Transformation optics and metamaterials
Source abstract
Abstract
Underpinned by the advent of metamaterials, transformation optics offers great versatility for controlling electromagnetic waves to create materials with specially designed properties. Here we review the potential of transformation optics to create functionalities in which the optical properties can be designed almost at will. This approach can be used to engineer various optical illusion effects, such as the invisibility cloak.
Source: europepmc · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Metamaterials and Metasurfaces Applications · Advanced Antenna and Metasurface Technologies · Electromagnetic Scattering and Analysis
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (100+)
Show source-provided references
1. Leonhardt, U. Optical conformal mapping. Science 312, 1777–1780 (2006).10.1126/science.1126493 ↗
2. Pendry, J. B., Schurig, D. & Smith, D. R. Controlling electromagnetic fields. Science 312, 1780–1782 (2006).10.1126/science.1125907 ↗
3. Ramo, S., Whinnery, J. R. & Van Duzer, T. Fields and Waves in Communication Electronics 3rd edn, Ch. 7 (Wiley, 1994).
4. Post, E. G. Formal Structure of Electromagnetics: General Covariance and Electromagnetics (Interscience Publishers, 1962).
5. Lax, M. & Nelson, D. F. Maxwell equations in material form. Phys. Rev. B 13, 1777–1784 (1976).10.1103/PhysRevB.13.1777 ↗
6. Schurig, D., Pendry, J. B. & Smith, D. R. Calculation of material properties and ray tracing in transformation media. Opt. Express 14, 9794–9804 (2006).10.1364/OE.14.009794 ↗
7. Leonhardt, U. & Philbin, T. G. General relativity in electrical engineering. New J. Phys. 8, 247 (2006).10.1088/1367-2630/8/10/247 ↗
8. Milton, G. W., Briane, M. & Willis, J. R. On cloaking for elasticity and physical equations with a transformation invariant form. New J. Phys. 8, 248 (2006).10.1088/1367-2630/8/10/248 ↗
9. Shalaev, V. M. Transforming light. Science 322, 384–386 (2008).10.1126/science.1166079 ↗
10. Leonhardt, U. & Philbin, T. G. Transformation optics and the geometry of light. Prog. Opt. 53, 69–152 (2009).10.1016/S0079-6638(08)00202-3 ↗
11. Dolin, L. S. On a possibility of comparing three-dimensional electromagnetic systems with inhomogeneous filling. Izv. Vuz. Radiofiz. 4, 964–967 (1961).
12. Pendry, J. B. et al. Extremely low frequency plasmons in metallic mesostructures. Phys. Rev. Lett. 76, 4773–4776 (1996).10.1103/PhysRevLett.76.4773 ↗
13. Pendry, J. B. et al. Magnetism from conductors and enhanced nonlinear phenomena. IEEE Trans. Microwave Theory 47, 2075–2084 (1999).10.1109/22.798002 ↗
14. Shelby, R. A., Smith, D. R. & Schultz, S. Experimental verification of a negative index of refraction. Science 292, 77–79 (2001).10.1126/science.1058847 ↗
15. Smith, D. R., Pendry, J. B. & Wiltshire, M. C. K. Metamaterials and negative refractive index. Science 305, 788–792 (2004).10.1126/science.1096796 ↗
16. Soukoulis, C. M., Linden, S. & Wegener, M. Negative refractive index at optical wavelengths. Science 315, 47–49 (2007).10.1126/science.1136481 ↗
17. Lezec, H. J., Dionne, J. A. & Atwater, H. A. Negative refraction at visible frequencies. Science 316, 430–432 (2007).10.1126/science.1139266 ↗
18. Yao, J. et al. Optical negative refraction in bulk metamaterials of nanowires. Science 321, 930 (2008).10.1126/science.1157566 ↗
19. Valentine, J. et al. Three-dimensional optical metamaterial with a negative refractive index. Nature 455, 376–379 (2008).10.1038/nature07247 ↗
20. Kerker, M. Invisible bodies. J. Opt. Soc. Am. 65, 376–379 (1975).10.1364/JOSA.65.000376 ↗
21. Nicorovici, N. A., McPhedran, R. C. & Milton, G. W. Optical and dielectric properties of partially resonant composites. Phys. Rev. B 49, 8479–8482 (1994).10.1103/PhysRevB.49.8479 ↗
22. Milton, G. W. & Nicorovici, N-A. P. On the cloaking effects associated with anomalous localized resonance. Proc. R. Soc. Lon. Ser.-A 462, 3027–3059 (2006).
