Abstract

The near-field radiative heat transfer (NFRHT) between two semi-infinite α-MoO3 biaxial crystals is investigated numerically based on the fluctuation–dissipation theorem combined with the modified 4 × 4 transfer matrix method in this paper. In the calculations, the near-field radiative heat flux (NFRHF) along each of the crystalline directions of α-MoO3 is obtained by controlling the orientation of the biaxial crystals. The results show that much larger heat flux than that between two semi-infinite hexagonal boron nitride can be achieved in the near-field regime, and the maximum heat flux is along the [001] crystalline direction. The mechanisms for the large radiative heat flux are explained as due to existence of hyperbolic phonon polaritons (HPPs) inside α-MoO3 and excitation of hyperbolic surface phonon polaritons (HSPhPs) at the vacuum/α-MoO3 interfaces. The effect of relative rotation between the emitter and the receiver on the heat flux is also investigated. It is found that the heat flux varies significantly with the relative rotation angle. The modulation contrast can be as large as two when the heat flux is along the [010] direction. We attribute the large modulation contrast mainly to the misalignment of HSPhPs and HPPs between the emitter and the receiver. Hence, the results obtained in this work may provide a promising way for manipulating near-field radiative heat transfer between anisotropic materials.

Issue Section:
Radiative Heat Transfer
Keywords:
near-field radiative heat transfer, anisotropic material, α-MoO3 biaxial crystal, hyperbolic phonon polariton, hyperbolic surface phonon polariton
Topics:
Crystals, Heat flux, Radiative heat transfer, Rotation, Anisotropy, Excitation, Phonons, Polaritons

References

1.
Laroche
,
M.
,
Carminati
,
R.
, and
Greffet
,
J. J.
,
2006
, “
Near-Field Thermophotovoltaic Energy Conversion
,”
J. Appl. Phys.
,
100
(
6
), p.
063704
.10.1063/1.2234560
2.
Messina
,
R.
, and
Ben-Abdallah
,
P.
,
2013
, “
Graphene-Based Photovoltaic Cells for Near-Field Thermal Energy Conversion
,”
Sci. Rep.
,
3
, p.
1383
.10.1038/srep01383
3.
Zhao
,
B.
,
Chen
,
K.
,
Buddhiraju
,
S.
,
Bhatt
,
G.
,
Lipson
,
M.
, and
Fan
,
S.
,
2017
, “
High-Performance Near-Field Thermophotovoltaics for Waste Heat Recovery
,”
Nano Energy
,
41
, pp.
344
–
350
.10.1016/j.nanoen.2017.09.054
4.
Zhu
,
L. X.
,
Otey
,
C. R.
, and
Fan
,
S. H.
,
2013
, “
Ultrahigh-Contrast and Large-Bandwidth Thermal Rectification in Near-Field Electromagnetic Thermal Transfer Between Nanoparticles
,”
Phys. Rev. B
,
88
(
18
), p.
184301
.10.1103/PhysRevB.88.184301
5.
Chen
,
K. F.
,
Santhanam
,
P.
, and
Fan
,
S. H.
,
2016
, “
Near-Field Enhanced Negative Luminescent Refrigeration
,”
Phys. Rev. Appl.
,
6
, p.
024014
.10.1103/PhysRevApplied.6.024014
6.
Ben-Abdallah
,
P.
, and
Biehs
,
S. A.
,
2014
, “
Near-Field Thermal Transistor
,”
Phys. Rev. Lett.
,
112
(
4
), p.
0443301
.10.1103/PhysRevLett.112.044301
7.
Basu
,
S.
,
Zhang
,
Z. M.
, and
Fu
,
C. J.
,
2009
, “
Review of Near-Field Radiation and Its Application to Energy Conversion
,”
Int. J. Energy Res.
,
33
(
13
), pp.
1203
–
1232
.10.1002/er.1607
8.
Shi
,
J. W.
,
Li
,
P. F.
,
Liu
,
B. A.
, and
Shen
,
S.
,
2013
, “
Tuning Near Field Radiation by Doped Silicon
,”
Appl. Phys. Lett.
,
102
(
18
), p.
183114
.10.1063/1.4804631
9.
Watjen
,
J. I.
,
Zhao
,
B.
, and
Zhang
,
Z. M.
,
2016
, “
Near-Field Radiative Heat Transfer Between Doped-Si Parallel Plates Separated by a Spacing Down to 200 nm
,”
Appl. Phys. Lett.
,
109
(
20
), p.
203112
.10.1063/1.4967384
10.
Lang
,
S.
,
Sharma
,
G.
