NANO LETTERS
Modal Decomposition of Surface-Plasmon Whispering Gallery Resonators
2009 Vol. 9, No. 9 3147-3150
Ernst Jan R. Vesseur,*,† F. Javier Garcı´a de Abajo,‡ and Albert Polman† Center for Nanophotonics, FOM Institute for Atomic and Molecular Physics (AMOLF), ´ pticasCSIC, Science Park 113, 1098 XG Amsterdam, The Netherlands, Instituto de O Serrano 121, 28006 Madrid, Spain Received April 22, 2009; Revised Manuscript Received July 7, 2009
ABSTRACT We resolve the resonant whispering gallery modes of plasmonic subwavelength ring cavities defined by circular grooves patterned into a gold surface. An interesting interplay is observed between subwavelength confinement and guiding along the groove. Full spatial and spectroscopic information is directly obtained using cathodoluminescence, including details of the nanoscale intensity distribution (spatial resolution 11 ( 8 nm). Excellent agreement between measurements and rigorous electromagnetic theory is obtained, thus allowing us to assess the symmetry, ordering, degree of confinement, and near-field enhancement of the modes with unprecedented detail.
Surface plasmons (SPs) are hybrid electromagnetic and conduction electron excitations1 that allow matching the micrometer-sized wavelength of light at optical frequencies with nanoscopic dimensions of patterned metallic structures. In particular, the interplay between localized and propagating surface plasmons has been intensely investigated with a view to integrated plasmonic devices like plasmon waveguides2-4 and plasmon lasers.5 However, exploiting the field concentration that is offered by such nanostructures requires a probe of the plasmonic modes at nanometer scale resolution. Scanning near-field optical microscopy (SNOM) provides a resolution down to ∼50 nm, although a coated tip can interact with the local modes thus producing distorted information. In contrast, fast electrons constitute a noninvasive probe of metal structures with the potential for true nanometer spatial resolution to retrieve spectral information through induced light emission (cathodoluminescence, CL)6 or via the analysis of electron energy loss in the case of thin samples.7 The field of a moving electron8 diverges close to its trajectory. The interaction of the electron with the photonic structure being probed is governed by this divergent field. Consequently, there is no limit to the resolution, which in experiment is only limited by the finite size of the electron beam. In this Letter, we investigate whispering gallery plasmon excitations9-13 supported by grooves of annular shape that share a unique combination of features associated to both standing wave modes and propagating modes. We pattern * To whom correspondence should be addressed. E-mail:
[email protected]. † Center for Nanophotonics, FOM Institute for Atomic and Molecular Physics (AMOLF). ‡ ´ pticasCSIC. Instituto de O 10.1021/nl9012826 CCC: $40.75 Published on Web 08/04/2009
2009 American Chemical Society
the grooves in a single-crystal gold surface and study the spatial and spectral evolution of the modes with unprecedented detail by using cathodoluminescence spectroscopy and boundary element method (BEM) calculations. We report excellent agreement between experiment and theory, which allows us to classify plasmon modes according to their azimuthal symmetry and radial order. We formulate a dispersion model relating circular grooves to straight grooves that explains satisfactorily the detailed dependence of mode frequencies and spatial distributions on ring radius and groove depth. Nanoresonators consisting of ring-shaped grooves (Figure 1a) were fabricated in a Czochralski grown and polished (rms roughness