23. Alù, A. & Engheta, N. Achieving transparency with plasmonic and metamaterial coatings. Phys. Rev. E 72, 016623 (2005).10.1103/PhysRevE.72.016623 ↗
24. Greenleaf, A., Lassas, M. & Uhlmann, G. On non-uniqueness for Calderon's inverse problem. Math. Res. Lett. 10, 685–693 (2003).10.4310/MRL.2003.v10.n5.a11 ↗
25. Greenleaf, A., Lassas, M. & Uhlmann, G. Anisotropic conductivities that cannot be detected by EIT. Physiol. Meas. 24, 413–419 (2003).10.1088/0967-3334/24/2/353 ↗
26. Cummer, S. A. et al. Full-wave simulations of electromagnetic cloaking structures. Phys. Rev. E 74, 036621 (2006).10.1103/PhysRevE.74.036621 ↗
27. Schurig, D. et al. Metamaterial electromagnetic cloak at microwave frequencies. Science 314, 977–980 (2006).10.1126/science.1133628 ↗
28. Chen, H. S. et al. Electromagnetic wave interactions with a metamaterial cloak. Phys. Rev. Lett. 99, 063903 (2007).10.1103/PhysRevLett.99.063903 ↗
29. Ruan, Z. C. et al. Ideal cylindrical cloak: perfect but sensitive to tiny perturbations. Phys. Rev. Lett. 99, 113903 (2007).10.1103/PhysRevLett.99.113903 ↗
30. Yan, M., Ruan, Z. & Qiu, M. Cylindrical invisibility cloak with simplified material parameters is inherently visible. Phys. Rev. Lett. 99, 233901 (2007).10.1103/PhysRevLett.99.233901 ↗
31. Liang, Z. X. et al. The physical picture and the essential elements of the dynamical process for dispersive cloaking structures. Appl. Phys. Lett. 92, 131118 (2008).10.1063/1.2840703 ↗
32. Chen, H. Y. & Chan, C. T. Time delays and energy transport velocities in three dimensional ideal cloaking devices. J. Appl. Phys. 104, 033113 (2008).10.1063/1.2967815 ↗
33. Leonhardt, U. Notes on conformal invisibility devices. New J. Phys. 8, 118 (2006).10.1088/1367-2630/8/7/118 ↗
34. Cai, W. S. et al. Optical cloaking with metamaterials. Nature Photon. 1, 224–227 (2007).10.1038/nphoton.2007.28 ↗
35. Cai, W. S. et al. Nonmagnetic cloak with minimized scattering. Appl. Phys. Lett. 91, 111105 (2007).10.1063/1.2783266 ↗
36. Wood, B. & Pendry, J. B. Metamaterials at zero frequency. J. Phys. Condens. Matter 19, 076208 (2007).10.1088/0953-8984/19/7/076208 ↗
37. Magnus, F. et al. A d.c. magnetic metamaterial. Nature Mater. 7, 295–297 (2008).10.1038/nmat2126 ↗
38. Yan, W. et al. Coordinate transformations make perfect invisibility cloaks with arbitrary shape. New J. Phys. 10, 043040 (2008).10.1088/1367-2630/10/4/043040 ↗
39. Jiang, W. X. et al. Arbitrarily elliptical–cylindrical invisible cloaking. J. Phys. D 41, 085504 (2008).10.1088/0022-3727/41/8/085504 ↗
40. Kwon, D.-H. & Werner, D. H. Two-dimensional eccentric elliptic electromagnetic cloaks. Appl. Phys. Lett. 92, 013505 (2008).10.1063/1.2830698 ↗
