Jun 23, 2006 the medium performs an optical conformal mapping to empty space. The state of the art conformal optics is described. This change implies to the change of refractive index of the fibre. Applications of optics have traditionally conformed to the difficulties and limitations imposed by the practical limits on designing and fabricating optical systems. Here the imperfections of invisibility can be made. The mode field characteristics of eccentric optical fibers are investigated theoretically. He has been involved with the science of cloaking objects since then he is a wolfson research merit award holder from the royal. By choosing an appropriate mapping function, the analyst can transform the inconvenient geometry into a much more convenient one. Notes on conformal invisibility devices iopscience institute of. Osa husimi functions at gradient index cavities designed. The optical carpet cloak is designed using quasiconformal mapping to conceal an object that is placed.
The paper shows that the time delays do not depend on the directions and impact parameters of incident light rays, although the refractiveindex profile of any conformal invisibility device is necessarily asymmetric. Notes on conformal invisibility devices iopscience. Worked examples conformal mappings and bilinear transfor. Study of bending losses in optical fibers using comsol. Perfect conformal invisible device with feasible refractive indexes lin xu and huanyang chen. Controlling refractive index of transformationoptics devices. Passive waveguides, electrooptic components, transmitters, receivers, and driving electronics can be integrated into one chip using planar technology, similar to microelectronics. The conformal cloak was proposed based on optical conformal mapping 1, thus only inhomogeneous refractive index pro. In this paper, we propose a simple method of illusion optics based on conformal mappings.
We present the design and analysis of an optical cloak of invisibility with nonmagnetic metamaterials. Ulf leonhardt, frse born 9 october 1965 in schlema, germany is a german and british scientist. Maximising the optical power collected in a waveguide from the diffracting field of a semiconductor laser is desirable in optical fibre communication systems. Various bend loss measurement in optical fiber cables. The transformation optics technique for designing novel electromagnetic and optical devices offers great control over wave behavior, but is difficult to implement primarily due to limitations in current metamaterial design and fabrication techniques. However, the spot size and phase front curvature of the laser field usually makes a poor overlap with the mode of the receiving waveguide. Examples of conformal maps and of critical points we know that an analytic function fz is conformal preserves angles and orientation at all points where the derivative fz is not zero. Conformal mapping of nuclei in 3d tomographic cell images to assess shape heterogeneity vivek nandakumar1,2, xing an3,4, yalin wang3, roger johnson2, deirdre meldrum1,2 1school of electrical, computer, and energy engineering, arizona state university, tempe, arizona 2center for biosignatures discovery automation, biodesign institute, tempe, arizona. Therefore its refractive index profile was obtained numerically. Conformal mappings to achieve simple material parameters for. Controlling refractive index of transformationoptics devices via.
Pdf 2011 cross section comparison of cloaks designed by. This kind of approximation may give valid results but with a compromise on accuracy. Ideal invisibility devices are impossible due to the wave nature of light. The medium performs an optical conformal mapping to empty space. Perfect conformal invisible device with feasible refractive. The optical carpet cloak is designed using quasi conformal mapping to conceal an object that is placed. Osa conformal optical devices based on geodesic lenses.
Both the conformal cloak and the pushforward cloak have singular. By setting a line current source in a properly tuned refractive index pro. This paper considers invisibility devices based on optical conformal mapping. The lens is an infinitelylong, gradientindex dielectric cylinder with a semielliptic crosssection.
The operational efficiency of devices, especially military systems, has frequently been compromised by the need to accommodate an adverse environment in a non optical manner. February 2, 2008 an invisibility device should guide light around an object as if nothing were there, regardless where the light comes from. Decoupling optical function and geometrical form using. In this letter, we propose a new carpet cloak based on the optical conformal mapping, with an analytical form of a refractive index profile, thereby facilitating future experimental designs.
Metamaterials direct and control the propagation and transmission of specified parts of the light spectrum and demonstrate the potential to render an object seemingly. Ingeneral, aquasi conformal map isrequired foran unchanged topology of space without creating additional singular points in the coordinate transformation 26. Optical waveguides are the key elements of photonic devices that perform guiding, coupling, switching, splitting, multiplexing and demultiplexing of optical signals. Conformal mapping in opt ical biosensor applications 537 section, we used the variables xf and zf, which were scaled by the dimensions of the. In the main text, starting from virtual space, versatile devices with isotropic optical media are introduced by various conformal mappings. In these two conformal mappings, the second sheet is finite in one direction because of the periodical property of the logarithm terms, which is quite different from the zhukowski conformal mapping mostly used for cloaking design 1,14. Leonhardt, optical conformal mapping, science 312, 17771780 2006. The integral of gz defines a map wz to new coordinates where, according to eq. How to find a conformal mapping that transfers the first quadrant onto the upper half plane. Optical conformal mapping has been used to construct several isotropic devices with novel functionalities. The modified refractive index obtained from conformal mapping is given by below equation. With a refractive index profile nwu, v applied, virtual space. Based on conformal mapping method, a two dimensional, multifunctional lens structure is proposed and designed in this work. Worked examples conformal mappings and bilinear transformations example 1 suppose we wish to.
