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We demonstrate an optical phased-array equipped with a 3D-printed facet-attached element for shaping and deflection of the emitted beam. The beam shaper combines freeform refractive surfaces with total-internal-reflection mirrors and is in-situ printed to edge-emitting waveguide facets using high-resolution multi-photon lithography, thereby ensuring precise alignment with respect to on-chip waveguide structures. In a proof-of-concept experiment, we achieve a grating-lobe free steering range of ± 30 ∘ and a full-width-half-maximum beam divergence of approximately 2 ∘ . The concept opens an attractive alternative to currently used grating structures and is applicable to a wide range of integration platforms.

Plasmonic nanorings provide the unique advantage of a pronounced plasmonic field enhancement inside their core. If filled with a polarizable medium, it may significantly enhance its optical effects. Here, we demonstrate this proposition by filling gold nanorings with lithium niobate. The generated second harmonic signal is compared to the signal originating from an unpatterned lithium niobate surface. Measurements and simulation confirm an enhancement of about 20. Applications requiring nanoscopic localized light sources like fluorescence spectroscopy or quantum communication will benefit from our findings.

An optical metamaterial, operating in between the MID/IR and the visible domain, which uses the effect of extreme coupling between closely spaced nanostructured gold metal plates and a planar gold substrate was realized by means of electron beam lithography and lift-off technique. This regime is only accessible by using an ultrathin oxide layer between metal plates and substrate, where the oxide layerisrealized by atomic layer deposition here. The involved fabrication is discussed in detail. The metamaterial shows the predicted effect of perfect absorption with multiple resonances in the spectral range from 100 THz to 600 THz. The plasmonic based resonance frequencies are very sensitive to the plate size of the grating and the spacer thickness.

The high potential of bottom-up fabrication strategies for realizing sophisticated optical sensors combining the high sensitivity of a surface plasmon resonance with the exceptional properties of stimuli-responsive hydrogel is demonstrated. The sensor is composed of a periodic hole array in a gold film whose holes are filled with gold-capped poly(N-isoproyl-acrylamide) (polyNIPAM) microspheres. The production of this sensor relies on a pure chemical approach enabling simple, time-efficient, and cost-efficient preparation of sensor platforms covering areas of cm(2). The transmission spectrum of this plasmonic sensor shows a strong interaction between propagating surface plasmon polaritons at the metal film surface and localized surface plasmon resonance of the gold cap on top of the polyNIPAM microspheres. Computer simulations support this experimental observation. These interactions lead to distinct changes in the transmission spectrum, which allow for the simultaneous, sensitive optical detection of refractive index changes in the surrounding medium and the swelling state of the embedded polyNIPAM microsphere under the gold cap. The volume of the polyNIPAM microsphere located underneath the gold cap can be changed by certain stimuli such as temperature, pH, ionic strength, and distinct molecules bound to the hydrogel matrix facilitating the detection of analytes which do not change the refractive index of the surrounding medium significantly.

We present, discuss, and validate an adapted $S$-matrix formalism for an efficient, simplified treatment of stacked homogeneous periodically structured metasurfaces operated under normally incident plane wave excitation. The proposed formalism can be applied to any material system, arbitrarily shaped metaatoms, at any frequency, and with arbitrary subwavelength periods. Circumventing the introduction of any kind of effective parameters we directly use the $S$ parameters of the individual metasurfaces to calculate the response of an arbitrary stack. In fact, the $S$ parameters are the complex parameters of choice fully characterizing the homogeneous metasurfaces, in particular with respect to its polarization manipulating properties. Just as effective material parameters like the permittivity and the permeability or wave parameters like the propagation constant and the impedance, the stacking based upon $S$ matrices can be applied as long as the individual layers are decoupled with respect to their near fields. This requirement eventually sets the limits for using the optical properties of the individual layers to calculate the response of the stacked system---this being the conceptual aim for any homogeneous metasurface or metamaterial layer and therefore the essence of what is eventually possible with homogeneous metasurfaces. As simple and appealing as this approach is, it is as powerful as well: Combining structured metasurfaces with each other as well as with isotropic, anisotropic, or chiral homogeneous layers is possible by simple semianalytical $S$-matrix multiplication. Hence, complex stacks and resonators can be set up, accurately treated and optimized with respect to their dispersive polarization sensitive optical functionality without the need for further rigorous full-wave simulations.

