# Light Propagation through Nanophotonics Wormholes

## Abstract

**:**

## 1. Introduction

## 2. Traversable Wormhole Spacetimes

## 3. Embedding Wormhole Surfaces

## 4. Surfaces of Revolution in the Laboratory

## 5. Wave Equations

## 6. Results

## 7. Conclusions

## Acknowledgments

## Conflicts of Interest

## References

- Shoresh, T.; Katanov, N.; Malka, N. 1 × 4 MMI visible light wavelength demultiplexer based on a GaN slot-waveguide structure. Photonics Nanostruct. Fundam. Appl.
**2018**, 30, 45–49. [Google Scholar] [CrossRef] - Nikolaevsky, L.; Shchori, T.; Malka, D. Modeling a 1 × 8 MMI green light power splitter based on Gallium-Nitride slot waveguide structure. IEEE Photonics Technol. Lett.
**2018**, 30, 720–723. [Google Scholar] [CrossRef] - Malka, D.; Danan, Y.; Ramon, Y.; Zalevsky, Z.A. Photonic 1 × 4 Power Splitter Based on Multimode Interference in Silicon-Gallium-Nitride Slot Waveguide Structures. Materials
**2016**, 9, 516. [Google Scholar] [CrossRef] - Leonhardt, U.; Philbin, T.G. General relativity in electrical engineering. New J. Phys.
**2006**, 8, 247. [Google Scholar] [CrossRef] - Schultheiss, V.H.; Batz, S.; Szameit, A.; Dreisow, F.; Nolte, S.; Tünnermann, A.; Peschel, U. Optics in curved space. Phys. Rev. Lett.
**2010**, 105, 149301. [Google Scholar] [CrossRef] - Bekenstein, R.; Nemirowsky, J.; Kaminer, I.; Segev, M. Shape-preserving accelerating electromagnetic wave-packets in curved space. Phys. Rev. X
**2014**, 4, 011038. [Google Scholar] [CrossRef] - Bekenstein, R.; Kabessa, Y.; Sharabi, Y.; Tal, O.; Engheta, N.; Eisenstein, G.; Segev, M. Control of light by curved space in nanophotonic structures. Nat. Photonics
**2017**, 11, 664. [Google Scholar] [CrossRef] - Misner, C.W.; Thorne, K.S.; Wheeler, J.A. Gravitation; W. H. Freeman: San Francisco, CA, USA, 1973. [Google Scholar]
- Ellis, H.G. Ether Flow Through a Drainhole: A Particle Model in General Relativity. J. Math. Phys.
**1973**, 14, 104–118. [Google Scholar] [CrossRef] - Morris, M.S.; Thorne, K.S.; Yurtsever, U. Wormholes, Time Machines, and the Weak Energy Condition. Phys. Rev. Lett.
**1988**, 61, 1446. [Google Scholar] [CrossRef] - Takahashi, R.; Asada, H. Observational upper bound on the cosmic abundances of negative-mass compact objects and Ellis wormholes from the Sloan digital sky survey quasar lens search. Astrophys. J. Lett.
**2013**, 768, L16. [Google Scholar] [CrossRef] - Morris, M.S.; Thorne, K.S. Wormholes in spacetime and their use for interstellar travel: A tool for teaching general relativity. Am. J. Phys.
**1988**, 56, 395–412. [Google Scholar] [CrossRef] - Hawking, S.W. Chronology protection conjecture. Phys. Rev. D
**1992**, 46, 603. [Google Scholar] [CrossRef] - Deutsch, D. Quantum mechanics near closed timelike lines. Phys. Rev. D
**1991**, 44, 3197. [Google Scholar] [CrossRef] - Ford, L.H.; Roman, T.A. Averaged energy conditions and quantum inequalities. Phys. Rev. D
**1995**, 51, 4277. [Google Scholar] [CrossRef] - Li, Z.; Bambi, C. Distinguishing black holes and wormholes with orbiting hot spots. Phys. Rev. D
**2014**, 90, 024071. [Google Scholar] [CrossRef] [Green Version] - Cardoso, V.; Franzin, E.; Pani, P. Is the Gravitational-Wave Ringdown a Probe of the Event Horizon? Phys. Rev. Lett.
**2016**, 116, 171101. [Google Scholar] [CrossRef] - Konoplya, R.A.; Zhidenko, A. Wormholes versus black holes: Quasinormal ringing at early and late times. J. Cosmol. Astropart. Phys.
**2016**, 12, 043. [Google Scholar] [CrossRef] - Yuan, X.; Assad, S.M.; Thompson, J.; Haw, J.-Y.; Vedral, V.; Ralph, T.C.; Gu, M. Replicating the benefits of Deutschian closed timelike curves without breaking causality. NPJ Quant. Inf.
**2015**, 1, 15007. [Google Scholar] [CrossRef] [Green Version] - Maldacena, J.; Susskind, L. Cool horizons for entangled black holes. Fortschritte del Physik
**2013**, 61, 781–811. [Google Scholar] [CrossRef] [Green Version] - Müller, T. Exact geometric optics in a Morris-Thorne wormhole spacetime. Phys. Rev. D
**2008**, 77, 044043. [Google Scholar] [CrossRef] - Taylor, P. Propagation of test particles and scalar fields on a class of wormhole space-times. Phys. Rev. D
**2014**, 90, 024057. [Google Scholar] [CrossRef] - Sabín, C. Mapping curved spacetimes into Dirac spinors. Sci. Rep.
**2017**, 7, 40346. [Google Scholar] [CrossRef] [Green Version] - Abe, F. Gravitational Microlensing by the Ellis Wormhole. Astrophys. J.
**2010**, 725, 787. [Google Scholar] [CrossRef] - Nakajima, K.; Asada, H. Deflection angle of light in an Ellis wormhole geometry. Phys. Rev. D
**2012**, 85, 107501. [Google Scholar] [CrossRef] - Ohgami, T.; Sakai, N. Wormhole shadows. Phys. Rev. D
**2015**, 91, 124020. [Google Scholar] [CrossRef] - Sabín, C. Quantum detection of wormholes. Sci. Rep.
**2017**, 7, 716. [Google Scholar] [CrossRef] - Peloquin, C.; Euvé, L.-P.; Philbin, T.; Rousseaux, G. Analogue wormholes and black hole LASER effect in hidrodynamics. Phys. Rev. D
**2016**, 93, 084032. [Google Scholar] [CrossRef] - Euvé, L.-P.; Rousseaux, G. Classical analogue of an interstellar travel through a hidrodynamic wormhole. Phys. Rev. D
**2017**, 96, 064042. [Google Scholar] [CrossRef] - Prat-Camps, J.; Navau, C.; Sanchez, A. A magnetic wormhole. Sci. Rep.
**2015**, 5, 12488. [Google Scholar] [CrossRef] - Sabín, C. Quantum simulation of traversable wormhole spacetimes in a dc-SQUID array. Phys. Rev. D
**2016**, 94, 081501. [Google Scholar] [CrossRef] [Green Version] - Mateos, J.; Sabín, C. Quantum simulation of traversable wormhole spacetimes in a Bose-Einstein condensate. Phys. Rev. D
**2018**, 97, 044045. [Google Scholar] [CrossRef] [Green Version] - Sabín, C. One-dimensional sections of exotic spacetimes with superconducting circuits. New J. Phys.
**2018**, 20, 053028. [Google Scholar] [CrossRef]

