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We present spatial frequency maps of power flow in metamaterials and photonic crystals in order to provide insights into their electromagnetic responses and further our understanding of backward power in periodic structures. Since 2001, many different structures across the electromagnetic spectrum have been presented in the literature as exhibiting an isotropic negative effective index. Although these structures all exhibit circular or spherical equifrequency contours that resemble those of left-handed media, here we show through $k$-space diagrams that the distribution of power in the spatial frequency domain can vary considerably across these structures. In particular, we show that backward power arises from high-order right-handed harmonics in photonic crystals, magnetodielectric crystals, and across the layers of coupled-plasmonic-waveguide metamaterials, while arising from left-handed harmonic pairs in split-ring resonator and wire composites, plasmonic crystals, and along the layers of coupled-plasmonic-waveguide metamaterials. We also show that the fishnet structure exhibits the same left-handed harmonic pairs as the latter group. These observations allow us to categorize different metamaterials according to their spatial spectral source of backward power and identify the mechanism behind negative refraction at a given interface. Finally, we discuss how $k$-space maps of power flow can be used to explain the high or low transmittance of power into different metamaterial or photonic crystal structures.

Almost a decade ago, transformation optics established a geometrical perspective to describe the interaction of light with structured matter, enhancing our understanding and control of light. However, despite their huge technological relevance in applications such as optical circuitry, optical detection, and actuation, guided electromagnetic waves along dielectric waveguides have not yet benefited from the flexibility and conceptual simplicity of transformation optics. Indeed, transformation optics inherently imposes metamaterials not only inside the waveguide's core but also in the surrounding substrate and cladding. Here we restore the two-dimensional nature of guided electromagnetic waves by introducing a thickness variation on an anisotropic dielectric core according to alternative two-dimensional equivalence relations. Our waveguides require metamaterials only inside the core with the additional advantage that the metamaterials need not be magnetic and, hence, our purely dielectric waveguides are low loss. We verify the versatility of our theory with full wave simulations of three crucial functionalities: beam bending, beam splitting, and lensing. Our method opens up the toolbox of transformation optics to a plethora of waveguide-based devices.

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 demonstrate that surface plasmons of a thin metal film interacting with a periodic array of nano-structures around it can be utilized to make bulk negative index metamaterials at visible spectrum with simultaneously negative permittivity and permeability. These surface plasmon driven metamaterials have high figure of merit and can be tuned arbitrarily to operate at any wavelength in the visible spectrum and possibly at ultraviolet spectrum. We numerically demonstrate the idea by a metamaterial structure which exhibits a strong magnetic response resulting in a negative index of refraction in the green region of the electromagnetic spectrum at 536nm with a figure of merit of 3.67. We also demonstrate by simply changing the constituent material only, hence by modifying the underlying surface plasmon dispersion, that the operating wavelength of the structure can be blue-shifted to the violet region at 406nm with a figure of merit of 2.27. In contrast to the fishnet-structure based approaches for visible metamaterials, our proposed approach offers a more frequency scalable way of achieving negative index of refraction in the visible and possibly at ultraviolet wavelengths with high figure of merit., Comment: Accepted for publication in Physical Review B, 7 journal page, 6 figures

We demonstrate that it is possible to confine electromagnetic radiation in cavities that are significantly smaller than the wavelength of the radiation it encapsulates. To this aim, we use the techniques of transformation optics. First, we present a "perfect cavity" of arbitrarily small size in which such confined modes can exist. Furthermore, we show that these eigenmodes have a continuous spectrum and that bending losses are absent, in contrast to what is observed in traditional microcavities. Finally, we introduce an alternative cavity configuration that is less sensitive to material imperfections and still exhibits deep subwavelength modes combined with high quality factor, even if considerable material losses are included. Such a cavity may be interesting for the storage of information in optical data processing and for applications in quantum optics., 5 pages, 4 figures

Plasmonic cloaking is a scattering-cancellation technique based on the local negative polarizability of metamaterials. Here we report its first experimental realization and measurement at microwave frequencies. An array of metallic fins embedded in a high-permittivity fluid has been used to create a metamaterial plasmonic shell capable of cloaking a dielectric cylinder, yielding over 75% reduction of total scattering width.

We demonstrate theoretically that electromagnetically induced transparency can be achieved in metamaterials, in which electromagnetic radiation is interacting resonantly with mesoscopic oscillators rather than with atoms. We describe novel metamaterial designs that can support a full dark resonant state upon interaction with an electromagnetic beam and we present results of its frequency-dependent effective permeability and permittivity. These results, showing a transparency window with extremely low absorption and strong dispersion, are confirmed by accurate simulations of the electromagnetic field propagation in the metamaterial.

In recent works, we have suggested that plasmonic covers may provide an interesting cloaking effect, dramatically reducing the overall visibility and scattering of a given object. While materials with the required properties may be directly available in nature at some specific infrared or optical frequencies, this is not necessarily the case for any given design frequency of interest. Here we discuss how such plasmonic covers may be specifically designed as metamaterials at terahertz, infrared, and optical frequencies using naturally available metals. Using full-wave simulations, we demonstrate that the response of a cover formed by metallic plasmonic implants may be tailored at will so that at a given frequency, it possesses the plasmonic-type properties required for cloaking applications.

