Abstract
The transformation electromagnetics technique provides a powerful tool to electromagnetic and optical designers by offering a blueprint for creating novel devices that feature a variety of unconventional wave-material interaction properties. Combined with the recent advances in metamaterials technology, the coordinate transformation-based design methodology paves the way to realizing devices that perform entirely new functions or traditional functions in different geometrical configurations that are advantageous in practical applications. Here, transformation electromagnetics techniques are applied to the design of invisibility cloaks, lenses, beam controllers, and antennas. Each device design is illustrated with an example, including the associated specifications and performance expectations. For the two-dimensional embedded antenna application, a microwave metamaterial design is also presented.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Leonhardt U (2006) Optical conformal mapping. Science 312:1777–1780
Pendry JB, Schurig D, Smith DR (2006) Controlling electromagnetic fields. Science 312:1780–1782
Schurig D, Pendry JB, Smith DR (2006) Calculation of material properties and ray tracing in transformation media. Opt Express 14:9794–9804
Schurig D, Mock JJ, Justice BJ, Cummer SA, Pendry JB, Starr AF, Smith DR (2006) Metamaterial electromagnetic cloak at microwave frequencies. Science 314:977–980
Huang Y, Feng Y, Jiang T (2007) Electromagnetic cloaking by layered structure of homogeneous isotropic materials. Opt Express 15:11133–11141
Gaillot DP, Croenne C, Lippens D (2008) An all-dielectric route for terahertz cloaking. Opt Express 16:3986–3992
Zolla F, Guenneau S, Nicolet A, Pendry JB (2007) Electromagnetic analysis of cylindrical invisibility cloaks and the mirage effect. Opt Lett 32:1069–1071
Zhang B, Chen H, Wu B-I, Kong JA (2008) Extraordinary surface voltage effect in the invisibility cloak with an active device inside. Phy Rev Lett 100:063904
Ruan Z, Yan M, Neff CW, Qiu M (2007) Ideal cylindrical cloaks: perfect but sensitive to tiny perturbations. Phy Rev Lett 99:113903
Chen H, Wu B-I, Zhang B, Kong JA (2007) Electromagnetic wave interactions with a metamaterial cloak. Phy Rev Lett 99:063903
Chen H, Chan CT (2008) Time delays and energy transport velocities in three dimensional ideal cloaking devices. J Appl Phys 104:033113
Leonhardt U, Tyc T (2009) Broadband invisibility by non-Euclidean cloaking. Science 323:110–112
Kwon D-H, Werner DH (2008) Two-dimensional eccentric elliptic electromagnetic cloaks. Appl Phys Lett 92:013503
Nicolet A, Zolla F, Guenneau S (2008) Finite-element analysis of cylindrical invisibility cloaks of elliptical cross section. IEEE Trans Magn 44:1150–1153
Rahm M, Schurig D, Roberts DA, Cummer SA, Smith DR, Pendry JB (2008) Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations. Photon Nanostruct Fundam Appl 6:87–95
Zhang J, Luo Y, Chen H, Wu B-I (2008) Cloak of arbitrary shape. J Opt Soc Amer B 25:1776–1779
Wu Q, Zhang K, Meng F, Li L (2008) Material parameters characterization for arbitrary N-sided regular polygonal invisible cloak. J Phys D 42:035408
Kwon D-H, Werner DH (2008) Two-dimensional electromagnetic cloak having a uniform thickness for elliptic cylindrical regions. Appl Phys Lett 92:113502
Nicolet A, Zolla F, Guenneau S (2008) Electromagnetic analysis of cylindrical cloaks of an arbitrary cross section. Opt Lett 33:1584–1586
Li C, Yao K, Li F (2008) Two-dimensional electromagnetic cloaks with non-conformal inner and outer boundaries. Opt Express 16:19366–19374