41. Nicolet, A., Zolla, F. & Guenneau, S. Electromagnetic analysis of cylindrical cloaks of an arbitrary cross section. Opt. Lett. 33, 1584–1586 (2008).10.1364/OL.33.001584 ↗
42. Lai, Y. et al. Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell. Phys. Rev. Lett. 102, 093901 (2009).10.1103/PhysRevLett.102.093901 ↗
43. Philbin, T. Cloaking at a distance. Physics 2, 17 (2009).10.1103/Physics.2.17 ↗
44. Chen, H. Y. et al. Extending the bandwidth of electromagnetic cloaks. Phys. Rev. B 76, 241104 (2007).10.1103/PhysRevB.76.241104 ↗
45. Yaghjian, A. D. & Maci, S. Alternative derivation of electromagnetic cloaks and concentrators. New J. Phys. 10, 115022 (2008).10.1088/1367-2630/10/11/115022 ↗
46. Kildishev, A. V. et al. Transformation optics: Approaching broadband electromagnetic cloaking. New J. Phys. 10, 115029 (2008).10.1088/1367-2630/10/11/115029 ↗
47. Chen, H. Y. & Chan, C. T. Electromagnetic wave manipulation by layered systems using the transformation media concept. Phys. Rev. B 78, 054204 (2008).10.1103/PhysRevB.78.054204 ↗
48. Li, J. & Pendry, J. B. Hiding under the carpet: A new strategy for cloaking. Phys. Rev. Lett. 101, 203901 (2008).10.1103/PhysRevLett.101.203901 ↗
49. Liu, R. et al. Broadband ground-plane cloak. Science 323, 366–369 (2009).10.1126/science.1166949 ↗
50. Valentine, J. et al. An optical cloak made of dielectrics. Nature Mater. 8, 568–571 (2009).10.1038/nmat2461 ↗
51. Gabrielli, L. H. et al. Silicon nanostructure cloak operating at optical frequencies. Nature Photon. 3, 461–463 (2009).10.1038/nphoton.2009.117 ↗
52. Leonhardt, U. & Tyc, T. Broadband invisibility by non-Euclidean cloaking. Science 323, 110–112 (2009).10.1126/science.1166332 ↗
53. Greenleaf, A., Lassas, M. & Uhlmann, G. Electromagnetic wormholes and virtual magnetic monopoles from metamaterials. Phys. Rev. Lett. 99, 183901 (2007).10.1103/PhysRevLett.99.183901 ↗
54. Luo, X. D. et al. Conceal an entrance by means of superscatterer. Appl. Phys. Lett. 94, 223513 (2009).10.1063/1.3149694 ↗
55. Chen, H. Y. et al. A simple route to a tunable electromagnetic gateway. New J. Phys. 11, 083012 (2009).10.1088/1367-2630/11/8/083012 ↗
56. Leonhardt, U. & Piwnicki, P. Optics of nonuniformly moving media. Phys. Rev. A 60, 4301–4312 (1999).10.1103/PhysRevA.60.4301 ↗
57. Genov, D. A., Zhang, S. & Zhang, X. Mimicking celestial mechanics in metamaterials. Nature Phys. 5, 687–692 (2009).10.1038/nphys1338 ↗
58. Narimanov, E. E. & Kildishev, A. V. Optical black hole: Broadband omnidirectional light absorber. Appl. Phys. Lett. 95, 041106 (2009).10.1063/1.3184594 ↗
59. Cheng, Q. & Cui, T. J. An electromagnetic black hole made of metamaterials. Preprint at http://arxiv.org/abs/0910.2159 (2009).