A method is described which elucidates propagation of an electromagnetic field generated by a stochastic, electromagnetic source within the short wavelength limit. The results can be used to determine statistical properties of fields using ray tracing methods.

We introduce an approach towards the design of metamaterials where the dielectric and magnetic activity is caused by resonances in dielectric nanocavities embedded in metal. The simplest implementation of this concept is a rectangular nanoaperture in a thin metallic stripe. We show that the electromagnetic field of the resonance eigenmodes is primarily concentrated in the dielectric medium. Even modes affect the effective permittivity, whereas odd modes evoke dispersion in the effective permeability. The negative permittivity provided by the metallic stripes allows potentially for a negative effective index near the first magnetic resonance. Advantages and disadvantages of this structure compared to metamaterials where the resonant eigenmodes are mainly localized at metallic nanoparticles are discussed.

It was shown some years ago that the spectrum of a stochastic scalar field depends not only on the source spectrum but also on the degree of coherence of the source. In this paper we show that there are electromagnetic fields for which not only the state of coherence of the source, but also its degree of polarization affect the spectrum of the radiated field. We illustrate the analysis by diagrams which show the far-zone spectra of some stochastic electromagnetic beams generated by sources of different states of coherence and different degrees of polarization. The spectra of the radiated field depend both on coherence properties of the source and its degree of polarization and are found to be different in different directions of observation.

We have studied the influence of space and time dispersion on the frequency dependence of the wave vectors of electromagnetic waves propagating in periodic dielectric structures. Two types of structures are considered: media with weak periodic modulation of the permittivity and photonic crystals composed of periodically arranged identical resonant dielectric particles embedded into nontransparent host medium. It is shown that in these systems, different types of excitations exist, for example, a peculiar kind of polaritons arises in the photonic crystals due to the interaction of the electromagnetic field, eigenoscillations of the dielectric medium, and the Debye resonance. Additional transparency bands and gaps appear in the frequency spectrum of photons due to the dispersion, and their widths depend on the wave vector. The widths of the transparency zones and of the band gaps have been calculated as functions of the frequency and of the parameters of the media. The interaction of different types of waves brings into existence a discontinuity of the frequency at some surfaces in $\stackrel{P\vec}{k}$ space. If such a surface is not a plane, the classical Bragg condition does not hold.

We present a class of artificial materials that exhibit a tailored response to the electrical component of electromagnetic radiation. These electric metamaterials are investigated theoretically, computationally, and experimentally using terahertz time-domain spectroscopy. These structures display a resonant response including regions of negative permittivity ${ϵ}_{1}(\ensuremath{\omega})l0$ ranging from $\ensuremath{\sim}500\phantom{\rule{0.3em}{0ex}}\mathrm{GHz}\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}1\phantom{\rule{0.3em}{0ex}}\mathrm{THz}$. Conventional electric media such as distributed wires are difficult to incorporate into metamaterials. In contrast, these localized structures will simplify the construction of future metamaterials, including those with negative index of refraction. As these structures generalize to three dimensions in a straightforward manner, they will significantly enhance the design and fabrication of functional terahertz devices.

We propose a complete set of periodic circuit networks which can realize electromagnetic wave propagation in different two-dimensional (2D) isotropic and anisotropic metamaterials (AMMs). We synthesize the periodic circuits with unit cells of series capacitor or inductor in orthogonal directions, together with either capacitor or inductor shunted to ground. The dispersion relations of the periodic circuits are derived by applying Bloch boundary conditions to the unit cell, which show either elliptic or hyperbolic dispersion surface in phase space. The effective constitutive parameters are obtained by choosing different types and values of the impedance elements in the unit cell. The validity of the circuit models is proved by showing examples that the anisotropic $L\text{\ensuremath{-}}C$ circuits could exhibit the wave propagation characteristics of two 2D AMMs with different cutoff properties, called never-cutoff or anti-cutoff medium. We construct interfaces between isotropic normal medium and AMMs with properly designed $L\text{\ensuremath{-}}C$ circuits and analyze the electromagnetic wave propagation using microwave circuit simulations. We demonstrate extraordinary electromagnetic wave reflection and refraction phenomena including negative refraction, total reflection with reversion of the critical angle and anomalous Brewster effect that have good agreements with the theoretical analysis. Furthermore, we show that the $L\text{\ensuremath{-}}C$ circuit models of AMMs could lead to different approach of actual implementation of 2D AMMs through capacitance loaded transmission line metamaterials. The simulation on actual microstrip line structure demonstrates similar wave propagation phenomena of AMMs, and the losses in the structure only affect the magnitude of the propagating energy.

We show that the two-photon temporal (longitudinal) correlation of light is limited by its classical optical spectral width. We present examples of the sources of two-photon light approaching this limit.

The two-photon emission spectrum of a strongly driven two-level atom is defined and calculated. Such a spectrum reveals details of non-Markovian dynamics which are not observable in the usual experiments. It is shown that a clear separation of Markovian and non-Markovian regimes is possible in the two-photon emission spectrum.

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