,
Molesky
,
S.
,
Kranzien
,
P. U.
,
Jalas
,
T.
,
Jacob
,
Z.
,
Petrov
,
A. Y.
, and
Eich
,
M.
,
2017
, “
Dynamic Measurement of Near-Field Radiative Heat Transfer
,”
Sci. Rep.
,
7
, p.
13916
.10.1038/s41598-017-14242-x
11.
Yang
,
J.
,
Du
,
W.
,
Su
,
Y. S.
,
Fu
,
Y.
,
Gong
,
S. X.
,
He
,
S. L.
, and
Ma
,
Y. G.
,
2018
, “
Observing of the Super-Planckian Near-Field Thermal Radiation Between Graphene Sheets
,”
Nat. Commun.
,
9
, p.
4033
.10.1038/s41467-018-06163-8
12.
Lim
,
M.
,
Song
,
J.
,
Lee
,
S. S.
, and
Lee
,
B. J.
,
2018
, “
Tailoring Near-Field Thermal Radiation Between Metallo-Dielectric Multilayers Using Coupled Surface Plasmon Polaritons
,”
Nat. Commun.
,
9
, p.
4302
.10.1038/s41467-018-06795-w
13.
Ghashami
,
M.
,
Geng
,
H. Y.
,
Kim
,
T.
,
Iacopino
,
N.
,
Cho
,
S. K.
, and
Park
,
K.
,
2018
, “
Precision Measurement of Phonon-Polaritonic Near-Field Energy Transfer Between Macroscale Planar Structures Under Large Thermal Gradients
,”
Phys. Rev. Lett.
,
120
(
17
), p.
175901
.10.1103/PhysRevLett.120.175901
14.
Fu
,
C. J.
, and
Tan
,
W. C.
,
2009
, “
Near-Field Radiative Heat Transfer Between Two Plane Surfaces With One Having a Dielectric Coating
,”
J. Quant. Spectrosc. Radiat. Transfer
,
110
(
12
), pp.
1027
–
1036
.10.1016/j.jqsrt.2009.02.007
15.
Ben-Abdallah
,
P.
,
Joulain
,
K.
,
Drevillon
,
J.
, and
Domingues
,
G.
,
2009
, “
Near-Field Heat Transfer Mediated by Surface Wave Hybridization Between Two Films
,”
J. Appl. Phys.
,
106
(
4
), p.
044306
.10.1063/1.3204481
16.
van Zwol
,
P. J.
,
Joulain
,
K.
,
Ben-Abdallah
,
P.
, and
Chevrier
,
J.
,
2011
, “
Phonon Polaritons Enhance Near-Field Thermal Transfer Across the Phase Transition of VO2
,”
Phys. Rev. B
,
84
(
16
), p.
161413(R)
.10.1103/PhysRevB.84.161413
17.
Liu
,
X. L.
,
Shen
,
J. D.
, and
Xuan
,
Y. M.
,
2019
, “
Near-Field Thermal Radiation of Nanopatterned Black Phosphorene Mediated by Topological Transitions of Phosphorene Plasmons
,”
Nanoscale Microscale Thermophys. Eng.
,
23
(
3
), pp.
188
–
199
.10.1080/15567265.2019.1578310
18.
Zhang
,
Y.
,
Yi
,
H. L.
, and
Tan
,
H. P.
,
2018
, “
Near-Field Radiative Heat Transfer Between Black Phosphorus Sheets Via Anisotropic Surface Plasmon Polaritons
,”
ACS Photonics
,
5
(
9
), pp.
3739
–
3747
.10.1021/acsphotonics.8b00776
19.
Salihoglu
,
H.
, and
Xu
,
X. F.
,
2019
, “
Near-Field Radiative Heat Transfer Enhancement Using Natural Hyperbolic Material
,”
J. Quant. Spectrosc. Radiat. Transfer
,
222–223
, pp.
115
–
121
.10.1016/j.jqsrt.2018.10.022
20.
Song
,
J. L.
,
Cheng
,
Q.
,
Lu
,
L.
,
Li
,
B. W.
,
Zhou
,
K.
,
Zhang
,
B.
,
Luo
,
Z. X.
, and
Zhou
,
X. P.
,
2020
, “
Magnetically Tunable Near-Field Radiative Heat Transfer in Hyperbolic Metamaterials
,”
Phys. Rev. Appl.
,
13
, p.
024054
.10.1103/PhysRevApplied.13.024054
21.
Biehs
,
S. A.
,
Tschikin
,
M.
, and
Ben-Abdallah
,
P.