We report on the investigation of an advanced circular plasmonic nanoantenna under ultrafast excitation using nonlinear photoemission electron microscopy (PEEM) under near-normal incidence. The circular nanoantenna is enhanced in its performance by a supporting grating and milled out from a gold film. The considered antenna shows a sophisticated physical resonance behavior that is ideal to demonstrate the possibilities of PEEM for the experimental investigations of plasmonic effects on the nanoscale. Field profiles of the antenna resonance for both possible linear polarizations of the incident field are measured with high spatial resolution. In addition, outward propagating Hankel plasmons, which are also excited by the structure, are measured and analyzed. We compare our findings to measurements of an isolated plasmonic nanodisc resonator and scanning near-field optical microscopy (SNOM) measurements of both structures. All results are in very good agreement with numerical simulations as well as analytial models that are also discussed in our paper.

We experimentally investigate the propagation of Airy surface plasmon polariton on a metallic film by using Multiphoton Photoemission Electron Microscopy and demonstrate a good agreement with large scale finite difference time domain simulations.

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 theoretically and experimentally investigate circular plasmonic disc nanoantennas enhanced in their performance by a surrounding Bragg grating ring structure. PEEM investigations are demonstrated to provide unprecedented insights into the field localization and enhancement.

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.

Understanding the impact of order and disorder is of fundamental importance to perceive and to appreciate the functionality of modern photonic metasurfaces. Metasurfaces with disordered and amorphous inner arrangements promise to mitigate problems that arise for their counterparts with strictly periodic lattices of elementary unit cells such as, e.g., spatial dispersion and allows the use of fabrication techniques that are suitable for large scale and cheap fabrication of metasurfaces. In this study, we analytically, numerically and experimentally investigate metasurfaces with different lattice arrangements and uncover the influence of lattice disorder on their electromagnetic properties. The considered metasurfaces are composed of metal-dielectric-metal elements that sustain both electric and magnetic resonances. Emphasis is placed on understanding the effect of the transition of the lattice symmetry from a periodic to an amorphous state and on studying oblique illumination. For this scenario, we develop a powerful analytical model that yields, for the first time, an adequate description of the scattering properties of amorphous metasurfaces, paving the way for their integration into future applications.

Genuinely homogeneous metamaterials, which may be characterized by local effective constitutive relations, are required for many spectacular metamaterial applications. Such metamaterials have to be made of meta-atoms, i.e., subwavelength resonators, which exhibit only electric and or magnetic dipole and negligible higher-order multipolar polarizabilities in the spectral range of interest. Here, we show that these desired meta-atoms can be designed by exploiting the extreme coupling regime. Appropriate meta-atoms are identified by performing a multipole analysis of the field scattered from the respective meta-atom. To design those particular meta-atoms it is important to disclose the frequency and angular-dependent polarizability of both dipole moments. We demonstrate the applicability of a purely analytical model to accurately calculate for a normally incident plane wave reflection and transmission from meta-surfaces made of periodically arranged meta-atoms. With our work we identify a possible route towards the engineering of artificial materials while only considering the response from its constituents. Our approach is generally applicable to all spectral domains and can be used to evaluate and design metamaterials made from different constituting materials, e.g., metals, dielectrics, or semiconductors.

We apply the concept of quasicrystals to metamaterials and experimentally demonstrate metasurfaces with isotropic properties and high resonance strength. By comparing quasicrystalline, periodic, and amorphous metasurfaces we quantify the impact of symmetry on their properties. This is achieved by studying the eigenpolarizations’ ellipticity and circular dichroism induced by mutual coupling of the meta-atoms. The advantage of the quasicrystalline in comparison to a periodic arrangement originates from the ability to reach a higher rotational symmetry in k space, therefore opening a route towards isotropic metasurfaces.

We compare, both experimentally and theoretically, metamaterials with three different symmetries: square lattice, hexagonal lattice, and quasicrystalline Penrose tiling. By relying on an advanced Jones calculus, we link the symmetry properties to the far-field optical response, such as ellipticity and circular dichroism, as the incident angle is varied. We show that hexagonal lattice metamaterials, when compared to the square ones, exhibit less circular dichroism and ellipticity due to their higher symmetry. Furthermore, we show that in contrast to periodic metamaterials, quasicrystalline metamaterials inhibit ellipticity and circular dichroism and open a new route to isotropy in metamaterials at oblique incidence.

