Transcript Presentation

Perfect absorption, gain and high-directive
super-Planckian thermal emission in asymmetric
hyperbolic metamaterials
Igor Nefedov and Leonid Melnikov
[email protected]
[email protected]
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.
Outline
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
Hyperbolic dispersion
usual uniaxial medium
3
kz/k
2
1
hyperbolic (ε-negative)
medium
0
-2
2
0
0
2 -2
kx/k
ky/k
Asymmetric hyperbolic metamaterials
Electromagnetic density of states in AHMM
E

TM
z
z’

h
Here is a schematic view of AHMM: red arrow shows direction of the
optical axis. Parallel (TM) polarization is considered.
h
x
x’
z
15
|K|>>k
propagating
waves
10
5
0
-2
-1
0
kx/k
1
2
2D hyperbolic dispersion. Interface with vacuum is parallel to the xaxis. Waves can go out of AHMM if |kx|<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.
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 dΩ between
isofrequency surfaces.
Waves with large wavenumbers in AHMM are coupled with plane waves in free space!
Eigenwaves, asymmetry with respect to
the Z-axis
Normal component of the wave
vector. Extremal asymmetry
appears in the special case:
Special case: εt =1; ε’zz =-1+iδ,
as in free space
Conditions for the perfect absorption
Perfect matcing of plasmonic structure with free
space. No reflection! Total absorption!
Higest interaction between plane wave in free
space and plasmonic system!
Example of AHMM. Graphene multilayer:
effective permittivity
εh= 1.01
d = 1.2 μm
τ = 10-12 s
E = 25 meV
f
Im(ε)
Re(ε)
The real part of effective permittivity
E is the Fermi energy
f
is negative
graphene substrate
d
I.S. Nefedov, C.A. Valagiannopoulos,
L.A. Melnikov J. Opt. 15 (2013) 114003
air
I. Absorption in graphene-based AHMM
1
0.8
3 nm
d=5 nm
A, |T|
2
1.5 nm
0.6
0.4
0.2
0
1.5
2
,  m
2.5
3
Absorption (black) and transmission (red) versus wavelength, calculated for
different distance between graphene sheets d. Chemical potential μc =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
II.Terahertz amplification
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
THz amplification in graphene AHMM
1.5
x 10
8
absorption
reflection
transmission
2
0
A, |T| , |R|
0.5
2
1
-0.5
-1
d=1.2 μm
h= 15 μm
θ=44°, φ=43°
Ef= 0.025 eV
-1.5
3
3.05
3.1
3.15
3.2
Frequency, THz
3.25
very strong negative absorption!
3.3
III. Thermal emission from AHMM
E
Mazwell equations
+ Fluctruation-dissipation theorem
z

TM
h

z’
d
x
+ Ergodic hypethesis
thermal emission into a solid angle
Green’s function method is used for calculations of Ex, Hy
x’
Emissivity in the near(mid)-IR
3
x 10
E
-6
z
2.5
=-45

=-50


TM
h

z’
x
emissivity
2
=-60
1.5
x’

1
=-40

0.5
0
2
2.2
2.4
h
d
2.6
,  m
2.8
3
μc = 0.5 eV
τ=10-13 s
εh =2.1+0.001i
d=2 nm
φ=-30°
Graphene-based multilayer is taken as example of asymmetric
hyperbolic metamaterial.
Emissivity of AHMM strongly differs from the black body emissivity
Electrically controllable, high directive
thermal emission from graphene AHMM
90
1
120
0.8
60
0.6
150
30
0.4
0.2
180
0
Chemical potential µc varies
from 0.1 5 eV to 0.45 eV with
the step 0.05 eV
 c=0.15 eV
210
330
 c=0.45 eV
240
300
270
Τ=10-13 s
λ=4.7 µm
d= 2 nm
φ=-35°
Publications on asymmetric hyperbolic
metamaterials
1. S. M. Hashemi and I. S. Nefedov, “Wideband perfect absorption in arrays of tilted
carbon nanotubes,” Physical Review B, vol. 86, no. 19, p. 195411, 2012.
2. I. S. Nefedov, C. Valagiannopoulos, S. M. Hashemi, and E. I. Nefedov, “Total
absorption in asymmetric hyperbolic media,” Scientific Reports, vol. 3, no. 2662, p.
2662, 2013.
3. S. M. Hashemi, I. S. Nefedov, and M. Soleimani, “Waves in asymmetric hyperbolic
media,” Photonics Letters of Poland, vol. 5, no. 2, pp. 72-74, 2013.
4. C. A. Valagiannopoulos and I. S. Nefedov, “Increasing the electromagnetic
attenuation below a quasi-matched surface with use of passive hyperbolic
metamaterials,” Photonics and Nanostructures: Fundamentals and Applications, no.
11, pp. 182-190, 2013.
5. I. S. Nefedov, C. A. Valagiannopoulos, and L. A. Melnikov, “Perfect absorption in
graphene multilayers,” Journal of Optics, vol. 15, no. 15, p. 114003, 2013.
6. I. S. Nefedov, L. A. Melnikov, “Super-Planckian far-zone thermal emission from
asymmetric hyperbolic metamaterials,” arXiv:1402.3507 [physics.optics]
Conclusions
• 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.