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Recent research has indicated considerable potential for millimeter-waves in copper access, with data-rate estimations up to 1 Terabit per second for a reach of 100 m. This line of research exploits millimeter-waves and their corresponding higher-order propagation modes inside the twisted pair cable binder. Unlike the conventionally used transmission-line mode (currents through copper wires), the approach relies on the copper and plastics present in these cables to form a low-loss waveguide. Here, we take a closer look at the potential of millimeter-wave propagation in twisted pair cables by refining the idealized assumptions, used by Cioffi et al., and identifying the limiting factors. To this end, we introduce the concept of transformation optics as an efficient method of calculating the propagating modes on a twisted pair. Leveraging this technique allows us to calculate modal propagation using realistic material parameters, exposing an important trade-off between loss and confinement. Our modeling results yield achievable data rates that are orders of magnitude lower than those achieved under idealized assumptions. According to our results, 1 Terabit per second can be achieved up to a distance of about 10 m over a twisted-pair with a plastic sheath.

Machine learning offers the potential to revolutionize the inverse design of complex nanophotonic components. Here, we propose a novel variant of this formalism specifically suited for the design of resonant nanophotonic components. Typically, the first step of an inverse design process based on machine learning is training a neural network to approximate the non-linear mapping from a set of input parameters to a given optical system’s features. The second step starts from the desired features, e.g. a transmission spectrum, and propagates back through the trained network to find the optimal input parameters. For resonant systems, this second step corresponds to a gradient descent in a highly oscillatory loss landscape. As a result, the algorithm often converges into a local minimum. We significantly improve this method’s efficiency by adding the Fourier transform of the desired spectrum to the optimization procedure. We demonstrate our method by retrieving the optimal design parameters for desired transmission and reflection spectra of Fabry–Pérot resonators and Bragg reflectors, two canonical optical components whose functionality is based on wave interference. Our results can be extended to the optimization of more complex nanophotonic components interacting with structured incident fields.

Orbital angular momentum (OAM) from lasers holds promise for compact, at-source solutions for applications ranging from imaging to communications. However, conjugate symmetry between circular spin and opposite helicity OAM states (±l) from conventional spin–orbit approaches has meant that complete control of light’s angular momentum from lasers has remained elusive. Here, we report a metasurface-enhanced laser that overcomes this limitation. We demonstrate new high-purity OAM states with quantum numbers reaching l = 100 and non-symmetric vector vortex beams that lase simultaneously on independent OAM states as much as Δl = 90 apart, an extreme violation of previous symmetric spin–orbit lasing devices. Our laser conveniently outputs in the visible, producing new OAM states of light as well as all previously reported OAM modes from lasers, offering a compact and power-scalable source that harnesses intracavity structured matter for the creation of arbitrary chiral states of structured light. A metasurface laser generates orbital angular momentum states with quantum numbers reaching l = 100. Simultaneous output vortex beams, with Δl as great as 90, are demonstrated in the visible regime.

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., Under review in J. Opt

The electromagnetic near field enables subwavelength applications such as near-field microscopy and nanoparticle manipulation. Present methods to structure the near field rely on optical antenna theory, involving nanostructures that locally convert propagating waves into confined near-field patterns. We developed a theory of remote rather than local near-field shaping, based on cascaded mode conversion and interference of counterpropagating guided waves with different propagation constants. We demonstrate how to structure at will the longitudinal and transverse variation of the near field, allowing for distributions beyond the conventional monotonic decay of the evanescent field. We provide an experimental realization that confirms our theory. Our method applies to fields with arbitrary polarization states and mode profiles, providing a path toward three-dimensional control of the near field.

A particular class of focused, pulsed light beams can propagate self-similarly in free space at a fixed group velocity. Now, scientists present a law of refraction that determines how the group velocity of these beams changes as they refract at an interface between two materials.