Electromagnetic properties of resonant metasurfaces are studied in transition from a periodic to an amorphous arrangement of their constituents. Emphasis is put to investigate the response at oblique incidence and for TM polarized light. Our metasurfaces possess both electric and magnetic resonances which makes them to be canonical samples that reflect properties of many metasurfaces. The suggested analytical model explains many if not to say all far-field optical properties that can be observed in resonant metasurfaces. For example, the resonance broadening and damping for the electric mode which contrasts with the persistence of these properties for the magnetic mode in transition from crystalline to the amorphous state can be fully explained. All theoretical predictions are verified with complementary numerical calculations and experimental measurements.

The availability of novel technologies that enable the fabrication of bulk metamaterials made it necessary to develop a theoretical language to discuss their properties appropriately. Here we use the fundamental Bloch mode approximation to explore bulk properties of metamaterials that operate at terahertz frequencies. We demonstrate that this approximation is valid in the case of terahertz meta-foil metamaterials. While relying on theoretical and experimental results, we show that the fundamental Bloch mode approximation can explain minuscule details that are unique to the bulk metamaterial. Various applications such as cylindrical lenses, terahertz cloaks, and sensors will benefit from our analysis.

We discuss the homogenization of metamaterials consisting of periodically arranged unit-cells from a Bloch mode perspective. This theory provides clear answers to the important questions of whether a metamaterial can be homogenized, which effective properties can be assigned, and how they are linked to properties of the Bloch mode. It is shown that material parameters can only be assigned to the metamaterial under certain circumstances, i.e. only if the propagation constant and the impedance obey a strict functional dependency. To achieve homogenous metamaterials fewer efforts are necessary but they still require a carefully balanced design.

By means of experiment and simulation, we achieve unprecedented insights into the formation of Talbot images to be observed in transmission for light diffracted at wavelength-scale amplitude gratings. Emphasis is put on disclosing the impact and the interplay of various diffraction orders to the formation of Talbot images. They can be manipulated by selective filtering in the Fourier plane. Experiments are performed with a high-resolution interference microscope that measures the amplitude and phase of fields in real-space. Simulations have been performed using rigorous diffraction theory. Specific phase features, such as singularities found in the Talbot images, are discussed. This detailed analysis helps to understand the response of fine gratings. It provides moreover new insights into the fundamental properties of gratings that often find use in applications such as, e.g., lithography, sensing, and imaging. (C) 2012 Optical Society of America

Recently perfect metamaterial absorbers triggered some fascination since they permit the observation of an extreme interaction of light with a nanostructured thin film. For the first time we evaluate here the functionality of such perfect absorbers if they are applied on curved surfaces. We probe their optical response and discuss potential novel applications. Examples are the complete suppression of back-scattered light from the covered objects, rendering it cloaked in reflection, and their action as optical black holes.

We demonstrate that planar metamaterial lacking of mirror symmetry shows asymmetric transmission of terahertz waves and bands of positive, negative and zero phase and group velocities indicating a polarization sensitive negative index and slow-light media.

International audience; The appropriate description of light scattering (transmission/reflection) at a bulky artificial medium, consisting of a sequence of functional metamaterial and natural material films, represents a major challenge in current theoretical nano-optics. Because in many relevant cases, in particular, in the optical domain, a metamaterial must not be described by an effective permittivity and permeability the usual Fresnel formalism cannot be applied. A reliable alternative consists in using a Bloch mode formalism known, e.g., from the theory of photonic crystals. It permits to split this complex issue into two more elementary ones, namely the study of light propagation in an infinitely extended metamaterial and the analysis of light scattering at interfaces between adjacent meta and natural materials. The first problem is routinely solved by calculating the relevant Bloch modes and theirdispersion relations. The second task is more involved and represents the subject of the present study. It consists in using the general Bloch mode orthogonality to derive rigorous expressions for the reflection and transmission coefficients at an interface between two three-dimensional absorptive periodic media for arbitrary incidence. A considerable simplification can be achieved if only the fundamental Bloch modes of both media govern the scattering properties at the interface. If this approximation is valid,which depends on the longitudinalmetamaterial period, the periodic metamaterial may be termed homogeneous. Only in this case the disentanglement of the fundamental modes of both media can be performed and the reflection/transmission coefficients can be expressed in terms of two impedances, each depending solely on the properties of the fundamental mode of the respectivemedium. In order to complement the picture, we apply the present formalism to the quite general problem ofreflection/transmission at a metamaterial film sandwiched between a dissimilar metamaterial. This situation asks for a devoted treatment where multiple modes have to be taken into account.

