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Transformation optics

Transformation optics is a branch of optics which 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.

Coordinate transformations
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 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==
Developments
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. ==Mimicking celestial mechanics==
Mimicking celestial mechanics
The interactions of light and matter with spacetime, as predicted by general relativity, can be studied using the new type of artificial optical materials that feature extraordinary abilities to bend light (which is actually electromagnetic radiation). This research creates a link between the newly emerging field of artificial optical metamaterials to that of celestial mechanics, thus opening a new possibility to investigate astronomical phenomena in a laboratory setting. The recently introduced, new class, of specially designed optical media can mimic the periodic, quasi-periodic and chaotic motions observed in celestial objects that have been subjected to gravitational fields. If a metamaterial could be produced that did not have high intrinsic loss and a narrow frequency range of operation then it could be employed as a type of media to simulate light motion in a curved spacetime vacuum. Such a proposal is brought forward, and metamaterials become prospective media in this type of study. The classical optical-mechanical analogy renders the possibility for the study of light propagation in homogeneous media as an accurate analogy to the motion of massive bodies, and light, in gravitational potentials. A direct mapping of the celestial phenomena is accomplished by observing photon motion in a controlled laboratory environment. The materials could facilitate periodic, quasi-periodic and chaotic light motion inherent to celestial objects subjected to complex gravitational fields. Twisting the optical metamaterial effects its "space" into new coordinates. The light that travels in real space will be curved in the twisted space, as applied in transformational optics. This effect is analogous to starlight when it moves through a closer gravitational field and experiences curved spacetime or a gravitational lensing effect. This analogue between classic electromagnetism and general relativity, shows the potential of optical metamaterials to study relativity phenomena such as the gravitational lens. The study also points toward the design of novel optical cavities and photon traps for application in microscopic devices and lasers systems. The first experimental demonstration of electromagnetic black hole at microwave frequencies occurred in October 2009. The proposed black hole was composed of non-resonant, and resonant, metamaterial structures, which can absorb electromagnetic waves efficiently coming from all directions due to the local control of electromagnetic fields. It was constructed of a thin cylinder at 21.6 centimeters in diameter comprising 60 concentric rings of metamaterials. This structure created a gradient index of refraction, necessary for bending light in this way. However, it was characterized as being artificially inferior substitute for a real black hole. The characterization was justified by an absorption of only 80% in the microwave range, and that it has no internal source of energy. It is singularly a light absorber. The light absorption capability could be beneficial if it could be adapted to technologies such as solar cells. However, the device is limited to the microwave range. Also in 2009, transformation optics were employed to mimic a black hole of Schwarzschild form. Similar properties of photon sphere were also found numerically for the metamaterial black hole. Several reduced versions of the black hole systems were proposed for easier implementations. MIT computer simulations by Fung along with lab experiments are designing a metamaterial with a multilayer sawtooth structure that slows and absorbs light over a wide range of wavelength frequencies, and at a wide range of incident angles, at 95% efficiency. This has an extremely wide window for colors of light. Multi-dimensional universe Engineering optical space with metamaterials could be useful to reproduce an accurate laboratory model of the physical multiverse. "''This 'metamaterial landscape' may include regions in which one or two spatial dimensions are compactified.''" Metamaterial models appear to be useful for non-trivial models such as 3D de Sitter space with one compactified dimension, 2D de Sitter space with two compactified dimensions, 4D de Sitter dS4, and anti-de Sitter AdS4 spaces. ==Gradient index lensing==
Gradient index lensing
Transformation optics is employed to increase capabilities of gradient index lenses. Conventional optical limitations Optical elements (lenses) perform a variety of functions, ranging from image formation, to light projection or light collection. The performance of these systems is frequently limited by their optical elements, which dominate system weight and cost, and force tradeoffs between system parameters such as focal length, field of view (or acceptance angle), resolution, and range. ==Battlefield applications==
Battlefield applications
Transformation optics has potential applications for the battlefield. The versatile properties of metamaterials can be tailored to fit almost any practical need, and transformation optics shows that space for light can be bent in almost any arbitrary way. This is perceived as providing new capabilities to soldiers in the battlefield. For battlefield scenarios benefits from metamaterials have both short term and long-term impacts. Harnessing subwavelength capabilities then allow for other advancements which appear to be beyond the battlefield. All kinds of materials could be manufactured with nano-manufacturing, which could go into electronic and optical devices from night vision goggles to distance sensors to other kinds of sensors. Longer-term views include the possibility for cloaking materials, which would provide "invisibility" by redirecting light around a cylindrical shape. ==See also==
Further reading and general references
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