Electromagnetic field radiated by a point
emitter on a graphene sheet
Alexey Nikitin
Instituto de Ciencia de Materiales de Aragón (Universidad de Zaragoza-CSIC)
In collaboration with:
Luis Martín-Moreno,
F. J. García-Vidal (UAM, Madrid)
Zaragoza, 03/02/2011
website: alexeynik.com
Outline of the presentation
Why graphene? Unusual properties
Surface EM waves in graphene
A point source: the fundamental problem
Radiation patterns: surface plasmons and free-space fields
Possible applications
Why graphene? Unusual properties
Why graphene? Unusual optical properties
Optical solutions: possible future of Electronics?
Thin metallic optical
interconnectors
Graphene optical
interconnectors
Why graphene? Unusual optical properties
Atomic structure and electronic properties
• One atomic layer-thick
• Zero mass of electrons
• High electron mobility
• Pronounced response to
external voltage
Graphene transistors and integrated circuits
Y.-M. Lin et al. (IBM),
Science 327, 662 (2010)
cutoff frequency of 100 GHz for a gate length of 240 nm
H. B. Heersche et al.,
Nature 446, 56 (2007)
supercurrent transistor
Why graphene? Unusual optical properties
Optical properties
• It absorbs 2.3% of white light
• Conductivity is sensible to external fields
• Saturable absorption
• Could be made luminescent
• Supports surface electromagnetic waves
Extremely thin, but seen with the naked eye
Graphene-based optoelectronics
Solar cell
LED
Flexible smart window
F. Bonaccorso et al., Nature Phot. 4, 611 (2010)
Surface EM waves in graphene
Surface EM waves in graphene
Surface plasmons (SPs) in metallic surafces
q
~ e x L
~ eiqx
q q
q
W. L. Barnes et al., Nature 424, 824 (2003)
Surface EM waves in graphene
Conductivity of graphene
T  300K
  0.2eV
Surface EM waves in graphene
Surface waves in graphene
~ e x L
~ eiqx
Im( )  0
Im( )  0
Surface EM waves in graphene
Graphene metamaterials and Transformation Optics
Ashkan Vakil and Nader Engheta, arXiv: optics/1101.3585
Spatial varying voltage
2D graphene plasmonic waveguide
2D graphene plasmonic prism
Transformation Optics devices
A point source: the fundamental problem
A point source: the fundamental problem
Possible sources for local excitation
molecule
Josephson
qubit
quantum dot
A point source: the fundamental problem
Electric dipole
E(r)?
A point source: the fundamental problem
Computational difficulties: asymptotic approach
E ( x)
 dq
oscillating
factor
eiqx
1  q 2  qzp
branch cut
branch cut
pole
pole
graphene
Radiowave propagation
problems
L. P. Felsen and N. Marcuvitz, Radiation and Scattering of Waves (IEEE Press, Piscataway, NJ, 1994)
Radiation patterns: SPs and free-space fields
Density of electromagnetic states
E ( x) ~  dq  DOS  eiqx
  0.024
  1.12
Radiation patterns: surface plasmons
and free-space fields
Radiation patterns: SPs and free-space fields
Vertical dipole
  0.31 mm,  0.97 THz
SP characteristics:
L  200
SP  
Radiation patterns: SPs and free-space fields
Vertical dipole
  41.3  m,  7.2 THz
SP characteristics:
L  3 SP  0.1
Radiation patterns: SPs and free-space fields
Vertical dipole
No SP excited
  1 (  6.2  m,  48.4 THz )
  2 (  3.1  m,  96.7 THz )
SP characteristics:
No SP excited
L  0.1 SP  0.01
Radiation patterns: SPs and free-space fields
Horizontal dipole
SP characteristics:
• long propagation length
• wavelength close to the vacuum one
  0.31 mm,  0.97 THz
Radiation patterns: SPs and free-space fields
Horizontal dipole
SP characteristics:
• medium propagation length (of order of several wavelengths)
• wavelength is quite less than the vacuum one
  15.5  m,  19.3 THz
Radiation patterns: SPs and free-space fields
Horizontal dipole
No SP excited
  3.1  m,  96.7 THz
Possible applications
Possible applications
Qubits coupling through
graphene SPs waveguides
A. Vakil et al.,
arXiv: optics/1101.3585
A. Gonzalez-Tudela et al.,
PRL 106, 020501 (2011)
EM fields created by
apertures in graphene
A. Yu. Nikitin et al.,
PRL 105, 073902 (2010)
Conclusions
Conclusions
In spite of being very transparent (97.7%), graphene can trap
electromagnetic fields on its surface.
The fields excited by point sources (like molecules or quantum
dots) can reach huge values.
The shape of the excited fields can be controlled by voltage,
wavelength or temperature.
Found properties of graphene are promising for using it in
different photonic or quantum circuits.