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 consist of a periodic or aperiodic arrangement of so-called meta-atoms. Usually their optical properties are derived from the collective response of this ensemble. However, it is highly desirable to deduce them from the scattering properties of individual meta-atoms because frequently the periodic arrangement has a spurious effect on the desired functionality. Moreover, understanding the scattering properties of individual meta-atoms permits introducing guidelines for their design and predicting effective properties of amorphous metamaterials. To achieve this we introduce a genuine approach to quantify the properties of individual meta-atoms. To this end we evaluate spectrally resolved the composition of the rigorously calculated scattered field in terms of contributions of electromagnetic multipoles, such as electric and magnetic dipoles, quadrupoles and, in principle, arbitrary higher order moments. Beyond its direct application to metamaterial's design and characterization, the approach will be significant in the entire field of nanooptics as, for example, for optical nanoantennas.

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.

We introduce a top-down fabricated metamaterial composed of three-dimensional, chiral, plasmonic nanostructures for visible and near-infrared wavelengths. Based on a combined spectroscopic and interferometric characterization, the entire complex transmission response in terms of a Jones matrix is disclosed. Particularly, the polarization output state of light after propagation through the nanostructures can be decoded from the measurements for any excitation configuration. We experimentally found a rotation of the polarization azimuth of linearly polarized light exceeding 50degrees at wavelengths around 1.08 mum. This corresponds to a specific rotation which is significantly larger than that of any linear, passive, and reciprocal medium reported to date.

Metamaterials are artificial media that allow tailoring the macroscopic properties of light propagation by a careful choice of nanoplasmonic inclusions it is made of. A simple and versatile analytical model describing propagation of electro magnetic waves in metamaterials is suggested. The model is based on the secondary averaging procedure in full analogy with the ordinary one accepted for Maxwell equations, where the nanoplasmonic inclusions (typically referred to as metaatoms or metamolecules) are considered similarly to natural atoms or molecules. The model turns out to be beneficial improvement in the theoretical description of metamaterials since it contributes to the physical understanding of optical phenomena in metamaterials and provides good quantitative correspondence with the results of rigorous numerical methods, and is able to predict new effects.

Homogenization of optical metamaterials is one of the fundamental problems of electrodynamics of composite materials. Here the homogenization approach using multipole expansion is analysed and compared with the phenomenological one. Applications of the developed model for different structures and various phenomena are presented.

By relying on an advanced Jones calculus we analyze the polarization properties of light upon propagation through metamaterial slabs in a comprehensive manner. Based on symmetry considerations, we show that all periodic metamaterials may be divided into five different classes only. It is shown that each class differently affects the polarization of the transmitted light and sustains different eigenmodes. We show how to deduce these five classes from symmetry considerations and provide a simple algorithm that can be applied to decide by measuring transmitted intensities to which class a given metamaterial is belonging to only.

Although optical metamaterials that show artificial magnetism are mesoscopic systems, they are frequently described in terms of effective material parameters. But due to intrinsic nonlocal (or spatially dispersive) effects it may be anticipated that this approach is usually only a crude approximation and is physically meaningless. In order to study the limitations regarding the assignment of effective material parameters, we present a technique to retrieve the frequency-dependent elements of the effective permittivity and permeability tensors for arbitrary angles of incidence and apply the method exemplarily to the fishnet metamaterial. It turns out that for the fishnet metamaterial, genuine effective material parameters can only be introduced if quite stringent constraints are imposed on the wavelength/unit cell size ratio. Unfortunately they are only met far away from the resonances that induce a magnetic response required for many envisioned applications of such a fishnet metamaterial. Our work clearly indicates that the mesoscopic nature and the related spatial dispersion of contemporary optical metamaterials that show artificial magnetism prohibits the meaningful introduction of conventional effective material parameters.

In the search for isotropic metamaterials we analyze isofrequency surfaces of the dispersion relation of highly symmetric metamaterials and show that they are optically anisotropic. Instead isotropic metamaterials are achieved by carefully designing multilayer structures.

Optically isotropic metamaterials (MMs) are required for the implementation of subwavelength imaging systems. At first glance one would expect that their design should be based on unit cells exhibiting a cubic symmetry being the highest crystal symmetry. It is anticipated that this is a sufficient condition since it is usually assumed that light does not resolve the spatial details of MM but experiences the properties of an effective medium, which is then optically isotropic. In this work we challenge this assumption by analyzing the isofrequency surfaces of the dispersion relation of the split-cube in carcass (SCiC) negative index MM. We show that this MM is basically optically isotropic, but not in the spectral domain where it exhibits negative refraction. The primary goal of this contribution is to introduce a tool that allows to probe a MM against optical isotropy.

