Thin hexagonal boron nitride layers have been shown to support highly confined hyperbolic phonon-polaritons, which are of interest for light guiding applications. Localized plasmon resonances in nanopatterned metal films can exhibit subwavelength-scale confinement as well as a high local field strength that is of importance to imaging and sensor applications. In this work, the interaction between hyperbolic phonon-polaritons in a hexagonal boron nitride thin film and plasmon-polaritons in a nanopatterned gold thin film is investigated by means of finite-difference time-domain simulations of a series of coupled and uncoupled layered devices. Both far-field and near-field properties are calculated and analyzed, enabling the features due to plasmon-polaritons and phonon-polaritons, individually, to be distinguished and the coupling between these excitations to be explored and characterized.

1.
J.
Wu
,
H.
Wang
,
L.
Jiang
,
J.
Guo
,
X.
Dai
,
Y.
Xiang
, and
S.
Wend
, “
Critical coupling using the hexagonal boron nitride crystals in the mid-infrared range
,”
J. Appl. Phys.
119
,
203107
(
2016
).
2.
P.
Pons-Valencia
,
F. J.
Alfaro-Mozaz
,
M. M.
Wiecha
,
V.
Biolek
,
I.
Dolado
,
S.
Vélez
,
P.
Li
,
P.
Alonso-González
,
F.
Casanova
,
L. E.
Hueso
,
L.
Martín-Moreno
,
R.
Hillenbrand
, and
A. Y.
Nikitin
, “
Launching of hyperbolic phonon-polaritons in h-BN slabs by resonant metal plasmonic antennas
,”
Nat. Commun.
10
,
3242
(
2019
).
3.
S. A.
Maier
and
H. A.
Atwater
, “
Plasmonics: Localization and guiding of electromagnetic energy in metal/dielectric structures
,”
J. Appl. Phys.
98
,
011101
(
2005
).
4.
M.
Losurdo
,
F.
Moreno
,
C.
Cobet
,
M.
Modreanu
, and
W.
Pernice
, “
Plasmonics: Enabling functionalities with novel materials
,”
J. Appl. Phys.
129
,
220401
(
2021
).
5.
K.
Tolpygo
, “
Physical properties of a rock salt lattice made up of deformable ions
,”
Zh. Eksp. Teor. Fiz.
20
,
497
509
(
1950
).
6.
K. U. N.
Huang
, “
Lattice vibrations and optical waves in ionic crystals
,”
Nature
167
,
779
780
(
1951
).
7.
A. J.
Huber
,
B.
Deutsch
,
L.
Novotny
, and
R.
Hillenbrand
, “
Focusing of surface phonon polaritons
,”
Appl. Phys. Lett.
92
,
203104
(
2008
).
8.
W. L.
Barnes
,
A.
Dereux
, and
T. W.
Ebbesen
, “
Surface plasmon subwavelength optics
,”
Nature
424
,
824
830
(
2003
).
9.
R. H.
Ritchie
, “
Plasma losses by fast electrons in thin films
,”
Phys. Rev.
106
,
874
881
(
1957
).
10.
D.
Pines
and
D.
Bohm
, “
A collective description of electron interactions: II. Collective vs individual particle aspects of the interactions
,”
Phys. Rev.
85
,
338
353
(
1952
).
11.
W. A.
Murray
and
W. L.
Barnes
, “
Plasmonic mater
,”
Adv. Mater.
19
,
3771
3782
(
2007
).
12.
J.
Pendry
, “
Playing tricks with light
,”
Science
285
,
1687
1688
(
1999
).
13.
J. D.
Caldwell
,
A. V.
Kretinin
,
Y.
Chen
,
V.
Giannini
,
M. M.
Fogler
,
Y.
Francescato
,
C. T.
Ellis
,
J. G.
Tischler
,
C. R.
Woods
,
A. J.
Giles
,
M.
Hong
,
K.
Watanabe
,
T.
