Session U44: Focus Session: Optical Properties of Metallic Nanostructures: Theory

Theory and modeling of light interactions with metallic nanostructures

Metallic nanostructures such as systems containing metal nanoparticles or metal films with nanoscale diameter holes or other nanostructured features are intriguing systems. Surface plasmons, special electronic excitations near the metallic surfaces, can then be excited with visible light. In addition to interest in their fundamental behavior and interactions, surface plasmons are useful in a variety of practical areas, including chemical and biological sensing and optoelectronics. Surface plasmons can be intense and localized, and correctly describing their behavior in complex systems can require numerically rigorous modeling techniques. This talk presents a discussion of the results of rigorous electrodynamics modeling using the finite-difference time-domain (FDTD) method. Such calculations may be used to validate ideas and concepts based on approximate models. Detailed inspection and analysis of the results can also lead to the development of new physical pictures . In particular, FDTD calculations are used to show (i) how it is possible to increase the propagation lengths surface plasmon polaritons with the use of appropriate dielectric underlayers, (ii) how to efficiently bend light in a subwavelength region, and, (iii) how nanoholes and wells in metal films can exhibit complex transmission spectra of relevance to sensing.   

General Properties of Local Plasmons in Metal Nanostructures

Local plasmon resonance in metal nanostructures offers the potential to concentrate electro-magnetic energies at nanoscale. Different designs of nanostructures have been proposed to achieve this goal. Here we investigate the general behavior of local plasmon resonances independent of specific structures. We study the local plasmon under quasi-static approximation given that nanostructure dimension is much smaller than optical wavelength.[1] We show that the plasmon resonance frequency depends on the fraction of plasmon energy residing in the metal through the real dielectric function of the metal. Further, at a given resonant frequency, the Q-factor of the resonance is determined only by the complex dielectric function of the metal material and does not depend on the nanostructure form or the dielectric environment. We will also discuss the effect of optical gain on the Q-factor of plasmon resonance. \newline [1] F. Wang and Y.R. Shen, Phys. Rev. Lett. \textbf{97}, 206806 (2006)   

Plasmonic properties of Nanorod Dimers

Using the plasmon hybridization and the FDTD methods, we investigate the plasmonic properties of nanorod dimers as a function of inter-particle separation and relative nanorod orientation. We show that the plasmonic structure of the dimer consists of bonding and anti-bonding combinations of individual nanorod plasmons localized on each particle. For short dimer separations, the plasmons consist of strongly hybridized individual nanorod plasmons of all multipolar orders. The bonding dipolar dimer plasmon displays a strong red shift with decreasing dimer separation and provides large electric field enhancements across the dimer junction.   

Plasmon Hybridization in finite and periodic structures

We have extended the plasmon hybridization method[1] to periodic structures of metallic nanoparticles. The approach allows for simple and intuitive calculations of the plasmonic band structure of periodic chains or arrays of nanoparticles. The method allows for the inclusion of arbitrarily high multipolar interactions between the individual nanoparticles and interaction distances beyond nearest neighbor couplings. We also present an investigation of how the plasmonic structure of a finite chain approaches that of an infinite periodic structure. The plasmonic structure of a nanostructure array is shown to consist of bands made up of hybridized plasmons of the individual nanoparticles. [1] E. Prodan, C. Radloff, N.J. Halas, and P. Nordlander, Science 302(2003) 419; E. Prodan and P. Nordlander, J. Chem. Phys.120(2004) 5444   

Laser Induced Forces Between Metallic Nanospheres; The Role of Collective Plasmon Resonances

We explore the theory of laser induced attractive forces between conducting nanospheres. Emphasis is placed on the influence of collective mode resonances on this force. As two spheres approach each other, the dipole active plasmon resonances drop in frequency and can pass through the laser frequency. This produces a dramatic enhancement of the force. We present explicit calculation for Ag nanospheres in solution. We compare the amplitude of the laser induced attractive force with the van der Waals forece.   