Homogenization of metamaterials is very important as it makes possible description in terms of effective parameters. In this contribution we consider the homogenization of chiral metamaterials. We show that for some metamaterials there is an optimal meta‐atom size which depends on the coupling between meta‐atoms. We introduce numerical criterion of homogeneity on the basis of the Bloch modes dispersion diagram calculation and a tool to predict the homogeneity limit. We show that some metamaterials with strong coupling between meta‐atoms cannot be considered as homogeneous at all.

We show for the first time that a planar metamaterial, an array of coupled metal split-ring resonators with a unit cell lacking mirror symmetry, exhibits asymmetric transmission of terahertz radiation (0.25-2.5 THz) propagating through it in opposite directions. This intriguing effect, that is compatible with Lorentz reciprocity and time-reversal, depends on a directional difference in conversion efficiency of the incident circularly polarized wave into one of opposite handedness, that is only possible in lossy low-symmetry planar chiral metamaterials. We show that asymmetric transmission is linked to excitation of enantiomerically sensitive plasmons, these are induced charge-field excitations that depend on the mutual handedness of incident wave and metamaterial pattern. Various bands of positive, negative and zero phase and group velocities have been identified indicating the opportunity to develop polarization sensitive negative index and slow light media based on such metamaterials., Comment: 5 pages, 6 figures (various minor improvements throughout)

We experimentally and numerically study the propagation of light through amorphous metamaterials. For this purpose we introduce a precisely controllable degree of positional disorder into a perfectly periodic system, transforming it to a partially disordered and ultimately an amorphous metamaterial. The observable spectral features occurring upon this transition and the impact of coherent interactions among neighboring unit cells are revealed. Backed by numerical simulations, the effective properties of the metamaterials are retrieved, most notably for the amorphous one. The most important finding with respect to negative index materials is that their magnetic properties are not affected by an arbitrarily high degree of disorder. This work enables the quantitative evaluation of effective properties of amorphous metamaterials fabricated by bottom-up approaches.

Metamaterials (MM) attracted an ever increasing research interest in the past. Their main fascination derives from the possibility to attribute conceptually effective properties to them, if their characteristic length scale (being the size of the metaatoms) is much smaller than the wavelength of light. Most notably, a negative effective negative index became possible. It implies that for a certain eigenmode that is allowed to propagate inside such a MM, the real part of the wave vector and its imaginary part have opposite signs. Such negative indices were obtained, thus far, in most cases by relying on plasmonic resonances that induce an artificial magnetization. However, by taking the definition above, it is naturally anticipated that such negative refraction is a feature that can be observed in various physical systems. Indeed, similar observations were made in, e.g. plasmonic waveguides or photonic crystals. Also recently, first experimental results were presented on a negative refractive index by relying on a chirality of the metaatoms. Interesting enough, the idea to achieve negative refraction by chirality was introduced by Pendry already in 2004 [1]. There his argumentation bases nearly entirely on the dispersion relation. Nevertheless, for the observation of negative refraction the chirality has to be strongly pronounced. To induce strong chirality one may resort to appropriately shaped three-dimensional metaatoms [2] instead of quasiplanar chiral metamaterials [3] or to rely on twisted unit cells. The latter would cause an ambi-chiral media.

In the past several years, optical metamaterials (MMs) have attracted a considerable deal of interest because it may be anticipated that their properties can be shaped to an unprecedented extent relieving optics from some of its natural limitations. An inevitable first step toward this goal is the evaluation of the optical properties of specifically designed MMs. To date, apart from identifying chiral properties of very specific configurations, this is primarily done in retrieving an effective refractive index---mostly---only for normal incidence. On this basis suggestions for a perfect lens, exploiting this negative refractive index have been put forward by taking advantage of geometrical optics arguments. We show that this approach is pointless for realistic MMs. Instead we prove that the dispersion relation of normal modes in these MMs provides all the required information. Most of the relevant optical parameters, such as refraction and diffraction coefficients, can be derived from this relation. Imaging properties follow straightforwardly from that data. This general approach holds for any optical material, in particular, for all MMs in question. As an example, we apply it to the fishnet structure: one of the most prominent and best studied design approaches to date. We show that both refraction and diffraction properties are strongly spatially and temporally dispersive and they can even change sign. In detail, we study the effect of these peculiarities on imaging and refraction of finite beams. In particular, we discuss both the effect of the specific dispersion relation and the losses on the imaging properties. All our physical predictions are backed by rigorous numerical calculations and the agreement is almost perfect. Ultimately the main conclusion to be drawn is that a negative index of refraction is by no means a sufficient criterion to achieve negative refraction and/or perfect imaging.