Taniguchi
,
S. A.
Maier
, and
K. S.
Novoselov
, “
Sub-diffractional volume-confined polaritons in the natural hyperbolic material hexagonal boron nitride
,”
Nat. Commun.
5
,
5221
(
2014
).
14.
R.
Estevâm da Silva
,
R.
Macêdo
,
T.
Dumelow
,
J. A. P.
da Costa
,
S. B.
Honorato
, and
A. P.
Ayala
, “
Far-infrared slab lensing and subwavelength imaging in crystal quartz
,”
Phys. Rev. B
86
,
155152
(
2012
).
15.
N.
Fang
,
H.
Lee
,
C.
Sun
, and
X.
Zhang
, “
Sub-diffraction-limited optical imaging with a silver superlens
,”
Science
308
,
534
537
(
2005
).
16.
K.
Kneipp
,
Y.
Wang
,
H.
Kneipp
,
L. T.
Perelman
,
I.
Itzkan
,
R. R.
Dasari
, and
M. S.
Feld
, “
Single molecule detection using surface-enhanced Raman scattering (SERS)
,”
Phys. Rev. Lett.
78
,
1667
(
1997
).
17.
C. E.
Talley
,
J. B.
Jackson
,
C.
Oubre
,
N. K.
Grady
,
C. W.
Hollars
,
S. M.
Lane
,
T. R.
Huser
,
P.
Nordlander
, and
N. J.
Halas
, “
Surface-enhanced Raman scattering from individual Au nanoparticles and nanoparticle dimer substrates
,”
Nano. Lett.
5
,
1569
1574
(
2005
).
18.
D.
Rodrigo
,
O.
Limaj
,
D.
Janner
,
D.
Etezadi
,
F. J.
García de Abajo
,
V.
Pruneri
, and
H.
Altug
, “
Mid-infrared plasmonic biosensing with graphene
,”
Science
349
,
165
168
(
2015
).
19.
A.
Fali
,
S. T.
White
,
T. G.
Folland
,
M.
He
,
N. A.
Aghamiri
,
S.
Liu
,
J. H.
Edgar
,
J. D.
Caldwell
,
R. F.
Haglund
, and
Y.
Abate
, “
Refractive index-based control of hyperbolic phonon-polariton propagation
,”
Nano. Lett.
19
,
7725
7734
(
2019
).
20.
D.
Chang
,
A. S.
Sørensen
,
P.
Hemmer
, and
M.
Lukin
, “
Quantum optics with surface plasmons
,”
Phys. Rev. Lett.
97
,
053002
(
2006
).
21.
A.
Gonzalez-Tudela
,
D.
Martin-Cano
,
E.
Moreno
,
L.
Martin-Moreno
,
C.
Tejedor
, and
F. J.
Garcia-Vidal
, “
Entanglement of two qubits mediated by one-dimensional plasmonic waveguides
,”
Phys. Rev. Lett.
106
,
020501
(
2011
).
22.
G. R.
Bhimanapati
,
Z.
Lin
,
V.
Meunier
,
Y.
Jung
,
J.
Cha
,
S.
Das
,
D.
Xiao
,
Y.
Son
,
M. S.
Strano
, and
V. R.
Cooper
, “
Recent advances in two-dimensional materials beyond graphene
,”
ACS Nano
9
,
11509
11539
(
2015
).
23.
F. H.
Koppens
,
D. E.
Chang
, and
F. J.
Garcia de Abajo
, “
Graphene plasmonics: A platform for strong light–matter interactions
,”
Nano. Lett.
11
,
3370
3377
(
2011
).
24.
S.
Dai
,
Z.
Fei
,
Q.
Ma
,
A.
Rodin
,
M.
Wagner
,
A.
McLeod
,
M.
Liu
,
W.
Gannett
,
W.
Regan
, and
K.
Watanabe
, “
Tunable phonon polaritons in atomically thin van der Waals crystals of boron nitride
,”
Science
343
,
1125
1129
(
2014
).
