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The interaction of light with superluminally moving matter entails unconventional phenomena, from Fresnel drag to Hawking radiation and to light amplification. While relativity makes these effects inaccessible using objects in motion, synthetic motion - enabled via space-time modulated internal degrees of freedom - is free from these constraints. Here we observe synthetic velocity of a reflectivity modulation travelling on an Indium-Tin-Oxide (ITO) interface, generated by ultrafast laser illumination at multiple positions and times. The interaction of the moving reflectivity modulation with a probe light beam acts as a non-separable spatio-temporal transformation that diffracts the light, changing its frequency and momentum content. The recorded frequency-momentum diffraction pattern is defined by the velocity of the diffracted probe wave relative to the modulation. Our experiments open a path towards mimicking relativistic mechanics and developing programmable spatio-temporal transformations of light., Comment: 9 pages, 3 figures

Experiments on Indium Tin Oxide (ITO) have revealed that a relatively broad 200THz pump pulse, roughly 30 cycles in width, can switch ITO from a transparent to a reflecting state within one or two optical cycles, a few Femtoseconds. So far the rapid switching has remained unexplained by theory. Here a very simple bare bones theory explains the key experimental features in terms of an avalanche model suggested by avalanche diodes., Comment: 9 pages, 6 figures

We investigate the frictional force arising from quantum fluctuations when two dissipative metallic plates are set in a shear motion. While early studies showed that the electromagnetic fields in the quantum friction setup reach nonequilibrium steady states, yielding a time-independent force, other works have demonstrated the failure to attain steady states, leading to instability and time-varying friction under sufficiently low-loss conditions. Here, we develop a fully quantum-mechanical theory without perturbative approximations and unveil the transition from stable to unstable regimes of the quantum friction setup. Due to the relative motion of the plates, their electromagnetic response may be active in some conditions, resulting in optical gain. We prove that the standard fluctuation-dissipation leads to inconsistent results when applied to our system, and, in particular, it predicts a vanishing frictional force. Using a modified fluctuation-dissipation relation tailored for gain media, we calculate the frictional force in terms of the system Green's function, thereby recovering early works on quantum friction. Remarkably, we also find that the frictional force diverges to infinity as the relative velocity of the plates approaches a threshold. This threshold is determined by the damping strength and the distance between the metal surfaces. Beyond this critical velocity, the system exhibits instability, akin to the behaviour of a laser cavity, where no steady state exists. In such a scenario, the frictional force escalates exponentially. Our findings pave the way for experimental exploration of the frictional force in proximity to this critical regime., Comment: Accepted for publication in Physical Review Research

We show that a grating amplitude stationary in space but oscillating in time can be accurately modelled as a set of independent gratings travelling in opposite directions, interacting almost exclusively with waves travelling in the same direction. This structure reproduces the key features of travelling gratings: amplification of a wave at points where the local wave speed equals the grating velocity. The same field compression and photon production is evident when even a single Fourier component of the grating profile has a velocity that matches the local wave speed. We speculate that these stationary but oscillating gratings may prove easier to realise experimentally than travelling gratings., Comment: 6 pages, 5 figures

In this study, we reveal noncontact frictional forces between surfaces in the presence of peristaltic permittivity modulation. Our setup comprises a conducting medium, an air gap, and a dielectric substrate on which we have a space-time-modulated grating that emits electromagnetic radiation. The radiation receives energy and momentum from the grating, which is eventually absorbed by the conducting medium or propagates away from the grating on the dielectric side, resulting in electromagnetic power loss and lateral forces at the surfaces.

Time dependent systems in general do not conserve photons nor do they conserve energy. However when parity time symmetry holds Maxwells equations can sometimes both conserve photon number and energy. Here we show that photon conservation is the more widely applicable law which can hold in circumstances where energy conservation is violated shedding further light on an amplification mechanism identified in previous papers as a process of conserved photons climbing a frequency ladder., Comment: 7 pages

Structures which appear to move at or near the velocity of light contain singular points. Energy generated by the motion accumulates at these points into ever-narrowing peaks. In this paper we show that energy is generated by a curious process that conserves the number of photons, adding energy by forcing photons already present to climb a ladder of increasing frequency. We present both a classical proof based on conservation of lines of force, and a more formal QED proof demonstrating the absence of unpaired creation and annihilation operators. Exceptions to this rule are found when negative frequencies make an appearance. Finally we make a connection to laboratory-based models of black holes and Hawking radiation., Comment: 13 pages, 4 figures