Twisted light carrying orbital angular momentum (OAM) has given rise to many developments ranging from optical manipulation to optical communications. Generating twisted light from solid-state lasers was initially achieved by amplitude and dynamic phase control, and more recently by manipulating the geometric phase of light. These lasers have been limited to generate superposition of OAM modes as well as scalar modes with OAM e = 10. Here we incorporate a metasurface device into a visible solid-state laser to control the angular momentum of light by arbitrary spin-to-orbit coupling. We demonstrate the generation of pure Laguerre Gaussian modes with OAM up to e = 100. Modal decomposition measurements of the output beams reveal the higher purity of the generated modes can reach up to 96% for e = 1 and 88% for e = 100. our approach offers a new route for high brightness OAM states at the source.

The use of beams carrying orbital angular momentum (OAM) has become ubiquitous and topical in a variety of research fields. More recently, there has been a growing interest in exotic OAM carrying beams with spatially variant polarisation, so called Poincare sphere beams. Structuring these beams at the source gives rise to compact solutions for a myriad of applications, from laser materials processing to microscopy. Here we present a visible laser that control's the angular momentum of light by arbitrary spin-orbit (SO) momentum conversion using novel metasurface devices. Further, we outline how to generate high purity OAM states in a deterministic manner with charge up to 100. Finally, we demonstrate the generation of symmetric and non-symmetric vector vortex beams from the same source with a large OAM differential between modes of up to 90. The performance and versatility in design of our approach offers a route to control light's angular momentum at the source.

Current day high speed optical communication systems employ photonic circuits using platforms such as silicon photonics. In these systems, the polarization state of light drifts due to effects such as polarization mode dispersion and nonlinear phenomena generated by photonic circuit building blocks. As the complexity, the number, and the variety of these building blocks grows, the demand increases for an in-situ polarization determination strategy. Here, we show that the transfer of the Belinfante momentum to particles in the evanescent field of waveguides depends in a non-trivial way on the polarization state of light within that waveguide. Surprisingly, we find that the maxima and minima of the lateral force are not produced with circularly polarized light, corresponding to the north and south poles of the Poincaré sphere. Instead, the maxima are shifted along the great circle of the sphere due to the phase differences between the scattered TE and TM components of light. This effect allows for an unambiguous reconstruction of the local polarization state of light inside a waveguide. Importantly, this technique depends on interaction with only the evanescent tails of the fields, allowing for a minimally invasive method to probe the polarization within a photonic chip.

Metasurfaces allow for agile manipulation of incoming light using a single layer of resonators. Despite recent progress, it remains difficult to generate new spectral components using nonlinear surfaces, because of the limited interaction length of a pulse traveling through a single surface. Time-dependent surfaces offer an exciting alternative to overcome this limitation, but a self-consistent framework to describe this mechanism is lacking. Based on an analytical model and finite-difference time-domain numerical simulations, we obtain physical insight into the frequency-shifting process that occurs when broadband electromagnetic pulses interact with time-varying surfaces. In particular, we find that there is an intriguing relationship between the bandwidth of the incident pulse, the targeted frequency shift, and the number of Lorentzian resonators that need to be implemented. We also demonstrate that in certain parameter regimes, pulse distortion and a deviation of pulse amplitude cannot be avoided. These results are independent of the mechanism that generates the time dependence. They are also independent of the frequency, the geometry, size, and material of the unit cell, but they are rather a direct result of the subtle interplay between time-dependent Lorentzian resonances.

Recently, it was shown that a Mie particle in an evanescent field ought to experience optical forces that depend on the helicity of the totally internally reflected beam. As yet, a direct measurement of such helicity-dependent forces has been elusive, as the widely differing force magnitudes in the three spatial dimensions place stringent demands on a measurement's sensitivity and range. In this study, we report the simultaneous measurement of all components of this polarization-dependent optical force by using a 3D force spectroscopy technique with femtonewton sensitivity. The vector force fields are compared quantitatively with our theoretical calculations as the polarization state of the incident light is varied and show excellent agreement. By plotting the 3D motion of the Mie particle in response to the switched force field, we offer visual evidence of the effect of spin momentum on the Poynting vector of an evanescent optical field.