25.
A.
Kumar
,
T.
Low
,
K. H.
Fung
,
P.
Avouris
, and
N. X.
Fang
, “
Tunable light–matter interaction and the role of hyperbolicity in graphene–hBN system
,”
Nano. Lett.
15
,
3172
3180
(
2015
).
26.
S. A.
Biehs
,
M.
Tschikin
, and
P.
Ben-Abdallah
, “
Hyperbolic metamaterials as an analog of a blackbody in the near field
,”
Phys. Rev. Lett.
109
,
104301
(
2012
).
27.
Y.
Guo
,
W.
Newman
,
C. L.
Cortes
, and
Z.
Jacob
, “
Applications of hyperbolic metamaterial substrates
,”
Adv. OptoElectron.
2012
,
452502
(
2012
).
28.
C. L.
Cortes
,
W.
Newman
,
S.
Molesky
, and
Z.
Jacob
, “
Quantum nanophotonics using hyperbolic metamaterials
,”
J. Opt.
14
,
063001
(
2012
).
29.
F.
Bonaccorso
,
Z.
Sun
,
T.
Hasan
, and
A. C.
Ferrari
, “
Graphene photonics and optoelectronics
,”
Nat. Photonics
4
,
611
622
(
2010
).
30.
Z.
Jacob
,
I. I.
Smolyaninov
, and
E. E.
Narimanov
, “
Broadband Purcell effect: Radiative decay engineering with metamaterials
,”
Appl. Phys. Lett.
100
,
181105
(
2012
).
31.
Z.
Liu
,
H.
Lee
,
Y.
Xiong
,
C.
Sun
, and
X.
Zhang
, “
Far-field optical hyperlens magnifying sub-diffraction-limited objects
,”
Science
315
,
1686
(
2007
).
32.
A. V.
Kretinin
,
Y.
Cao
,
J. S.
Tu
,
G. L.
Yu
,
R.
Jalil
,
K. S.
Novoselov
,
S. J.
Haigh
,
A.
Gholinia
,
A.
Mishchenko
,
M.
Lozada
,
T.
Georgiou
,
C. R.
Woods
,
F.
Withers
,
P.
Blake
,
G.
Eda
,
A.
Wirsig
,
C.
Hucho
,
K.
Watanabe
,
T.
Taniguchi
,
A. K.
Geim
, and
R. V.
Gorbachev
, “
Electronic properties of graphene encapsulated with different two-dimensional atomic crystals
,”
Nano. Lett.
14
,
3270
3276
(
2014
).
33.
C. R.
Dean
,
A. F.
Young
,
I.
Meric
,
C.
Lee
,
L.
Wang
,
S.
Sorgenfrei
,
K.
Watanabe
,
T.
Taniguchi
,
P.
Kim
,
K. L.
Shepard
, and
J.
Hone
, “
Boron nitride substrates for high-quality graphene electronics
,”
Nat. Nanotechnol.
5
,
722
726
(
2010
).
34.
C. R.
Dean
,
L.
Wang
,
P.
Maher
,
C.
Forsythe
,
F.
Ghahari
,
Y.
Gao
,
J.
Katoch
,
M.
Ishigami
,
P.
Moon
,
M.
Koshino
,
T.
Taniguchi
,
K.
Watanabe
,
K. L.
Shepard
,
J.
Hone
, and
P.
Kim
, “
Hofstadter’s butterfly and the fractal quantum Hall effect in moiré superlattices
,”
Nature
497
,
598
602
(
2013
).
35.
B.
Hunt
,
J. D.
Sanchez-Yamagishi
,
A. F.
Young
,
M.
Yankowitz
,
B. J.
LeRoy
,
K.
Watanabe
,
T.
Taniguchi
,
P.
Moon
,
M.
Koshino
,
P.