,
2012
, “
Hyperbolic Metamaterials as an Analog of a Blackbody in the Near Field
,”
Phys. Rev. Lett.
,
109
(
10
), p.
104301
.10.1103/PhysRevLett.109.104301
22.
Biehs
,
S. A.
,
Tschikin
,
M.
,
Messina
,
R.
, and
Ben-Abdallah
,
P.
,
2013
, “
Super-Planckian Near-Field Thermal Emission With Phonon-Polaritonic Hyperbolic Metamaterials
,”
Appl. Phys. Lett.
,
102
(
13
), p.
131106
.10.1063/1.4800233
23.
Biehs
,
S. A.
, and
Ben-Abdallah
,
P.
,
2017
, “
Near-Field Heat Transfer Between Multilayer Hyperbolic Metamaterials
,”
Z. Naturforsch. A
,
72
(
2
), pp.
115
–
127
.10.1515/zna-2016-0351
24.
Liu
,
X. L.
,
Bright
,
T. J.
, and
Zhang
,
Z. M.
,
2014
, “
Applications Conditions of Effective Medium Theory in Near-Field Radiative Heat Transfer Between Multilayered Metamaterials
,”
ASME J. Heat Transfer
,
136
, p.
092703
.10.1115/1.4027802
25.
Liu
,
X. L.
,
Zhang
,
R. Z.
, and
Zhang
,
Z. M.
,
2013
, “
Near-Field Thermal Radiation Between Hyperbolic Metamaterials: Graphite and Carbon Nanotubes
,”
Appl. Phys. Lett.
,
103
(
21
), p.
213102
.10.1063/1.4832057
26.
Song
,
J. L.
, and
Cheng
,
Q.
,
2016
, “
Near-Field Radiative Heat Transfer Between Graphene and Anisotropic Magneto-Dielectric Hyperbolic Metamaterials
,”
Phys. Rev. B
,
94
(
12
), p.
125419
.10.1103/PhysRevB.94.125419
27.
Zhao
,
B.
,
Guizal
,
B.
,
Zhang
,
Z. M.
,
Fan
,
S. H.
, and
Antezza
,
M.
,
2017
, “
Near-Field Transfer Between Graphene/hBN Multilayers
,”
Phys. Rev. B
,
95
(
24
), p.
245437
.10.1103/PhysRevB.95.245437
28.
Zhao
,
B.
, and
Zhang
,
Z. M.
,
2017
, “
Enhanced Photon Tunneling by Surface Plasmon-Phonon Polaritons in Graphene/hBN Heterostructures
,”
ASME J. Heat Transfer
,
139
, p.
022701
.10.1115/1.4034793
29.
Shi
,
K. Z.
,
Bao
,
F. L.
, and
He
,
S. L.
,
2017
, “
Enhanced Near-Field Thermal Radiation Based on Multilayer Graphene-hBN Heterostructures
,”
ACS Photonics
,
4
(
4
), pp.
971
–
978
.10.1021/acsphotonics.7b00037
30.
Shi
,
K. Z.
,
Liao
,
R.
,
Cao
,
G. J.
,
Bao
,
F. L.
, and
He
,
S. L.
,
2018
, “
Enhancing Thermal Radiation by Graphene-Assisted hBN/SiO2 Hybrid Structures at the Nanoscale
,”
Opt. Exp.
,
26
(
10
), pp.
A591
–
A601
.10.1364/OE.26.00A591
31.
Liu
,
X. L.
, and
Xuan
,
Y. M.
,
2016
, “
Super-Planckian Thermal Radiation Enabled by Hyperbolic Surface Phonon Polaritons
,”
Sci. China Technol. Sci.
,
59
(
11
), pp.
1680
–
1686
.10.1007/s11431-016-0480-9
32.
Liu
,
X. L.
,
Shen
,
J. D.
, and
Xuan
,
Y. M.
,
2017
, “
Pattern-Free Thermal Modulator Via Thermal Radiation Between Van Der Waals Materials
,”
J. Quant. Spectrosc. Radiat. Transfer
,
200
, pp.
100
–
107
.10.1016/j.jqsrt.2017.06.010
33.
Wu
,
X. H.
,
Fu
,
C. J.
, and
Zhang
,
Z. M.
,
2018
, “
Influence of hBN Orientation on the Near-Field Radiative Heat Transfer Between Graphene/hBN Heterostructures
,”
J. Photonics Energy
,
9
(
3
), p.
1
.10.1117/1.JPE.9.032702
34.
Zheng
,
Z. B.
,
Chen
,
J. N.
,
Wang
,
Y.