So far we have constructed a conformal lens or a mikaelian lens in fig. Here we describe a perfect conformal invisible device with full impedance matching. When a fibre is bent, the optical path of the light changes as we move away from the centre of the bend. Transformation optical design is generally complicated by the requirement for highly anisotropic and inhomogeneous constituent materials. Request pdf carpet cloak from optical conformal mapping the original carpet cloak phys.
Quasi conformal mappings have appeared as an attractive subset of the general transformation optics method because they only require isotropic, dielectriconly materials. Crosssection comparisons of cloaks designed by transformation optical and optical conformal mapping approaches yaroslav a urzhumov 1, nathan b kundtz,2,davidrsmith1 and john b pendry3 1 center for metamaterials and integrated plasmonics, pratt school of engineering, duke university, durham, nc 27708, usa. Quasiconformal approaches for two and threedimensional. Designing whispering gallery modes via transformation optics. By carefully developing designs with specific conformal mappings, one can make an object look like another with a significantly different shape. It is important to note, optical conformal mapping usually requires materials to be filled in the whole space. However, as a consequence of the riemann mapping theorem 15 nontrivial w coordinates occupy riemann. Boundary integral equation method for resonances in. The analytical conformal mapping is carefully chosen such that branch cut is a quarter of a great circle in virtual space. Conformal mapping in optical biosensor applications 537 section, we used the variables xf and zf, which were scaled by the dimensions of the. Chapter 3 conformal mapping technique an overview 3. Conformal mapping preserves the optical path rather than the measure of euclidian length between physical space and virtual space.
Logarithm conformal mapping brings the cloaking effect. However, in dealing with problems in fibre optics, conformal. Now we will employ a practical experimental system to demonstrate its properties. The quasi conformal mapping minimized the anisotropy needed in the optical constants, which meant that the cloak could be. This change can be estimated using a technique known as conformal mapping 6. The original carpet cloak was designed by a numerical method, the quasi conformal mapping.
Consequently, in w coordinates, the wave propagation is indistinguishable from empty space where light rays propagate along straight lines. Conformal mapping and its applications suman ganguli1 1department of physics, university of tennessee, knoxville, tn 37996 dated. The challenges and solutions to overcome the challenges associated with developing the tools and techniques that enable the use of conformal optics is described. The eccentric optical fiber is converted to be a concentric threelayered optical fiber through the conformal representation and the corresponding field distribution is given by solving eigenvalue equation of a general threelayered optical fiber waveguide. In this paper, we propose a new approach for estimating bend losses in optical fibers. Conformal mapping in optical biosensor applications. Various proposals have been made to improve this coupling. This alignment has not been observed in other galaxies because surface density maps are most easily made for faceon galaxies where there is. Carpet cloak from optical conformal mapping request pdf. We notice that both mappings allow us to put two kissing mirrored maxwells fisheye lenses proposed by wu et al 14 in the second sheet, leading light. Consider a conformal mapping w fz that connects two spaces zspace and wspace. Now that we are interested in the reaction kinetics, we introduce the variables x and z, which are scaled by the dimensions of the reacting zone. Design of metamaterialcoated arrays through quasiconformal. We remark that compared with the optical conformal mapping 10, the technique of quasi conformal mapping allows the conformal module of the two domains to di.
For the case of the recently proposed gradient index dielectric cavities called as transformation cavities designed by optical conformal mapping, we show that the phase space structure of resonant modes can be revealed through the conventional husimi functions by constructing a reciprocal virtual space. Optical conformal mapping and dielectric invisibility. Optm enables 3d imaging of individual cells with an isotropic spatial resolution of 350 nm. The lens can first be considered like a flattened luneburg lens, which produces highlydirective electromagnetic waves by adjusting the feed position along the line. The phase delay problem of invisibility cloaks designed by optical conformal mapping is referred to the optical path difference between the waves in upper and lower riemann sheets. Design of metamaterialcoated arrays through quasi conformal transformation optics ephrem t. Despite much interest and progress in optical spatial cloaking, a threedimensional 3d, transmitting, continuously multidirectional cloak in the visible regime has not yet been demonstrated. In 2006, he published the first scientific paper on invisibility cloaking with metamaterials at the same time pendrys group published their paper in the journal science. The method of optical conformal mapping is used to design two isotropic devices through which light travels in a unidirectional manner.
