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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 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)].

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)].

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 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].