Fractional Effective Charges and Misner-Wheeler Charge without Charge Effect in Metamaterials
"> Figure 1
<p>(<b>a</b>) “Optical space” in an anisotropic uniaxial metamaterial may mimic such topologically non-trivial 3D space as R<sub>2</sub> × S<sub>1</sub>, which is a product of a 2D plane R<sub>2</sub> and a circle S<sub>1</sub>. (<b>b</b>) Schematic view of the “layered” 3D hyperbolic metamaterial made of subwavelength metal and dielectric layers, which can be used to emulate the R<sub>2</sub> × S<sub>1</sub> space. (<b>c</b>) Example of numerical calculations of electromagnetic field distribution in the <span class="html-italic">xz</span> plane inside the R<sub>2</sub> × S<sub>1</sub> metamaterial space using Comsol Multiphysics 4.2a (COMSOL, Inc., Burlington, MA, USA). The distances in the <span class="html-italic">xz</span> plane are measured in the units of wavelength. The power flow distribution (calculated using the scattering boundary conditions) is similar to power flow in a multimode planar waveguide.</p> "> Figure 2
<p>(<b>a</b>) Schematic view of a toroidal handlebody, which connects two points of the R<sub>2</sub> × S<sub>1</sub> metamaterial space and changes its effective topology. (<b>b</b>,<b>c</b>) Numerical simulations of the electromagnetic wormhole performed using the scattering boundary conditions: (b) spatial distribution of <span class="html-italic">ε<sub>1</sub></span>, and (c) corresponding spatial distribution of <span class="html-italic">B<sub>y</sub></span>. The distances in the <span class="html-italic">xz</span> plane are measured in the units of wavelength.</p> "> Figure 2 Cont.
<p>(<b>a</b>) Schematic view of a toroidal handlebody, which connects two points of the R<sub>2</sub> × S<sub>1</sub> metamaterial space and changes its effective topology. (<b>b</b>,<b>c</b>) Numerical simulations of the electromagnetic wormhole performed using the scattering boundary conditions: (b) spatial distribution of <span class="html-italic">ε<sub>1</sub></span>, and (c) corresponding spatial distribution of <span class="html-italic">B<sub>y</sub></span>. The distances in the <span class="html-italic">xz</span> plane are measured in the units of wavelength.</p> "> Figure 3
<p>Numerical simulations of power flow near the electromagnetic wormhole in the same geometry as in <a href="#photonics-03-00043-f002" class="html-fig">Figure 2</a>b,c, which demonstrates “charge without charge” effect. The average Poynting vector direction is indicated by black arrows. Near the wormhole openings the <span class="html-italic">z</span> components of the Poynting vector <span class="html-italic">S<sub>3</sub></span> are nonzero and have opposite signs, which according to Equations (11)–(14) leads to appearance of opposite contributions to the effective charge of the wormhole openings (the openings are marked by dashed lines).</p> "> Figure 4
<p>If the wormhole geometry exhibits some symmetry (such as symmetry under rotation by either π (<b>a</b>) or 2π/3 (<b>b</b>) radian, the allowed values of effective charges of the wormhole openings may become restricted to some simple fractions of the “elementary charge” <span class="html-italic">e</span>: if such a rotational symmetry is imposed on electromagnetic field configurations, the integer effective charge inside <span class="html-italic">A</span> must be divided equally between the wormhole openings.</p> "> Figure 4 Cont.
