Vol. 149

Front:[PDF file] Back:[PDF file]
Latest Volume
All Volumes
All Issues
2014-11-10

Transformation Optics and Applications in Microwave Frequencies (Invited Paper)

By Wei Xiang Jiang, Wen Xuan Tang, and Tie-Jun Cui
Progress In Electromagnetics Research, Vol. 149, 251-273, 2014
doi:10.2528/PIER14102506

Abstract

Modern electrical and communication technologies benefit from classical electrodynamics and electric circuits, both of which are based on the Maxwell's equations. Using the property of metric invariance in Maxwell's Equations, transformation optics has been proposed and achieves a rapid progress in the past decade. Transformation optics is a method for the conceptual design of complex electromagnetic media, offering opportunities for the control of electromagnetic waves. In this paper, we introduce the general theory of transformation optics and discuss the recent development on the transformation devices in the microwave band, such as non-singular invisibility cloak and its realization in dc circuit, three-dimensional ground-plane cloaks, flattened Luneburg lens, high-performance antennas, and high-resolution imaging lens. Some of the transformation-optics-based devices are expected to have further impact on the microwave engineering applications.

Citation


Wei Xiang Jiang, Wen Xuan Tang, and Tie-Jun Cui, "Transformation Optics and Applications in Microwave Frequencies (Invited Paper)," Progress In Electromagnetics Research, Vol. 149, 251-273, 2014.
doi:10.2528/PIER14102506
http://jpier.org/PIER/pier.php?paper=14102506

References


    1. Maxwell, J. C., "A dynamical theory of the electromagnetic field," Philosophical Transactions of the Royal Society of London, Vol. 155, 459-512, 1865.
    doi:10.1098/rstl.1865.0008

    2. Pendry, J. B., D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science, Vol. 312, 1780, 2006.
    doi:10.1126/science.1125907

    3. Pendry, J. B., "Perfect cylindrical lenses," Opt. Express, Vol. 11, 755, 2003.
    doi:10.1364/OE.11.000755

    4. Yan, M., W. Yan, and M. Qiu, "Cylindrical superlens by a coordinate transformation," Phys. Rev. B, Vol. 78, 125113, 2008.
    doi:10.1103/PhysRevB.78.125113

    5. Kundtz, N. and D. R. Smith, "Extreme-angle broadband metamaterial lens," Nat. Mat., Vol. 9, 129-132, 2010.
    doi:10.1038/nmat2610

    6. Ma, H. F. and T. J. Cui, "Three-dimensional broadband and broad-angle transformation-optics lens," Nat. Comm., Vol. 1, 124, 2010.
    doi:10.1038/ncomms1126

    7. Leonhardt, U. and T. G. Philbin, "General relativity in electrical engineering," New J. Phys., Vol. 8, 2006.
    doi:10.1088/1367-2630/8/8/124

    8. Leonhardt, U. and T. G. Philbin, "Transformation optics and the geometry of light," Prog. Opt., Vol. 53, 69-152, 2009.
    doi:10.1016/S0079-6638(08)00202-3

    9. Schurig, D., J. B. Pendry, and D. R. Smith, "Calculation of material properties and ray tracing in transformation media," Opt. Express, Vol. 14, No. 9704, 2006.

    10. Leonhardt, U., "Optical conformal mapping," Science, Vol. 312, 1777, 2006.
    doi:10.1126/science.1126493

    11. Cummer, S. A., B.-I. Popa, D. Schurig, D. R. Smith, and J. B. Pendry, "Full-wave simulations of electromagnetic cloaking structures," Phys. Rev. E, Vol. 74, 036621, 2006.
    doi:10.1103/PhysRevE.74.036621

    12. Schurig, D., J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science, Vol. 314, 977, 2006.
    doi:10.1126/science.1133628

    13. Cai, W., U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Optical cloaking with metamaterials," Nat. Photon., Vol. 1, 224, 2007.
    doi:10.1038/nphoton.2007.28

