Electromagnetic field radiated by a point emitter on a graphene sheet

Alexey NikitinInstituto de Ciencia de Materiales de Aragón (Universidad de Zaragoza-CSIC)

Zaragoza, 03/02/2011

In collaboration with:Luis Martín-Moreno, F. J. García-Vidal (UAM, Madrid)

website: alexeynik.com

Outline of the presentation

Why graphene? Unusual properties

Surface EM waves in graphene

Radiation patterns: surface plasmons and free-space fields

A point source: the fundamental problem

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

H. B. Heersche et al., Nature 446, 56 (2007)

Y.-M. Lin et al. (IBM), Science 327, 662 (2010)

cutoff frequency of 100 GHz for a gate length of 240 nm supercurrent transistor

Why graphene? Unusual optical properties

Optical properties

Extremely thin, but seen with the naked eye

• It absorbs of white light

• Conductivity is sensible to external fields

• Saturable absorption

• Could be made luminescent

• Supports surface electromagnetic waves

F. Bonaccorso et al., Nature Phot. 4, 611 (2010)

Graphene-based optoelectronics

LEDSolar cell

Flexible smart window

2.3%

Surface EM waves in graphene

Surface EM waves in graphene

Surface plasmons (SPs) in metallic surafces

Ligh

t con

e

SP

sW. L. Barnes et al., Nature 424, 824 (2003)

~ iqxe

~ x Le

q

qqq

SP

Surface EM waves in graphene

Conductivity of graphene

300T K0.2eV

Surface EM waves in graphene

Surface waves in graphene

~ iqxe

~ x Le

Im( ) 0

Im( ) 0

Surface EM waves in graphene

Graphene metamaterials and Transformation OpticsAshkan Vakil and Nader Engheta, arXiv: optics/1101.3585

Spatial varying voltage 2D graphene plasmonic prism

2D graphene plasmonic waveguide Transformation Optics devices

A point source: the fundamental problem

A point source: the fundamental problem

Possible sources for local excitation

molecule

quantum dot

Josephson qubit

A point source: the fundamental problem

Electric dipole

( )?E r

A point source: the fundamental problem

Computational difficulties: asymptotic approach

2( )

1

iqx

zp

eE x dq

q q

polebranch cutpole

branch cut

L. P. Felsen and N. Marcuvitz, Radiation and Scattering of Waves (IEEE Press, Piscataway, NJ, 1994)

Radiowave propagation problems

graphene

oscillating factor

Radiation patterns: SPs and free-space fields

Density of electromagnetic states

( ) ~ iqxE x dq DOS e

0.024 1.12

Radiation patterns: surface plasmons and free-space fields

Radiation patterns: SPs and free-space fields

Vertical dipole

0.31 , 0.97mm THz

SP characteristics:

SP 200L

Radiation patterns: SPs and free-space fields

Vertical dipole

41.3 , 7.2m THz

SP characteristics:

0.1SP 3L

Radiation patterns: SPs and free-space fields

Vertical dipole

1 ( 6.2 , 48.4 )m THz

2 ( 3.1 , 96.7 )m THz No SP excited

SP characteristics:

0.01SP 0.1L

No SP excited

Radiation patterns: SPs and free-space fields

Horizontal dipole

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

0.31 , 0.97mm THz

Radiation patterns: SPs and free-space fields

Horizontal dipole

15.5 , 19.3m THz SP characteristics:• medium propagation length (of order of several wavelengths)• wavelength is quite less than the vacuum one

Radiation patterns: SPs and free-space fields

Horizontal dipole

No SP excited

3.1 , 96.7m THz

Possible applications

Possible applications

A. Gonzalez-Tudela et al., PRL 106, 020501 (2011)

Qubits coupling through graphene SPs waveguides

A. Vakil et al.,arXiv: optics/1101.3585

EM fields created by apertures in graphene

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

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.

Conclusions