Time-varying media have recently emerged as a new paradigm for wave manipulation, thanks to thesynergy between the discovery of novel, highly nonlinear materials, such as epsilon-near-zero materials, and the questfor novel wave applications, such as magnet-free nonreciprocity, multi-mode light shaping, and ultrafast switching. Inthis review we provide a comprehensive discussion of the recent progress achieved with photonic metamaterials whoseproperties stem from their modulation in time. We review the basic concepts underpinning temporal switching and itsrelation with spatial scattering, and deploy the resulting insight to review photonic time-crystals and their emergentresearch avenues such as topological and non-Hermitian physics. We then extend our discussion to account for spa-tiotemporal modulation and its applications to nonreciprocity, synthetic motion, giant anisotropy, amplification andother effects. Finally, we conclude with a review of the most attractive experimental avenues recently demonstrated,and provide a few perspectives on emerging trends for future implementations of time-modulation in photonics.

We ask the question 'what happens to Bloch waves in gratings synthetically moving at near the speed of light?'. First we define a constant refractive index (CRI) model in which Bloch waves remain well defined as they break the light barrier, then show their dispersion rotating through 360 degrees from negative to positive and back again. Next we introduce the effective medium approximation (EMA) then refine it into a 4-wave model which proves to be highly accurate. Finally using the Bloch waves to expand a pulse of light we demonstrate sudden inflation of pulse amplitude combined with reversal of propagation direction as a luminal grating is turned on., Comment: 11 pages, 5 figures

An Archimedes' Screw captures water, feeding energy into it by lifting it to a higher level. We introduce the first instance of an optical Archimedes' Screw, and demonstrate how this system is capable of capturing light, dragging it and amplifying it. We unveil new exact analytic solutions to Maxwell's Equations for a wide family of chiral space-time media, and show their potential to achieve chirally selective amplification within widely tunable parity-time-broken phases. Our work, which may be readily implemented via pump-probe experiments with circularly polarized beams, opens a new direction in the physics of time-varying media by merging the rising field of space-time metamaterials and that of chiral systems, and may form a new playground for topology and non-Hermitian physics, with potential applications to chiral spectroscopy and sensing.

Nothing can physically travel faster than light in vacuum. This is why it has been considered that there is no \v{C}erenkov radiation (\v{C}R) without an effective refractive index due to some background field. In this Letter, we theoretically predict \v{C}R in vacuum from a spatiotemporally modulated boundary. We consider the modulation of traveling wave type and apply a uniform electrostatic field on the boundary to generate electric dipoles. Since the induced dipoles stick to the interface, they travel at the modulation speed. When the grating travels faster than light, it emits \v{C}R. In order to quantitatively examine this argument, we need to calculate the field scattered at the boundary. We utilise a dynamical differential method, which we developed in the previous paper, to quantitatively evaluate the field distribution in such a situation. We can confirm that all scattered fields are evanescent if the modulation speed is slower than light while some become propagating if the modulation is faster than light.

Our ability to generate new distributions of light has been remarkably enhanced in recent years. At the most fundamental level, these light patterns are obtained by ingeniously combining different electromagnetic modes. Interestingly, the modal superposition occurs in the spatial, temporal as well as spatio-temporal domain. This generalized concept of structured light is being applied across the entire spectrum of optics: generating classical and quantum states of light, harnessing linear and nonlinear light-matter interactions, and advancing applications in microscopy, spectroscopy, holography, communication, and synchronization. This Roadmap highlights the common roots of these different techniques and thus establishes links between research areas that complement each other seamlessly. We provide an overview of all these areas, their backgrounds, current research, and future developments. We highlight the power of multimodal light manipulation and want to inspire new eclectic approaches in this vibrant research community., Comment: Under review in J. Opt

Electromagnetic waves in a system with a space and time dependent boundary experience both diffraction and Doppler-like frequency conversion. In order to analyse such situations, conventional methods call for either the eigenmodes or the dyadic Green's function in space and time dependent media. Here, we propose a dynamical differential method which does not require either of them. Our method utilises a dynamical coordinate transformation in order to simplify the calculation of the optical response of the space and time dependent system. We reveal that the diffraction symmetry is broken in the presence of traveling-wave type spatiotemporal modulation.

