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Open AccessArticle

Aperiodic Photonics of Elliptic Curves

1
Department of Electrical and Computer Engineering, Boston University, 8 Saint Mary’s Street, Boston, MA 02215, USA
2
Division of Material Science and Engineering, Boston University, 15 Saint Mary’s Street, Brookline, MA 02446, USA
3
Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, MA 02215, USA
*
Author to whom correspondence should be addressed.
Crystals 2019, 9(9), 482; https://doi.org/10.3390/cryst9090482
Received: 12 August 2019 / Revised: 2 September 2019 / Accepted: 3 September 2019 / Published: 14 September 2019
(This article belongs to the Collection Structure and Properties of Quasicrystals)
In this paper we propose a novel approach to aperiodic order in optical science and technology that leverages the intrinsic structural complexity of certain non-polynomial (hard) problems in number theory and cryptography for the engineering of optical media with novel transport and wave localization properties. In particular, we address structure-property relationships in a large number (900) of light scattering systems that physically manifest the distinctive aperiodic order of elliptic curves and the associated discrete logarithm problem over finite fields. Besides defining an extremely rich subject with profound connections to diverse mathematical areas, elliptic curves offer unprecedented opportunities to engineer light scattering phenomena in aperiodic environments beyond the limitations of traditional random media. Our theoretical analysis combines the interdisciplinary methods of point patterns spatial statistics with the rigorous Green’s matrix solution of the multiple wave scattering problem for electric and magnetic dipoles and provides access to the spectral and light scattering properties of novel deterministic aperiodic structures with enhanced light-matter coupling for nanophotonics and metamaterials applications to imaging and spectroscopy. View Full-Text
Keywords: aperiodic structures; light scattering; light localization; number theory; cryptography aperiodic structures; light scattering; light localization; number theory; cryptography
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MDPI and ACS Style

Dal Negro, L.; Chen, Y.; Sgrignuoli, F. Aperiodic Photonics of Elliptic Curves. Crystals 2019, 9, 482.

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