We reveal the surprising polarization dependence of lateral forces acting on reso-nant Mie particles in evanescent fields. This effect can be utilized to retrieve the polarization state of light inside birefringent waveguides.

Artificially structured metasurfaces make use of specific configurations of subwavelength resonators to efficiently manipulate electromagnetic waves. Additionally, optomechanical metasurfaces have the desired property that their actual configuration may be tuned by adjusting the power of a pump beam, as resonators move to balance pump-induced electromagnetic forces with forces due to elastic filaments or substrates. Although the reconfiguration time of optomechanical metasurfaces crucially determines their performance, the transient dynamics of unit cells from one equilibrium state to another is not understood. Here, we make use of tools from nonlinear dynamics to analyze the transient dynamics of generic optomechanical metasurfaces based on a damped-resonator model with one configuration parameter. We show that the reconfiguration time of optomechanical metasurfaces is not only limited by the elastic properties of the unit cell but also by the nonlinear dependence of equilibrium states on the pump power. For example, when switching is enabled by hysteresis phenomena, the reconfiguration time is seen to increase by over an order of magnitude. To illustrate these results, we analyze the nonlinear dynamics of a bilayer cross-wire metasurface whose optical activity is tuned by an electromagnetic torque. Moreover, we provide a lower bound for the configuration time of generic optomechanical metasurfaces. This lower bound shows that optomechanical metasurfaces cannot be faster than state-of-the-art switches at reasonable powers, even at optical frequencies.

Significance Using a highly sensitive particle-tracking scheme, we report an observation of elliptical motion of microparticles driven by a single evanescent field. We show that this behavior is highly tunable and predictable using a theoretical model that accounts for Mie scattering and hydrodynamic drag. The significance is twofold. First, our work represents an important step in understanding the detailed dynamics of microparticles in a fluidic environment—especially near a surface—a prerequisite for effective application of optically driven microparticles as functional elements in optofluidic devices. Second, our method could complement current structured-light approaches for inducing orbital motion in microparticles, with readily tunable parameters of motion including orbital frequency, radius, and ellipticity.

The enhancement of optical forces has enabled a variety of technological applications that rely on the optical control of small objects and devices. Unfortunately, optical forces are still too small for the convenient actuation of integrated switches and waveguide couplers. Here we show how the optical gradient force can be enhanced by an order of magnitude by making use of gauge materials inside two evanescently coupled waveguides. To this end, the gauge materials inside the cores should emulate imaginary vector potentials for photons pointing perpendicularly to the waveguide plane. Depending on the relative orientation of the vector potentials in neighboring waveguides, i.e., pointing away from or towards each other, the conventional attractive force due to an even mode profile may be enhanced, suppressed, or may even become repulsive. This and other new features indicate that the implementation of complex-valued vector potentials with non-Hermitian waveguide cores may further enhance our control over mode profiles and the associated optical forces.

Transformation optics makes use of coordinate transformations to explore the possibilities offered by artificially structured metamaterials for the manipulation of a wide variety of electromagnetic phenomena. Since a decade, transformation optics has consistently extended its scope. Initially, coordinate transformations were only applied to the transformation of light in the simplest of optical setups, i.e., empty space [1,2]. In particular, straight light trajectories were being transformed into curved ones, e.g., avoiding a specific region in space (invisibility devices), bending over a specific angle (benders and splitters), and focussing to a particular point (lenses). Today, research efforts go beyond the transformation of empty space, allowing metamaterials to further enhance our control on electromagnetic phenomena other than light propagation. In this contribution, I will review our work on transformation optics to manipulate guided modes along and optical forces between metamaterial waveguides [3,4], the emission of Cerenkov radiation due to fast charged particles [5,6], and the Goos-Hanchen shift at metamaterial surfaces [7].