60. Rahm, M. et al. Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwells equations. Photon. Nanostr. 6, 87–95 (2008).10.1016/j.photonics.2007.07.013 ↗
61. Kildishev, A. V. & Narimanov, E. E. Impedance-matched hyperlens. Opt. Lett. 32, 3432–3434 (2007).10.1364/OL.32.003432 ↗
62. Chen, H. Y. & Chan, C. T. Transformation media that rotate electromagnetic fields. Appl. Phys. Lett. 90, 241105 (2007).10.1063/1.2748302 ↗
63. Chen, H. Y. et al. Design and experimental realization of a broadband transformation media field rotator at microwave frequencies. Phys. Rev. Lett. 102, 183903 (2009).10.1103/PhysRevLett.102.183903 ↗
64. Rahm, M. et al. Optical design of reflectionless complex media by finite embedded coordinate transformations. Phys. Rev. Lett. 100, 063903 (2008).10.1103/PhysRevLett.100.063903 ↗
65. Huangfu, J. T. et al. Application of coordinate transformation in bent waveguides. J. Appl. Phys. 104, 014502 (2008).10.1063/1.2949272 ↗
66. Roberts, D. A. et al. Transformation-optical design of sharp waveguide bends and corners. Appl. Phys. Lett. 93, 251111 (2008).10.1063/1.3055604 ↗
67. Rahm, M. et al. Transformation-optical design of adaptive beam bends and beam expanders. Opt. Express 16, 11555–11567 (2008).10.1364/OE.16.011555 ↗
68. Jiang, W. X. et al. Arbitrary bending of electromagnetic waves using realizable inhomogeneous and anisotropic materials. Phys. Rev. E 78, 066607 (2008).10.1103/PhysRevE.78.066607 ↗
69. Mei, Z. L. & Cui, T. J. Arbitrary bending of electromagnetic waves using isotropic materials. J. Appl. Phys. 105, 104913 (2009).10.1063/1.3132842 ↗
70. Mei, Z. L. & Cui, T. J. Experimental realization of a broadband bend structure using gradient index metamaterials. Opt. Express 17, 18354–18363 (2009).10.1364/OE.17.018354 ↗
71. Tsang, M. & Psaltis, D. Magnifying perfect lens and superlens design by coordinate transformation. Phys. Rev. B 77, 035122 (2008).10.1103/PhysRevB.77.035122 ↗
72. Yan, M., Yan, W. & Qiu, M. Cylindrical superlens by a coordinate transformation. Phys. Rev. B 78, 125113 (2008).10.1103/PhysRevB.78.125113 ↗
73. Jiang, W. X. et al. Layered high-gain lens antennas via discrete optical transformation. Appl. Phys. Lett. 93, 221906 (2008).10.1063/1.3040307 ↗
74. Kwon, D-H. & Werner, D. H. Flat focusing lens designs having minimized reflection based on coordinate transformation techniques. Opt. Express 17, 7807–7817 (2009).10.1364/OE.17.007807 ↗
75. Roberts, D. A., Kundtz, N. & Smith, D. R. Optical lens compression via transformation optics. Opt. Express 17, 16535–16542 (2009).10.1364/OE.17.016535 ↗
76. Li, J. et al. Designing the Fourier space with transformation optics. Opt. Lett. 34, 3128–3130 (2009).10.1364/OL.34.003128 ↗
77. Tyc, T. & Leonhardt, U. Transmutation of singularities in optical instruments. New J. Phys. 10, 115038 (2008).10.1088/1367-2630/10/11/115038 ↗
78. Ma, Y. G. et al. An omnidirectional retroreflector based on the transmutation of dielectric singularities. Nature Mater. 8, 639–642 (2009).10.1038/nmat2489 ↗
