Surface-plasmon dispersion relations in chains of metallic nanoparticles: An exact quasistatic calculation (original) (raw)

Nonradiative limitations to plasmon propagation in chains of metallic nanoparticles

Physical Review B

We investigate the collective plasmonic modes in a chain of metallic nanoparticles that are coupled by nearfield interactions. The size-and momentum-dependent nonradiative Landau damping and radiative decay rates are calculated analytically within an open quantum system approach. These decay rates determine the excitation propagation along the chain. In particular, the behavior of the radiative decay rate as a function of the plasmon wavelength leads to a transition from an exponential decay of the collective excitation for short distances to an algebraic decay for large distances. Importantly, we show that the exponential decay is of a purely nonradiative origin. Our transparent model enables us to provide analytical expressions for the polarization-dependent plasmon excitation profile along the chain and for the associated propagation length. Our theoretical analysis constitutes an important step in the quest for the optimal conditions for plasmonic propagation in nanoparticle chains.

Propagation of surface plasmons in ordered and disordered chains of metal nanospheres

Physical Review B, 2007

We report a numerical investigation of surface plasmon (SP) propagation in ordered and disordered linear chains of metal nanospheres. In our simulations, SPs are excited at one end of a chain by a near-field tip. We then find numerically the SP amplitude as a function of propagation distance. Two types of SPs are discovered. The first SP, which we call the ordinary or quasistatic, is mediated by short-range, near-field electromagnetic interaction in the chain. This excitation is strongly affected by Ohmic losses in the metal and by disorder in the chain. These two effects result in spatial decay of the quasistatic SP by means of absorptive and radiative losses, respectively.

Dispersion relations in metal nanoparticle chains: necessity of the multipole approach

Journal of the Optical Society of America B, 2012

Lorenz-Mie multiple-scattering theory is used to perform semi-analytical calculations of the lossy dispersion relations of propagating modes in infinite chains of metallic spheres. Lossy modes are described by allowing the projection of the wavevector along the chain axis to be a complex number rather than the more common complex frequency description. We show that even when the constituent particles are much smaller than the wavelength, one generally needs to go well beyond the coupled dipole approximation to achieve stable predictions.

Collective plasmonic modes in two-dimensional periodic arrays of metal nanoparticles

Physical Review B, 2008

We investigate the collective plasmonic modes of metal nanoparticles in periodic two-dimensional (2D) arrays within a point-dipole description. The dynamic dispersion relations of the 2D arrays are obtained through a method which gives an effective polarizability describing the collective response of a system. Both the dispersion relations and mode qualities are simultaneously related to the imaginary part of the effective polarizability, which has contributions from the single-particle response as well as the interparticle coupling. The transverse long-range dipolar interaction is dominated by a wave term together with a purely geometrical constant representing the static geometrical contribution to resonant frequencies. As concrete examples, we considered small Ag spheres arranged in a square lattice. We find that inside the light cone, the transverse quasimode has a reasonably high mode quality, while the two in-plane modes show significant radiation damping. Near the light line, we observe strong coupling with free photons for the bands of the transverse mode and the transverse in-plane mode, and the longitudinal in-plane mode exhibits a negative group velocity inside the light cone. Vanishing group velocities in the light cone for all the quasimodes are found to be intrinsic properties of the 2D metal nanosphere dense arrays.

Plasmonic Resonances of Closely Coupled Gold Nanosphere Chains

The Journal of Physical Chemistry C, 2009

The optical properties of an ordered array of gold nanospheres have been calculated using the T-matrix method in the regime where the near-fields of the particles are strongly coupled. The array consists of a one-dimensional chain of spheres of 15 nm diameter where the number of spheres in the chain and interparticle spacing is varied. Calculations have been performed with chains up to 150 particles in length and with an interparticle spacing between 0.5 and 30 nm. Incident light polarized along the axis of the chain (longitudinal) and perpendicular (transverse) to it are considered, and in the latter case for wavevectors along and perpendicular to the chain axis. For fixed chain length the longitudinal plasmon resonance red shifts, relative to the resonance of an isolated sphere, as the interparticle spacing is reduced. The shift in the plasmon resonance does not appear to follow an exponential dependence upon gap size for these extended arrays of particles. The peak shift is inversely proportional to the distance, a result that is consistent with the van der Waals attraction between two spheres at short range, which also varies as 1/d. The transverse plasmon resonance shifts in the opposite direction as the interparticle gap is reduced; this shift is considerably smaller and approaches 500 nm as the gap tends to zero. Increasing the number of particles in the chain for a fixed gap has a similar effect on the longitudinal and transverse plasmon. In this case, however, the longitudinal plasmon tends toward an asymptotic value with increasing chain length, with the asymptotic value determined by the interparticle spacing. Here, the approach to the asymptote is exponential with a characteristic length of approximately two particles, at small interparticle spacings. This approach to an asymptote as the chain length becomes infinite has been verified in a finite element calculation with periodic boundary conditions.

Analysis of plasmon propagation along a chain of metal nanospheres using the generalized multipole technique

Journal of the Optical Society of America B, 2011

We compute the dispersion diagram of an infinite chain of silver nanospheres. The Drude model is used to define the permittivity of nanospheres, and the generalized multipole technique (GMT) is applied to solve the Maxwell's equation and, thus, to analyze the plasmon excitation. The obtained dispersion diagram using the GMT is compared with the result of the dipolar interacting model as well as the quasistatic model. Results of the finite element method are also presented to verify the accuracy of our results. Finally, a finite chain of metal nanospheres is examined for its scattering and propagation length of the guided modes.

On surface plasmon damping in metallic nanoparticles

Applied Physics B Lasers and Optics, 2004

Two possible mechanisms of damping of surface plasmon (SP) oscillations in metallic nanoparticles (MNPs), not connected with the electron-phonon interaction, are investigated theoretically: (a) radiation damping of SPs and (b) resonant coupling of SP oscillations with electronic transitions in the matrix. For the mechanism (a) it is shown that the radiation damping rate is proportional to the number of electrons in a MNP and therefore this channel of energy outflow from the MNP becomes essential for relatively large particles. The strong frequency and size dependence of the radiation damping rate obtained allows us to separate the contributions of radiative processes and the electron-phonon interaction to the energy leakage. The investigation of the mechanism (b) shows that the rate of energy leakage of SP oscillations from a MNP does not depend on particle size and is fully determined by the optical characteristics of the matrix. It is demonstrated that for very small MNPs of --3 5nm size, where the strong three-dimensional size quantization effect suppresses the electron-phonon interaction, the resonance coupling in certain cases provides an effective energy outflow.

Plasmonic modes in periodic metal nanoparticle chains: a direct dynamic eigenmode analysis

Optics Letters, 2007

We demonstrate an efficient eigen-decomposition method for analyzing the guided modes in metal nanoparticle chains. The proposed method has the advantage of showing the dispersion relation and mode quality simultaneously. It can also separate the material and geometrical properties, so its efficiency does not depend on the complexity of the material polarizability. The method is applied to analyze the guided modes of a single and a pair of metal chains. The more accurate dynamic dipole polarizability typically gives a red-shift compared with the results obtained with the broadly used quasistatic dipole polarizability with radiation correction.