Jarillo-Herrero
, and
R. C.
Ashoori
, “
Massive Dirac fermions and Hofstadter butterfly in a van der Waals heterostructure
,”
Science
340
,
1427
1430
(
2013
).
36.
G. L.
Yu
,
R. V.
Gorbachev
,
J. S.
Tu
,
A. V.
Kretinin
,
Y.
Cao
,
R.
Jalil
,
F.
Withers
,
L. A.
Ponomarenko
,
B. A.
Piot
,
M.
Potemski
,
D. C.
Elias
,
X.
Chen
,
K.
Watanabe
,
T.
Taniguchi
,
I. V.
Grigorieva
,
K. S.
Novoselov
,
V. I.
Fal’ko
,
A. K.
Geim
, and
A.
Mishchenko
, “
Hierarchy of Hofstadter states and replica quantum Hall ferromagnetism in graphene superlattices
,”
Nat. Phys.
10
,
525
529
(
2014
).
37.
F. D. M.
Haldane
and
S.
Raghu
, “
Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry
,”
Phys. Rev. Lett.
100
,
013904
(
2008
).
38.
S.
Raghu
and
F. D. M.
Haldane
, “
Analogs of quantum-Hall-effect edge states in photonic crystals
,”
Phys. Rev. A
78
,
033834
(
2008
).
39.
G.
Chen
,
A. L.
Sharpe
,
P.
Gallagher
,
I. T.
Rosen
,
E. J.
Fox
,
L.
Jiang
,
B.
Lyu
,
H.
Li
,
K.
Watanabe
,
T.
Taniguchi
,
J.
Jung
,
Z.
Shi
,
D.
Goldhaber-Gordon
,
Y.
Zhang
, and
F.
Wang
, “
Signatures of tunable superconductivity in a trilayer graphene moiré superlattice
,”
Nature
572
,
215
219
(
2019
).
40.
G.
Chen
,
A. L.
Sharpe
,
E. J.
Fox
,
Y.-H.
Zhang
,
S.
Wang
,
L.
Jiang
,
B.
Lyu
,
H.
Li
,
K.
Watanabe
,
T.
Taniguchi
,
Z.
Shi
,
T.
Senthil
,
D.
Goldhaber-Gordon
,
Y.
Zhang
, and
F.
Wang
, “
Tunable correlated Chern insulator and ferromagnetism in a moiré superlattice
,”
Nature
579
,
56
61
(
2020
).
41.
K. S.
Novoselov
,
A.
Mishchenko
,
A.
Carvalho
, and
A. H.
Castro Neto
, “
2D materials and van der Waals heterostructures
,”
Science
353
,
aac9439
(
2016
).
42.
A. K.
Geim
and
I. V.
Grigorieva
, “
Van der Waals heterostructures
,”
Nature
499
,
419
425
(
2013
).
43.
A.
Woessner
,
M. B.
Lundeberg
,
Y.
Gao
,
A.
Principi
,
P.
Alonso-González
,
M.
Carrega
,
K.
Watanabe
,
T.
Taniguchi
,
G.
Vignale
,
M.
Polini
,
J.
Hone
,
R.
Hillenbrand
, and
F. H. L.
Koppens
, “
Highly confined low-loss plasmons in graphene–boron nitride heterostructures
,”
Nat. Mater.
14
,
421
425
(
2015
).
44.
B.
Zhao
and
Z. M.
Zhang
, “
Perfect mid-infrared absorption by hybrid phonon-plasmon polaritons in hBN/metal-grating anisotropic structures
,”
Int. J. Heat Mass Transf.
106
,
1025
1034
(
2017
).
45.
J.
Yang
,
M.
Mayyas
,
J.
Tang
,
M. B.
Ghasemian
,
H.
Yang
,
K.
Watanabe
,
T.
Taniguchi
,
Q.
Ou
,
L. H.
Li
,
Q.
Bao
, and
K.
