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Published on: February 6, 2014
Two-Dimensional Pulse Propagation without Anomalous Dispersion
Carl M Bender1,2, Francisco J Rodríguez-Fortuño2, Sarben Sarkar2
1Department of Physics, Washington University, St. Louis, Missouri 63130, USA.
Abstract:
Anomalous dispersion is a surprising phenomenon associated with wave propagation in an even number of space dimensions. In particular, wave pulses propagating in two-dimensional space change shape and develop a tail even in the absence of a dispersive medium. We show mathematically that this dispersion can be eliminated by considering a modified wave equation with two geometric spatial dimensions and, unconventionally, two timelike dimensions. Experimentally, such a wave equation describes pulse propagation in an optical or acoustic medium with hyperbolic dispersion, leading to a fundamental understanding and new approaches to ultrashort pulse shaping in nanostructured metamaterials.
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