Abstract
Van der Waals surface polariton nanostructures are promising candidates for miniaturisation of electromagnetic devices through the nanoscale confinement of infrared light. To fully exploit these nanoresonators, a computationally efficient model is necessary to predict polariton behaviour in complex geometries. Here, we develop a general wave model of surface polaritons in 2D geometries smaller than the polariton wavelength. Using geometric approximation widely tuneable infrared nanoimaging and local work function microscopy, we test this model against complex mono-/bi-layer graphene plasmon nanoresonators. Direct imaging of highly resonant graphene plasmon hotspots confirms that the model provides quantitatively accurate, analytical predictions of nanoresonator behaviour. The insights built with such models are crucial to the development of practical plasmonic nanodevices.
Highlights
Scattering scanning near-field optical microscopy (s-SNOM) has enabled direct imaging of plasmon modes in nanoresonators [17, 19]
Plasmon nano-imaging S-SNOM is a type of scanning probe microscopy that relies on ‘tapping mode’ atomic force microscopy (AFM), i.e. with a vertical dither applied to the probe at its mechanical resonance frequency ( f0 ≈ 280 kHz), which tracks the sample surface height
This was obtained by first calibrating the Kelvin probe force microscopy (KPFM) probe’s work function, ΦProbe, against gold, ΦAu = 4.82 eV, using ΦProbe = ΦAu + eVSP(Au), where VSP is the surface potential measured on gold, followedbyapplyingΦSample = ΦProbe − eVSP(Sample) to the surface potential image to obtain the work function of the sample [27]
Summary
Scattering scanning near-field optical microscopy (s-SNOM) has enabled direct imaging of plasmon modes in nanoresonators [17, 19]. The theoretical understanding of such experiments has required time-consuming and computationally expensive simulations using finite or boundary element methods [16, 17, 19], which require the input of a free parameter, the Fermi energy. These drawbacks mean that only simple 2D geometries, such as discs and rectangles [16, 19] or ribbons [11, 17, 22], have been studied. We introduce a simple wave model of how polaritons, including plasmons, behave in 2D geometries of length scales, L, smaller than the polariton wavelength (i.e. L < λsp). This model allows simple analytical calculations, which provide quantitatively accurate predictions of polariton behaviour in nanoresonators
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