Kalantar-Zadeh
, “
Boundary-induced auxiliary features in scattering-type near-field Fourier transform infrared spectroscopy
,”
ACS Nano
14
,
1123
1132
(
2020
).
46.
F. J.
Alfaro-Mozaz
,
P.
Alonso-González
,
S.
Vélez
,
I.
Dolado
,
M.
Autore
,
S.
Mastel
,
F.
Casanova
,
L. E.
Hueso
,
P.
Li
,
A. Y.
Nikitin
, and
R.
Hillenbrand
, “
Nanoimaging of resonating hyperbolic polaritons in linear boron nitride antennas
,”
Nat. Commun.
8
,
15624
(
2017
).
47.
M.
Autore
,
P.
Li
,
I.
Dolado
,
F. J.
Alfaro-Mozaz
,
R.
Esteban
,
A.
Atxabal
,
F.
Casanova
,
L. E.
Hueso
,
P.
Alonso-González
,
J.
Aizpurua
,
A. Y.
Nikitin
,
S.
Vélez
, and
R.
Hillenbrand
, “
Boron nitride nanoresonators for phonon-enhanced molecular vibrational spectroscopy at the strong coupling limit
,”
Light Sci. Appl.
7
,
17172
(
2018
).
48.
T. G.
Folland
,
A.
Fali
,
S. T.
White
,
J. R.
Matson
,
S.
Liu
,
N. A.
Aghamiri
,
J. H.
Edgar
,
R. F.
Haglund
,
Y.
Abate
, and
J. D.
Caldwell
, “
Reconfigurable infrared hyperbolic metasurfaces using phase change materials
,”
Nat. Commun.
9
,
4371
(
2018
).
49.
F.
Cheng
,
X.
Yang
, and
J.
Gao
, “
Ultrasensitive detection and characterization of molecules with infrared plasmonic metamaterials
,”
Sci. Rep.
5
,
14327
(
2015
).
50.
W.
Wan
,
X.
Yang
, and
J.
Gao
, “
Strong coupling between mid-infrared localized plasmons and phonons
,”
Opt. Express
24
,
12367
12374
(
2016
).
51.
A.
Bylinkin
,
M.
Schnell
,
M.
Autore
,
F.
Calavalle
,
P.
Li
,
J.
Taboada-Gutièrrez
,
S.
Liu
,
J. H.
Edgar
,
F.
Casanova
,
L. E.
Hueso
,
P.
Alonso-Gonzalez
,
A. Y.
Nikitin
, and
R.
Hillenbrand
, “
Real-space observation of vibrational strong coupling between propagating phonon polaritons and organic molecules
,”
Nat. Photon.
15
,
197
202
(
2021
).
52.
K. S.
Yee
, “
Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media
,”
IEEE Trans. Antennas Propag.
14
,
302
307
(
1966
).
53.
The in-house code is written in the C programming language and uses the NVIDIA OpenACC and CUDA frameworks to implement parallel execution on a GPU. Code capabilities include Bloch periodic boundary conditions, UPML, and CPML implementations of perfectly matched layers. In addition to isotropic dielectric and metallic materials, the code implements anisotropic frequency dependent materials such as hBN and magnetic plasmas.
54.
A.
Taflove
and
S.
Hagness
,
Computational Electrodynamics: The Finite-Difference Time-Domain Method
(
Artech House
,
2005
).
55.
“PGI Compilers and Tools: OpenACC Getting Started Guide, NVIDIA,” (2020); available at https://www.pgroup.com/resources/docs/20.1/pdf/openacc20_gs.pdf
56.
N.
Ricker
, “
Further developments in the wavelet theory of seismogram structure
,”
Bull. Seismol. Soc. Am.
33
,
197
228
(
1943
).
57.
D.
Merewether
,
R.
Fisher
, and
F.
Smith
, “
On implementing a numeric Huygen’s source scheme in a finite difference program to illuminate scattering bodies
,”
IEEE Trans. Nucl. Sci.
27
,
1829
1833
(
1980
).