In gratings travelling at nearly the velocity of light a symmetry breaking transition is observed between free-flowing fluid-like Bloch waves observed at lower grating velocities and, at luminal velocities, condensed, localised states of light captured in each period of the grating and locked to its velocity. We introduce a new technique for calculating in this regime and use it to study the transition in detail shedding light on the critical exponents, and the periodic oscillations in transmitted intensity seen in the pre-transition regime., Comment: 11 pages, 5 figures

Time dependent systems do not in general conserve energy invalidating much of the theory developed for static systems and turning our intuition on its head. This is particularly acute in luminal space time crystals where the structure moves at or close to the velocity of light. Conventional Bloch wave theory no longer applies, energy grows exponentially with time, and a new perspective is required to understand the phenomenology. In this letter we identify a new mechanism for amplification: the compression of lines of force that are nevertheless conserved in number., Comment: 9 pages, 3 figures

We present a general framework for the homogenisation theory of space-time metamaterials. By mapping to a frame co-moving with the space-time modulation, we derive analytical formulae for the effective material parameters for travelling wave modulations in the low frequency limit: electric permittivity, magnetic permeability and magnetoelectric coupling. Remarkably, we show that the theory is exact at all frequencies in the absence of back-reflections, and exact at low frequencies when that condition is relaxed. This allows us to derive exact formulae for the Fresnel drag experienced by light travelling through travelling-wave modulations of electromagnetic media.

In order to confine waves beyond the diffraction limit, advances in fabrication techniques have enabled subwavelength structuring of matter, achieving near-field control of light and other types of waves. The price is often expensive fabrication needs and the irreversibility of device functionality, as well as the introduction of impurities, a major contributor to losses. In this Letter, we propose temporal inhomogeneities, such as a periodic drive in the electromagnetic properties of a surface which supports guided modes, to circumvent the need for subwavelength fabrication in the coupling of propagating waves to evanescent modes across the light line, achieving the temporal counterpart of the Wood anomaly. We show analytically and numerically how this concept is valid for any material platform and at any frequency, and propose and model a realistic experiment in graphene to couple terahertz radiation to plasmons with unit efficiency, demonstrating that time-modulation of material properties could be a tunable, lower-loss and fast-switchable alternative to the subwavelength structuring of matter for near-field wave control., Comment: 5 pages, 4 figures

Surface plasmons subject to a surface distortion split asymmetrically in energy resulting in a net lowering of zero-point energy. This is because surface plasmon eigenvalues are the square of frequencies, a statement generally true for electromagnetic excitations. We utilize the method based on conformal mapping to demonstrate asymmetric splitting under surface corrugations leading to a decrease in zero-point energy of a single corrugated metallic surface contributing to surface reconstructions but too small on its own to drive the reconstruction. However, by introducing a second metallic surface more significant lowering of energy is seen sufficient to drive the instability of a mercury thin film., Comment: 13 pages, 4 figures

Singular graphene metasurfaces, conductivity gratings realized by periodically suppressing the local doping level of a graphene sheet, have recently been proposed to efficiently harvest THz light and couple it to surface plasmons over broad absorption bands, achieving remarkably high field enhancement. However, the large momentum wavevectors thus attained are sensitive to the nonlocal behaviour of the underlying electron liquid. Here, we extend the theory of singular graphene metasurfaces to account for the full nonlocal optical response of graphene and discuss the resulting impact on the plasmon resonance spectrum. Finally, we propose a simple local analogue model that is able to reproduce the effect of nonlocality in local-response calculations by introducing a constant conductivity offset, which could prove a valuable tool in the modelling of more complex experimental graphene-based platforms., Comment: 8 pages, 5 figures

A moving medium drags light along with it as measured by Fizeau and explained by Einstein's theory of special relativity. Here we show that the same effect can be obtained in a situation where there is no physical motion of the medium. Modulations of both the permittivity and permeability, phased in space and time in the form of travelling waves, are the basis of our model. Space-time metamaterials are represented by effective bianisotropic parameters, which can in turn be mapped to a moving homogeneous medium. Hence these metamaterials mimic a relativistic effect without the need for any actual material motion. We discuss how both the permittivity and permeability need to be modulated in order to achieve these effects, and we present an equivalent transmission line model.