Transformation optics has revolutionized our approach to material design in several scientific disciplines by determining the material properties that implement the desired effects of a coordinate transformation. Unfortunately, the performance of several coordinate-based devices, such as beam splitters and invisibility cloaks, suffers from the necessary implementation of singularities with extreme material parameters. Here, we make use of transformation optics to eliminate these singularities in an isotropic way for the improvement of coordinate-based metamaterial waveguides. In particular, singularities that lead to vanishing material properties are softened with a global rescaling of the coordinates, while singular terms that lead to infinite material properties are strategically replaced by well-behaved curve factors. Detailed full-wave simulations confirm that the resulting waveguide devices are as efficient as their singular counterparts despite the fact that they consist of materials with much more moderate optical properties.

Transformation optics, a geometrical recipe for metamaterial design, was originally conceived as a tool to smoothly modify the trajectory of light using continuous coordinate transformations. Here, we show how discontinuous transformations can be used as a geometric framework to understand and manipulate phenomena at the surface of nanophotonic structures. In particular, we show how the Goos-Hanchen shift - a lateral shift exhibited by totally reflected beams - can be tailored and we provide a classification and complete analytical description of this effect in existing complex media.

Transformation optics provides a geometry-based tool to create new components taking advantage of artificial metamaterials with optical properties that are not available in nature. Unfortunately, although guided electromagnetic waves are crucial for optical circuitry, transformation optics is not yet compatible with two-dimensional slab waveguides. Indeed, after determining the propagation of confined waves along the waveguide with a two-dimensional coordinate transformation, the conventional application of transformation optics results in metamaterials whose properties are insensitive to the coordinate perpendicular to the waveguide, leading to bulky, and therefore impractical, designs. In this contribution, we formulate an alternative framework that leads to feasible coordinate-based designs of two-dimensional waveguides. To this end, we characterize a guided transverse-magnetic light mode by relevant electromagnetic equations: a Helmholtz equation to account for wave propagation and a dispersion relation to impose a continuous light profile at the interface. By considering how two-dimensional conformal transformations transform these equations, we are able to materialize the coordinate-designed flows with a nonmagnetic metamaterial core of varying thickness, obtaining a two-dimensional device. We numerically demonstrate the effectiveness and versatility of our equivalence relations with three crucial functionalities, a beam bender, a beam splitter and a conformal lens, on a qualitative and quantitative level, by respectively comparing the electromagnetic fields inside and the transmission of our two-dimensional metamaterial devices to that of their three-dimensional counterparts at telecom wavelengths. As a result, we envision that one coordinate-based multifunctional waveguide component may seamlessly split and bend light beams on the landscape of an optical chip. © (2016) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.

Metamaterials make use of subwavelength building blocks to enhance our control on the propagation of light. To determine the required material properties for a given functionality, i.e., a set of desired light flows inside a metamaterial device, metamaterial designs often rely on a geometrical design tool known as transformation optics. In recent years, applications in integrated photonics motivated several research groups to develop two-dimensional versions of transformation optics capable of routing surface waves along graphene-dielectric and metal-dielectric interfaces. Although guided electromagnetic waves are highly relevant to applications in integrated optics, no consistent transformation-optical framework has so far been developed for slab waveguides. Indeed, the conventional application of transformation optics to dielectric slab waveguides leads to bulky three-dimensional devices with metamaterial implementations both inside and outside of the waveguide's core. In this contribution, we develop a transformation-optical framework that still results in thin metamaterial waveguide devices consisting of a nonmagnetic metamaterial core of varying thickness [Phys. Rev. B 93.8, 085429 (2016)]. We numerically demonstrate the effectiveness and versatility of our equivalence relations with three crucial functionalities: a beam bender, a beam splitter and a conformal lens. Our devices perform well on a qualitative (comparison of fields) and quantitative (comparison of transmitted power) level compared to their bulky counterparts. As a result, the geometrical toolbox of transformation optics may lead to a plethora of integrated metamaterial devices to route guided waves along optical chips.

