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 promise the possibility to tailor the propagation properties of light at the nano-scale. With this
contribution we explore the possibility to combine the concept of metamaterials with integrated optics.
We investigate a system consisting of a one-dimensional array of double cut-wires (two very thin gold sheets
separated by a dielectric spacer) placed on top of a dielectric slab waveguide, which supports only the fundamental
TE and TM mode in the near infrared spectral region around 1550 nm. Strong coupling of the waveguide modes
to the plasmonic eigenmodes of the double cut-wire is achieved via the longitudinal component of the electric
field, being relatively large for an asymmetric refractive index profile. By tuning the length of the double cutwires,
we can tune the spectral position of the occurring hybrid resonance. We will show by rigorous calculations,
that the resonance is anti-symmetric and hence produces artificial magnetism at optical frequencies in this simple
To further explore the physics of the system, we investigate the dispersion relation of a periodic array of
double cut-wires with varying lattice periods. The slab waveguide mode leads to a coupling of the individual
plasmonic nanostructures. We find that for short lattice periods the dispersion closely resembles that of the
slab waveguide. However when the Bragg frequency approaches the plasmonic resonance frequency, a strong
interaction takes place and leads to a back-bending of the dispersion relation with regions of negative group
velocity near to the band edge while an avoided crossing of both resonances takes place.
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.
A simple analytical model has been developed within the scopes of the macroscopic Maxwell's equations. In the
framework of this model the dispersion relation for plane waves has been calculated for the case of Cut-Wire (CW) and
Split Ring Resonator (SRR) geometries. The dispersion relation has been compared with rigorous numerical calculations.
A possible way to introduce the electric and magnetic material parameters has been suggested. Validity criteria and
applicability limitations of the developed model are discussed. A new type of nonlinearity specific for the metamaterials
- Multipole Nonlinearity - is identified based on the developed model, wheras the second harmonic generation (SHG)
process is considered in detail
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.
In modern optical engineering the simulation of imaging and non-imaging optical systems on the basis of wave optics is of increasing importance. A simulation based on wave optics means on one hand to use everywhere in the optical system a wave-optical description of light. This allows the evaluation of more general merit functions for the description of the system quality which requires, for example, access to amplitude, phase, polarization, coherence information of light. On the other hand, including wave optics in optical simulations means to model the light propagation exact enough to describe wave-optical propagation effects. That means in general not to perform all simulations without physical approximations but to use light propagation models that work with sufficient physical precision within the optical system. The authors will discuss which needs follow for modern optical simulation software. This discussion includes a flexible handling of different models for simulation of light propagation, descriptions of different wave-optical light representations and considerations of numerical and physical simulation precision.
In wave-optical engineering the propagation of light through an optical system can be simulated by using several physical approximations. Independent of the used method it is necessary to have full access to the complete electromagnetic field information in the desired regions. In this article we firstly go into the question what the required information is to get access to the whole electromagnetic field and as a second step we give some insights into physical modeling accuracy and numerical accuracy which is of high importance to evaluate the quality of the calculated results.