Electromagnetic field radiated by a point emitter on a graphene sheet

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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)
website alexeynik.com
Zaragoza, 03/02/2011
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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

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Why graphene? Unusual properties
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Why graphene? Unusual optical properties
Optical solutions possible future of Electronics?
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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
H. B. Heersche et al., Nature 446, 56 (2007)
Y.-M. Lin et al. (IBM), Science 327, 662 (2010)
supercurrent transistor
cutoff frequency of 100 GHz for a gate length of
240 nm
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Why graphene? Unusual optical properties
Optical properties

• It absorbs 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
LED
Solar cell
Flexible smart window
F. Bonaccorso et al., Nature Phot. 4, 611 (2010)
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Surface EM waves in graphene
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Surface EM waves in graphene
Surface plasmons (SPs) in metallic surafces
Light cone
SPs
SP
W. L. Barnes et al., Nature 424, 824 (2003)
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Surface EM waves in graphene
Conductivity of graphene
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Surface EM waves in graphene
Surface waves in graphene
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Surface EM waves in graphene
Graphene metamaterials and Transformation Optics
Ashkan Vakil and Nader Engheta, arXiv
optics/1101.3585
2D graphene plasmonic prism
Spatial varying voltage
Transformation Optics devices
2D graphene plasmonic waveguide
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A point source the fundamental problem

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A point source the fundamental problem
Possible sources for local excitation
molecule
Josephson qubit
quantum dot
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A point source the fundamental problem
Electric dipole
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A point source the fundamental problem
Computational difficulties asymptotic approach
oscillating factor
pole
branch cut
L. P. Felsen and N. Marcuvitz, Radiation and
Scattering of Waves (IEEE Press, Piscataway, NJ,
1994)
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Radiation patterns SPs and free-space
fields
Density of electromagnetic states
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Radiation patterns surface plasmons and
free-space fields
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Radiation patterns SPs and free-space
fields
Vertical dipole
SP characteristics
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Radiation patterns SPs and free-space
fields
Vertical dipole
SP characteristics
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Radiation patterns SPs and free-space
fields
Vertical dipole
No SP excited
SP characteristics
No SP excited
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Radiation patterns SPs and free-space
fields
Horizontal dipole

• SP characteristics
• long propagation length
• wavelength close to the vacuum one

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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

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Radiation patterns SPs and free-space
fields
Horizontal dipole
No SP excited
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Possible applications
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Possible applications
EM fields created by apertures in graphene
Qubits coupling through graphene SPs waveguides
A. Gonzalez-Tudela et al., PRL 106, 020501 (2011)

• Vakil et al.,
• arXiv optics/1101.3585

A. Yu. Nikitin et al., PRL 105, 073902 (2010)
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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.