In this work, an electromagnetic energy harvester operating at microwave frequencies is designed based on a cut- wire metasurface. This metamaterial is known to contain a quasistatic electric dipole resonator leading to a strong resonant electric response when illuminated by electromagnetic fields.1 Starting from an equivalent electrical circuit, we analytically design the parameters of the system to tune the resonance frequency of the harvester at the desired frequency band. Subsequently, we compare these results with numerical simulations, which have been obtained using finite elements numerical simulations. Finally, we optimize the design by investigating the best arrangement for energy harvesting by coupling in parallel and in series many single layers of cut-wire metasurfaces. We also discuss the implementation of different geometries and sizes of the cut-wire metasurface for achieving different center frequencies and bandwidths.

Since its first observation in 1947, the Goos-Hänchen effect—an electromagnetic wave phenomenon where a totally reflected beam with finite cross section undergoes a lateral displacement from its position predicted by geometric optics—has been extensively investigated for various types of optical media such as dielectrics, metals and photonic crystals. Given their huge potential for guiding and sensing applications, the search for giant and tunable Goos-Hänchen shifts is still an open question in the field of optics and photonics. Metamaterials allow for unprecedented control over electromagnetic properties and thus provide an interesting platform in this quest for Goos-Hänchen shift enhancement. Over the last few years, the Goos-Hänchen effect has been investigated for specific metamaterial interfaces including graphene-on-dielectric surfaces, negative index materials and epsilon- near-zero materials. In this contribution, we generalize the approach for the investigation of the Goos-Hänchen effect based on the geometric formalism of transformation optics. Although this metamaterial design methodology is generally applied to manipulate the propagation of light through continuous media, we show how it can also be used to describe the reflections arising at the interface between a vacuum region and a transformed region with a metamaterial implementation. Furthermore, we establish an analytical model that relates the magnitude of the Goos-Hänchen shift to the underlying geometry of the transformed medium. This model shows how the dependence of the Goos-Hänchen shift on geometric parameters can be used to dramatically enhance the size of the shift by an appropriate choice of permittivity and permeability tensors. Numerical simulations of a beam with spatial Gaussian profile incident upon metamaterial interfaces verify the model and firmly establish a novel route towards Goos-Hänchen shift engineering using transformation optics. © (2016) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.

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.

In this contribution, we explore the generation of light in transformation-optical media. When charged particles move through a transformation-optical material with a speed larger than the phase velocity of light in the medium, Cherenkov light is emitted. We show that the emitted Cherenkov cone can be modified with longitudinal and transverse stretching of the coordinates. Transverse coordinates stretching alters only the dimensions of the cone, whereas longitudinal stretching also changes the apparent velocity of the charged particle. These results demonstrate that the geometric formalism of transformation optics can be used not only for the manipulation of light beam trajectories, but also for controlling the emission of light, here for describing the Cherenkov cone in an arbitrary anisotropic medium. Subsequently, we illustrate this point by designing a radiator for a ring imaging Cherenkov radiator. Cherenkov radiators are used to identify unknown elementary particles by determining their mass from the Cherenkov radiation cone that is emitted as they pass through the detector apparatus. However, at higher particle momentum, the angle of the Cherenkov cone saturates to a value independent of the mass of the generating particle, making it difficult to effectively distinguish between different particles. Using our transformation optics description, we show how the Cherenkov cone and the cut-off can be controlled to yield a radiator medium with enhanced sensitivity for particle identification at higher momentum [Phys. Rev. Lett. 113, 167402 (2014)].

Since its inception in 2006, transformation optics has become an established tool to understand and design electromagnetic systems. It provides a geometrical perspective into the properties of light waves without the need for a ray approximation. Most studies have focused on modifying the trajectories of light rays, e.g. beam benders, lenses, invisibility cloaks, etc. In this contribution, we explore transformation optics beyond the manipulation of light trajectories. With a few well-chosen examples, we demonstrate that transformation optics can be used to manipulate electromagnetic fields up to an unprecedented level. In the first example, we introduce an electromagnetic cavity that allows for deep subwavelength confinement of light. The cavity is designed with transformation optics even though the concept of trajectory ceases to have any meaning in a structure as small as this cavity. In the second example, we show that the properties of Cherenkov light emitted in a transformation-optical material can be understood and modified from simple geometric considerations. Finally, we show that optical forces—a quadratic function of the fields—follow the rules of transformation optics too. By applying a folded coordinate transformation to a pair of waveguides, optical forces can be enhanced just as if the waveguides were closer together. With these examples, we open up an entirely new spectrum of devices that can be conceived using transformation optics.

