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![Page 1: Optical properties of asymmetrical hyperbolic media, based on graphene multilayers Igor Nefedov and Leonid Melnikov.](https://reader036.fdocuments.us/reader036/viewer/2022062304/56649eea5503460f94bfbcb7/html5/thumbnails/1.jpg)
Optical properties of asymmetrical hyperbolic media, based on
graphene multilayers
Igor Nefedov and Leonid Melnikov
![Page 2: Optical properties of asymmetrical hyperbolic media, based on graphene multilayers Igor Nefedov and Leonid Melnikov.](https://reader036.fdocuments.us/reader036/viewer/2022062304/56649eea5503460f94bfbcb7/html5/thumbnails/2.jpg)
1. Hyperbolic dispersion of electromagnetic waves in graphene multilayers
2. Properties of asymmetric hyperbolic media
3. Total absorption in asymmetric graphene multilayers
4. Thermal emission from asymmetric hyperbolic metamaterial, made of graphene multilayers
5. Spontaneous emission in hyperbolic media
6. Radiation of a small dipole, placed inside the asymmetric hyperbolic medium
Outline
![Page 3: Optical properties of asymmetrical hyperbolic media, based on graphene multilayers Igor Nefedov and Leonid Melnikov.](https://reader036.fdocuments.us/reader036/viewer/2022062304/56649eea5503460f94bfbcb7/html5/thumbnails/3.jpg)
Hyperbolic media
L.F. Felsen, N. Marcuvitz, Radiation and Scattering of Waves, 1973 (references to E. Arbel, L.B. Felsen, 1963)
infinite power, radiated by a point-like source
D.R. Smith, D. Schurig, PRL 90 2003 Term indefinite medium, negative refraction, near-field focusing
M. A. Noginov, et al. Optics Letters 35, 1863 (2010)Control of spontaneous emission
I.S. Nefedov, PRB, 82, 155423 (2010) Hyperbolic dispersion in 2D periodic arrays of metallic carbon nanotubes.
I.S. Nefedov, C.R. Simovski, PRB, 84, 195459 (2011) Giant radiation thermal heat transfer through micron gaps.
Illustration of inifinite density of modes in hyperbolic media
![Page 4: Optical properties of asymmetrical hyperbolic media, based on graphene multilayers Igor Nefedov and Leonid Melnikov.](https://reader036.fdocuments.us/reader036/viewer/2022062304/56649eea5503460f94bfbcb7/html5/thumbnails/4.jpg)
Model of graphene conductivity
intraband conductivity (the Kubo formula)
interband conductivity,
G.W. Hanson, JAP, 103, 064302 (2008)
![Page 5: Optical properties of asymmetrical hyperbolic media, based on graphene multilayers Igor Nefedov and Leonid Melnikov.](https://reader036.fdocuments.us/reader036/viewer/2022062304/56649eea5503460f94bfbcb7/html5/thumbnails/5.jpg)
Effective permittivity
0.5 1 1.5 2-12
-10
-8
-6
-4
-2
0
2
4
, m
c=0.8 eV
c=1. eV
c=1.2 eV
d=1,5 nm
![Page 6: Optical properties of asymmetrical hyperbolic media, based on graphene multilayers Igor Nefedov and Leonid Melnikov.](https://reader036.fdocuments.us/reader036/viewer/2022062304/56649eea5503460f94bfbcb7/html5/thumbnails/6.jpg)
Schematic view
z´
x´
![Page 7: Optical properties of asymmetrical hyperbolic media, based on graphene multilayers Igor Nefedov and Leonid Melnikov.](https://reader036.fdocuments.us/reader036/viewer/2022062304/56649eea5503460f94bfbcb7/html5/thumbnails/7.jpg)
Indefinite medium: εt =1; ε’zz =-1+iδ,
Eigenwaves, non-symmetry with respect to the Z-axis
special case:
![Page 8: Optical properties of asymmetrical hyperbolic media, based on graphene multilayers Igor Nefedov and Leonid Melnikov.](https://reader036.fdocuments.us/reader036/viewer/2022062304/56649eea5503460f94bfbcb7/html5/thumbnails/8.jpg)
Isofrequencies. Hyperbolic dispersion
-1.5 -1 -0.5 0 0.5 1 1.50
5
10
15
20
25
30
35
40
kx/k
k z/k
=45
=90
=1.2 m
=1.16 m
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Conditions for the perfect absorption
No reflection! Perfect absorption!
