Achieving control of light-material interactions for photonic device applications at nanoscale dimensions will require structures that guide electromagnetic energy with a lateral mode confinement below the diffraction limit of light. This cannot be achieved by using conventional waveguides or photonic crystals. It has been suggested that electromagnetic energy can be guided below the diffraction limit along chains of closely spaced metal nanoparticles that convert the optical mode into non-radiating surface plasmons. A variety of methods such as electron beam lithography and self-assembly have been used to construct metal nanoparticle plasmon waveguides. However, all investigations of the optical properties of these waveguides have so far been confined to collective excitations, and direct experimental evidence for energy transport along plasmon waveguides has proved elusive. Here we present observations of electromagnetic energy transport from a localized subwavelength source to a localized detector over distances of about 0.5 microm in plasmon waveguides consisting of closely spaced silver rods. The waveguides are excited by the tip of a near-field scanning optical microscope, and energy transport is probed by using fluorescent nanospheres.

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Near-field interactions between closely spaced Au nanoparticles were characterized by studying the spectral position of the extinction bands corresponding to longitudinal (L) and transverse (T) plasmon-polariton modes of Au nanoparticle chains. Far-field spectroscopy and finite-difference time-domain simulations on arrays of 50 nm diameter Au spheres with an interparticle spacing of 75 nm both show a splitting ⌬E between the L and T modes that increases with chain length and saturates at a length of seven particles at ⌬Eϭ65 meV. We show that the measured splitting will result in a propagation loss of 3 dB/15 nm for energy transport. Calculations indicate that this loss can be reduced by at least one order of magnitude by modifying the shape of the constituent particles. © 2002 American Institute of Physics. ͓DOI: 10.1063/1.1503870͔In a recent paper, a method was proposed for guiding electromagnetic energy below the diffraction limit at visible frequencies using ordered arrays of closely spaced noble metal nanoparticles. 1 Energy transport in these plasmon waveguides relies on near-field coupling between surface plasmon-polariton modes of neighboring particles. In contrast to conventional optical waveguides, the minimum size of the guided modes is not limited by the diffraction limit /2n of light, enabling the fabrication of nanoscale optical devices. This type of guiding due to near-field coupling was recently demonstrated experimentally in macroscopic structures operating in the microwave regime. 2 At the submicron scale, a theoretical analysis of plasmon waveguides was done using a point-dipole model, allowing for the determination of the dispersion relation (k) and group velocities v g for energy transport. 3,4 The predictions of the point-dipole model for the collective ͑in-phase͒ excitation of the longwavelength mode ͑wavevector kϭ0͒ of plasmon waveguides consisting of 80 Au nanoparticles were confirmed using farfield spectroscopy. 5 Energy transport in plasmon waveguides relies on the excitation of modes with a finite wave vector (k 0). The functional form (k), the group velocity, and the energy propagation loss all depend on the number of directly interacting nanoparticles. In this letter, we investigate this optical near-field interaction range via a determination of the collective plasmon resonance frequencies for structures with 3, 5, and 7 Au nanoparticles using finite-difference time-domain ͑FDTD͒ simulations. The results are compared with far-field extinction measurements on arrays of plasmon waveguides fabricated using electron-beam lithography. Additionally, a simple mathematical formula is deduced relating the far-field extinction data and the expected waveguide loss.Figure 1 outlines our simulation approach for the determination of the surface plasmon resonance energies E L,T of nanoparticles in plasmon waveguides, where L and T correspond to polarization along ͑longitudinal mode L͒ or perpendicular ͑transverse mode T͒ to the chain axis. The simulation volume is chosen as a rectangular box of di...