In high energy physics, unknown particles are identified by determining their mass from the Cherenkov radiation cone that is emitted as they pass through the detector apparatus. However, at higher particle momentum, the angle of the Cherenkov cone saturates to a value independent of the mass of the generating particle, making it difficult to effectively distinguish between different particles. Here, we show how the geometric formalism of transformation optics can be applied to describe the Cherenkov cone in an arbitrary anisotropic medium. On the basis of these results, we propose a specific anisotropic metamaterial to control Cherenkov radiation, leading to enhanced sensitivity for particle identification at higher momentum.

The interaction between light and matter involves not only an energy transfer, but also the transfer of linear momentum. In everyday life applications this linear momentum of light is too small to play any significant role. However, in nanoscale dimensions, the associated optical forces start to play an increasingly important role. These forces are, e.g., large enough for exiting experiments in the fields of cavity-optomechanics, laser cooling and optical trapping of small particles. Recently, it has been suggested that optical gradient forces can also be employed for all-optical actuation in micro- and nanophotonic systems. The typical setup consists of two slab waveguides positioned in each others vicinity such that they are coupled through the interaction of the evanescent tails. Although the gradient forces between these waveguides can be enhanced considerably using electromagnetic resonators or slow-light techniques, the resulting displacements remain relatively small. In this contribution, we present an alternative approach to enhance optical gradient forces between waveguides using a combination of transformation optics and metamaterials. Our design starts from the observation that gradient forces exponentially decay with the separation distance between the waveguides. Therefore, we employ transformation optics to annihilate the apparent distance for light between the waveguides. Analytical calculations confirm that the resulting forces indeed increase when such an annihilating cladding is inserted. Subsequently, we discuss the metamaterial implementation of this annihilating medium. Such lensing media automatically translate into anisotropic metamaterials with negative components in the permittivity and permeability tensors. Our full-wave numerical simulations show that the overall amplification is highly limited by the loss-tangent of the metamaterial cladding. However, as this cladding only needs to operate in the near-field for a specific polarization, we can also consider single-negative metamaterial implementations. We finally demonstrate that in this way metamaterials can support optical forces enhanced by more than 200 times [Phys. Rev. Lett. 110, 057401 (2013)].

We show how transformation optics can enhance optical gradient forces between two optical waveguides by several orders of magnitude. The technique is based on a coordinate transformation that alters the perceived distance between the waveguides. This transformation can be implemented using single-negative metamaterial thin films. The process is remarkably robust to the dissipative loss normally observed in metamaterials. Therefore, our results provide an alternative way to enhance optical forces in nanophotonic actuation systems and may be combined with existing resonator-based enhancement methods to produce optical gradient forces with unprecedented amplitude [Phys. Rev. Lett. 110, 057401 (2013)].

In the interaction between light and matter, linear momentum can be transferred from electromagnetic waves to particles to generate so-called optical forces. Recently, it has been suggested that optical gradient forces can be used to actuate nanophotonic devices since measurable displacements can be achieved [1]. The typical setup consists of two waveguides positioned in each other's vicinity such that they are coupled through the interaction of the evanescent tails [2]. Although the gradient forces between these waveguides can be enhanced considerably with the use of electromagnetic resonators, the resulting displacements remain relatively small [1,2].