S.M. Hashemi, I.S. Nefedov, PRB, 86, 195411 (2012).
![Page 10: Optical properties of asymmetrical hyperbolic media, based on graphene multilayers Igor Nefedov and Leonid Melnikov.](https://reader036.fdocuments.us/reader036/viewer/2022062304/56649eea5503460f94bfbcb7/html5/thumbnails/10.jpg)
Normal components of wave vectors
z - components of wave vectors for waves propagating in opposite directions under the fixed transverse component kx =ksin(θ)
1 1.05 1.1 1.15 1.2-30
-20
-10
0
10
20
30
40
50
60
, m
Re
(kz)/
k, I
m(k
z)/k
Re(kz(2))
Re(kz(1))
Im(kz(2))
-50 0 50-20
0
20
40
60
80
R
e(k
z)/k,
Im
(kz)/
k
Re(kz(2))
Im(kz(2))
Re(kz(1))
θ=45°
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Absorption in graphene multilayers
0.8 1 1.2 1.4 1.60
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
, m
A,
|T|2
A, =10-13
|R|2
|T|2, =10-13
A, =10-14
|T|2, =10-14
A, =10-12
|T|2, =10-12
c=1eV
d=1.5 nmh=80 nm
Absorption (black) and transmission (red) versus wavelength, calculated for different relaxation times τ. Green line shows absorption in the same thickness multilayer with horizontally arranged graphene sheets
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Different interlayer distances
1.5 2 2.5 30
0.2
0.4
0.6
0.8
1
, m
A,
|T|2
d=5 nm
1.5 nm3 nm
Absorption (black) and transmission (red) versus wavelength, calculated for different distance between graphene sheets d. Chemical potential μc =0.5 eV.Number of graphene sheets Ng =100.
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Absorption, dependence on the incidence angle
-50 0 500
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
A,
|T|2 ,
|R|2
A
|R|2
|T|2
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h=λ/10
![Page 15: Optical properties of asymmetrical hyperbolic media, based on graphene multilayers Igor Nefedov and Leonid Melnikov.](https://reader036.fdocuments.us/reader036/viewer/2022062304/56649eea5503460f94bfbcb7/html5/thumbnails/15.jpg)
h=λ/10
![Page 16: Optical properties of asymmetrical hyperbolic media, based on graphene multilayers Igor Nefedov and Leonid Melnikov.](https://reader036.fdocuments.us/reader036/viewer/2022062304/56649eea5503460f94bfbcb7/html5/thumbnails/16.jpg)
Thermal emission
Ergodic hypethesis
Energy of Planck’s oscillator
z
x
z ’
x ’
E
TM
h d
thermal emission into a solid angle
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Thermal emissionHyperbolic isofrequencies
-1.5 -1 -0.5 0 0.5 1 1.50
5
10
15
20
25
30
35
40
kx/k
k z/k
=45
=90
=1.2 m
=1.16 m
z
x
z ’
x ’
E
TM
h d
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Far-zone thermal emissionDensity of modes
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Thermal emission
-0.5 0 0.50
2
4
6
8
10
Sz/
(,T
)
emission angle
=48
=45
=90
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A model of spontaneous emission in HM: two-level atom
- basic states
Equations:
- initial conditions
- ratio of energy stored in the field and in the atoms
w
a
b
n k
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Angular dependence of spontaneous radiation rate
Angle-averaged spontaneous radiation rate in dependence on a and b
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Electric dipole radiation, HFSS simulation
dipole in vacuum
dipole in hyperbolic medium
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• Graphene multilayers can exhibit properties of hyperbolic media in the near-infrared and visible ranges
• Perfect absorption of TM-polarized waves in a considerably wide wavelength range can be achieved in optically ultra-thin graphene multilayer structures with tilted anisotropy axes
• The perfect absorption is provided by the perfect matching with free space and a very large attenuation constant.
• High-directive thermal emission can be obtained from asymmetric graphene multilayer structures. This effect is caused by enhanced level of spontaneous emission inside hyperbolic media and ability of modes with a very high density to be emitted from ASHM without total internal reflection.
• A small source, placed incide a slab of asymmetric hyperbolic medium, can produce a high-directive radiation in far zone.
Conclusions