79. Kwon, D-H. & Werner, D. H. Polarization splitter and polarization rotator designs based on transformation optics. Opt. Express 16, 18731–18738 (2008).10.1364/OE.16.018731 ↗
80. Jiang, W. X. et al. Cylindrical-to-plane-wave conversion via embedded optical transformation. Appl. Phys. Lett. 92, 261903 (2008).10.1063/1.2953447 ↗
81. Ma, H. et al. Wave-shape-keeping media. Opt. Lett. 34, 127–129 (2009).10.1364/OL.34.000127 ↗
82. Zhai, T. R. et al. Polarization controller based on embedded optical transformation. Opt. Express 17, 17206–17213 (2009).10.1364/OE.17.017206 ↗
83. Pendry, J. B. Negative refraction makes a perfect lens. Phys. Rev. Lett. 85, 3966–3969 (2000).10.1103/PhysRevLett.85.3966 ↗
84. Milton, G. W. et al. Solutions in folded geometries, and associated cloaking due to anomalous resonance. New J. Phys. 10, 115021 (2008).10.1088/1367-2630/10/11/115021 ↗
85. Yang, T. et al. Superscatterer: Enhancement of scattering with complementary media. Opt. Express 16, 18545–18550 (2008).10.1364/OE.16.018545 ↗
86. Luo, Y. et al. Wave and ray analysis of a type of cloak exhibiting magnified and shifted scattering effect. Pr. Electromag. Res. S. 95, 167–178 (2009).10.2528/PIER09070805 ↗
87. Ng, J., Chen, H. Y. & Chan, C. T. Metamaterial frequency-selective superabsorber. Opt. Lett. 34, 644–646 (2009).10.1364/OL.34.000644 ↗
88. Zhang, J. J. et al. Guiding waves through an invisible tunnel. Opt. Express 17, 6203–6208 (2009).10.1364/OE.17.006203 ↗
89. Lu, W. L. et al. Transformation media based super focusing antenna. J. Phys. D 42, 212002 (2009).10.1088/0022-3727/42/21/212002 ↗
90. Luo, Y. et al. High-directivity antenna with small antenna aperture. Appl. Phys. Lett. 95, 193506 (2009).10.1063/1.3264085 ↗
91. Lai, Y. et al. Illusion optics: The optical transformation of an object into another object. Phys. Rev. Lett. 102, 253902 (2009).10.1103/PhysRevLett.102.253902 ↗
92. Pendry, J. B. Optics: All smoke and metamaterials. Nature 460, 579–580 (2009).10.1038/460579a ↗
93. Cummer, S. A. & Schurig, D. One path to acoustic cloaking. New J. Phys. 9, 45 (2007).10.1088/1367-2630/9/3/045 ↗
94. Chen, H. Y. & Chan, C. T. Acoustic cloaking in three dimensions using acoustic metamaterials. Appl. Phys. Lett. 91, 183518 (2007).10.1063/1.2803315 ↗
95. Cummer, S. A. et al. Scattering theory derivation of a 3D acoustic cloaking shell. Phys. Rev. Lett. 100, 024301 (2008).10.1103/PhysRevLett.100.024301 ↗
96. Brun, M., Guenneau, S. & Movchan, A. B. Achieving control of in-plane elastic waves. Appl. Phys. Lett. 94, 061903 (2009).10.1063/1.3068491 ↗
97. Farhat, M. et al. Cloaking bending waves propagating in thin elastic plates. Phys. Rev. B 79, 033102 (2009).10.1103/PhysRevB.79.033102 ↗
98. Farhat, M., Guenneau, S. & Enoch, S. Ultrabroadband elastic cloaking in thin plates. Phys. Rev. Lett. 103, 024301 (2009).10.1103/PhysRevLett.103.024301 ↗
99. Zhang, S. et al. Cloaking of matter waves. Phys. Rev. Lett. 100, 123002 (2008).10.1103/PhysRevLett.100.123002 ↗
100. Lin, D-H. & Luan, P-G. Cloaking of matter waves under the global Aharonov–Bohm effect. Phys. Rev. A 79, 051605 (2009).10.1103/PhysRevA.79.051605 ↗