Skip to main content

FDTD Modelling of Transformation Electromagnetics Based Devices

  • Chapter
  • First Online:
Computational Electromagnetics

Abstract

Transformation Electromagnetics (TE), often referred to as Transformation Optics (TO), is a subject area of much interest worldwide, along with the topic of metamaterials. The concept was introduced through a demonstration of invisible cloaks, comprised of a shell of metamaterials engineered to route electromagnetic waves around an object, so as to render it “invisible”. Although the performance of an invisible cloak does not always live up to its expectations, the potential of the underlying TE approach has a much wider applicability than cloaking alone, covering important areas such as communications, energy transfer, sensors and security. In this chapter, the fundamental design issues pertaining to TE-based devices are examined from the perspective of numerical modelling. The FDTD technique is employed to illustrate the key concepts and to identify the challenges encountered in implementing the TE-based designs. Current and future trends of FDTD modelling related to this topic are discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Veselago VG (1968) The electrodynamics of substances with simultaneously negative values of ε and μ. Sov Phys Usp 10:509–514

    Article  Google Scholar 

  2. Tretyakov S (2005) Research on negative refraction and backward-wave media: a historical perspective. In: Negative refraction: revisiting electromagnetics from microwave to optics, EPFL Latsis symposium, Lausanne, pp 30–35

    Google Scholar 

  3. Pendry JB, Holden AJ, Stewart WJ, Youngs I (1996) Extremely low frequency plasmons in metallic mesostructures. Phys Rev Lett 76(25):4773–4776

    Article  Google Scholar 

  4. Pendry J, Holden A, Robbins D, Stewart W (1999) Magnetism from conductors and enhanced nonlinear phenomena. IEEE Trans Microw Theory Tech 47(11):2075–2084

    Article  Google Scholar 

  5. Smith D, Padilla W, Vier D, Nemat-Nasser S, Schultz S (2000) Composite medium with simultaneously negative permeability and permittivity. Phys Rev Lett 84(18):4184–4187

    Article  Google Scholar 

  6. Pendry J (2000) Negative refraction makes a perfect lens. Phys Rev Lett 85(18):3966–3969

    Article  Google Scholar 

  7. Ziolkowski RW (2001) Superluminal transmission of information through an electromagnetic metamaterial. Phys Rev E 63(4):046604

    Article  Google Scholar 

  8. Smith DR, Pendry JB, Wiltshire MCK (2004) Metamaterials and negative refractive index. Science 305:788–792

    Article  Google Scholar 

  9. Shelby RA, Smith DR, Schultz S (2001) Experimental verification of a negative index of refraction. Science 292:77–79

    Article  Google Scholar 

  10. Greegor R, Parazzoli C, Li K, Tanielian M (2003) Origin of dissipative losses in negative index of refraction materials. Appl Phys Lett 82(14):2356

    Article  Google Scholar 

  11. Pendry J, Ramakrishna S (2003) Focusing light using negative refraction. J Phys Cond Matter 15:6345

    Article  Google Scholar 

  12. Grbic A, Eleftheriades G (2004) Overcoming the diffraction limit with a planar left-handed transmission-line lens. Phys Rev Lett 92(11):117403

    Article  Google Scholar 

  13. Baena J, Jelinek L, Marqu´es R, Medina F (2005) Near-perfect tunneling and amplification of evanescent electromagnetic waves in a waveguide filled by a metamaterial: theory and experiments. Phys Rev B 72(7):075116

    Article  Google Scholar 

  14. Leonhardt U (2006) Optical conformal mapping. Science 312:1777–1780

    Article  MathSciNet  MATH  Google Scholar 

  15. Pendry JB, Schurig D, Smith DR (2006) Controlling electromagnetic fields. Science 312:1780–1782

    Article  MathSciNet  Google Scholar 

  16. 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

    Article  Google Scholar 

  17. Schurig D, Pendry JB, Smith DR (2006) Calculation of material properties and ray tracing in transformation media. Opt Express 14(21):9794–9804

    Article  Google Scholar 

  18. Jiang W, Chin J, Li Z, Cheng Q, Liu R, Cui T (2008) Analytical design of conformally invisible cloaks for arbitrarily shaped objects. Phys Rev E 77(6):66607

    Article  Google Scholar 

  19. Cai W, Chettiar U, Kildishev A, Shalaev V (2007) Optical cloaking with metamaterials. Nat Photon 1(4):224–227

    Article  Google Scholar 

  20. Alu A, Engheta N (2008) Multifrequency optical invisibility cloak with layered plasmonic shells. Phys Rev Lett 100(11):113901

    Article  Google Scholar 

  21. Gaillot D, Croënne C, Lippens D et al (2008) An all-dielectric route for terahertz cloaking. Opt Express 16(6):3986–3992

