Perfect absorption, gain and high-directive super-Planckian thermal emission in asymmetric hyperbolic metamaterials
Igor Nefedov and Leonid Melnikov igor.nefedov@aalto.fi lam-pels@yandex.ru
Media, characterized by permittivity (or permeability) tensors with opposite signs of diagonal components, exhibit hyperbolic-type dispersion in space of wave vectors. Such media are referred as hyperbolic metamaterials (HMMs). A distinctive feature of such media is a capability to support propagation of electromagnetic waves with huge wave vector components, or by other words, electromagnetic density of states (DOS) may be very high. As a result, the spontaneous emission rate and all processes of the wave-matter interaction can be strongly enhanced.
However, high DOS photons cannot be emitted from HMMs to vacuum due to the total internal reflection. Nevertheless, high DOS photons in HMMs can be coupled with plane waves in free space if to tilt an optical axis of HMM with respect to the interface. We called such HMMs the asymmetric hyperbolic metamaterials (AHMMs) due to a strong difference in properties of waves propagating upward and downward to media interfaces. Huge normal component of the wave vector in AHMM and a perfect matching with free space result in a perfect absorption and gain in optically thin layers of AHMMs and a high-directive thermal emission, exceeding Planck's limit.

1. General properties of hyperbolic and asymmetric hyperbolic metamaterials (AHMMs)
2. Perfect absorption in graphene-based AHMMs
3. Terahertz amplification in graphene-based AHMMs
4. High-directive thermal emission from AHMMs

usual uniaxial medium
3
2
1
0
-2
0 k x
/k
2 -2
0 k y
/k
2 hyperbolic ( ε-negative) medium

15
10
5 h
TM
Asymmetric hyperbolic metamaterials
Electromagnetic d ensity of states in AHMM
E
 z
 z’
 h x
Here is a schematic view of AHMM: red arrow shows direction of the optical axis. Parallel (TM) polarization is considered.
x’
|K|>>k propagating waves
2D hyperbolic dispersion. Interface with vacuum is parallel to the x axis. Waves can go out of AHMM if | k x
|< k, yellow area. Red line is the upper part of isofrequency, corresponding to free space.
If the optical axis is tilted, the waves with large modules of the wave vector can leave the AHMM without total internal reflection.
0
-2 -1 0 k x
/k 1 2
Similar for the 3D case.
Isofrequency surfaces for waves in
AHMM and vacuum.
Density of states dN is proportional to the volume, enclosed within the body angle cone d
Ω between isofrequency surfaces.
Waves with large wavenumbers in AHMM are coupled with plane waves in free space!

Normal component of the wave vector. Extremal asymmetry appears in the special case:
Special case: ε t
=1; ε’ zz
=-1+i δ, as in free space

Perfect matcing of plasmonic structure with free space. No reflection! Total absorption!
Higest interaction between plane wave in free space and plasmonic system!

Im( ε )
Re( ε )
ε h
= 1.01
d = 1.2 μm
τ = 10 -12 s
E f
= 25 meV
The real part of effective permittivity is negative
E f is the Fermi energy graphene d substrate air
I.S. Nefedov, C.A. Valagiannopoulos,
L.A. Melnikov J. Opt. 15 (2013) 114003

1
0.8
0.6
0.4
0.2
1.5 nm
3 nm d=5 nm
0
1.5
2 2.5
3

,

m
Absorption (black) and transmission (red) versus wavelength, calculated for different distance between graphene sheets d . Chemical potential μ c
=0.5 eV.
I.S. Nefedov, C.A. Valagiannopoulos, and L.A. Melnikov, Perfect absorption in graphene multilayers, J. Opt. 15 (2013) 114003

Result of HFSS simulation, absorption in optically ultra-thin layer h= λ /10.
Animation

Stimulated generation of plasmons in graphene:
A.A. Dubinov et al. J. Phys.: Condens. Matter 23 145302 (2011)
THz amplification and lasing in graphene Bragg resonator:
V.V. Popov et al., PRB 86 , 195437 (2012)
V.V. Popov et al., J. Opt. 15 , 114009 (2013)
Page 10

1.5
x 10
8
1 absorption reflection transmission
0.5
d=1.2 μm h= 15 μm
θ=44 ° , φ=43 °
E f
= 0.025 eV
0
-0.5
-1
-1.5
3 3.05
3.1
3.15
3.2
Frequency, THz
3.25
3.3
very strong negative absorption !

Mazwell equations
+ Fluctruation-dissipation theorem
+ Ergodic hypethesis z
 h
TM
E
 d x x’ z’ thermal emission into a solid angle
Green’s function method is used for calculations of
E x
, H y

3 x 10
-6
2.5
2
1.5
1
0.5
0
2
E z TM
 z’

=-45


=-50
  h d x
 h x’

=-40


=-60

μ c
= 0.5 eV
τ=10 -13 s
ε h
=2.1+0.001i
d=2 nm
φ=-30 °
2.2
2.4

,

m
2.6
2.8
3
Graphene-based multilayer is taken as example of asymmetric hyperbolic metamaterial.
Emissivity of AHMM strongly differs from the black body emissivity

150
120
90
1
0.8
0.6
0.4
0.2
60
30 Chemical potential µ c varies from 0.1 5 eV to 0.45 eV with the step 0.05 eV
180
 c
=0.15 eV
0
210
 c
=0.45 eV
240
270
300
330
Τ =10 -13 s
λ=4.7 µm d= 2 nm
φ=-35 °

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4.
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5.
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6.
I. S. Nefedov, L. A. Melnikov, “Super-Planckian far-zone thermal emission from asymmetric hyperbolic metamaterials,” arXiv:1402.3507 [physics.optics]

• A perfect coupling of wave with very large wavenumbers in hyperbolic media with free space can be achieved if to tilt the optical axis with respect to interface that results in a very efficient interaction of electromagnetic radiation in vacuum with plasmonic systems without any external elements like prisms or gratings.
• Exploitation of AHMMs may be prospective for creation of perfect absorbers, amplifiers and high-directive thermal emitters.