Transformation optics

Transformation optics applies metamaterials to produce spatial variations, derived from coordinate transformations, which can direct chosen bandwidths of electromagnetic radiation. This can allow for the construction of new composite artificial devices, which probably could not exist without metamaterials and coordinate transformation. Computing power that became available in the late 1990s enables prescribed quantitative values for the permittivity and permeability, the constitutive parameters, which produce localized spatial variations. The aggregate value of all the constitutive parameters produces an effective value, which yields the intended or desired results. Transformation optics applies metamaterials to produce spatial variations, derived from coordinate transformations, which can direct chosen bandwidths of electromagnetic radiation. This can allow for the construction of new composite artificial devices, which probably could not exist without metamaterials and coordinate transformation. Computing power that became available in the late 1990s enables prescribed quantitative values for the permittivity and permeability, the constitutive parameters, which produce localized spatial variations. The aggregate value of all the constitutive parameters produces an effective value, which yields the intended or desired results. Hence, complex artificial materials, known as metamaterials, are used to produce transformations in optical space. The mathematics underpinning transformation optics is similar to the equations that describe how gravity warps space and time, in general relativity. However, instead of space and time, these equations show how light can be directed in a chosen manner, analogous to warping space. For example, one potential application is collecting sunlight with novel solar cells by concentrating the light in one area. Hence, a wide array of conventional devices could be markedly enhanced by applying transformation optics. Transformation optics has its beginnings in two research endeavors, and their conclusions. They were published on May 25, 2006, in the same issue of the peer-reviewed journal Science. The two papers describe tenable theories on bending or distorting light to electromagnetically conceal an object. Both papers notably map the initial configuration of the electromagnetic fields on to a Cartesian mesh. Twisting the Cartesian mesh, in essence, transforms the coordinates of the electromagnetic fields, which in turn conceal a given object. Hence, with these two papers, transformation optics is born. Transformation optics subscribes to the capability of bending light, or electromagnetic waves and energy, in any preferred or desired fashion, for a desired application. Maxwell's equations do not vary even though coordinates transform. Instead values of chosen parameters of materials 'transform', or alter, during a certain time period. Transformation optics developed from the capability to choose which parameters for a given material, known as a metamaterial. Hence, since Maxwell's equations retain the same form, it is the successive values of permittivity and permeability that change, over time. Permittivity and permeability are in a sense responses to the electric and magnetic fields of a radiated light source respectively, among other descriptions. The precise degree of electric and magnetic response can be controlled in a metamaterial, point by point. Since so much control can be maintained over the responses of the material, this leads to an enhanced and highly flexible gradient-index material. Conventionally predetermined refractive index of ordinary materials become independent spatial gradients, that can be controlled at will. Therefore, transformation optics is a new method for creating novel and unique optical devices. Transformation optics can go beyond cloaking (mimic celestial mechanics) because its control of the trajectory and path of light is highly effective. Transformation optics is a field of optical and material engineering and science embracing nanophotonics, plasmonics, and optical metamaterials. Developments in this field focus on advances in research of transformation optics. Transformation optics is the foundation for exploring a diverse set of theoretical, numerical, and experimental developments, involving the perspectives of the physics and engineering communities. The multi-disciplinary perspectives for inquiry and designing of materials develop understanding of their behaviors, properties, and potential applications for this field. If a coordinate transformation can be derived or described, a ray of light (in the optical limit) will follow lines of a constant coordinate. There are constraints on the transformations, as listed in the references. In general, however, a particular goal can be accomplished using more than one transformation. The classic cylindrical cloak (first both simulated and demonstrated experimentally) can be created with many transformations. The simplest, and most often used, is a linear coordinate mapping in the radial coordinate. There is significant ongoing research into determining advantages and disadvantages of particular types of transformations, and what attributes are desirable for realistic transformations. One example of this is the broadband carpet cloak: the transformation used was quasi-conformal. Such a transformation can yield a cloak that uses non-extreme values of permittivity and permeability, unlike the classic cylindrical cloak, which required some parameters to vary towards infinity at the inner radius of the cloak. General coordinate transformations can be derived which compress or expand space, bend or twist space, or even change the topology (e.g. by mimicking a wormhole). Much current interest involves designing invisibility cloaks, event cloaks, field concentrators, or beam-bending waveguides.