Electromagnetic field radiated by a point emitter on a graphene sheet Alexey Nikitin Instituto 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

Surface EM waves in graphene

Surface EM waves in graphene Surface plasmons (SPs) in metallic surafces Light cone SPs W. L. Barnes et al., Nature 424, 824 (2003) q q q q SP

Surface EM waves in graphene Conductivity of graphene

Surface EM waves in graphene Surface waves in graphene

Surface EM waves in graphene Graphene metamaterials and Transformation Optics Ashkan Vakil and Nader Engheta, arXiv: optics/ 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

A point source: the fundamental problem Computational difficulties: asymptotic approach pole branch cut pole 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

Radiation patterns: surface plasmons and free-space fields

Radiation patterns: SPs and free-space fields Vertical dipole SP characteristics:

Radiation patterns: SPs and free-space fields Vertical dipole SP characteristics:

Radiation patterns: SPs and free-space fields Vertical dipole No SP excited SP characteristics: No SP excited

Radiation patterns: SPs and free-space fields Horizontal dipole SP characteristics: long propagation length wavelength close to the vacuum one

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

Radiation patterns: SPs and free-space fields Horizontal dipole No SP excited

Possible applications

Possible applications A. Gonzalez-Tudela et al., PRL 106, (2011) Qubits coupling through graphene SPs waveguides A.Vakil et al., arXiv: optics/ EM fields created by apertures in graphene A. Yu. Nikitin et al., PRL 105, (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