Far-field polarization spectroscopy on chains of Au nanoparticles reveals the existence of longitudinal ͑L͒ and transverse ͑T͒ plasmon-polariton modes. The experimental results provide support for the validity of a recently published dipole model for electromagnetic energy transfer below the diffraction limit along chains of closely spaced metal nanoparticles. The key parameters that govern the energy transport are determined for various interparticle spacings using measurements of the resonance frequencies of L and T modes, yielding a bandwidth of 1.4ϫ10 14 rad/s and a maximum group velocity of v g ϭ4.0ϫ10 6 m/s for a 75 nm-spacing. DOI: 10.1103/PhysRevB.65.193408 PACS number͑s͒: 78.67.Bf, 42.70.Qs, 42.82.Et, 71.45.Gm In recent years, the interaction of light with metal nanoparticles has been the focus of intensive research.1,2 From work on single noble-metal nanoparticles, it is well established that light at the surface plasmon resonance frequency interacts strongly with metal particles and excites a collective electron motion, or plasmon.3 These resonance frequencies are typically in the visible or infrared part of the spectrum.1 For particles with a diameter much smaller than the wavelength of the exciting light, plasmon excitations produce an oscillating dipole field.Whereas until recently most work focused on large numbers of particles in disordered arrays, advances in particle synthesis and fabrication techniques allow for studies of ordered arrays of noble-metal particles. Since each excited metal nanoparticle with a diameter much smaller than the wavelength of the exciting light acts as an electric dipole, two types of electromagnetic interactions between particles can be distinguished: near-field coupling and far-field dipolar interaction. For particle spacings d larger than the wavelength of light, far-field dipolar interactions with a d Ϫ1 dependence dominate. Indeed, using broad beam illumination of regular two-dimensional gratings of Au nanoparticles with grating constants of several 100 nm, it was shown that the far-field dipolar interactions lead to changes in the position and the width of the dipole resonance. 4 -6 Most work has focused on these far-field interactions between metal nanoparticles and their possible applications for the fabrication of optoelectronic materials, but relatively little is known about the nature and properties of near-field interactions of closely spaced metal nanoparticles. However, recently it was suggested that chains of closely spaced noble-metal nanoparticles could be used as linear waveguides for electromagnetic energy below the diffraction limit.7 Analysis of Au nanoparticle chains using near-field optical microscopy has indeed shown signs of collective behavior of such chains. 8 It has also been shown that straight solid noble-metal nanowires can allow for electromagnetic energy transport over micrometer distances. 9In a number of recent publications, we presented experiments on macroscopic microwave analog systems 10,11 and theoretical models for metal n...

Finite-difference time-domain simulations show direct evidence of optical pulse propagation below the diffraction limit of light along linear arrays of spherical noble metal nanoparticles with group velocities up to 0.06c. The calculated dispersion relation and group velocities correlate remarkably well with predictions from a simple point-dipole model. A change in particle shape to spheroidal particles shows up to a threefold increase in group velocity. Pulses with transverse polarization are shown to propagate with negative phase velocities antiparallel to the energy flow. DOI: 10.1103/PhysRevB.67.205402 PACS number͑s͒: 78.67.Bf, 42.70.Qs, 42.82.Et, 71.45.Gm Investigations of the interaction of light with metal nanoparticles have led to a wealth of knowledge about the fundamental electromagnetic processes occurring on length scales smaller than the wavelength of light.1,2 Near-field investigations of the optical properties of single noble metal nanoparticles have confirmed the century old prediction that light at the surface plasmon resonance frequency interacts strongly with a single metal nanoparticle and excites a coherent collective electron motion, or plasmon.3,4 For a particle with a diameter DӶ, the light-matter interactions lead to an oscillating homogeneous polarization of the nanoparticle volume, resulting in an oscillating dipole field. For spherical Au and Ag nanoparticles in air, the dipole plasmon resonance frequencies lie in the visible part of the spectrum. Advances in particle synthesis and fabrication enable a study of the electromagnetic interactions between metal nanoparticles in ordered arrays with various particle spacings d. Such nanoparticle arrays exhibit collective dipole resonances. For dу, the collective dipole resonance frequencies and the lifetime of the plasmon oscillations are influenced predominantly by far-field dipolar interactions with a d Ϫ1 distance dependence. 5,6 For closely spaced metal nanoparticles (dϽ), interactions mediated by the high local electromagnetic fields near the particle surface dominate with a d Ϫ3 distance dependence. Far-field polarization spectroscopy on ordered linear arrays of closely spaced Au nanoparticles indeed showed a distance dependence of d Ϫ3 of the interparticle coupling. 7,8 An intriguing application of the interaction between metal nanoparticles is the construction of waveguides for electromagnetic energy at visible or near-infrared frequencies. It was shown that far-field interactions between Au particles in a grating can establish a surface plasmon-polariton bandgap in analogy to photonic crystals, allowing for the construction of line defect waveguides. 9 It has also been shown that the minimum size of these defect waveguides is determined by the diffraction limit /2n of light due to the large spacing d between adjacent particles that is necessary for the establishment of the bandgap.Two recent publications have discussed the possibility of guiding electromagnetic energy with a lateral confinement below the diffraction limit of li...