Faraday-Talbot effect: Alternating phase and circular arrays

• Published in: Chaos (Woodbury, N.Y.) Vol. 28; no. 9; pp. 096101 - 96107
• Main Authors: Sungar, N., Sharpe, J. P., Pilgram, J. J., Bernard, J., Tambasco, L. D.
• Format: Journal Article
• Language: English
• Published: United States American Institute of Physics 01.09.2018
• Subjects: Arrays; Curvature; Ridges; Superposition (mathematics); Talbot effect
• ISSN: 1054-1500; 1089-7682; 1089-7682
• DOI: 10.1063/1.5031442

A hydrodynamic analog to the optical Talbot effect may be realized on the surface of a vertically shaken fluid bath when a periodic array of pillars protrudes from the fluid surface. When the pillar spacing is twice or one and a half times the Faraday wavelength, we observe repeated images of the pillars projected in front of the array. Sloshing inter-pillar ridges act as sources of Faraday waves, giving rise to self-images. Here, we explore the emergence of Faraday-Talbot patterns when the sloshing ridges between pillars have alternating phases. We present a simple model of linear wave superposition and use it to calculate the expected self-image locations, comparing them to experimental observations. We explore how alternating phase sources affect the Faraday-Talbot patterns for linear and circular arrays of pillars, where curvature allows for magnification and demagnification of the self-imaging pattern. The use of an underlying wavefield is a subject of current interest in hydrodynamic quantum analog experiments, as it may provide a means to trap walking droplets.