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.
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.
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 transformationoptical
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.
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)].
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. There- fore, 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 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
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,
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].