A. Chipouline

The origin of magnetic polarizability in metamaterials at optical frequencies - an electrodynamic approach

We explain the origin of the electric and particular the magnetic polarizabiltiy of metamaterials employing a fully electromagnetic plasmonic picture. As example we study an U-shaped split-ring resonator based metamaterial at optical frequencies. The relevance of the split-ring resonator orientation relative to the illuminating field for obtaining a strong magnetic response is outlined. We reveal higher-order magnetic resonances and explain their origin on the basis of higher-order plasmonic eigenmodes caused by an appropriate current flow in the split-ring resonator. Finally, the conditions required for obtaining a negative index at optical frequencies in a metamaterial consisting of split-ring resonators and wires are investigated.

Nonlinear thermal effects in optical microspheres at different wavelength sweeping speeds.

Results of detailed experimental investigations of the power and sweeping speed dependent resonance bandwidth and resonance wavelength shift in microsphere resonators are presented. The experimental manifestations of the nonlinear effects for the different sweeping modes are considered and a possibility of separation between the Kerr and thermal nonlinearities is discussed. As it follows from the detailed comparison between theory and experiments, a single mode theoretical model, based on the mean field approximation, gives a satisfactory description of the experimental data only at small coupling powers and fast sweeping. For example, the values of Kerr nonlinearity, obtained through the fitting of the experimental data, are far from the expected, commonly used ones.

THz bandwidth optical switching with carbon nanotube metamaterial

We provide the first demonstration of exceptional light-with-light optical switching performance of a carbon nanotube metamaterial - a hybrid nanostructure of a plasmonic metamaterial with semiconducting single-walled carbon nanotubes. A modulation depth of 10% in the near-IR with sub-500 fs response time is achieved with a pump fluence of just 10 μJ/cm², which is an order of magnitude lower than in previously reported artificial nanostructures. The improved switching characteristics of the carbon nanotube metamaterial are defined by an excitonic nonlinearity of carbon nanotubes resonantly enhanced by a concentration of local fields in the metamaterial. Since the spectral position of the excitonic response and metamaterial plasmonic resonance can be adjusted by using carbon nanotubes of different diameter and scaling of the metamaterial design, the giant nonlinear response of the hybrid metamaterial - in principle - can be engineered to cover the entire second and third telecom windows, from O- to U-band.

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.

Experimental determination of the dispersion relation of light in metamaterials by white-light interferometry

We present a method to experimentally measure the complex reflection and transmission coefficients of optical waves at metamaterials under normal incidence. This allows us to determine their pertinent dispersion relation without resorting to numerical simulations. For this purpose we employ a spectrometer and a white light interferometer for amplitude and phase measurements, respectively. To demonstrate the reliability of the method, it is applied to two referential metamaterial geometries, namely, the fishnet and the double-element structure. Involved aspects of the phase measurements as well as the accuracy of the method are discussed.

Simple and versatile analytical approach for planar metamaterials

We present a simple model which permits to access the optical properties of planar metamaterials made of unit cells (meta-atoms) which are formed by a set of elementary building blocks, namely, thin metallic wires. In the model, the wires are represented as oscillating electric dipoles which are mutually coupled. The parameters describing the building blocks have to be matched once to let the model reproduce the results of a rigorous simulation or measurement. But afterwards the building blocks can be arranged in quite a different way and the achievable optical properties can be fully explored within the model without further rigorous simulations. The optical properties are accessed at normal incidence only and, for convenience, they can be described in terms of effective material tensors which are assigned to a conceptually homogenous medium causing the same optical response. As an example the model is applied to reveal the occurrence of elliptical dichroism if the split ring resonator meta-atom is modified to L- or S-shaped meta-atoms. The model constitutes an excellent tool to explore new designs of metamaterials.

Understanding the electric and magnetic response of isolated metaatoms by means of a multipolar field decomposition

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 Mies theory. By relating these cylindrical 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 particular, 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.

Double-element metamaterial with negative index at near-infrared wavelengths

We present the realization of a metamaterial that combines double cut wires and continuous wires in its unit cell. This double-element geometry together with the applied layer-by-layer fabrication technique permits an independent tuning of the geometry of the unit-cell components. The characterization of the samples is based on the measurement of transmission and reflection spectra combined with rigorous numerical simulations. The results show that the metamaterial exhibits an effective refractive index of n=-0.5+1.9i at the wavelength lambda=2.1 microm.

Basics of averaging of the Maxwell equations for bulk materials

Abstract Volume or statistical averaging of the microscopic Maxwell equations (MEs), i.e. transition from microscopic MEs to their macroscopic counterparts, is one of the main steps in electrodynamics of materials. In spite of the fundamental importance of the averaging procedure, it is quite rarely properly discussed in university courses and respective books; up to now there is no established consensus about how the averaging procedure has to be performed. In this paper we show that there are some basic principles for the averaging procedure (irrespective to what type of material is studied) which have to be satisfied. Any homogenization model has to be consistent with the basic principles. In case of absence of this correlation of a particular model with the basic principles the model could not be accepted as a credible one. Another goal of this paper is to establish the averaging procedure for bulk MM, which is rather close to the case of compound materials but should include magnetic response of the inclusions and their clusters. In the vast majority of cases the consideration of bulk materials means that we consider propagation of an electromagnetic wave far from the interfaces, where the eigenwave in the medium has been already formed and stabilized. In other words, in this paper we consider the possible eigenmodes, which could exist in the equivalent homogenized media, and the necessary math apparatus for an adequate description of these waves. It has to be again clearly emphasized, that the presented paper does not suggest new recipes for the homogenization procedure, but rather summarizes known basics in order to establish solid basis for more particular cases. Nevertheless, it is believed that any homogenization model has to be compatible with the presented in this paper general structure. A discussion about boundary conditions and layered MM is a subject of separate publication and will be done elsewhere.

Genuine effectively biaxial left-handed metamaterials due to extreme coupling

Most left-handed metamaterials cannot be described by local effective permittivity or permeability tensors in the visible or near-infrared due to the mesoscopic size of the respective unit cells and the related strong spatial dispersion. We lift this problem and propose a metamaterial exhibiting artificial magnetism that does not suffer from this restriction. The artificial magnetism arises from the extreme coupling between both metallic films forming the unit cell. We show that its electromagnetic response can be properly described by biaxial local constitutive relations. A genuine biaxial left-handed fishnet metamaterial is suggested, which can be realized by atomic layer deposition to fabricate the nanoscaled spacing layers required for extreme coupling.