    14. Chen, H., B.-I. Wu, B. Zhang, and J. A. Kong, "Electromagnetic wave interactions with a metamaterial cloak," Phys. Rev. Lett., Vol. 99, 063903, 2007.
    doi:10.1103/PhysRevLett.99.063903

    15. Ruan, Z., M. Yan, C. W. Neff, and M. Qiu, "Ideal cylindrical cloak: Perfect but sensitive to tiny perturbations," Phys. Rev. Lett., Vol. 99, 113903, 2007.
    doi:10.1103/PhysRevLett.99.113903

    16. Yan, M., Z. Ruan, and M. Qiu, "Cylindrical invisibility cloak with simplified material parameters is inherently visible," Phys. Rev. Lett., Vol. 99, 233901, 2007.
    doi:10.1103/PhysRevLett.99.233901

    17. Chen, H. and C. T. Chan, "Transformation media that rotate electromagnetic fields," Appl. Phys. Lett, Vol. 90, 241105, 2007.
    doi:10.1063/1.2748302

    18. Chen, H., B. Hou, S. Chen, X. Ao, W. Wen, and C. T. Chan, "Design and experimental realization of a broadband transformation media field rotator at microwave frequencies," Phys. Rev. Lett., Vol. 102, 183903, 2009.
    doi:10.1103/PhysRevLett.102.183903

    19. Rahm, M., D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, "Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations," Photo. Nano. Fund. Appl., Vol. 6, 87, 2008.
    doi:10.1016/j.photonics.2007.07.013

    20. Jiang, W. X., T. J. Cui, Q. Cheng, J. Y. Chin, X. M. Yang, R. Liu, and D. R. Smith, "Design of arbitrarily shaped concentrators based on conformally optical transformation of nonuniform rational B-spline surfaces," Appl. Phys. Lett., Vol. 92, 264101, 2008.
    doi:10.1063/1.2951485

    21. Kong, F., B.-I. Wu, J. A. Kong, J. Huangfu, S. Xi, and H. Chen, "Planar focusing antenna design by using coordinate transformation technology," Appl. Phys. Lett., Vol. 91, 253509, 2007.
    doi:10.1063/1.2826283

    22. Schurig, D., J. B. Pendry, and D. R. Smith, "Transformation-designed optical elements," Opt. Express, Vol. 15, 14772, 2007.
    doi:10.1364/OE.15.014772

    23. Kwon, D.-H. and D. H. Werner, "Transformation optical designs for wave collimators, flat lenses and right-angle bends," New J. Phys., Vol. 10, 115023, 2008.
    doi:10.1088/1367-2630/10/11/115023

    24. Rahm, M., S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, "Optical design of reflectionless complex media by finite embedded coordinate transformations," Phys. Rev. Lett., Vol. 100, 063903, 2008.
    doi:10.1103/PhysRevLett.100.063903

    25. Moon, P. and D. E. Spencer, Field Thoery Handbook, Springer-Verlag, Berlin, 1961.
    doi:10.1007/978-3-642-53060-9

    26. Li, J. and J. B. Pendry, "Hiding under the carpet: A new strategy for cloaking," Phys. Rev. Lett., Vol. 101, 203901, 2008.
    doi:10.1103/PhysRevLett.101.203901

    27. Liu, R., C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, "Broadband ground-plane cloak," Science, Vol. 323, 366, 2009.
    doi:10.1126/science.1166949

    28. Jiang, W. X., T. J. Cui, X. M. Yang, Q. Cheng, R. Liu, and D. R. Smith, "Invisibility cloak without singularity," Appl. Phys. Lett., Vol. 93, 194102, 2008.
    doi:10.1063/1.3026532

    29. Yang, F., Z. L. Mei, T. Y. Jin, and T. J. Cui, "DC electric invisibility cloak," Phys. Rev. Lett., Vol. 109, 053902, 2012.
    doi:10.1103/PhysRevLett.109.053902

    30. Jiang, W. X., C. Y. Luo, Z. L. Mei, and T. J. Cui, "An ultrathin but nearly perfect direct current electric cloak," Appl. Phys. Lett., Vol. 102, No. 014102, 2013.

