Light in curved two-dimensional space

Schultheiß V, Schultheiß V, Batz S, Peschel U (2020)

Publication Type: Journal article, Review article

Publication year: 2020

Journal

Advances in Physics: X Taylor & Francis

Book Volume: 5

Journal Issue: 1

DOI: 10.1080/23746149.2020.1759451

Abstract

The extrinsic and intrinsic curvature of a two-dimensional wave-guide influences wave propagation therein. While this can already be apprehended from a geometric point of view in terms of geodesics generalizing straight lines as the shortest distance between any two points, in wave optics interference phenomena strongly govern the field evolution, too. Radii of curvature in the order of the wavelength of light modify the local effective refractive index by altering the mode profile. Macroscopic radii only influence light propagation for non-vanishing intrinsic (or Gaussian) curvature. A positive Gaussian curvature leads to refocusing and thus an imaging behavior, whereas negative Gaussian curvature forces the field profile to diverge exponentially. These effects can be explained by an effective transverse potential acting on the electromagnetic field distribution's envelope. This can also be extended to nonlinear beam propagation. In this review paper we give a thorough introduction to differential geometry in two-dimensional manifolds and its incorporation with Maxwell's equations. We report on first fundamental experiments in this newly emerging field, which may lead to applications in integrated optical circuits. The dose conceptual analogy to phenomena in four-dimensional spacetime with constant curvature as well as toy-models of the Schwarzschild metric and a wormhole topology are also discussed.

Authors with CRIS profile

Vincent Schultheiß Institut für Optik, Information und Photonik Ulf Peschel

Involved external institutions

Friedrich-Schiller-Universität Jena DE Germany (DE)

How to cite

APA:

Schultheiß, V., Schultheiß, V., Batz, S., & Peschel, U. (2020). Light in curved two-dimensional space. Advances in Physics: X, 5(1). https://dx.doi.org/10.1080/23746149.2020.1759451

MLA:

Schultheiß, Vincent, et al. "Light in curved two-dimensional space." Advances in Physics: X 5.1 (2020).

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