Rahm M, Cummer SA, Schurig D, Pendry JB, Smith DR (2008) Optical design of reflectionless complex media by finite embedded coordinate transformations. Phys Rev Lett 100:063903
Kwon D-H, Werner DH (2008) Transformation optical designs for wave collimators, flat lenses and right-angle bends. New J Phys 10:115023
Donderici B, Teixeira FL (2008) Metamaterial blueprints for reflectionless waveguide bends. IEEE Microw Wireless Comp Lett 18:233–235
Huangfu J, Xi S, Kong F, Zhang J, Chen H, Wang D, Wu B-I, Ran L, Kong JA (2008) Application of coordinate transformation in bent waveguides. J Appl Phys 104:014502
Rahm M, Roberts DA, Pendry JB, Smith DR (2008) Transformation-optical design of adaptive beam bends and beam expanders. Opt Express 16:11555–11567
Emiroglu CD, Kwon D-H (2010) Impedance-matched three-dimensional beam expander and compressor designs via transformation optics. J Appl Phys 107:084502
Jiang WX, Cui TJ, Ma HF, Zhou XY, Cheng Q (2008) Cylindrical-to-plane-wave conversion via embedded optical transformation. Appl Phys Lett 92:261903
Zhang JJ, Luo Y, Xi S, Chen HS, Ran LX, Wu B-I, Kong JA (2008) Directive emission obtained by coordinate transformation. Prog Electromagn Res 81:437–446
Roberts DA, Kindtz N, Smith DR (2009) Optical lens compression via transformation optics. Opt Express 17:16535–16542
Pendry JB (2000) Negative refraction makes a perfect lens. Phys Rev Lett 85:3966–3969
Shelby RA, Smith DR, Schultz S (2001) Experimental verification of a negative index of refraction. Science 292:77–79
Valentine J, Zhang S, Zentgraf T, Ulin-Avila E, Genov DA, Bartal G, Zhang X (2008) Three-dimensional optical metamaterial with a negative refractive index. Nature 455:376–380
Yan M, Yan W, Qiu M (2008) Cylindrical superlens by a coordinate transformation. Phy Rev B 78:125113
Chen H, Luo X, Ma H, Chan CT (2008) The anti-cloak. Opt Express 16:14603–14608
Yang T, Chen H, Luo X, Ma H (2008) Superscatterer: enhancement of scattering with complementary media. Opt Express 16:18545–18550
Ng J, Chen H, Chan CT (2009) Metamaterial frequency-selective superabsorber. Opt Lett 34:644–646
Lai Y, Zheng H, Zhang Z-Q, Chan CT (2011) Manipulating sources using transformation optics with ‘folded geometry’. J Opt 13:024009
Leonhardt U, Philbin TG (2006) General relativity in electrical engineering. New J Phys 8:247
Lai Y, Chen H, Zhang Z-Q, Chan CT (2009) Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell. Phys Rev Lett 102:093901
Lai Y, Ng J, Chen H, Han D, Xiao J, Zhang Z-Q, Chan CT (2009) Illusion optics: the optical transformation of an object into another object. Phys Rev Lett 102:253902
Kwon D-H, Werner DH (2008) Restoration of antenna parameters in scattering environments using electromagnetic cloaking. Appl Phys Lett 92:113507
Popa B-I, Allen J, Cummer SA (2009) Conformal array design with transformation electromagnetics. Appl Phys Lett 94:244102
Kwon D-H (2009) Virtual circular array using material-embedded linear source distributions. Appl Phys Lett 95:173503
Tichit P-H, Burokur SN, de Lustrac A (2009) Ultradirective antenna via transformation optics. J Appl Phys 105:104912
Tichit P-H, Burokur SN, Germain D, de Lustrac A (2011) Design and experimental demonstration of a high-directive emission with transformation optics. Phy Rev B 83:115108
Kwon D-H (2010) Transformation electromagnetic design of an embedded monopole in a ground recess for conformal applications. IEEE Antennas Wireless Propag Lett 9:432–435
Li J, Pendry JB (2008) Hiding under the carpet: a new strategy for cloaking. Phys Rev Lett 101:203901
Liu R, Ji C, Mock JJ, Chin JY, Cui TJ, Smith DR (2009) Broadband ground-plane cloak. Science 323:366–369
