Directive surface plasmons on tunable two-dimensional hyperbolic metasurfaces and black phosphorus

Green's function and complex plane analysis

Seyyed Ali Hassani Gangaraj, Tony Low, Andrei Nemilentsau, George W. Hanson

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

We study the electromagnetic response of two- and quasi-two-dimensional (2-D) hyperbolic materials, on which a simple dipole source can excite a well-confined and tunable surface plasmon polariton (SPP). The analysis is based on the Green's function for an anisotropic 2-D surface, which nominally requires the evaluation of a 2-D Sommerfeld integral. We show that for the SPP contribution, this integral can be evaluated efficiently in a mixed continuous-discrete form as a continuous spectrum contribution (branch cut integral) of a residue term, in distinction to the isotropic case, where the SPP is simply given as a discrete residue term. The regime of strong SPP excitation is discussed, and the complex-plane singularities are identified, leading to physical insight into the excited SPP. We also present a stationary phase solution valid for large radial distances. Examples are presented using graphene strips to form a hyperbolic metasurface and thin-film black phosphorus. Green's function and complex-plane analysis developed allows for the exploration of hyperbolic plasmons in general 2-D materials.

Original languageEnglish (US)
Article number7762740
Pages (from-to)1174-1186
Number of pages13
JournalIEEE Transactions on Antennas and Propagation
Volume65
Issue number3
DOIs
StatePublished - Mar 1 2017

Fingerprint

Plasmons
plasmons
Green's function
phosphorus
Phosphorus
Green's functions
polaritons
continuous spectra
Graphene
strip
graphene
electromagnetism
dipoles
Thin films
evaluation
thin films
excitation

Keywords

  • Anisotropy
  • complex plane analysis
  • directed surface plasmon
  • Green's function
  • hyperbolic surface

How much support was provided by MRSEC?

  • Partial

Reporting period for MRSEC

  • Period 3

Cite this

Directive surface plasmons on tunable two-dimensional hyperbolic metasurfaces and black phosphorus : Green's function and complex plane analysis. / Gangaraj, Seyyed Ali Hassani; Low, Tony; Nemilentsau, Andrei; Hanson, George W.

In: IEEE Transactions on Antennas and Propagation, Vol. 65, No. 3, 7762740, 01.03.2017, p. 1174-1186.

Research output: Contribution to journalArticle

@article{67a25b47d2334fc0b9f2254d8b5b77a9,
title = "Directive surface plasmons on tunable two-dimensional hyperbolic metasurfaces and black phosphorus: Green's function and complex plane analysis",
abstract = "We study the electromagnetic response of two- and quasi-two-dimensional (2-D) hyperbolic materials, on which a simple dipole source can excite a well-confined and tunable surface plasmon polariton (SPP). The analysis is based on the Green's function for an anisotropic 2-D surface, which nominally requires the evaluation of a 2-D Sommerfeld integral. We show that for the SPP contribution, this integral can be evaluated efficiently in a mixed continuous-discrete form as a continuous spectrum contribution (branch cut integral) of a residue term, in distinction to the isotropic case, where the SPP is simply given as a discrete residue term. The regime of strong SPP excitation is discussed, and the complex-plane singularities are identified, leading to physical insight into the excited SPP. We also present a stationary phase solution valid for large radial distances. Examples are presented using graphene strips to form a hyperbolic metasurface and thin-film black phosphorus. Green's function and complex-plane analysis developed allows for the exploration of hyperbolic plasmons in general 2-D materials.",
keywords = "Anisotropy, complex plane analysis, directed surface plasmon, Green's function, hyperbolic surface",
author = "Gangaraj, {Seyyed Ali Hassani} and Tony Low and Andrei Nemilentsau and Hanson, {George W.}",
year = "2017",
month = "3",
day = "1",
doi = "10.1109/TAP.2016.2633900",
language = "English (US)",
volume = "65",
pages = "1174--1186",
journal = "IEEE Transactions on Antennas and Propagation",
issn = "0018-926X",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "3",

}

TY - JOUR

T1 - Directive surface plasmons on tunable two-dimensional hyperbolic metasurfaces and black phosphorus

T2 - Green's function and complex plane analysis

AU - Gangaraj, Seyyed Ali Hassani

AU - Low, Tony

AU - Nemilentsau, Andrei

AU - Hanson, George W.

PY - 2017/3/1

Y1 - 2017/3/1

N2 - We study the electromagnetic response of two- and quasi-two-dimensional (2-D) hyperbolic materials, on which a simple dipole source can excite a well-confined and tunable surface plasmon polariton (SPP). The analysis is based on the Green's function for an anisotropic 2-D surface, which nominally requires the evaluation of a 2-D Sommerfeld integral. We show that for the SPP contribution, this integral can be evaluated efficiently in a mixed continuous-discrete form as a continuous spectrum contribution (branch cut integral) of a residue term, in distinction to the isotropic case, where the SPP is simply given as a discrete residue term. The regime of strong SPP excitation is discussed, and the complex-plane singularities are identified, leading to physical insight into the excited SPP. We also present a stationary phase solution valid for large radial distances. Examples are presented using graphene strips to form a hyperbolic metasurface and thin-film black phosphorus. Green's function and complex-plane analysis developed allows for the exploration of hyperbolic plasmons in general 2-D materials.

AB - We study the electromagnetic response of two- and quasi-two-dimensional (2-D) hyperbolic materials, on which a simple dipole source can excite a well-confined and tunable surface plasmon polariton (SPP). The analysis is based on the Green's function for an anisotropic 2-D surface, which nominally requires the evaluation of a 2-D Sommerfeld integral. We show that for the SPP contribution, this integral can be evaluated efficiently in a mixed continuous-discrete form as a continuous spectrum contribution (branch cut integral) of a residue term, in distinction to the isotropic case, where the SPP is simply given as a discrete residue term. The regime of strong SPP excitation is discussed, and the complex-plane singularities are identified, leading to physical insight into the excited SPP. We also present a stationary phase solution valid for large radial distances. Examples are presented using graphene strips to form a hyperbolic metasurface and thin-film black phosphorus. Green's function and complex-plane analysis developed allows for the exploration of hyperbolic plasmons in general 2-D materials.

KW - Anisotropy

KW - complex plane analysis

KW - directed surface plasmon

KW - Green's function

KW - hyperbolic surface

UR - http://www.scopus.com/inward/record.url?scp=85015163161&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85015163161&partnerID=8YFLogxK

U2 - 10.1109/TAP.2016.2633900

DO - 10.1109/TAP.2016.2633900

M3 - Article

VL - 65

SP - 1174

EP - 1186

JO - IEEE Transactions on Antennas and Propagation

JF - IEEE Transactions on Antennas and Propagation

SN - 0018-926X

IS - 3

M1 - 7762740

ER -