Klein tunneling near the Dirac points in metal-dielectric multilayer metamaterials

Lei Sun,Jie Gao,Xiaodong Yang

doi:10.1038/s41598-017-09899-3

Lei Sun, Jie Gao + Show 1 more

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https://doi.org/10.1038/s41598-017-09899-3

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Abstract

The Klein tunneling of optical waves near the Dirac points in the metal-dielectric multilayer metamaterials is theoretically investigated and demonstrated through the coupled-mode theory under the tight-binding approximation and the rigorous band structure analysis based on the transfer-matrix method. The optical analogue of Klein tunneling for the relativistic electrons passing across a potential barrier is revealed by the iso-frequency contour analysis and numerical simulation to describe the optical beam propagation and refraction across the interface of two metal-dielectric multilayer metamaterial stacks. The transmission and reflection spectra of the Klein tunneling of optical waves are also explained by the coupled mode theory.

Highlights

Klein tunneling represents the phenomenon that the relativistic fermions can pass across a high potential barrier without the exponential damping, which is a particular property that arising from the existence of negative-energy solutions of the Dirac equation[1,2,3,4,5]
Compared with the binary dielectric superlattices that previously applied to study the Klein tunneling for optical waves[9, 10], the lossless metal-dielectric multilayer metamaterials have a simpler structure, which can be tuned to achieve the Klein tunneling and possess a special band structure associated with the two surface plasmon polariton (SPP) eigenmodes, which can be degenerated to form the Dirac point, resulting in a better analogue to the Klein tunneling in graphene
According to the specified coupled-mode theory under the tight-binding approximation, the connection between the metal-dielectric multilayer metamaterials and the relativistic fermions system described by the Dirac equation is revealed

Summary

Introduction

Klein tunneling represents the phenomenon that the relativistic fermions can pass across a high potential barrier without the exponential damping, which is a particular property that arising from the existence of negative-energy solutions of the Dirac equation[1,2,3,4,5]. The Klein tunneling of optical waves near the Dirac points in the lossless metal-dielectric multilayer metamaterials is investigated and demonstrated through theoretical analysis and numerical simulation. Compared with the binary dielectric superlattices that previously applied to study the Klein tunneling for optical waves[9, 10], the lossless metal-dielectric multilayer metamaterials have a simpler structure, which can be tuned to achieve the Klein tunneling and possess a special band structure associated with the two SPP eigenmodes, which can be degenerated to form the Dirac point, resulting in a better analogue to the Klein tunneling in graphene. For the relativistic electrons passing across a potential barrier is further illustrated by the iso-frequency contour analysis to describe the optical wave propagation and refraction across the interface between two metal-dielectric multilayer metamaterial stacks, which is coincident with the optical beam tunneling visualized from numerical simulation. The transmission and reflection spectra of the Klein tunneling of optical waves across the interface of two multilayer metamaterial stacks are explained based on the coupled-mode theory

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