Ab initio theory of Fano resonances in plasmonic nanostructures and metamaterials

An ab initio theory for Fano resonances in plasmonic nanostructures and metamaterials is developed using Feshbach formalism. It reveals the role played by the electromagnetic modes and material losses in the system, and enables the engineering of Fano resonances in arbitrary geometries. A general formula for the asymmetric resonance in a non-conservative system is derived. The influence of the electromagnetic interactions on the resonance line shape is discussed and it is shown that intrinsic losses drive the resonance contrast, while its width is mostly determined by the coupling strength between the non-radiative mode and the continuum. The analytical model is in perfect agreement with numerical simulations.Comment: 13 pages, 5 figure

Fano Resonances in Plasmonic Nanostructures:Fundamentals, Numerical Modeling and Applications

Surface plasmons are able to generate extremely strong and confined optical fields at a deep-subwavelength scale, far beyond the diffraction limit, and now play a central role in nanosciences. A proper combination of plasmonic nanostructures can support Fano resonances arising from the interference between a non-radiative mode and a continuum of radiative electromagnetic waves. Fano resonances are able to confine light more efficiently and are characterized by a steeper dispersion than conventional plasmon resonances, which make them promising for nanoscale biochemical sensing, switching or lasing applications. Unfortunately, these technological developments are hindered by a lack of theoretical and numerical models able to deliver insights into the mechanisms of Fano resonances in plasmonic systems; e.g. to determine the best configuration for specific applications based on this phenomenon. In this thesis, the fundamental properties of Fano resonances in plasmonic nanostructures, and more generally in non-conservative systems, are investigated. An ab initio framework to describe their properties is developed and an analytical formula for their spectral response is derived. An equivalence between the derived resonance formula and the model of two coupled oscillators is also drawn, which confirms the general character of the developed framework. Furthermore, an original surface integral formulation for light scattering by periodic structures is developed and implemented. With this versatile numerical method, a very large variety of geometries can be simulated. The surface discretization using finite elements provides a high flexibility, allowing the investigation of irregular shapes. Thanks to the singularity subtraction technique, insights into the extreme near-field of the scatterers as well as into the corresponding far-field can be obtained with great accuracy. This particular advantage of the surface integral formulation, compared to other numerical methods, enables the detailed study of all the different aspects of Fano resonances in realistic plasmonic systems. The developed theoretical and numerical models are then used to elaborate a methodology to tailor the optical response of plasmonic Fano resonances in the far-field and the near-field. It is also shown that there exist three different coupling regimes in Fano-resonant systems, each regime exhibiting specific properties: in the weak coupling regime, a very high sensitivity to the opening of a radiative channel for the dark mode is observed. An optimal regime of highest electromagnetic field enhancement is obtained only when the in and out-coupling balance intrinsic losses. Finally, for stronger coupling, the specific features of Fano resonances are altered. In the last part, this knowledge of the mechanisms of Fano-resonant plasmonic systems is translated to the optimization of nanoplasmonic systems for a broad range of applications. In the weak coupling regime, radiative losses of the dark mode are almost suppressed and the modulation depth becomes a physical value extremely sensitive to the modes coupling, which can be used for nanoscale plasmon rulers to measure nanometric displacements. In the intermediate regime, the best electromagnetic field enhancement is obtained, which optimizes devices for second harmonic generation, as well as for surface enhanced Raman scattering or antenna-based trapping for biomolecular recognition. The sensitivity of Fano-resonant systems to local perturbations of the refractive index is then discussed. Higher figures of merit than conventional plasmon resonances can be obtained because the contribution of radiative and non-radiative losses to the spectral width can be controlled. This analysis finally leads to the introduction of an intrinsic figure of merit for refractive index sensing using Fano-resonant systems

Refractive Index Sensing with Subradiant Modes: A Framework To Reduce Losses in Plasmonic Nanostructures

Plasmonic modes with long radiative lifetimes, subradiant modes, combine strong confinement of the electromagnetic energy at the nanoscale with a steep spectral dispersion, which makes them promising for biochemical sensors or immunoassays. Subradiant modes have three decay channels: Ohmic losses, their extrinsic coupling to radiation, and possibly their intrinsic dipole moment. In this work, the performance of subradiant modes for refractive index sensing is studied with a general analytical and numerical approach. We introduce a model for the impact that has different decay channels of subradiant modes on the spectral resolution and contrast. It is shown analytically and verified numerically that there exists an optimal value of the mode coupling for which the spectral dispersion of the resonance line shape is maximal The intrinsic width of subradiant modes determines the value of the dispersion maximum and depends on the penetration of the electric field in the metallic nanostructure. A figure of merit given by the ratio of the sensitivity to the intrinsic width, which are both intrinsic properties of subradiant modes, is introduced. This figure of merit can be directly calculated from the line shape in the far field optical spectrum and accounts for the fact that both the spectral resolution and contrast determine the limit of detection. An expression for the intrinsic width of a plasmonic mode is derived and calculated from the line shape parameters and using perturbation theory. The method of analysis introduced in this work is illustrated for dolmen and heptamer nanostructures. Fano-resonant systems have the potential to act as very efficient refractive index sensing platforms compared to Lorentz-resonant systems due to control of their radiative losses. This study paves the way toward sensitive nanoscale biochemical sensors and immunoassays with a low limit of detection and in general, any nano-optical device where Ohmic, losses limit the performance

