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The excitation of surface plasmon polaritons in metallic nanostructures significantly enhances light-matter interactions at sub-wavelength scales. This enables novel optical effects that rely on artificial materials, so-called metamaterials. Metamaterials are made from densely packed and sufficiently small nanostructured unit cells. The purpose of metamaterials is to act comparable to bulk materials but with effective properties that can be tailored by the geometry of the unit cells. However, recently it became obvious that many appealing applications are already in reach by employing an ultrathin layer of metamaterial. Exploiting the metamaterials’ primary optical properties in the form of their dispersive complex reflection and transmission coefficients, single functional layers instead of bulk metamaterials are already sufficient for achieving sophisticated device properties. In particular, if the unit cells change across the functional layer, a new class of devices can be perceived that shape the light in the far-field according to predefined patterns. These metamaterial layers, usually referred to as metasurfaces, possess major advantages when compared to traditional optical elements. Here, we provide an overview of the burgeoning field of research that explores metasurfaces to affect an incident field spatially and spectrally in a deterministic way to enable functional diffractive optical elements.

We systematically study both experimentally and theoretically the links between the lattice symmetries of metasurfaces and their optical properties at both normal and oblique illumination. We attribute different symmetry elements to number of polarization phenomena. In particular, we predict analytically and verify experimentally the influence of rotational axes, mirror planes and inversion centres on optical activity, circular dichroism and asymmetric transmission. We fabricate and test nanostructured optical metasurfaces with four different inner structures: square and hexagonal lattices, quasicrystalline layout, and amorphous arrangement. We demonstrate the ability to enhance/suppress particular optical response by appropriate choice of the metasurface’s symmetry.

Properties of metamaterials are usually discussed in terms of biaxial anisotropic material parameters. To consider the underlying constitutive relations as valid, it is required that only weak spatial dispersion occurs. At operational frequencies of optical metamaterials this assumption often ceases to be valid. A description using effective material properties tends to be inadequate and new approaches are required. We outline here our latest achievements along this direction and discuss two approaches. The first one assumes that if it is not possible to introduce useful effective properties, a more primary source of information should be used to quantify metamaterials, leading to a characterization of metamaterials in terms of Jones matrices. We discuss the implications of this description and show that all metamaterials can be categorized into five classes, each with distinct properties. The second approach resorts to an effective description but restricts its considerations to a dispersion relation, characterizing the propagation of light in bulk metamaterials, and an impedance, characterizing the coupling between metamaterials and their surroundings. Definitions of both properties linked to a single Bloch mode are discussed and metamaterials are introduced which can be homogenized while considering only this single mode.

Metamaterials are composites consisting of artificial meta-atoms/metamolecules with typical sizes less than the wavelength of operation. One of the key properties that makes metamaterials distinctly different form the natural media is a very strong magnetic response that can be engineered in the visible and infra-red part of the spectrum. In this work we summarize our multipole expansion approach that can be used to describe analytically optical properties of metamaterials composed of, in particular, the split-ring and cut-wire resonators. An important feature of our formalism is the possibility of describing nonlinear response of a metamaterial, such as second harmonic generation, which arises due to induced high-order multipoles. Our model has recently been extended to the case of hybrid metamaterials composed of plasmonic nano-resonators coupled with quantum elements (such as quantum dots, carbon nano tubes etc). It has also been shown that apart from metamaterials various other physical systems can be successfully modelled within framework of the developed approach. For example, transient dynamics and steady-state regime of a nano-laser, as well as its stochastic properties (e.g. linewidth of generation) have been described using this model.

The realm of nanooptics is usually characterized by the interaction of light with structures having relevant feature sizes much smaller than the wavelength. To model such problems, a large variety of methods exists. However, most of them either require a periodic arrangement of a unit cell or can handle only single entities. But there exists a great variety of functional devices which may have either a spatial extent much larger than the wavelength and which comprise structural details with sizes in the order of a fraction of the wavelength or they may consist of an amorphous arrangement of strongly scattering entities. Such structures require large scale simulations where the fine details are retained. In this contribution we outline our latest research on such devices and detail the computational peculiarities we have to overcome. Presenting several examples, we show how simulations support the physical understanding of these devices. Examples are randomly textured surfaces used for solar cells, where guided modes excited in the light absorbing layers strongly affect the solar cell efficiency, amorphous metamaterials and stochastically arranged nanoantennas. The usage of computational experiments will be motivated by the unprecedented insight into the functionality of such components.

The properties of metamaterials made of an increasing number of discrete functional layers are analyzed. Convergence of the effective properties towards their bulk counterparts is observed if the light propagation in the metamaterial is dominated by a single eigenmode. The effective properties of the finite structure will be compared to the properties of the infinite structure for which an effective refractive index can be derived from the dispersion relation. The dispersion relation is furthermore shown to be useful in deriving angle dependent effective material parameters. They are compared to the effective properties obtained from a finite slab by applying a dedicated retrieval procedure.

An analytical description for plane wave propagation in metamaterials (MM) is presented. It follows the usual approach for describing light propagation in homogenous media on the basis of Maxwell's equations, though applied to a medium composed of metallic nanostructures. Here, as an example, these nanostructures are double (or cut) wires. In the present approach the multipole expansion technique is used to account for the electric and magnetic dipole as well as the electric quadrupole moments of the carrier distribution within the nanostructure where a model of coupled oscillators is used for the description of the internal charge density dynamics. It is shown how expressions for the effective permittivity and permeability can be derived from analytical expressions for the dispersion relation, the magnetization and the electric displacement field. Results of the analytical model are compared with rigorous simulations of Maxwell's equations yielding the limitations and applicability of the proposed model.