Time has emerged as a new degree of freedom for metamaterials, promising new pathways in wave control. However, electromagnetism suffers from limitations in the modulation speed of material parameters. Here we argue that these limitations can be circumvented by introducing a traveling-wave refractive index modulation, with the same phase velocity of the waves. We show how the concept of "luminal grating" can yield giant nonreciprocity, achieve efficient one-way amplification, pulse compression and frequency up-conversion, proposing a realistic implementation in double-layer graphene., Comment: 6 pages, 3 figures

Plasmonic gratings constitute a paradigmatic instance of the wide range of applications enabled by plasmonics. While subwavelength metal gratings find applications in optical biosensing and photovoltaics, atomically thin gratings achieved by periodically doping a graphene monolayer perform as metasurfaces for the control of terahertz radiation. In this paper we show how these two instances of plasmonic gratings inherit their spectral properties from an underlying slab with translational symmetry.We develop an analytical formalism to accurately derive the mode spectrum of the gratings that provides a great physical insight.

As the continual experimental advances made in Electron energy loss spectroscopy (EELS) and cathodoluminescence (CL) open the door to practical exploitations of plasmonic effects in metal nanoparticles, there is an increasing need for precise interpretation and guidance of such experiments. Numerical simulations are available but lack physical insight, while traditional analytical approaches are rare and limited to studying specific, simple structures. Here, we propose a versatile and efficient method based on transformation optics which can fully characterize and model the EELS problems of nanoparticles of complex geometries. Detailed discussions are given on 2D and 3D nanoparticle dimers, where the frequency and time domain responses under electron beam excitations are derived.

Electron energy loss spectroscopy (EELS) and Cathodoluminescence (CL) play a pivotal role in many of the cutting edge experiments in plasmonics. EELS and CL experiments are usually supported by numerical simulations, which, whilst accurate, may not provide as much physical insight as analytical calculations do. Fully analytical solutions to EELS and CL systems in plasmonics are rare and difficult to obtain. This paper aims to narrow this gap by introducing a new method based on Transformation optics that allows to calculate the quasi-static frequency and time-domain response of plasmonic particles under electron beam excitation.

We present a simple design to achieve bianisotropy at visible wavelengths: an ultrathin plasmonic grating made of a gold grating covered by a thin flat layer of gold. We show experimentally and through simulations that the grating exhibits magneto-electric coupling and features asymmetric reflection and absorption, all that with a device thickness of a tenth of the operating wavelength. We compared the spectral results and retrieved the effective material parameters of different polarizations and devices. We show that both asymmetry and strong coupling between the incoming light and the optically interacting surfaces are required for obtaining asymmetric optical behavior in metasurfaces.

Transformation optics (TO) is a new tool for controlling electromagnetic fields. In the context of metamaterial technology, it provides a direct link between a desired electromagnetic (EM) phenomenon and the material response required for its occurrence. Recently, this powerful framework has been successfully exploited to study surface plasmon assisted phenomena such as light harvesting. Here, we review the general strategy based on TO to design plasmonic devices capable of harvesting light over a broadband spectrum and achieving considerable field confinement and enhancement. The methodology starts with two-dimensional (2D) cases, such as 2D metal edges, crescent-shaped cylinders, nanowire dimers, and rough metal surfaces, and has been well extended to fully-fledged three-dimensional (3D) situations. The largely analytic approach gives physical insights into the processes involved and suggests the way forward to study a wide variety of plasmonic nanostructures., Comment: 20 pages, 10 figures, Accepted for publication by Science China Information Sciences

Surface plasmons on metals can concentrate light into sub-nanometric volumes and on these near atomic length scales the electronic response at the metal interface is smeared out over a Thomas-Fermi screening length. This nonlocality is a barrier to a good understanding of atomic scale response to light and complicates the practical matter of computing the fields. In this letter, we present a local analogue model and show that spatial nonlocality can be represented by replacing the nonlocal metal with a composite material, comprising a thin dielectric layer on top of a local metal. This method not only makes possible the quantitative analysis of nonlocal effects in complex plasmonic phenomena with unprecedented simplicity and physical insight, but also offers great practical advantages in their numerical treatment., Comment: 16 pages, 4 figures, Accepted for publication by Physical Review Letters

We investigate the frictional forces due to quantum fluctuations acting on a small sphere rotating near a surface. At zero temperature, we find the frictional force near a surface to be several orders of magnitude larger than that for the sphere rotating in vacuum. For metallic materials with typical conductivity, quantum friction is maximized by matching the frequency of rotation with the conductivity. Materials with poor conductivity are favored to obtain large quantum frictions. For semiconductor materials that are able to support surface plasmon polaritons, quantum friction can be further enhanced by several orders of magnitude due to the excitation of surface plasmon polaritons., Comment: Published on PRL as Editors' Suggestion

A new type of cloak is discussed: one that gives all cloaked objects the appearance of a flat conducting sheet. It has the advantage that none of the parameters of the cloak is singular and can in fact be made isotropic. It makes broadband cloaking in the optical frequencies one step closer.