Transformation optics can go beyond cloaking mimic celestial mechanics because its control of the trajectory and path of light is highly effective. Chalkboard photos, reading assignments, and exercises solutions pdf 2. Metamaterial cloaking is the usage of metamaterials in an invisibility cloak. For this reason, our scheme takes advantage of conformal mapping and isotropic dielectric materials. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed. November 20, 2008 conformal same form or shape mapping is an important technique used in complex analysis and has many applications in di erent physical situations. Selffocusing and the talbot effect in conformal transformation optics xiangyang wang,1 huanyang chen,2, hui liu,1, lin xu,2 chong sheng,1 and shining zhu1 1national laboratory of solid state microstructures and school of physics, collaborative innovation center of advanced microstructures, nanjing university, nanjing, jiangsu 210093, china. Transformation optics and applications in microwave. Granted application number us15975,521 other versions us10267957b2 en inventor seyedeh. Conformal mapping article about conformal mapping by the. Conformal mapping has many applications in physics. This paper demonstrates that restricting the spatial transformation to a conformal mapping can lead to much simpler material parameters for more. The general recipe for the implementation of such a device is provided. Optical conformal mapping and dielectric invisibility devices.
However, there is usually discontinuity for refractive index profile at branch cuts of different virtual riemann sheets, hence compromising the functionalities. Conformal transformations to achieve unidirectional. A transformation w fz is said to beconformalif it preserves angel between oriented curves in magnitude as well as in orientation. Transformation optics is a field of optical and material engineering and science embracing nanophotonics, plasmonics, and optical. This paper develops a general recipe for the design of media that create perfect invisibility within the accuracy of geometrical optics.
Carpet cloak from optical conformal mapping springerlink. Oct 31, 2014 in these two conformal mappings, the second sheet is finite in one direction because of the periodical property of the logarithm terms, which is quite different from the zhukowski conformal mapping mostly used for cloaking design 1,14. Coating defects detection, causes and cures edward d. Here we look at some examples of analytic functions that illustrate that they are conformal maps. In section 2, we describe the possible sources of modification of. Request pdf conformal mappings to achieve simple material parameters for transformation optics devices the transformation optics technique for designing.
May 19, 2016 the conformal metasurface concept is highly versatile for developing arbitrarily shaped multifunctional optical devices. However, it can only work in the geometrical optics realm and is con. To deal with that, we present a special method for conformal transformation optics based on geodesic lenses. Conformal mapping is used to find the exact cutoff frequency of optical fibres with a dip in the. In the original work of optical conformal mapping, an isotropic medium with a nonuniform refractive index profile was used4. Crosssection comparisons of cloaks designed by transformation optical and optical conformal mapping approaches yaroslav a urzhumov 1, nathan b kundtz,2,davidrsmith1 and john b pendry3 1 center for metamaterials and integrated plasmonics, pratt school of engineering, duke university, durham, nc. The paper shows that the time delays do not depend on the directions and impact. Correspondingly light rays are shown in colored curves in fig. In mathematics, a conformal map is a function that locally preserves angles, but not necessarily lengths more formally, let and be open subsets of. Broadband illusion optical devices based on conformal mappings. Realizing components with decoupled geometrical form and optical function. We present a general method of designing optical devices based on optical conformal mapping and rescaling the optical path along a given.
Conformal optics refers to the design, fabrication and use of optical windows and domes that are neither flat nor a section of a sphere. A conformal mapping is a function that locally keeps the angle of any two lines unchanged, but not the. So far, we have achieved a conformal optical transparency by gcto, which is a composition of one geodesic conformal mapping and two analytical. It is not difficult to ascertain that in this case the halflines parallel to the sides of the angle are transformed into halfparabolas with a common focus at o figure 3. From the above observation if f is analytic in a domain d and z 0 2d with f0z 0 6 0 then f is conformal at z 0. Optical conformal mapping and dielectric invisibility devices ulf leonhardt school of physics and astronomy, university of st andrews, north haugh, st andrews ky16 9ss, scotland dated. Mode field analysis of eccentric optical fibers by. Tem eigenmode, usinga generalization of the schwarzchristoe l conformal mapping of the spiral transverse section, is provided together with the analysis of the impedances and the poynting vector of the line. Conformal mappings to achieve simple material parameters. This is accomplished by manipulating the paths traversed by light through a novel optical material. An invisibility device should guide light around an object as if nothing were there, regardless where the light comes from.
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