We present and evaluate theoretically and experimentally a design for a negative-index metamaterial that is termed the "Swiss cross" structure. Compared with the established fishnet structure, the proposed design eliminates the drawback of polarization-dependent effective optical parameters. The new design is fabricated by means of e-beam technology and experimentally analyzed using spectroscopic techniques. The thorough comparison with numerical simulations reveals an effective refractive index of n=-1.9 at an operational wavelength of 1400 nm that is independent of the incident polarization. The resonances of the system are comprehensively discussed. (C) 2009 Optical Society of America

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 figures

The multipole reinterpretation of plasmonic resonances occurring in metaatoms is presented. The approach allows us to determine effective metamaterial parameters and inherently induces nonlinear optical response by considering higher order multipoles beyond the electric dipole.

We measure the angular dependent response of a Swiss-cross metamaterial that has an effective index of n = −1.9 at normal incidence. It is experimentally shown how the effective properties depend on the incidence angle.

We introduce a procedure to retrieve anisotropic effective parameters of metamaterials at oblique incidence. We show that such a homogenization fails near plasmonic resonances for all reasonable aspect ratios and discuss possible implications.

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.

We derive the dispersion relation of Bloch modes in a fishnet metamaterial in the optical frequency domain. The dependence of the longitudinal wave vector component on the transverse one and the frequency, which governs diffraction and dispersive spreading of localized light excitations, respectively, are analyzed. We show that this type of metamaterial exhibits an involved anisotropic behavior with diffraction changing the sign in passing even a zero diffraction point. For completeness we derive furthermore a formal angle-dependent effective refractive index which exhibits discontinuities. Thus we conclude that an effective refractive index tends to get meaningless and that only the dispersion relation predicts reliably light propagation in metamaterials. The results are double checked with those obtained from a retrieval algorithm based on angular resolved reflection/transmission data of a finite slab. Excellent agreement is observed.

We introduce a technique to retrieve effective metamaterial parameters for arbitrary angles of incidence. It employs the complex reflection and/or transmission coefficients of a finite slab. Explicit expressions for both polarizations are derived and the constraints to be met for obtaining unique solutions are discussed. The method is applied to the fishnet structure. It turns out that all retrieved parameters strongly depend on the lateral wave vector component due to the complexity of the metamaterial structure. Thus, these parameters are mere wave parameters rather than global material parameters. The physical effects behind this behavior are very likely anisotropy and spatial dispersion.

We show that a longitudinal (Goos-H\"anchen) and a transverse (Imbert-Fedorov) beam displacement can be observed upon total internal reflection at two-dimensional photonic crystal slabs. By inspecting only the dispersion relation of the photonic crystal we derive qualitative criteria for the direction of the beam shift. Furthermore, it will be shown that the beam shift can be strongly enhanced at particular angles of incidence where Fabry-P\'erot resonances of the slab are excited. The Renard model, which predicts the strength of the shifts based on the Poynting vector in the totally reflecting medium, has been adapted to quantitatively analyze the beam shift.

We introduce a procedure to retrieve angle- and polarization-dependent effective parameters of metamaterials based on reflection and transmission at a finite slab. Their meaning in the presence of strong spatial dispersion and anisotropy is discussed.

We analyze beam displacements that occur upon reflection at interfaces between homogeneous media and metamaterials. Emphasis is put on system requirements, the techniques to predict the shift and the peculiarities in the presence of metamaterials.

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.

We analyze the transverse shift (Imbert-Fedorov shift) of a focused beam upon reflection at stratified (doubly dispersive) metamaterials. In deriving analytical expressions for the reflection of a focused beam at such an interface this shift can be quantitatively forecast. Solely based on symmetry considerations of the vectorial reflection coefficient we analyze potential geometries where such a shift occurs. Contrary to the common belief, this shift is observable for a linearly polarized beam at total internal reflection. Furthermore, we predict a giant Imbert-Fedorov shift if light is partially reflected at impedance-matched media.

Upon evaluating the dispersion relation of light propagating in metamaterials, we elucidate the impact of encountered normal and anomalous diffraction regimes on refraction, diffraction and the imaging properties of metamaterials.