Abstract
We study the analogy between propagation of light rays in a stationary curved spacetime and in a toroidal (meta-)material. After introducing a novel gravitational analog of the index of refraction of a magneto-electric medium, it is argued that light rays not only feel a Lorentz-like force in a magneto-electric medium due to the non-vanishing curl of the toroidal moment, but also there exists an optical analog of Aharonov–Bohm effect for the rays traveling in a region with a curl-free toroidal moment. Experimental realization of this effect could utilize either a multiferroic material or a toroidal metamaterial.
Highlights
Apart from yet being the most successful theory of gravity, general relativity and the exact solutions of Einstein field equations, in recent years have turned into a very powerful tool to study linear and nonlinear phenomena in other branches of physics
In the present article, motivated by the gravitational Aharonov-Bohm effect, first we use the 1 + 3 formulation of spacetime decomposition to exhibit an interesting analogy between electromagnetic wave propagation in a stationary curved spcetime and in a magneto-electricmaterial, and employ this analogy to show that there should be an optical analog of this effect inmaterials with toroidal moment
In section five after a brief introduction of the gravitational Aharonov-Bohm effect we discuss our prediction of the optical analog of the Aharonov-Bohm effect in toroidalmaterials with any value for the toroidal moment and show that it reduces to the previous result in the limit of small toroidal moment
Summary
Apart from yet being the most successful theory of gravity, general relativity and the exact solutions of Einstein field equations, in recent years have turned into a very powerful tool to study linear and nonlinear phenomena in other branches of physics. Their nontrivial properties, such as negative refractive index [3], originate not from the composition of their constituents, but from the way these subwavelength macroscopic constituents are assembled Another key development was the introduction of transformation optics [4], which formulates how electromagnetic field lines and the corresponding light rays could be redirected by deforming the underlying space in which they are embedded, very much like rerouting a river by deforming its bed. For a stationary spacetime we arrive at a novel form for the spacetime index of refraction, introduced here for the first time in the literature, which enables us to interpret it as the gravitational analog of the magneto-electric index of refraction in a material with toroidal moment In section three this analogy is extended to Maxwell equations in a stationary spacetime and their corresponding constitutive equations which include magneto-electric terms. Throughout we use the (+,-,-,-) signature for spacetime metric and our convention for indices is such that the Latin indices run from 1 to 3 while the Greek ones run from 0 to 3
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
