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2014-11-10
Transformation Optics and Applications in Microwave Frequencies (Invited Paper)
By
Progress In Electromagnetics Research, Vol. 149, 251-273, 2014
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 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://www.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