<p>If the wormhole geometry exhibits some symmetry (such as symmetry under rotation by either π (<b>a</b>) or 2π/3 (<b>b</b>) radian, the allowed values of effective charges of the wormhole openings may become restricted to some simple fractions of the “elementary charge” <span class="html-italic">e</span>: if such a rotational symmetry is imposed on electromagnetic field configurations, the integer effective charge inside <span class="html-italic">A</span> must be divided equally between the wormhole openings.</p> ">
Abstract
:1. Introduction
2. Methods
3. Results
4. Discussion
5. Conclusions
Conflicts of Interest
References
- Pendry, J.B.; Schurig, D.; Smith, D.R. Controlling electromagnetic fields. Science 2006, 312, 1780–1782. [Google Scholar] [CrossRef] [PubMed]
- Leonhardt, U. Optical conformal mapping. Science 2006, 312, 1777–1780. [Google Scholar] [CrossRef] [PubMed]
- Leonhardt, U.; Philbin, T.G. General relativity in electrical engineering. New J. Phys. 2006, 8. [Google Scholar] [CrossRef]
- Smolyaninov, I.I.; Hwang, E.; Narimanov, E.E. Hyperbolic metamaterial interfaces: Hawking radiation from Rindler horizons and spacetime signature transitions. Phys. Rev. B 2012, 85, 235122. [Google Scholar] [CrossRef]
- Greenleaf, A.; Kurylev, Y.; Lassas, M.; Uhlmann, G. Electromagnetic Wormholes and Virtual Magnetic Monopoles from Metamaterials. Phys. Rev. Lett. 2007, 99, 183901. [Google Scholar] [CrossRef] [PubMed]
- Kadic, M.; Dupont, G.; Guenneau, S.; Enoch, S. Invisible waveguides on metal plates for plasmonic analogs of electromagnetic wormholes. Phys. Rev. A 2014, 90, 043812. [Google Scholar] [CrossRef]
- Smolyaninov, I.I. Metamaterial “multiverse”. J. Opt. 2011, 13, 024004. [Google Scholar] [CrossRef]
- Smolyaninov, I.I. Analog of gravitational force in hyperbolic metamaterials. Phys. Rev. A 2013, 88, 033843. [Google Scholar] [CrossRef]
- Smolyaninov, I.I. Holographic duality in nonlinear hyperbolic metamaterials. J. Opt. 2014, 16, 075101. [Google Scholar] [CrossRef]
- Landau, L.D.; Lifshitz, E.M. Electrodynamics of Continuous Media; Elsevier: Oxford, UK, 2004. [Google Scholar]
- Wangberg, R.; Elser, J.; Narimanov, E.E.; Podolskiy, V.A. Nonmagnetic nanocomposites for optical and infrared negative-refractive-index media. J. Opt. Soc. Am. B 2006, 23, 498–505. [Google Scholar] [CrossRef]
- Smolyaninov, I.I.; Hung, Y.J.; Davis, C.C. Magnifying superlens in the visible frequency range. Science 2007, 315, 1699–1701. [Google Scholar] [CrossRef] [PubMed]
- Liu, Z.; Lee, H.; Xiong, Y.; Sun, C.; Zhang, X. Far-field optical hyperlens magnifying sub-diffraction-limited objects. Science 2007, 315, 1686. [Google Scholar] [CrossRef] [PubMed]
- Lencina, A.; Vaveliuk, P. Squared-field amplitude modulus and radiation intensity nonequivalence within nonlinear slabs. Phys. Rev. E 2005, 71, 056614. [Google Scholar] [CrossRef] [PubMed]
- Greiner, W.; Schäfer, A. Quantum Chromodynamics; Springer: Berlin/Heidelberg, Germany, 1994. [Google Scholar]
- Kane, C.L.; Fisher, M.P.A. Nonequilibrium noise and fractional charge in the quantum Hall effect. Phys. Rev. Lett. 1994, 72, 724–727. [Google Scholar]
- Jensen, K.; Karch, A. Holographic dual of an Einstein-Podolsky-Rosen pair has a wormhole. Phys. Rev. Lett. 2013, 111, 211602. [Google Scholar] [CrossRef] [PubMed]
- Sonner, J. Holographic Schwinger effect and the geometry of entanglement. Phys. Rev. Lett. 2013, 111, 211603. [Google Scholar] [CrossRef] [PubMed]
- Smolyaninov, I.I. Vacuum in a strong magnetic field as a hyperbolic metamaterial. Phys. Rev. Letters 2011, 107, 253903. [Google Scholar] [CrossRef] [PubMed]
- Misner, C.; Wheeler, J.A. Classical physics as geometry. Ann. Phys. 1957, 2, 525–603. [Google Scholar] [CrossRef]
- Guendelman, E.; Kaganovich, A.; Nissimov, E.; Pacheva, S. Hiding charge in a wormhole. Open Nucl. Part. Phys. J. 2011, 4, 27–34. [Google Scholar] [CrossRef]
- Olmo, G.; Rubiera-Garcia, D.; Sanchez-Puente, A. Classical resolution of black hole singularities via wormholes. Eur. Phys. J. C 2016, 76, 143. [Google Scholar] [CrossRef]
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Smolyaninov, I. Fractional Effective Charges and Misner-Wheeler Charge without Charge Effect in Metamaterials. Photonics 2016, 3, 43. https://doi.org/10.3390/photonics3030043
Smolyaninov I. Fractional Effective Charges and Misner-Wheeler Charge without Charge Effect in Metamaterials. Photonics. 2016; 3(3):43. https://doi.org/10.3390/photonics3030043
Chicago/Turabian StyleSmolyaninov, Igor. 2016. "Fractional Effective Charges and Misner-Wheeler Charge without Charge Effect in Metamaterials" Photonics 3, no. 3: 43. https://doi.org/10.3390/photonics3030043