    Article  Google Scholar 

  22. Ward AJ, Pendry JB (1996) Refraction and geometry in Maxwell’s equations. J Mod Opt 43(4):773–793

    Article  MathSciNet  Google Scholar 

  23. Chen H, Hou B, Chen S, Ao X, Wen W, Chan C (2009) Design and experimental realization of a broadband transformation media field rotator at microwave frequencies. Phys Rev Lett 102(18):183903

    Article  Google Scholar 

  24. Luo Y, Chen H, Zhang J, Ran L, Kong J (2008) Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations. Phys Rev B 77(12):125127

    Article  MATH  Google Scholar 

  25. Rahm M, Schurig D, Roberts D, Cummer S, Smith D, Pendry J (2008) Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations. Photon Nanostruct Fundam Appl 6(1):87–95

    Article  Google Scholar 

  26. Yaghjian A, Maci S (2008) Alternative derivation of electromagnetic cloaks and concentrators. New J Phys 10:115022

    Article  Google Scholar 

  27. Jiang W, Cui T, Cheng Q, Chin J, Yang X, Liu R, Smith D (2008) Design of arbitrarily shaped concentrators based on conformally optical transformation of nonuniform rational B-spline surfaces. Appl Phys Lett 92:264101

    Article  Google Scholar 

  28. Alu A, Engheta N (2009) Cloaking a sensor. Phys Rev Lett 102(23):233901

    Article  Google Scholar 

  29. Narimanov E, Kildishev A (2009) Optical black hole: broadband omnidirectional light absorber. Appl Phys Lett 95(4):041106

    Article  Google Scholar 

  30. Cheng Q, Cui T, Jiang W, Cai B (2010) An omnidirectional electromagnetic absorber made of metamaterials. New J Phys 12:063006

    Article  Google Scholar 

  31. Kong F, Wu B, Kong J, Huangfu J, Xi S, Chen H (2007) Planar focusing antenna design by using coordinate transformation technology. Appl Phys Lett 91:253509

    Article  Google Scholar 

  32. Kundtz N, Smith D (2010) Extreme-angle broadband metamaterial lens. Nat Mater 9:129–132

    Article  Google Scholar 

  33. Li J, Pendry J (2008) Hiding under the carpet: a new strategy for cloaking. Phys Rev Lett 101(20):203901

    Article  Google Scholar 

  34. Liu R, Ji C, Mock JJ, Chin JY, Cui TJ, Smith DR (2009) Broadband ground-plane cloak. Science 323(5912):366–369

    Article  Google Scholar 

  35. Ma H, Jiang W, Yang X, Zhou X, Cui T (2009) Compact-sized and broadband carpet cloak and free-space cloak. Opt Express 17(22):19947–19959

    Article  Google Scholar 

  36. Valentine J, Li J, Zentgraf T, Bartal G, Zhang X (2009) An optical cloak made of dielectrics. Nat Mater 8(7):568–571

    Article  Google Scholar 

  37. Bao D, Rajab KZ, Hao Y, Kallos E, Tang W, Argyropoulos C, Piao Y, Yang S (2011) All-dielectric invisibility cloak made of BaTiO3-loaded polyurethane foam. New J Phys 13:103023

    Article  Google Scholar 

  38. Taflove A, Hagness SC (2005) Computational electrodynamics: the finite-difference time-domain method, 3rd edn. Artech House, Boston

    Google Scholar 

  39. Hao Y, Mittra R (2009) FDTD modelling of metamaterials: theory and applications. Artech House, Boston

    Google Scholar 

  40. Yee K (1966) Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media. IEEE Trans Antennas Propag 14(3):302–307

    MATH  Google Scholar 

  41. Feise M, Schneider J, Bevelacqua P (2004) Finite-difference and pseudospectral time-domain methods applied to backward-wave metamaterials. IEEE Trans Antennas Propag 52(11):2955–2962

    Article  Google Scholar 

  42. Panoiu N, Osgood R Jr (2003) Influence of the dispersive properties of metals on the transmission characteristics of left-handed materials. Phys Rev E 68(1):016611

    Article  Google Scholar 

  43. Lee J, Lee J, Kim H, Kang N, Jung H (2005) Effective medium approach of left-handed material using a dispersive FDTD method. IEEE Trans Magn 41(5):1484–1487

    Article  Google Scholar 

  44. Zhao Y, Argyropoulos C, Hao Y (2008) Full-wave finite-difference time-domain simulation of electromagnetic cloaking structures. Opt Express 16(9):6717–6730

    Article  Google Scholar 

  45. Argyropoulos C, Zhao Y, Hao Y (2009) A radially-dependent dispersive finite difference time-domain method for the evaluation of electromagnetic cloaks. IEEE Trans Antennas Propag 57(5):1432–1441