Valentine J, Li J, Zentgraf T, Bartal G, Zhang X (2009) An optical cloak made of dielectrics. Nat Mater 8:568–571
Kundtz N, Smith DR (2009) Extreme-angle broadband metamaterial lens. Nat Mater 9:129–132
Demetriadou A, Hao Y (2011) Slim Luneburg lens for antenna applications. Opt Express 19:19925–19934
Mei ZL, Bai J, Cui TJ (2011) Experimental verification of a broadband planar focusing antenna based on transformation optics. New J Phys 13:063028
Garcia-Meca C, Martinez A, Leonhardt U (2011) Engineering antenna radiation patterns via quasi-conformal mappings. Opt Express 19:23743–23750
Kwon D-H, Werner DH (2010) Transformation electromagnetics: an overview of the theory and applications. IEEE Antennas Propag Mag 52:24–46
Chen H, Chan CT, Sheng P (2010) Transformation optics and metamaterials. Nat Mater 9:387–396
Kuntz N, Smith DR, Pendry JB (2011) Electromagnetic design with transformation optics. Proc IEEE 99:1622–1633
Milton GW, Briane M, Willis JR (2006) On cloaking for elasticity and physical equations with a transformation invariant form. New J Phys 8:248
Gabrielli LH, Cardenas J, Poitras CB, Lipson M (2009) Silicon nanostructure cloak operating at optical frequencies. Nat Photon 3:461–463
Lee J, Blair J, Tamma V, Wu Q, Rhee S, Summers C, Park W (2009) Direct visualization of optical frequency invisibility cloak based on silicon nanorod array. Opt Express 17:12922–12928
Ma HF, Cui TJ (2010) Three-dimensional broadband ground-plane cloak made of metamaterials. Nat Commun 1:1–6
Ergin T, Stenger N, Brenner P, Pendry JB, Wegener M (2010) Three-dimensional invisibility cloak at optical wavelengths. Science 328:337–339
Ma HF, Cui TJ (2010) Three-dimensional broadband and broad-angle transformation-optics lens. Nat Commun 1:124
Kundtz NB, Smith DR, Urzhumov Y, Landy NI (2010) Enhancing imaging systems using transformation optics. Opt Express 18:21238–21251
Tang W, Argyropoulos C, Kallos E, Song W, Hao Y (2010) Discrete coordinate transformation for designing all-dielectric flat antennas. IEEE Trans Antennas Propag 58:3795–3804
Yang R, Tang W, Hao Y (2011) A broadband zone plate lens from transformation optics. Opt Express 19:12348–12355
Zentgraf T, Valentine J, Tapia N, Li J, Zhang X (2010) An optical “Janus” device for integrated photonics. Adv Mater 22:2561–2564
Hunt J, Tyler T, Dhar S, Tsai Y-J, Bowen P, Larouche S, Jokerst NM, Smith DR (2012) Planar, flattened Luneburg lens at infrared wavelengths. Opt Express 20:1706–1713
Bao D, Rajab KZ, Tang W, Hao Y (2012) Experimental demonstration of broadband transmission through subwavelength aperture. Appl Phys Lett 97:134105
Yang R, Tang W, Hao Y, Youngs I (2011) A coordinate transformation-based broadband flat lens via microstrip array. IEEE Antennas Wireless Propag Lett 10:99–102
Mei ZL, Bai J, Cui TJ (2010) Illusion devices with quasi-conformal mapping. J Electromagn Waves Appl 24:2561–2573
Mastin CW, Thompson JF (1984) Quasiconformal mappings and grid generation. SIAM J Sci Stat Comp 5:305–310
Ives DC, Zacharias RM (1989) Conformal mapping and orthogonal grid generation. J Propul Power 5:327–333
Thompson JF, Soni BK, Weatherill NP (1999) Handbook of grid generation. CRC Press, Boca Raton
Chang Z, Zhou X, Hu J, Hu G (2012) Design method for quasi-isotropic transformation materials based on inverse Laplace’s equation with sliding boundaries. Opt Express 18:6089–6096
Turpin JP, Massoud AT, Jiang ZH, Werner PL, Werner DH (2010) Conformal mappings to achieve simple material parameters for transformation optics devices. Opt Express 18:244–252
