Transformation optics

About: Transformation optics is a research topic. Over the lifetime, 2687 publications have been published within this topic receiving 102378 citations.

Bidirectional invisibility in Kramers-Kronig optical media.

Abstract: A broad class of planar dielectric media with complex permittivity profiles that are fully invisible, for both left and right incidence sides, is introduced. Such optical media are locally isotropic, non-magnetic, and belong to the recently discovered class of Kramers-Kronig media [Nat. Photonics9, 436 (2015)], i.e., the spatial profiles of the real and imaginary parts of the dielectric permittivity are related each other by a Hilbert transform. The transition from unidirectional to bidirectional invisibility, and the possibility to realize sharp reflection above a cut-off incidence angle, are also discussed.

Transformation seismology: composite soil lenses for steering surface elastic Rayleigh waves

Abstract: Metamaterials are artificially structured media that exibit properties beyond those usually encountered in nature. Typically they are developed for electromagnetic waves at millimetric down to nanometric scales, or for acoustics, at centimeter scales. By applying ideas from transformation optics we can steer Rayleigh-surface waves that are solutions of the vector Navier equations of elastodynamics. As a paradigm of the conformal geophysics that we are creating, we design a square arrangement of Luneburg lenses to reroute Rayleigh waves around a building with the dual aim of protection and minimizing the effect on the wavefront (cloaking). To show that this is practically realisable we deliberately choose to use material parameters readily available and this metalens consists of a composite soil structured with buried pillars made of softer material. The regular lattice of inclusions is homogenized to give an effective material with a radially varying velocity profile and hence varying the refractive index of the lens. We develop the theory and then use full 3D numerical simulations to conclusively demonstrate, at frequencies of seismological relevance 3–10 Hz, and for low-speed sedimentary soil (vs: 300–500 m/s), that the vibration of a structure is reduced by up to 6 dB at its resonance frequency.

Flat-lens design using Field Transformation and its comparison with those based on Transformation Optics and Ray Optics

Abstract: This paper proposes a technique for designing flat lenses using Field Transformation (FT), as opposed to Ray Optics (RO) or Transformation Optics (TO). The lens design consists of 10 layers of graded index dielectric in the radial direction and 5 layers in the longitudinal direction. The central layer in the longitudinal direction primarily contributes to a bulk of the phase transformation, while the other four layers, above and below this middle layer on either side, act as matching layers that help reduce the reflections introduced by the impedance mismatch at the interfaces of the middle layer. The paper compares the performance of the lens, so designed, with those based on the RO and TO techniques. We show that the proposed lens design using field transformation is broadband, has a better than 1 dB higher gain compared to the RO and TO based designs over a wider frequency band, and that its scan capability is superior as well.

Enhanced control of light and sound trajectories with three-dimensional gradient index lenses

Abstract: We numerically study the focusing and bending effects of light and sound waves through heterogeneous isotropic cylindrical and spherical devices. We first point out that transformation optics and acoustics show that the control of light requires spatially varying anisotropic permittivity and permeability, while the control of sound is achieved via spatially anisotropic density and isotropic compressibility. Moreover, homogenization theory applied to electromagnetic and acoustic periodic structures leads to such artificial (although not spatially varying) anisotropic permittivity, permeability and density. We stress that homogenization is thus a natural mathematical tool for the design of structured metamaterials. To illustrate the two-step geometric transform-homogenization approach, we consider the design of cylindrical and spherical electromagnetic and acoustic lenses displaying some artificial anisotropy along their optical axis (direction of periodicity of the structural elements). Applications are sought in the design of Eaton and Luneburg lenses bending light at angles ranging from 90° to 360°, or mimicking a Schwartzchild metric, i.e. a black hole. All of these spherical metamaterials are characterized by a refractive index varying inversely with the radius which is approximated by concentric layers of homogeneous material. We finally propose some structured cylindrical metamaterials consisting of infinitely conducting or rigid toroidal channels in a homogeneous bulk material focusing light or sound waves. The functionality of these metamaterials is demonstrated via full-wave three-dimensional computations using nodal elements in the context of acoustics, and finite edge-elements in electromagnetics.