,
Wang
,
X. M.
,
Chen
,
X. B.
,
Liu
,
P. Y.
,
Xu
,
J. B.
,
Xie
,
W. G.
,
Chen
,
H. J.
,
Deng
,
S. Z.
, and
Xu
,
N. S.
,
2018
, “
Highly Confined and Tunable Hyperbolic Phonon Polaritons in Van Der Waals Semiconducting Transition Metal Oxides
,”
Adv. Mater.
,
30
(
13
), p.
1705318
.10.1002/adma.201705318
35.
Zheng
,
Z. B.
,
Xu
,
N. S.
,
Oscurato
,
S. L.
,
Tamagnone
,
M.
,
Sun
,
F. S.
,
Jiang
,
Y. Z.
,
Ke
,
Y. L.
,
Chen
,
J. N.
,
Huang
,
W. C.
,
Wilson
,
W. L.
,
Ambrosio
,
A.
,
Deng
,
S. Z.
, and
Chen
,
H. J.
,
2019
, “
A Mid-Infrared Biaxial Hyperbolic Van Der Waals Crystal
,”
Sci. Adv.
,
5
(
5
), p.
eaav8690
.10.1126/sciadv.aav8690
36.
Biehs
,
S. A.
,
Rosa
,
F. S. S.
, and
Ben-Abdallah
,
P.
,
2011
, “
Modulation of Near-Field Heat Transfer Between Two Gratings
,”
Appl. Phys. Lett.
,
98
(
24
), p.
243102
.10.1063/1.3596707
37.
Biehs
,
S. A.
,
Ben-Abdallah
,
P.
,
Rosa
,
F. S. S.
,
Joulain
,
K.
, and
Greffet
,
J. J.
,
2011
, “
Nanoscale Heat Flux Between Nanoporous Materials
,”
Opt. Exp.
,
19
(
S5
), pp.
A1088
–
A1103
.10.1364/OE.19.0A1088
38.
Moharam
,
M. G.
,
Pommet
,
D. A.
,
Grann
,
E. B.
, and
Gaylord
,
T. K.
,
1995
, “
Stable Implementation of the Rigorous Coupled-Wave Analysis for Surface-Relief Gratings: Enhanced Transmittance Matrix Approach
,”
J. Opt. Soc. Am. A
,
12
(
5
), pp.
1077
–
1086
.10.1364/JOSAA.12.001077
39.
Ma
,
W.
,
Alonso-González
,
P.
,
Li
,
S.
,
Nikitin
,
A. Y.
,
Yuan
,
J.
,
Martín-Sánchez
,
J.
,
Taboada-Gutiérrez
,
J.
,
Amenabar
,
I.
,
Li
,
P.
,
Vélez
,
S.
,
Tollan
,
C.
,
Dai
,
Z.
,
Zhang
,
Y.
,
Sriram
,
S.
,
Kalantar-Zadeh
,
K.
,
Lee
,
S.-T.
,
Hillenbrand
,
R.
, and
Bao
,
Q.
,
2018
, “
In-Plane Anisotropic and Ultra-Low-Loss Polaritons in a Natural Van Der Waals Crystal
,”
Nature
,
562
(
7728
), pp.
557
–
562
.10.1038/s41586-018-0618-9
40.
Cojocaru
,
E.
,
2015
, “
Dyakonov Hybrid Surface Waves at the Isotropic-Biaxial Media Interface
,”
J. Opt. Soc. Am. A
,
32
(
5
), pp.
782
–
789
.10.1364/JOSAA.32.000782
41.
Walker
,
D. B.
,
Glytsis
,
E. N.
, and
Gaylord
,
T. K.
,
1998
, “
Surface Mode at Isotropic-Uniaxial and Isotropic-Biaxial Interfaces
,”
J. Opt. Soc. Am. A
,
15
(
1
), pp.
248
–
260
.10.1364/JOSAA.15.000248
42.
Takayama
,
O.
,
Crasovan
,
L.-C.
,
Johansen
,
S. K.
,
Mihalache
,
D.
,
Artigas
,
D.
, and
Torner
,
L.
,
2008
, “
Dyakonov Surface Waves: A Review
,”
Electromagnetics
,
28
(
3
), pp.
126
–
145
.10.1080/02726340801921403
43.
Narimanov
,
E. E.
,
2018
, “
Dyakonov Waves in Biaxial Anisotropic Crystals
,”
Phys. Rev. A
,
98
(
1
), p.
013818
.10.1103/PhysRevA.98.013818
Copyright © 2020 by ASME
You do not currently have access to this content.