    31. Wang, W., L. Lin, J. Ma, C. Wang, J. Cui, and C. Du, "Electromagnetic concentrators with reduced material parameters based on coordinate transformation," Opt. Express, Vol. 16, 11431, 2008.
    doi:10.1364/OE.16.011431

    32. Piegl, L. and W. Tiller, The NURBS Book, 2nd Edition, Springer-Verlag, New York, 1996.

    33. Luo, Y., H. Chen, J. Zhang, L. Ran, and J. Kong, "Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations," Phys. Rev. B, Vol. 77, 125127, 2008.
    doi:10.1103/PhysRevB.77.125127

    34. Jiang, W. X., C. Y. Luo, H. F. Ma, Z. L. Mei, and T. J. Cui, "Enhancement of current density by dc electric concentrator," Scientific Reports, Vol. 2, 956, 2012.

    35. Ma, H., S. Qu, Z. Xu, and J. Wang, "Wave-shape-keeping media," Opt. Lett., Vol. 34, 127-129, 2009.
    doi:10.1364/OL.34.000127

    36. Kraus, J. D. and R. J. Marhefka, Antennas for All Applications, 3rd Edition, McGraw-Hill, New York, 2002.

    37. Jiang, W. X., T. J. Cui, H. F. Ma, X. Y. Zhou, and Q. Cheng, "Cylindrical-to-plane-wave conversion via embedded optical transformation," Appl. Phys. Lett., Vol. 92, 261903, 2008.
    doi:10.1063/1.2953447

    38. Jiang, W. X., T. J. Cui, H. F. Ma, X. M. Yang, and Q. Cheng, "Layered high-gain lens antennas via discrete optical transformation," Appl. Phys. Lett., Vol. 93, 221906, 2008.
    doi:10.1063/1.3040307

    39. Zhang, J. J., Y. Luo, S. Xi, H. Chen, L.-X. Ran, B.-I. Wu, and J. A. Kong, "Directive emission obtained by coordinate transformation," Progress In Electromagnetics Research, Vol. 81, 437-446, 2008.
    doi:10.2528/PIER08011002

    40. Kundtz, N., D. A. Roberts, J. Allen, S. Cummer, and D. R. Smith, "Optical source transformations," Opt. Express, Vol. 16, 21215, 2008.
    doi:10.1364/OE.16.021215

    41. Zhang, J., Y. Luo, H. Chen, and B.-I. Wu, "Manipulating the directivity of antennas with metamaterial," Opt. Express, Vol. 16, 10962, 2008.
    doi:10.1364/OE.16.010962

    42. Ma, H., S. Qu, Z. Xu, and J. Wang, "General method for designing wave shape transformers," Opt. Express, Vol. 16, 22072-22082, 2008.
    doi:10.1364/OE.16.022072

    43. Jiang, Z. H., M. D. Gregory, and D. H. Werner, "Experimental demonstration of a broadband transformation optics lens for highly directive multibeam emission," Phys. Rev. B, Vol. 84, 165111, 2009.

    44. Gabrielli, L. H., J. Cardenas, C. B. Poitras, and M. Lipson, "Silicon nanostructure cloak operating at optical frequencies," Nat. Photon., Vol. 3, 461, 2009.
    doi:10.1038/nphoton.2009.117

    45. Valentine, J., J. Li, T. Zentgraf, G. Bartal, and X. Zhang, "An optical cloak made of dielectrics," Nat. Materials, Vol. 8, 568, 2009.
    doi:10.1038/nmat2461

    46. Ma, H. F., W. X. Jiang, X. M. Yang, X. Y. Zhou, and T. J. Cui, "Compact-sized and broadband carpet cloak and free-space cloak," Opt. Express, Vol. 17, 19947, 2009.
    doi:10.1364/OE.17.019947

    47. Ma, H. F. and T. J. Cui, "Three-dimensional broadband ground-plane cloak made of metamaterials," Nat. Comm., Vol. 1, 21, 2010.