58.
B. D.
Gvozdic
and
D. Z.
Djurdjevic
, “
Performance advantages of CPML over UPML absorbing boundary conditions in FDTD algorithm
,”
J. Electr. Eng.
68
,
47
53
(
2017
).
59.
Z. S.
Sacks
,
D. M.
Kingsland
,
R.
Lee
, and
J.-F.
Lee
, “
A perfectly matched anisotropic absorber for use as an absorbing boundary condition
,”
IEEE Trans. Antennas Propag.
43
,
1460
1463
(
1995
).
60.
R. C.
Rumpf
, “Formulation of plane wave expansion method, EMPossible” (2020) (last accessed 7 July 2021); available at https://empossible.net/academics/emp5337/ [Online; accessed 7-July-2021]
61.
Y.
Jiang
,
X.
Lin
,
T.
Low
,
B.
Zhang
, and
H.
Chen
, “
Group-velocity-controlled and gate-tunable directional excitation of polaritons in graphene-boron nitride heterostructures
,”
Laser Photonics Rev.
12
,
1800049
(
2018
).
62.
A.
Ciesielski
,
L.
Skowronski
,
M.
Trzcinski
,
E.
Górecka
,
P.
Trautman
, and
T.
Szoplik
, “
Evidence of germanium segregation in gold thin films
,”
Surf. Sci.
674
,
73
78
(
2018
).
63.
D. M.
Sullivan
, “
Z-transform theory and the FDTD method
,”
IEEE Trans. Antennas Propag.
44
,
28
34
(
1996
).
64.
D. M.
Sullivan
,
Electromagnetic Simulation Using the FDTD Method
, 2nd ed. (
Wiley
,
2013
).
65.
H.
MacLeod
,
Thin-Film Optical Filters
(
CRC Press
,
2001
).
66.
Peak positions were initially found using a naive peak finding algorithm that sequentially determined all local maxima. This procedure was validated by comparing to a fit to multiple Gaussian functions, although the latter approach would fail in regions where multiple peaks and shoulders were close in frequency. In the case of the inflections in the vicinity of the TO frequency, side peaks or shoulders were determined by calculating the second derivative of the spectrum; the resulting curve was then multiplied by 1 and the above peak finding algorithm was reapplied.
67.
R. W.
Wood
, “
On a remarkable case of uneven distribution of light in a diffraction grating spectrum
,”
London Edinburg Dublin Philos. Mag. J. Sci.
4
,
396
402
(
1902
).
68.
J. W.
Strutt
, “
On the dynamical theory of gratings
,”
Proc. R. Soc. A
79
,
399
416
(
1907
).
69.
H.
Gao
,
J. M.
McMahon
,
M. H.
Lee
,
J.
Henzie
,
S. K.
Gray
,
G. C.
Schatz
, and
T. W.
Odom
, “
Rayleigh anomaly-surface plasmon polariton resonances in palladium and gold subwavelength hole arrays
,”
Opt. Express
17
,
2334
2340
(
2009
).
70.
A. E.
Klein
,
N.
Janunts
,
M.
Steinert
,
A.
Tünnermann
, and
T.
Pertsch
, “
Polarization-resolved near-field mapping of plasmonic aperture emission by a dual-SNOM system
,”
Nano. Lett.
14
,
5010
5015
(
2014
).
71.
W. H.
Press
,
S. A.
Teukolsky
,
W. T.
Vetterling
, and
B. P.
Flannery
,
Numerical Recipes: The Art of Scientific Computing
, 3rd ed. (
Cambridge University Press
,
2007
), p.
607
.
72.
S. J.
Orfanidis
,
Electromagnetic Waves and Antennas
(
Rutgers University
,
2016
).
73.
P.
Bloomfield
,
Fourier Analysis of Time Series: An Introduction
, 2nd ed. (
Wiley-Interscience
,
2000
), p.
69
You do not currently have access to this content.