In this contribution we show that the fundamental diffraction limit of optical cavities can be overcome using a transformation-optical approach. Transformation optics has recently provided a new method for the design of devices to control electromagnetic fields, based on the analogy between the macroscopic Maxwell's equations in complex dielectrics and the free-space Maxwell's equations in a curved coordinate system. It offers an elegant approach to exploit the full potential of metamaterials. We show how transformation optics can be used to achieve the opposite e ect of an invisibility cloak; instead of prohibiting the electromagnetic waves from entering a predefi ned region, we encapsulate the light waves within such a finite region. This allows us to design cavities with extraordinary properties. We have been able to demonstrate theoretically the existence of eigenmodes whose wavelength is much larger than the characteristic dimensions of the device. Furthermore, our cavities avoid the bending losses observed in traditional microcavities, so the quality factor is only limited by the intrinsic absorption of the materials. Finally, we also demonstrate how the combination of radial and angular transformations allows developing cavities without bending losses using right-handed material parameters only. 1, 2

We develop a novel approach to create optical resonators by applying the geometrical technique of transformation optics and we show that the fundamental diffraction limit can be overcome inside metamaterials with right-handed material parameters.

We demonstrate how transformation optics can be used to amplify optical gradient forces. We show how meta-materials allow to enhance optical forces between waveguides over several orders of magnitude, even when realistic losses are included.

Based on the analogy between the Maxwell equations in complex metamaterials and the free-space Maxwell equations on the background of an arbitrary metric, transformation optics allows for the design of metamaterial devices using a geometrical perspective. This intuitive geometrical approach has already generated various novel applications within the elds of invisibility cloaking, electromagnetic beam manipulation, optical information storage, and imaging. Nevertheless, the framework of transformation optics is not limited to three-dimensional transformations and can be extended to four-dimensional metrics, which allow for the implementation of metrics that occur in general relativistic or cosmological models. This enables, for example, the implementation of black hole phenomena and space-time cloaks inside dielectrics with exotic material parameters. In this contribution, we present a time-dependent metamaterial device that mimics the cosmological redshift. Theoretically, the transformation-optical analogy requires an innite medium with a permittivity and a permeability that vary monotonically as a function of time. We demonstrate that the cosmological frequency shift can also be reproduced in more realistic devices, considering the fact that practical devices have a nite extent and bound material parameters. Indeed, our recent numerical results indicate that it is possible to alter the frequency of optical pulses in a medium with solely a modulated permittivity. Furthermore, it is shown that the overall frequency shift does not depend on the actual variation of the permittivity. The performance of a nite frequency converter is, for example, not aected by introducing the saw tooth evolution of the material parameters. Finally, we studied the eect of the introduction of realistic metamaterial losses and, surprisingly, we found a very high robustness with respect to this parameter. These results open up the possibility to fabricate this frequency converting device with currently available metamaterials [V. Ginis, P. Tassin, B. Craps, and I. Veretennico, Opt. Express 18, 5350{5355 (2010) 1 ].

Recently, there has been a lot of interest in electromagnetic analogues of general relativistic effects. Using the techniques of transformation optics, the material parameters of table-top devices have been calculated such that they implement several effects that occur in outer space, e.g., the implementation of an artificial event horizon inside an optical fiber, an inhomogeneous refractive index profile to mimic celestial mechanics, or an omnidirectional absorber based on an equivalence with black holes. In this communication, we show how we have extended the framework of transformation optics to a time-dependent metric-the Robertson-Walker metric, a popular model for our universe describing the cosmological redshift. This redshift occurs due to the expansion of the universe, where a photon of frequency ωem emitted at instance tem, will be measured at a different frequency ωobs at time tobs. The relation between these two frequencies is given by ωobsa(tobs) = ωema(tem), where a(t) is the time-dependent scale factor of the expanding universe. Our results show that the transformation-optical analogue of the Robertson-Walker metric is a medium with linear, isotropic, and homogeneous material parameters that evolve as a given function of time. The electromagnetic solutions inside such a medium are frequency shifted according to the cosmological redshift formula. Furthermore, we have demonstrated that a finite slab of such a material allows for the frequency conversion of an optical signal without the creation of unwanted sidebands. Because the medium is linear, the superposition principle remains applicable and arbitrary wavepackets can be converted [V. Ginis, P. Tassin, B. Craps, and I. Veretennicoff Opt. Express 18, 5350-5355 (2010)1].