    Article  MathSciNet  Google Scholar 

  46. Leonhardt U, Philbin TG (2010) Geometry and light: the science of invisibility. Dover, Mineola, 288 pp

    Google Scholar 

  47. Dolin LS (1961) On a possibility of comparing three-dimensional electromagnetic systems with inhomogeneous filling. Izv Vyssh Uchebn Zaved Radiofiz 4:964–967

    Google Scholar 

  48. Post EG (1962) Formal structure of electromagnetics; general covariance and electromagnetics. Interscience, New York

    MATH  Google Scholar 

  49. Lax M, Nelson DF (1976) Maxwell equations in material form. Phys Rev B 13:1777

    Article  MathSciNet  Google Scholar 

  50. Cummer SA, Popa B-I, Schurig D, Smith DR, Pendry JB (2006) Fullwave simulations of electromagnetic cloaking structures. Phys Rev E 74:036621

    Article  Google Scholar 

  51. Kwon D-H, Werner DH (2008) Two-dimensional eccentric elliptic electromagnetic cloaks. Appl Phys Lett 92:013505

    Article  Google Scholar 

  52. Jiang W, Cui T, Yu G, Lin X, Cheng Q, Chin J (2008) Arbitrarily elliptical–cylindrical invisible cloaking. J Phys D: Appl Phys 41:199801

    Article  Google Scholar 

  53. Maci S (2010) A cloaking metamaterial based on an inhomogeneous linear field transformation. IEEE Trans Antennas Propag 58(4):1136–1143

    Article  MathSciNet  Google Scholar 

  54. CST 3D EM field simulation-CST computer simulation technology. http://www.cst.com

  55. HFSS 3D full-wave electromagnetic field simulation. http://www.ansoft.com/products/hf/hfss

  56. COMSOL Multiphysics modelling and simulation. http://www.comsol.com

  57. Jiang WX, Cui TJ (2010) Optical transformation theory. In: Cui TJ, Liu RP, Smith DR (eds) Metamaterials: theory, design, and applications. Springer, New York, pp 21–48, ch. 2

    Google Scholar 

  58. Berenger J (1994) A perfectly matched layer for the absorption of electromagnetic waves. J Comput Phys 114(2):185–200

    Google Scholar 

  59. Alu A, Engheta N (2005) Achieving transparency with plasmonic and metamaterial coatings. Phys Rev E 72:016623

    Article  Google Scholar 

  60. Milton GW, Nicorovici NP (2006) On the cloaking effects associated with anomalous localized resonance. Proc R Soc A 462:3027–3059

    Article  MathSciNet  MATH  Google Scholar 

  61. Garcia de Abajo FJ, Gomez-Santos G, Blanco LA, Borisov AG, Shabanov SV (2005) Tunneling mechanism of light transmission through metallic films. Phys Rev Lett 95:067403

    Article  Google Scholar 

  62. Cory H, Lee YJ, Hao Y, Parini CG (2007) Use of conjugate dielectric and metamaterial slabs as radomes. IET Microw Antenna Propag 1:137–143

    Article  Google Scholar 

  63. Zolla F, Guenneau S, Nicolet A, Pendry JB (2007) Electromagnetic analysis of cylindrical invisibility cloaks and the mirage effect. Opt Lett 32:1069–1071

    Article  Google Scholar 

  64. Yan M, Ruan Z, Qiu M (2007) Cylindrical invisibility cloak with simplified material parameters is inherently visible. Phys Rev Lett 99:233901

    Article  Google Scholar 

  65. Lin L, Wang W, Cui J, Du C, Luo X (2008) Design of electromagnetic refractor and phase transformer using coordinate transformation theory. Opt Express 16(10):6815–6821

    Article  Google Scholar 

  66. Zhao AP, Juntunen J, Raisanen AV (1998) Generalized material-independent PML absorbers for the FDTD simulation of electromagnetic waves in arbitrary anisotropic dielectric and magnetic media. IEEE Microw Guid Wave Lett 8:52–54

    Article  Google Scholar 

  67. Chen H, Chan CT (2007) Transformation media that rotate electromagnetic fields. Appl Phys Lett 90:241105

    Article  Google Scholar 

  68. Genov DA, Zhang S, Zhang X (2009) Mimicking celestial mechanics in metamaterials. Nat Phys 5(9):687–692

    Article  Google Scholar 

  69. Landy NI, Sajuyigbe S, Mock JJ, Smith DR, Padilla WJ (2008) Perfect metamaterialabsorber. Phys Rev Lett 100:207402

    Article  Google Scholar 

  70. Atwater HA, Polman A (2010) Plasmonics for improved photovoltaic devices. Nat Mater 9(3):205–213

    Article  Google Scholar 

  71. Schuller JA, Barnard ES, Cai W, Jun YC, White JS, Brongersma ML (2010) Plasmonics for extreme light concentration and manipulation. Nat Mater 9(3):193–204