Schmiele M, Varma VS, Rockstuhl C, Lederer F (2010) Designing optical elements from isotropic materials by using transformation optics. Phys Rev A 81:033837
Tang L, Yin J, Yuan G, Du J, Gao H, Dong X, Lu Y, Du C (2011) General conformal transformation method based on Schwarz-Christoffel approach. Opt Express 19:15119–15126
Ma YG, Wang N, Ong CK (2010) Application of inverse, strict conformal transformation to design waveguide devices. J Opt Soc Am A: 27:968–972
Landy NI, Padilla WJ (2009) Guiding light with conformal transformations. Opt Express 17:14872–14879
Cummer SA, Popa B-I, Schurig D, Smith DR, Pendry JB (2006) Full-wave simulations of electromagnetic cloaking structures. Phys Rev E 74:036621
Haupt RL, Werner DL (2007) Genetic algorithms in electromagnetics. Wiley, Hoboken, NJ
Chen H, Chan CT (2007) Transformation media that rotate electromagnetic fields. Appl Phys Lett 90:241105
Kwon D-H, Werner DH (2008) Polarization splitter and polarization rotator designs based on transformation optics. Opt Express 16:18731–18738
Kwon D-H, Werner DH (2009) Flat focusing lens designs having minimized reflection based on coordinate transformation techniques. Opt Express 17:7807–7817
Xu X, Feng Y, Jiang T (2008) Electromagnetic beam modulation through transformation optical structures. New J Phys 10:115027
Cummer SA, Kundtz N, Popa B-I (2009) Electromagnetic surface and line sources under coordinate transformations. Phys Rev A 80:033820
Kwon D-H, Emiroglu CD (2012) Two-dimensional metamaterial designs for line-source radiation from a virtual location. In: Proceedings of the 6th European conference on antennas and propagation, Prague, 26–30 March 2012, pp 1706–1710
Pendry JB, Holden AJ, Robbins DJ, Stewart WJ (1999) Magnetism from condcutors and enhanced nonlinear phenomena. IEEE Trans Microw Theory Tech 47:2075–2084
Smith DR, Schultz S, Markos P, Soukoulis CM (2002) Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients. Phys Rev B 65:195104
Schurig D, Mock JJ, Smith DR (2006) Elecric-field-coupled resonators for negative permittivity metamaterials. Appl Phys Lett 88:041109
Lifante G (2003) Integrated photonics: fundamentals. Wiley, Chichester
Pollock CR, Lipson M (2003) Integrated photonics. Kluwer Academic Publishers, Norwell
Wu Q, Turpin JP, Werner DH (2012) Integrated photonic systems based on transformation optics enabled gradient index devices. Light Sci Appl 1:e38
Tichit P-H, Burokur SN, de Lustrac A (2010) Waveguide taper engineering using coordinate transformation technology. Opt Express 18:767–772
Johnson SG, Manolatou C, Fan S, Villeneuve PR, Joannopoulos JD, Haus HA (1998) Elimination of cross talk in waveguide intersections. Opt Lett 23:1855–1857
Bogaerts W, Dumon P, Thourhout D, Baets R (2007) Low-loss, low cross-talk crossings for silicon-on-insulator nanophotonic waveguides. Opt Lett 32:2801–2803
Acknowledgments
This work was partially supported by the NSF MRSEC program under grant number DMR-0820404. Kwon acknowledges the support by the ECE Department of UMass Amherst for this work.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer-Verlag London
About this chapter
Cite this chapter
Kwon, DH., Wu, Q., Werner, D.H. (2014). Transformation Electromagnetics for Cloaking, Lensing, and Radiation Applications. In: Werner, D., Kwon, DH. (eds) Transformation Electromagnetics and Metamaterials. Springer, London. https://doi.org/10.1007/978-1-4471-4996-5_2
Download citation
DOI: https://doi.org/10.1007/978-1-4471-4996-5_2
Published:
Publisher Name: Springer, London
Print ISBN: 978-1-4471-4995-8
Online ISBN: 978-1-4471-4996-5
eBook Packages: EngineeringEngineering (R0)