Observation of coupled plasmon-polariton modes in Au nanoparticle chain waveguides of different lengths: Estimation of waveguide loss

Abstract

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...

Enhanced Förster Resonance Energy Transfer on Single Metal Particle. 2. Dependence on Donor−Acceptor Separation Distance, Particle Size, and Distance from Metal Surface

“…FDTD is now the start-of-the-art method for solving Maxwell's equations for complex geometries. [24][25][26][27][28][29][30][31][32][33][34][35][36][37] Being a direct time and space solution, FDTD offers the user a unique insight into all types of problems in photonics. Furthermore, FDTD can also be used to obtain the frequency solution by exploiting Fourier transforms, thus enabling a full range of useful quantities such as the complex Poynting vector and the transmission/reflection of light, in addition to fields around particles to be calculated.…”

Single-Molecule Studies on Fluorescently Labeled Silver Particles: Effects of Particle Size

“…[22][23][24][25][26][27][28][29][30][31][32][33][34] Since FDTD is a direct time and space solution, it offers the user a unique insight into all types of problems in electromagnetics and photonics. Furthermore, FDTD can also be used to obtain the frequency solution by exploiting Fourier transforms; thus, a full range of useful quantities in addition to fields around particles can be calculated, such as the complex Poynting vector and the transmission/reflection of light.…”

“…In the FDTD technique, Maxwell's curl equations are discretized by using finite-difference approximations in both time and space that are easy to program and are accurate. [22][23][24][25][26][27][28][29][30][31][32][33][34] To achieve high accuracy for realizing the spatial derivatives involved, the algorithm positions the components of the electric and magnetic field about a unit cell of the lattice that constitutes the FDTD computational domain. Each individual cube in the grid is called the Yee cell as it was first designed elegantly by Yee.…”

Parallel-chain optical transmission line for a low-loss ultraconfined light beam

“…The curves are obtained using full-wave analysis, consistent with the solutions in Refs. [4][5][6][7][8][9][10][11][12][13][14][15][16], which for the case of linear chains take into account all the dynamic coupling among the infinite number of particles in the array. Figure 1 reports the propagation length ͑defined as the length after which the guided field is e −1 of the original value͒ and Re͓␤͔ / k 0 for these two geometries, as depicted in the inset.…”

“…1,2 If one wants to squeeze the beam so that its total transverse cross-section is subwavelength, plasmonic waveguides may be realized in the form of cylindrical waveguides ͑nanorods͒ 3,4 or linear chains of closely spaced nanoparticles. [5][6][7][8][9][10][11][12][13][14][15][16][17] Due to their design flexibility, the propagation properties of linear chains may be tailored at will, effectively realizing laterally confined optical connectors. Experimental realization of such devices in the nanoscale, however, has shown severe losses, mainly caused by material absorption and disorder.…”