The combination of transformation optics [1,2] and metamaterials [3,4] was one of the groundbraking ideas of the last decade. It has generated a novel formalism to design devices that control the properties of light up to a unprecedented level [5]. The first device that was designed within the formalism of transformation optics was the invisibility cloak. An invisibility cloak turns a finite region in space invisible by guiding light around it. For an ideal cloak, it is impossible for light of any wavelength to enter the cloaked region. But if no light can go in, then perhaps no light can go out? This idea suggests that one could approach an invisibility cloak as an optical cavity.

In recent years, transformation optics [1,2] has led to the design of a number of optical devices with exceptional properties, such as invisibility cloaks, beam transformers, electromagnetic concentrators, and subwavelength cavities [1–4]. These devices are derived from three-dimensional spatial coordinate transformations. However, it is shown that transformation optics can be applied to the four-dimensional metrics known from general relativity [5].

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

We use transformation optics to design an optical cavity that allows for the subwavelength confinement of light. Our cavity combines a deep subwavelength mode volume with the absence of intrinsic (bending) losses.

The storage of light is of crucial importance for applications involving optical data processing and certain quantum-optical devices, where it can be used to control the rate of spontaneous emission of light sources. Nowadays, light can be confined using optical microresonators or stopped-light techniques. Two important figures of merit determine the quality of these devices: the quality factor Q and the mode volume V , respectively quantifying the temporal and spatial confinement of light. Most applications require small mode volumes in combination with high quality factors. However, due to the wavelike nature of light, it is generally admitted that it is impossible to store light in a volume with subwavelength dimensions in combination with a high quality factor. In this contribution, we overcome this fundamental limitation by designing an optical cavity based on a transformation-optical approach [Ginis et al., arXiv: 0911.4216v1].

We apply the framework of transformation optics to the Robertson-Walker metric. We describe how a medium with controlled time-dependent material properties can change the optical frequency, even though it supports linear electromagnetic waves and we demonstrate perfect redshifting or blueshifting of an electromagnetic wave without the creation of sidebands.

According to general relativity, the frequency of electromagnetic radiation is altered by the expansion of the universe. This effect--commonly referred to as the cosmological redshift--is of utmost importance for observations in cosmology. Here we show that this redshift can be reproduced on a much smaller scale using an optical analogue inside a dielectric metamaterial with time-dependent material parameters. To this aim, we apply the framework of transformation optics to the Robertson-Walker metric. We demonstrate theoretically how perfect redshifting or blueshifting of an electromagnetic wave can be achieved without the creation of sidebands with a device of finite length., 6 pages, 3 figures

In this contribution, we apply the framework of transformation optics to the Robertson-Walker metric of general relativity. We describe how a medium with controlled time-dependent material properties can change the optical frequency, even though it supports linear electromagnetic waves, and we demonstrate perfect redshifting or blueshifting of an electromagnetic wave without creation of sidebands.

We investigate the potential of transformation optics for the design of novel electromagnetic cavities. First, we determine the dispersion relation of bound modes in a device performing an arbitrary radial coordinate transformation and we discuss a number of such cavity structures. Subsequently, we generalize our study to media that implement azimuthal transformations and we show that such transformations can manipulate the azimuthal mode number. Finally, we discuss how the combination of radial and azimuthal coordinate transformations allows for perfect confinement of subwavelength modes inside a cavity consisting of right-handed materials only., 17 pages, 6 figures

We apply the framework of transformation optics to mimic the cosmological redshift inside metamaterials and describe how a medium with well-defined time-dependent material parameters changes the optical frequency even though it supports linear electromagnetic waves.

We show how plasmonic metamaterials can enhance optical forces between two optical waveguides by several orders of magnitude. The result is based on the observation that plasmonic thin films reduce the optical distance between objects.