Electromagnetic metamaterials are a class of materials which have been artificially structured on a subwavelength scale. They are currently the focus of a great deal of interest because they allow access to previously unrealisable properties like a negative refractive index. Most metamaterial designs have so far been based on resonant elements, like split rings, and research has concentrated on microwave frequencies and above. In this work, we present the first experimental realisation of a non-resonant metamaterial designed to operate at zero frequency. Our samples are based on a recently-proposed template for an anisotropic magnetic metamaterial consisting of an array of superconducting plates. Magnetometry experiments show a strong, adjustable diamagnetic response when a field is applied perpendicular to the plates. We have calculated the corresponding effective permeability, which agrees well with theoretical predictions. Applications for this metamaterial may include non-intrusive screening of weak DC magnetic fields., Comment: 6 pages, 3 figures

We show that two-dimensional arrays of thin metallic wires can guide transverse electromagnetic (TEM) waves and focus them to the spatial dimensions much smaller that the vacuum wavelength. This guiding property is retained for the tapered wire bundles which can be used as multi-channel TEM endoscopes: they capture a detailed electromagnetic field profile created by deeply sub-wavelength features of the studied sample and magnify it for observation. The resulting imaging method is superior to the conventional scanning microscopy because of the parallel nature of the image acquisition by multiple metal wires. Possible applications include terahertz and mid-infrared endoscopy with nanoscale resolution., Comment: 3 figures

In this paper, we investigate the effect of spatial dispersion on a double-lattice metamaterial which has both magnetic and electric response. A numerical scheme based on a dipolar model is developed to extract the non-local effective medium of the metamaterial. We found a structure-induced bianisotropy near the resonance gap even if the artificial particles are free from cross-coupling. A cross-coupled resonance also results from spatial dispersion and it can be understood using a Lorentz frequency dispersion model. The strength of the cross-coupled resonance depends on the microstructure and it is larger at a higher normalized frequency., Comment: 11 pages,10 figures, 2 tables

We examine some of the optical properties of a metamaterial consisting of thin layers of alternating metal and dielectric. We can model this material as a homogeneous effective medium with anisotropic dielectric permittivity. When the components of this permittivity have different signs, the behavior of the system becomes very interesting: the normally evanescent parts of a P-polarized incident field are now transmitted, and there is a preferred direction of propagation. We show that a slab of this material can form an image with sub-wavelength details, at a position which depends on the frequency of light used. The quality of the image is affected by absorption and by the finite width of the layers; we go beyond the effective medium approximation to predict how thin the layers need to be in order to obtain subwavelength resolution., Comment: Accepted for publication in Physical Review B

Complex and interesting electromagnetic behavior can be found in spaces with non-flat topology. When considering the properties of an electromagnetic medium under an arbitrary coordinate transformation an alternative interpretation presents itself. The transformed material property tensors may be interpreted as a different set of material properties in a flat, Cartesian space. We describe the calculation of these material properties for coordinate transformations that describe spaces with spherical or cylindrical holes in them. The resulting material properties can then implement invisibility cloaks in flat space. We also describe a method for performing geometric ray tracing in these materials which are both inhomogeneous and anisotropic in their electric permittivity and magnetic permeability.

It has been recently proved that a slab of negative refractive index material acts as a perfect lens in that it makes accessible the sub-wavelength image information contained in the evanescent modes of a source. Here we elaborate on perfect lens solutions to spherical shells of negative refractive material where magnification of the near-field images becomes possible. The negative refractive materials then need to be spatially dispersive with $\epsilon(r) \sim 1/r$ and $\mu(r)\sim 1/r$. We concentrate on lens-like solutions for the extreme near-field limit. Then the conditions for the TM and TE polarized modes become independent of $\mu$ and $\epsilon$ respectively., Comment: Revtex4, 9 pages, 2 figures (eps)

A slab of negatively refracting material, thickness d, can focus an image at a distance 2d from the object. The negative slab cancels an equal thickness of positive space. This result is a special case of a much wider class of focussing: any medium can be optically cancelled by an equal thickness of material constructed to be an inverted mirror image of the medium, with, $\epsilon$ and $\mu$ reversed in sign. We introduce the powerful technique of coordinate transformation, mapping a known system into an equivalent system, to extend the result to a much wider class of structures including cylinders, spheres, and intersecting planes and hence show how to produce magnified images. All the images are perfect in the sense that both the near and far fields are brought to a focus and hence reveal sub wavelength details., Comment: pdf file only