Plasmons in Metallic Nanoparticles: Effect of Nanoparticle Shape

Plasmonic oscillations of valence electrons determine the optical response of metallic nanoparticles. The energy and strength of these surface oscillations are a function of the size and shape of the nanoparticles. With the use of the boundary element method, we solve Maxwell's equations to calculate light scattering and surface modes in Au nanorods that are commonly used in field enhanced nanoantennas and scanned probe microscopies and spectroscopies. We calculate the near field and far field response of the nanorods to show how the shape of the nanorod determines its optical response. Although it is often assumed that the plasmon wavelength scales with the nanorod aspect ratio, we find that scaling with the aspect ratio does not apply. For small rod radii, the plasmon response blueshifts with increasing radii, as would be expected for scaling with the aspect ratio. However, the plasmon response still depends on both the rod length and radius and does not scale with the aspect ratio. For larger radii, the plasmon response redshifts with increasing radii, in contradiction to scaling with aspect ratio. We discuss the mechanisms that determine the shape dependence in these two regimes.   

FDTD calculations of the optical properties of nanostars

Using the Finite-Difference Time-Domain (FDTD) method, we calculate the near- and far-field properties of a gold nanostar. The nanostar is modeled as a solid core with protruding tips of prolate spheroidal shape. The shape of this nanostar agrees qualitatively with the shape inferred from an SEM picture. The calculated extinction spectra agree very well with the experimentally observed scattering spectra for different polarization angles of incident light. We show that the plasmon resonances of the nanostar can be viewed as resulting from hybridization of short wavelength primitive plasmons associated with the core and long wavelengths plasmons associated with the individual tips. Due to the asymmetric orientation of the tips, several nanostars plasmons can be observed for an arbitrary polarization of the incident light. The intensity of these plasmons resonances vary with polarization angle. The plasmon hybridization results in bonding and antibonding nanostar plasmons. The bonding plasmons are primarily composed of primitive tip plasmons but with a small but finite admixture of the core plasmons. The admixture of the core plasmon dramatically increases the cross section for excitation of the bonding plasmons and result in enormous local electric field enhancements compared to those for individual tips.   

Optical Properties of Semiconducting and Metallic Nanoparticle Structures by TDDFT

Superstructures of semiconducting and metallic nanoparticles display substantially novel properties compared to homogeneous materials or single nanoparticles due to the coupling of elementary excitations between different nanoparticles, i.e. the confined plasmons in the metallic nanoparticles and excitons in semiconductor quantum dots. We use time-dependent density functional theory (TDDFT) to examine the optical response of such structures. This method allows a quantitative, fully quantum mechanical treatment of the electronic response of both the semiconducting and metallic components.   

Optical Properties of 2D hexagonal arrays of gold nanoshells

Using periodic boundary conditions, we employ the Finite Difference Time Domain method to calculate the optical properties of a two dimensional close-packed array of gold nanoshells for different polarizations under normal incidence. The calculated extinction spectrum agrees very well with experimental data. We show that compared with an individual nanoshell or a nanoshell trimer, the nanoshell array shows a significantly red shifted dipolar resonance while the quadrupolar peak remains at almost the same wavelength for all structures. The local field enhancement of the nanoshell array is a factor of 10 higher than that of an individual nanoshell. The calculated Surface Enhanced Raman Spectroscopy (SERS) efficiency of the close-packed array is around three orders of magnitude higher than that for an individual nanoshell. The largest efficiencies occur for incident wavelengths around six microns in the infrared. The 2D hexagonal array of gold nanoshells is therefore highly suitable as a substrate for both SERS and Surface Enhanced Infrared Absorption (SEIRA) applications.   

Coherent acoustic vibrations of metal nanoshells

We study vibrational modes of gold nanoshells grown on dielectric core by means of time-resolved pump-probe spectroscopy. The fundamental breathing mode launched by a femtosecond pump pulse manifests itself in a pronounced time-domain modulation of the differential transmission probed at the frequency of the nanoshell surface plasmon resonance. The modulation amplitude is significantly stronger while the period is longer than in a gold nanoparticle of the same overall size. A theoretical model describing breathing mode frequency and damping for a nanoshell in a medium is developed. A distinct acoustical signature of nanoshells provides a new and efficient method for identifying these versatile nanostructures and for studying their mechanical and structural properties.   

Surface plasmon polaritons in co-metal nanostructures.

Co-metal structures, such as a strip-line or coaxial cable, are well-known from radio engineering. They are capable of subwavelength guiding of TEM modes, and therefore their visible range analogs are of great interest. At these very high frequencies, however, the propagating modes acquire a plasmon polariton character. I study in detail these plasmon polaritons in co-metal structures, and show that for properly chosen materials and geometry, these modes reduce to the conventional, radio TEM modes. I show, how a metamedium made of an array of such co-metal nanostructures, can simulate negative refraction, suerlensisng and cloaking.