholtz equation. (c) An illustration of Gaussian (top) and Airy (bottom) wavefunctions which are solutions of the Schrödinger equation of a free particle
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