Decomposing the scattered field of two-dimensional metaatoms into multipole contributions

We introduce a technique to decompose the scattered near field of two-dimensional arbitrary metaatoms into its multipole contributions. To this end we expand the scattered field upon plane wave illumination into cylindrical harmonics as known from Mie theory. By relating these cylin- drical harmonics to the field radiated by Cartesian multipoles, the contribution of the lowest order electric and magnetic multipoles can be identified. Revealing these multipoles is essential for the design of metamaterials because they largely determine the character of light propagation. In par- ticular, having this information at hand it is straightforward to distinguish between effects that result either from the arrangement of the metaatoms or from their particular design

Analytical Model for Metamaterials with Quantum Ingredients

We present an analytical model for describing complex dynamics of a hybrid system consisting of interacting classical and quantum resonant structures. Classical structures in our model correspond to plasmonic nano-resonators of different geometries, as well as other types of nano- and micro-structures optical response of which can be described without invoking quantum-mechanical treatment. Quantum structures are represented by atoms or molecules, or their aggregates (for example, quantum dots and carbon nanotubes), which can be accurately modelled only with the use of quantum approach. Our model is based on the set of equations that combines well-established density matrix formalism appropriate for quantum systems, coupled with harmonic-oscillator equations ideal for modelling sub-wavelength plasmonic and optical resonators. This model can also be straightforwardly adopted for describing electromagnetic dynamics of various hybrid systems outside the photonics realm, such as Josephson-junction metamaterials, or SQUID elements coupled with an RF strip resonator.Comment: 9 pages, no figure

Multipole nonlinearity of metamaterials

We report on the linear and nonlinear optical response of metamaterials evoked by first and second order multipoles. The analytical ground on which our approach bases permits for new insights into the functionality of metamaterials. For the sake of clarity we focus here on a key geometry, namely the split-ring resonator, although the introduced formalism can be applied to arbitrary structures. We derive the equations that describe linear and nonlinear light propagation where special emphasis is put on second harmonic generation. This contribution basically aims at stretching versatile and existing concepts to describe light propagation in nonlinear media towards the realm of metamaterials.Comment: 7 pages, 3 figure

Contribution of the magnetic resonance to the third harmonic generation from a fishnet metamaterial

We investigate experimentally and theoretically the third harmonic generated by a double-layer fishnet metamaterial. To unambiguously disclose most notably the influence of the magnetic resonance, the generated third harmonic was measured as a function of the angle of incidence. It is shown experimentally and numerically that when the magnetic resonance is excited by pump beam, the angular dependence of the third harmonic signal has a local maximum at an incidence angle of {\theta} \simeq 20{\deg}. This maximum is shown to be a fingerprint of the antisymmetric distribution of currents in the gold layers. An analytical model based on the nonlinear dynamics of the electrons inside the gold shows excellent agreement with experimental and numerical results. This clearly indicates the difference in the third harmonic angular pattern at electric and magnetic resonances of the metamaterial.Comment: 7 pages, 5 figure