In the original work of optical conformal mapping, an isotropic medium with a nonuniform refractive index profile was used4. Correspondingly light rays are shown in colored curves in fig. Conformal mappings to achieve simple material parameters. Quasiconformal approaches for two and threedimensional. Conformal mapping is used to find the exact cutoff frequency of optical fibres with a dip in the. However, as a consequence of the riemann mapping theorem 15 nontrivial w coordinates occupy riemann. The analytical conformal mapping is carefully chosen such that branch cut is a quarter of a great circle in virtual space. 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. An invisibility device should guide light around an object as if nothing were there, regardless where the light comes from. 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. Pdf 2011 cross section comparison of cloaks designed by. By carefully developing designs with specific conformal mappings, one can make an object look like another with a significantly different shape. The method of optical conformal mapping is used to design two isotropic devices through which light travels in a unidirectional manner. How to find a conformal mapping that transfers the first quadrant onto the upper half plane.
Optical conformal mapping and dielectric invisibility devices. Consider a conformal mapping w fz that connects two spaces zspace and wspace. Realizing components with decoupled geometrical form and optical function. Optical waveguides are the key elements of photonic devices that perform guiding, coupling, switching, splitting, multiplexing and demultiplexing of optical signals. 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.
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. 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. Conformal mapping has many applications in physics. When a fibre is bent, the optical path of the light changes as we move away from the centre of the bend. Transformation optics is a field of optical and material engineering and science embracing nanophotonics, plasmonics, and optical. Various proposals have been made to improve this coupling. 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. 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. Chapter 3 conformal mapping technique an overview 3. Optical conformal mapping and dielectric invisibility. Transformation optics can go beyond cloaking mimic celestial mechanics because its control of the trajectory and path of light is highly effective.
In the main text, starting from virtual space, versatile devices with isotropic optical media are introduced by various conformal mappings. The modified refractive index obtained from conformal mapping is given by below equation. Transformation optics and applications in microwave. Decoupling optical function and geometrical form using. The lens can first be considered like a flattened luneburg lens, which produces highlydirective electromagnetic waves by adjusting the feed position along the line. Leonhardt, optical conformal mapping, science 312, 17771780 2006. Osa multifunctional lens based on conformal mapping. Worked examples conformal mappings and bilinear transformations example 1 suppose we wish to.
Here the imperfections of invisibility can be made. The integral of gz defines a map wz to new coordinates where, according to eq. Boundary integral equation method for resonances in. Conformal mapping preserves the optical path rather than the measure of euclidian length between physical space and virtual space. 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. 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. In this paper, we propose a simple method of illusion optics based on conformal mappings. This is accomplished by manipulating the paths traversed by light through a novel optical material. Controlling refractive index of transformationoptics devices via.
Perfect conformal invisible device with feasible refractive indexes lin xu and huanyang chen. The optical carpet cloak is designed using quasiconformal mapping to conceal an object that is placed. However, it can only work in the geometrical optics realm and is con. 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 quasi conformal mapping minimized the anisotropy needed in the optical constants, which meant that the cloak could be. 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. This alignment has not been observed in other galaxies because surface density maps are most easily made for faceon galaxies where there is.
In this paper, we propose a new approach for estimating bend losses in optical fibers. By choosing an appropriate mapping function, the analyst can transform the inconvenient geometry into a much more convenient one. Conformal transformations to achieve unidirectional. 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. Transformation optical design is generally complicated by the requirement for highly anisotropic and inhomogeneous constituent materials. The paper shows that the time delays do not depend on the directions and impact. A conformal mapping is a function that locally keeps the angle of any two lines unchanged, but not the. Design of metamaterialcoated arrays through quasi conformal transformation optics ephrem t. Chalkboard photos, reading assignments, and exercises solutions pdf 2.
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. Conformal mapping and its applications suman ganguli1 1department of physics, university of tennessee, knoxville, tn 37996 dated. 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. With a refractive index profile nwu, v applied, virtual space. The lens is an infinitelylong, gradientindex dielectric cylinder with a semielliptic crosssection. He has been involved with the science of cloaking objects since then he is a wolfson research merit award holder from the royal. Notes on conformal invisibility devices iopscience institute of. 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.
Request pdf carpet cloak from optical conformal mapping the original carpet cloak phys. 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. However, in dealing with problems in fibre optics, conformal. Metamaterial cloaking is the usage of metamaterials in an invisibility cloak. Various bend loss measurement in optical fiber cables. A transformation w fz is said to beconformalif it preserves angel between oriented curves in magnitude as well as in orientation. The conformal cloak was proposed based on optical conformal mapping 1, thus only inhomogeneous refractive index pro. Conformal mapping in optical biosensor applications.
