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Two-Dimensional Pulse Propagation without Anomalous Dispersion.

Carl M Bender1,2, Francisco J Rodríguez-Fortuño2, Sarben Sarkar2

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|September 27, 2017
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Summary
This summary is machine-generated.

Anomalous dispersion in two-dimensional wave propagation can be eliminated by modifying the wave equation to include two time dimensions. This offers new methods for ultrashort pulse shaping in metamaterials.

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Area of Science:

  • Physics
  • Wave Propagation
  • Optics and Acoustics

Background:

  • Anomalous dispersion is observed in wave propagation across even spatial dimensions.
  • Wave pulses in 2D space develop tails without a dispersive medium.

Purpose of the Study:

  • To mathematically eliminate anomalous dispersion in 2D wave propagation.
  • To explore a modified wave equation with two spatial and two timelike dimensions.

Main Methods:

  • Mathematical analysis of a modified wave equation.
  • Investigating wave pulse behavior in a novel spacetime.

Main Results:

  • Demonstrated elimination of anomalous dispersion using the modified wave equation.
  • The modified equation describes hyperbolic dispersion in optical/acoustic media.

Conclusions:

  • A new theoretical framework for understanding and controlling wave dispersion.
  • Enables novel approaches for ultrashort pulse shaping in nanostructured metamaterials.