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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, 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
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        Google Scholar

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

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

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        Google Scholar

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

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        Google Scholar

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        Google Scholar

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        Google Scholar

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.        Google Scholar

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

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        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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.        Google Scholar

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        Google Scholar

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        Google Scholar

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.        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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.        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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

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        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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

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        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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