Transcript graphene
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.