    48. Chen, X., H. F. Ma, X. Y. Zou, W. X. Jiang, and T. J. Cui, "Three-dimensional broadband and high-directivity lens antenna made of metamaterials," J. Appl. Phys., Vol. 110, 044904, 2011.
    doi:10.1063/1.3622596

    49. Born, M. and E. Wolf, Principles of Optics, Cambridge University Press, Cambridge , 1999.
    doi:10.1017/CBO9781139644181

    50. Pendry, J. B., "Negative refraction makes a perfect lens," Phys. Rev. Lett., Vol. 85, 3966, 2000.
    doi:10.1103/PhysRevLett.85.3966

    51. Veselago, V. G., "The electrodynamics of substances with simultaneously negative values of ε and μ," Sov. Phys. Usp., Vol. 10, 509, 1968.
    doi:10.1070/PU1968v010n04ABEH003699

    52. Kildishev, A. V. and V. M. Shalaev, "Engineering space for light via transformation optics," Opt. Lett., Vol. 33, 43, 2008.
    doi:10.1364/OL.33.000043

    53. Tsang, M. and D. Psaltis, "Magnifying perfect lens and superlens design by coordinate transformation," Phys. Rev. B, Vol. 77, 035122, 2008.
    doi:10.1103/PhysRevB.77.035122

    54. Fang, N., H. Lee, C. Sun, and X. Zhang, "Sub-diffraction-limited optical imaging with a silver superlens," Science, Vol. 308, 534, 2005.
    doi:10.1126/science.1108759

    55. Taubner, T., D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, "Near-field microscopy through a SiC superlens," Science, Vol. 313, 1595, 2006.
    doi:10.1126/science.1131025

    56. Zhang, X. and Z. W. Liu, "Superlenses to overcome the diffraction limit," Nat. Mater., Vol. 7, 435, 2008.
    doi:10.1038/nmat2141

    57. Liu, Z. W., S. Durant, H. Lee, Y. Pikus, N. Fang, Y. Xiong, C. Sun, and X. Zhang, "Far field optical superlens," Nano Lett., Vol. 7, 403, 2007.
    doi:10.1021/nl062635n

    58. Jacob, Z., L. V. Alekseyev, and E. Narimanov, "Optical hyperlens: Far-field imaging beyond the diffraction limit," Opt. Express, Vol. 14, 8247, 2006.
    doi:10.1364/OE.14.008247

    59. Salandrino, A. and N. Engheta, "Far-field subdiffraction optical microscopy using metamaterial crystals: Theory and simulations," Phys. Rev. B, Vol. 74, 075103, 2006.
    doi:10.1103/PhysRevB.74.075103

    60. Smolyaninov, I. I., Y. J. Huang, and C. C. Davis, "Magnifying superlens in the visible frequency range," Science, Vol. 315, 1699, 2007.
    doi:10.1126/science.1138746

    61. Liu, Z. W., H. Lee, Y. Xiong, C. Sun, and X. Zhang, "Optical hyperlens magnifying sub-diffractionlimited objects," Science, Vol. 315, 1686, 2007.
    doi:10.1126/science.1137368

    62. Rho, J., Z. Ye, Y. Xiong, X. Yin, Z. Liu, H. Choi, G. Bartal, and X. Zhang, "Spherical hyperlens for two-dimensional sub-diffractional imaging at visible frequencies," Nat. Commun., Vol. 1, 143, 2010.
    doi:10.1038/ncomms1148

    63. Zhang, B. L. and G. Barbastathis, "Dielectric metamaterial magnifiercreating a virtual color image withfar-field subwavelength information," Opt. Express, Vol. 18, 11216, 2010.
    doi:10.1364/OE.18.011216

    64. Jiang, W. X., C.-W. Qiu, T. C. Han, Q. Cheng, H. F. Ma, S. Zhang, and T. J. Cui, "Broadband all-dielectric magnifying lens for far-field high-resolution imaging," Adv. Mater., Vol. 25, 6963-6968, 2013.
    doi:10.1002/adma.201303657

    65. Mansfield, S. M. and G. S. Kino, "Solid immersion microscope," Appl. Phys. Lett., Vol. 57, 2615, 1990.
    doi:10.1063/1.103828