Perfect conformal invisible device with feasible refractive. February 2, 2008 an invisibility device should guide light around an object as if nothing were there, regardless where the light comes from. Here we describe a perfect conformal invisible device with full impedance matching. This paper demonstrates that restricting the spatial transformation to a conformal mapping can lead to much simpler material parameters for more. Study of bending losses in optical fibers using comsol. Optm enables 3d imaging of individual cells with an isotropic spatial resolution of 350 nm. Therefore its refractive index profile was obtained numerically. 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. May 19, 2016 the conformal metasurface concept is highly versatile for developing arbitrarily shaped multifunctional optical devices. Consequently, in w coordinates, the wave propagation is indistinguishable from empty space where light rays propagate along straight lines. Broadband illusion optical devices based on conformal mappings. In section 2, we describe the possible sources of modification of. Ingeneral, aquasi conformal map isrequired foran unchanged topology of space without creating additional singular points in the coordinate transformation 26.
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. The state of the art conformal optics is described. Ulf leonhardt, frse born 9 october 1965 in schlema, germany is a german and british scientist. This paper considers invisibility devices based on optical conformal mapping. Applications of optics have traditionally conformed to the difficulties and limitations imposed by the practical limits on designing and fabricating optical systems. Passive waveguides, electrooptic components, transmitters, receivers, and driving electronics can be integrated into one chip using planar technology, similar to microelectronics. By setting a line current source in a properly tuned refractive index pro. This change can be estimated using a technique known as conformal mapping 6.
Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed. This kind of approximation may give valid results but with a compromise on accuracy. Notes on conformal invisibility devices iopscience. Ideal invisibility devices are impossible due to the wave nature of light. The medium performs an optical conformal mapping to empty space. Osa conformal optical devices based on geodesic lenses. Carpet cloak from optical conformal mapping request pdf. The optical carpet cloak is designed using quasi conformal mapping to conceal an object that is placed. 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. We present the design and analysis of an optical cloak of invisibility with nonmagnetic metamaterials. 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. The general recipe for the implementation of such a device is provided. Carpet cloak from optical conformal mapping springerlink. Granted application number us15975,521 other versions us10267957b2 en inventor seyedeh.
Based on conformal mapping method, a two dimensional, multifunctional lens structure is proposed and designed in this work. Both the conformal cloak and the pushforward cloak have singular. So far we have constructed a conformal lens or a mikaelian lens in fig. Maximising the optical power collected in a waveguide from the diffracting field of a semiconductor laser is desirable in optical fibre communication systems. 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. 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. Quasi conformal mappings have appeared as an attractive subset of the general transformation optics method because they only require isotropic, dielectriconly materials.
Design of metamaterialcoated arrays through quasiconformal. 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. 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. Coating defects detection, causes and cures edward d. Conformal mapping in opt ical biosensor applications 537 section, we used the variables xf and zf, which were scaled by the dimensions of the. Now we will employ a practical experimental system to demonstrate its properties. Jun 23, 2006 the medium performs an optical conformal mapping to empty space. This paper develops a general recipe for the design of media that create perfect invisibility within the accuracy of geometrical optics. Logarithm conformal mapping brings the cloaking effect.
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. However, there is usually discontinuity for refractive index profile at branch cuts of different virtual riemann sheets, hence compromising the functionalities. Metamaterials direct and control the propagation and transmission of specified parts of the light spectrum and demonstrate the potential to render an object seemingly. Worked examples conformal mappings and bilinear transfor. Designing whispering gallery modes via transformation optics. So far, we have achieved a conformal optical transparency by gcto, which is a composition of one geodesic conformal mapping and two analytical. Osa husimi functions at gradient index cavities designed. The original carpet cloak was designed by a numerical method, the quasi conformal mapping. Conformal optics refers to the design, fabrication and use of optical windows and domes that are neither flat nor a section of a sphere. Conformal mapping in optical biosensor applications 537 section, we used the variables xf and zf, which were scaled by the dimensions of the. Controlling refractive index of transformationoptics devices. We present a general method of designing optical devices based on optical conformal mapping and rescaling the optical path along a given bunch of rays. In mathematics, a conformal map is a function that locally preserves angles, but not necessarily lengths more formally, let and be open subsets of.
Request pdf conformal mappings to achieve simple material parameters for transformation optics devices the transformation optics technique for designing novel electromagnetic and optical. Optical conformal mapping has been used to construct several isotropic devices with novel functionalities. Conformal mappings to achieve simple material parameters for. This change implies to the change of refractive index of the fibre. For this reason, our scheme takes advantage of conformal mapping and isotropic dielectric materials. An application of conformal mapping in fibre optics. Conformal mapping article about conformal mapping by the.
Conformal transformation optics provides a simple scheme for manipulating light rays with inhomogeneous isotropic dielectrics. The mode field characteristics of eccentric optical fibers are investigated theoretically. Request pdf conformal mappings to achieve simple material parameters for transformation optics devices the transformation optics technique for designing. To deal with that, we present a special method for conformal transformation optics based on geodesic lenses. Here we look at some examples of analytic functions that illustrate that they are conformal maps.
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