Analytical description of Fano resonances in plasmonic nanostructures

We report on the derivation of analytical formulas for the lineshape of Fano resonances in plasmonic nanostructures as a function of their electromagnetic response. Contrary to the original work of Fano, the formalism proposed here includes losses in the materials composing the system. As a result, a more general formula is obtained for the response of the system and general conclusions for the determination of the resonance parameters are drawn, in particular on its width and asymmetry. The insights into the physical understanding of Fano resonances gained this way will be of great interest for the design of plasmonic sensing platforms and metamaterials

Influence of electromagnetic interactions on the lineshape of plasmonic Fano resonances

The optical properties of plasmonic nanostructures supporting Fano resonances are investigated with an electromagnetic theory. Contrary to the original work of Fano, this theory includes losses in the materials composing the system. As a result, a more general formula is obtained for the response of the system and general conclusions for the determination of the resonance parameters are drawn. These predictions are verified with surface integral numerical calculations in a broad variety of plasmonic nanostructures including dolmens, oligomers, and gratings. This work presents a robust and consistent analysis of plasmonic Fano resonances and enables the control of their line shape based on Maxwell's equations. The insights into the physical understanding of Fano resonances gained this way will be of great interest for the design of plasmonic systems with specific spectral responses for applications such as sensing and optical metamaterials

Scattering on plasmonic nanostructures arrays modeled with a surface integral formulation

The surface integral formulation is a flexible, multiscale and accurate tool to simulate light scattering on nanostructures. Its generalization to periodic arrays is introduced in this paper. The general electromagnetic scattering problem is reduced to a discretizated model using the Method of Moments on the surface of the scatterers in the unit cell. The study of the resonances of an array of bowtie antennas illustrates the main features of the method. When placed into an array, the bowtie antennas show additional resonances compared to those of an individual antenna. Using the surface integral formulation, we are able to investigate both near-field and far-field properties of these resonances, with a high level of accuracy. (C) 2010 Elsevier B.V. All rights reserved

Relation between near–field and far–field properties of plasmonic Fano resonances

The relation between the near–field and far–field properties of plasmonic nanostructures that exhibit Fano resonances is investigated in detail. We show that specific features visible in the asymmetric lineshape far–field response of such structures originate from particular polarization distributions in their near–field. In particular we extract the central frequency and width of plasmonic Fano resonances and show that they cannot be directly found from far–field spectra. We also address the effect of the modes coupling onto the frequency, width, asymmetry and modulation depth of the Fano resonance. The methodology described in this article should be useful to analyze and design a broad variety of Fano plasmonic systems with tailored near–field and far–field spectral properties

Electromagnetic Scattering of Finite and Infinite 3D Lattices in Polarizable Backgrounds

A novel method is elaborated for the electromagnetic scattering from periodical arrays of scatterers embedded in a polarizable background. A dyadic periodic Green's function is introduced to calculate the scattered electric field in a lattice of dielectric or metallic objects. The method exhibits strong advantages: discretization and computation of the field are restricted to the volume of the scatterers in the unit cell, open and periodic boundary conditions for the electric field are included in the Green's tensor, and finally both near and far-fields physics are directly revealed, without any additional computational effort. Promising applications include the design of periodic structures such as frequency-selective surfaces, photonic crystals and metamaterials

High refractive index dielectric nanoparticles for optically-enhanced activity of water-splitting photoanodes

Metal oxide semiconductors have shown considerable potential for photoelectrochemical water-splitting. However, no ideal material has emerged which benefit from both an attractive sunlight absorption and efficient charge transport properties. In this work, we show that decorating photoanodes with high refractive index nanoparticles such as amorphous titania can result in reduced reflection losses at the electrolyte/photoanode interface, thereby increasing the performances under illumina- tion from the electrolyte side. A proof of concept is obtained for a bismuth vanadate photoanode including a surface catalyst and a hematite photoanode. The photocurrent density and external quantum efficiency are improved by up to 10% upon nanoparticle decoration, quantitatively matching the decrease in reflectance. Simulations show that a similar enhancement happens when a thick bismuth vanadate photoanode with optimal charge transport properties is considered, thereby suggesting that this strategy can improve photoanodes suffer- ing from high reflection losses regardless of the bare sample performance

Symmetry and selection rules for localized surface plasmon resonances in nanostructures

We describe a general theoretical framework based on the Bergman spectral representation to study how a nanostructure interacts with an external electromagnetic field. The selection rules for localized surface plasmon resonances (LSPRs) are obtained by implementing the group theory upon the electric vector field. The influence of symmetry breaking on the splitting of degenerated modes and the switching of dark modes by specific illuminations are discussed. These results emphasize the fact that the selection rules for a vector field are different from the case of a scalar field and essentially induced by the geometry of the structure. Finally, this work not only points out that measurements of LSPRs may result in very different results with different external fields, but also provides a strategy to selectively excite specific LSPRs of plasmonic structures