In an earlier paper we introduced the concept of the perfect lens which focuses both near and far electromagnetic fields, hence attaining perfect resolution. Here we consider refinements of the original prescription designed to overcome the limitations of imperfect materials. In particular we show that a multi-layer stack of positive and negative refractive media is less sensitive to imperfections. It has the novel property of behaving like a fibre-optic bundle but one that acts on the near field, not just the radiative component. The effects of retardation are included and minimized by making the slabs thinner. Absorption then dominates image resolution in the near-field. The deleterious effects of absorption in the metal are reduced for thinner layers., Comment: RevTeX, (9 pages, 8 figures)

We extend the ideas of the recently proposed perfect lens [J.B. Pendry, Phys. Rev. Lett. {\bf 85}, 3966 (2000)] to an alternative structure. We show that a slab of a medium with negative refractive index bounded by media of different positive refractive index also amplifies evanescent waves and can act as a near-perfect lens. We examine the role of the surface states in the amplification of the evanescent waves. The image resolution obtained by this asymmetric lens is more robust against the effects of absorption in the lens. In particular, we study the case of a slab of silver, which has negative dielectric constant, with air on one side and other media such as glass or GaAs on the other side as an `asymmetric' lossy near-perfect lens for P-polarized waves. It is found that retardation has an adverse effect on the imaging due to the positive magnetic permeability of silver, but we conclude that subwavelength image resolution is possible inspite of it., Comment: RevTeX, To appear in J. Mod. Optics

A recent paper showed how to construct a lens that focuses near field radiation and hence produce resolution unlimited by wavelength. The prescription requires lossless materials with negative refractive index: finite loss cuts off the finer details of the image. In this paper we suggest compensating for losses by introducing optical gain media into the lens design. Calculations demonstrate a dramatic improvement in performance for a silver/gain composite medium at optical frequencies., Comment: RevTeX4, 4 pages

In a recent Physical Review Letter [1] Garcia and Nieto Vesperinas (GNV) dispute the claim of perfect lensing made in [2]. The thrust of the GVN paper is that the solutions proposed in [2] imply infinite energy density and are therefore inadmissible. They claim that finite absorption leads to catastrophic collapse of the amplifying solutions vital to focussing and that no useful effect can be achieved. In this Comment I show that, on the contrary, careful consideration of absorption results in solutions that are always well behaved and evolve smoothly and continuously to perfect resolution in the limiting case of zero absorption., Comment: 1 page PDF file, Comment on Phys. Rev.Lett., v.88, 207403 (2002), by N. Garcia and M. Nieto-Vesperinas

Recently it has been proposed that a planar slab of material, for which both the permittivity and permeability have the values of -1, could bring not only the propagating fields associated with a source to a focus, but could also refocus the nonpropagating near-fields, thereby achieving a subdiffraction image. In this work we discuss the sensitivity of the subwavelength focus to various slab parameters, pointing out the connection to slab plasmon modes. We also note and resolve a paradox associated with the perfect imaging of a point source. We conclude that subwavelength resolution is achievable with available technology, but only by implementation of a critical set of design parameters., Comment: pdf file

It has been shown that a slab of materials with refractive index = -1 behaves like a perfect lens focussing all light to an exact electromagnetic copy of an object. The original lens is limited to producing images the same size as the object, but here we generalise the concept so that images can be magnified. For two dimensional systems, over distances much shorter than the free space wavelength, we apply conformal transformations to the original parallel sided slab generating a variety of new lenses. Although the new lenses are not `perfect' they are able to magnify two dimensional objects. The results apply equally to imaging of electric or magnetic sub wavelength objects in two dimensions. The concepts have potential applications ranging from microwave frequencies to the visible., Comment: PDF file

We present a fully three-dimensional theoretical study of the extraordinary transmission of light through subwavelength hole arrays in optically thick metal films. Good agreement is obtained with experimental data. An analytical minimal model is also developed, which conclusively shows that the enhancement of transmission is due to tunneling through surface plasmons formed on each metal-dielectric interfaces. Different regimes of tunneling (resonant through a ''surface plasmon molecule", or sequential through two isolated surface plasmons) are found depending on the geometrical parameters defining the system., Comment: 4 pages, 4 figures