title: Raman Radiation Patterns of Graphene.
abstract: We report the angular distribution of the G and 2D Raman scattering from graphene on glass by detecting back focal plane patterns. The G Raman emission can be described by a superposition of two incoherent orthogonal point dipoles oriented in the graphene plane. Due to double resonant Raman scattering, the 2D emission can be represented by the sum of either three incoherent dipoles oriented 120° with respect to each other, or two orthogonal incoherent ones with a 3:1 weight ratio. Parameter-free calculations of the G and 2D intensities are in excellent agreement with the experimental radiation patterns. We show that the 2D polarization ratio and the 2D/G intensity ratio depend on the numerical aperture of the microscope objective. This is due to the depolarization of the emission and excitation light when graphene is on a dielectric substrate, as well as to tight focusing. The polarization contrast decreases substantially for increasing collection angle, due to polarization mixing caused by the air-dielectric interface. This also influences the intensity ratio I(2D)/I(G), a crucial quantity for estimating the doping in graphene. Our results are thus important for the quantitative analysis of the Raman intensities in confocal microscopy. In addition, they are relevant for understanding the influence of signal enhancing plasmonic antenna structures, which typically modify the sample's radiation pattern.
authors.affiliation: Department Chemie & CeNS, LMU Munich , Butenandtstr. 5-13E, 81377 Munich, Germany.
authors.forename: Harald
authors.initials: H
authors.lastname: Budde
authors.affiliation: Department Chemie & CeNS, LMU Munich , Butenandtstr. 5-13E, 81377 Munich, Germany.
authors.forename: Nicolás
authors.initials: N
authors.lastname: Coca-López
authors.affiliation: Department Chemie & CeNS, LMU Munich , Butenandtstr. 5-13E, 81377 Munich, Germany.
authors.forename: Xian
authors.initials: X
authors.lastname: Shi
authors.affiliation: Department Chemie & CeNS, LMU Munich , Butenandtstr. 5-13E, 81377 Munich, Germany.
authors.forename: Richard
authors.initials: R
authors.lastname: Ciesielski
authors.affiliation: Cambridge Graphene Centre, University of Cambridge , Cambridge CB3 0FA, United Kingdom.
authors.forename: Antonio
authors.initials: A
authors.lastname: Lombardo
authors.affiliation: Cambridge Graphene Centre, University of Cambridge , Cambridge CB3 0FA, United Kingdom.
authors.forename: Duhee
authors.initials: D
authors.lastname: Yoon
authors.affiliation: Cambridge Graphene Centre, University of Cambridge , Cambridge CB3 0FA, United Kingdom.
authors.forename: Andrea C
authors.initials: AC
authors.lastname: Ferrari
authors.affiliation: Department Chemie & CeNS, LMU Munich , Butenandtstr. 5-13E, 81377 Munich, Germany.
authors.forename: Achim
authors.initials: A
authors.lastname: Hartschuh
keywords: Raman scattering; graphene; radiation patterns