Spatial Coherence in Near-Field Raman Scattering

Ryan Beams, Luiz Gustavo Cançado, Sang-Hyun Oh, Ado Jorio, and Lukas Novotny

Phys. Rev. Lett. 113, 186101 – Published 28 October 2014

Abstract

Inelastic light scattering in crystals has historically been treated as a spatially incoherent process, giving rise to incoherent optical radiation. Here we demonstrate that Raman scattering can be spatially coherent, in which case it depends on the dimensionality and symmetry of the scatterer. Using near-field spectroscopy, we measure a correlation length of $\sim 30 nm$ for the optical phonons in graphene, the results varying with vibrational symmetries and spatial confinement of the phonons.

Received 13 June 2014

DOI:https://doi.org/10.1103/PhysRevLett.113.186101

Authors & Affiliations

Ryan Beams¹, Luiz Gustavo Cançado², Sang-Hyun Oh³, Ado Jorio², and Lukas Novotny⁴

¹Institute of Optics, University of Rochester, Rochester, New York 14627, USA
²Departamento de Física, Universidade Federal de Minas Gerais, Belo Horizonte, MG 30123-970, Brazil
³Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, Minnesota 55455, USA
⁴Photonics Laboratory, ETH Zürich, 8093 Zürich, Switzerland*

^*www.nano-optics.org www.labns.com.br/en

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Issue

Vol. 113, Iss. 18 — 31 October 2014

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Images

Figure 1
TERS characterization of a graphene flake. (a) Sketch of the experiment. An incident electric field, $E$ , inelasically scatters off the graphene lattice creating the outgoing field $E_{s}$ . A gold tip is used to measure the correlations on the sample. (b) TERS image of the $G^{'}$ band of a single graphene flake. The black line indicates the location of the hyperspecral line scan in Fig. 2. Inset: confocal image of the same area with the color contrast scaled by $\times 3$ . (c) Raman spectra with (red) and without (black) the tip acquired in the center (top panel) and at the edge (bottom panel) of the flake. The locations are indicated by the black square and circle in (b), respectively.
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Figure 2
TERS hyperspectral line scan acquired along the black line in Fig. 1. (a) Color map showing the intensities of the Raman bands as one moves from the inside (position equals 0 nm) to the outside of the flake (position equals 500 nm). The edge of the flake is indicated by the dashed line. (b),(c) Plots of the amplitudes for the $D$ (black triangles), $G$ (blue circles), and $G^{'}$ (red squares) bands from the hyperspectral line scan shown in (a). The tip-down spectra are normalized by the far-field value at each location. The $D$ band profile is fit with two Gaussians: one for the confocal focus and one for the near-field signal. The bump near the edge in the $G^{'}$ band data is likely due to strain and dopants.
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Figure 3
Theoretical description of the TERS signal. (a),(b) Dependence of the signal on the tip-sample separation ( $z_{ts}$ ) for the $D$ , $G$ , and $G^{'}$ bands. The curves are calculated with two different phonon correlation lengths: $L_{c} = 0 nm$ and $L_{c} = 50 nm$ . The signal $S (r_{o})$ is normalized to 1 for $z_{ts} = 25 nm$ , which corresponds to the closest tip-sample distance. (c),(d) Sketches of the TERS process. The incident field induces a vertical dipole in the tip that interacts with the sample (green arrows), which in turn acts back on the tip at the Raman frequency (green arrows) before the fields are scattered out to the detector. The strength of the scattered signal depends on the relative phase of the induced dipoles in the sample (horizontal red and blue arrows). The emission dipoles on the sample add constructively for the $G^{'}$ band and destructively for the $G$ band, as shown in (c),(d), respectively.
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Figure 4
Experimental tip-sample distance curves for the Raman $D$ (black triangles), $G$ (blue circles), and $G^{'}$ (red squares) bands of two graphene samples. Top row: acquired at the edge of a pristine graphene flake. Bottom row: ion bombarded flake with uniformly distributed defects. (a),(c) Amplitudes of the Raman bands. (b),(d) Normalized data from (a) and (b), respectively, with the far-field values subtracted. The data are overlayed with the theoretical curves evaluated in Ref. [26], and shown Fig. 3. The values for the enhancement factor ( ${\tilde{f}}_{e}$ ), correlation length ( $L_{c}$ ), and tip radius ( $r_{tip}$ ) are indicated in the plots.
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