**Figure 1.**(

**a**) Flamm paraboloid corresponding to Schwarzschild black-hole metric. (

**b**) Embedding surface of Ellis traversable-wormhole metric. Schwarzschild radius in (

**a**) is equal to wormhole’s throat radius in (

**b**) ${b}_{0}=30$ $\mathsf{\mu}$m. Notice the similarity between both figures. (

**b**) does not seem to entail additional experimental challenges.

**Figure 2.**Group velocity ${v}_{g}/c$ vs the spatial coordinate z for ${b}_{0}=30$ $\mathsf{\mu}$m, ${k}_{0}=2\pi /\lambda $, $\lambda =780\mathrm{nm}$, ${n}_{0}=1.5$, $q=5.9\xb7{10}^{6}$ m${}^{-1}$ and the values of ${k}_{x}$ indicated. The group velocity can significantly decrease near the wormhole throat at $z=0$.

**Figure 3.**Phase velocity ${v}_{p}h/c$ vs the spatial coordinate z for ${b}_{0}=30$ $\mathsf{\mu}$m, ${k}_{0}=2\pi /\lambda $, $\lambda =780\mathrm{nm}$, ${n}_{0}=1.5$, $q=5.9\xb7{10}^{6}$ m${}^{-1}$ and the values of ${k}_{x}$ indicated. The phase velocity increases and can become superluminal near the throat.

© 2018 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Sabín, C.
Light Propagation through Nanophotonics Wormholes. *Universe* **2018**, *4*, 137.
https://doi.org/10.3390/universe4120137

**AMA Style**

Sabín C.
Light Propagation through Nanophotonics Wormholes. *Universe*. 2018; 4(12):137.
https://doi.org/10.3390/universe4120137

**Chicago/Turabian Style**

Sabín, Carlos.
2018. "Light Propagation through Nanophotonics Wormholes" *Universe* 4, no. 12: 137.
https://doi.org/10.3390/universe4120137