    Article  Google Scholar 

  72. Kallos E, Argyropoulos C, Hao Y (2009) Ground-plane quasi-cloaking for free space. Phys Rev A 79(6):063825

    Article  Google Scholar 

  73. Demetriadou A, Hao Y (2011) Slim Luneburg lens for antenna applications. Opt Express 19(21):19925–19934

    Article  Google Scholar 

  74. Yang R, Tang W-X, Hao Y (2011) A broadband zone plate lens from transformation optics. Opt Express 19(13):12348–12355

    Article  Google Scholar 

  75. Yang R, Tang W-X, Hao Y, Youngs I (2011) A coordinate transformation based broadband flat lens via microstrip array. IEEE Antennas Wirel Propag Lett 10:99–102

    Article  Google Scholar 

  76. Yang R, Tang W-X, Hao Y (2011) Wideband beam-steerable flat reflectors via transformation optics. IEEE Antennas Wirel Propag Lett 10:1290–1294

    Article  Google Scholar 

  77. Tang W-X, Hao Y, Mittra R (2012) Design of a carpet cloak to conceal an antenna located underneath. IEEE Trans Antennas Propag 60(9):4444–4449

    Article  Google Scholar 

  78. Zhang XL, Song JF, Li XB, Sun HB (2012) FDTD study on the invisibility performance of two-dimensional cylindrical cloak with off-plane incidence. J Lightwave Technol 30(12):1835–1842

    Article  Google Scholar 

  79. Lee YY, Ahn D (2013) Dispersive full-wave finite-difference time-domain analysis of the bipolar cylindrical cloak based on the effective medium approach. J Opt Soc Am B Opt Phys 30(1):140–148

    Article  Google Scholar 

  80. Okada N, Cole JB (2012) Cylindrical invisibility cloak based on photonic crystal layers that permits communication with the outside. J Opt Soc Am B Opt Phys 29(12):3344–3348

    Article  Google Scholar 

  81. Hao Y, Railton CJ (1998) Analyzing electromagnetic structures with curved boundaries on Cartesian FDTD meshes. IEEE Trans Microw Theory Tech 46(1):82–88

    Article  Google Scholar 

  82. Zhao Y, Hao Y (2007) Finite-difference time-domain study of guided modes in nano-plasmonic waveguides. IEEE Trans Antennas Propag 55(11):3070–3077

    Article  Google Scholar 

  83. Zhao S, Wei GW (2004) High-order FDTD methods via derivative matching for Maxwell’s equations with material interface. J Comput Phys 200:60–103

    Article  MathSciNet  MATH  Google Scholar 

  84. Li JC, Huang YQ, Yang W (2012) Developing a time-domain finite-element method for modeling of electromagnetic cylindrical cloaks. J Comput Phys 231(7):2880–2891

    Article  MathSciNet  MATH  Google Scholar 

  85. Blanchard C, Porti J, Wu B-I, Morente JA, Salinas A, Kong JA (2008) Time domain simulation of electromagnetic cloaking structures with TLM method. Opt Express 16:6461–6470

    Article  Google Scholar 

  86. Shibayama J, Ando R, Yamauchi J, Nakano H (2011) Frequency-dependent 3-D LOD-FDTD method for the analysis of plasmonic devices. Photonics Technol Lett IEEE 23(15):1070–1072

    Article  Google Scholar 

  87. Shibayama J, Nomura A, Ando R, Yamauchi J, Nakano H (2010) Frequency-dependent LOD-FDTD method and its application to the analyses of plasmonic waveguide devices. IEEE J Quantum Electron 46(1):40–49

    Article  Google Scholar 

  88. Siushansian R, LoVetri J (1995) A comparison of numerical techniques for modeling electromagnetic dispersive media. IEEE Microw Guid Wave Lett 5(12):426–428

    Article  Google Scholar 

  89. Luebbers RJ, Hunsberger F (1992) FDTD for Nth-order dispersive media. IEEE Trans Antennas Propag 40(11):1297–1301

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yang Hao .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer Science+Business Media New York

About this chapter

Cite this chapter

Hao, Y., Argyropoulos, C., Tang, W.X. (2014). FDTD Modelling of Transformation Electromagnetics Based Devices. In: Mittra, R. (eds) Computational Electromagnetics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4382-7_13

Download citation

  • DOI: https://doi.org/10.1007/978-1-4614-4382-7_13

  • Published:

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4614-4381-0

  • Online ISBN: 978-1-4614-4382-7

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics