Advertisement

Theoretical Basis

  • Xiangang LuoEmail author
Chapter

Abstract

This chapter first describes the theories and laws in classic optics, and highlights their drawbacks and challenges in engineering applications. Then the macroscopic and microscopic theories of meta-surface-waves are presented as a cornerstone of EO 2.0. Subsequently, the generalized theories and laws of diffraction, reflection and refraction, absorption, and radiation are discussed in detail.

Keywords

Snell’s law Fresnel’s equations Diffraction limit Generalized laws of reflection and refraction 

References

  1. 1.
    Fermat’s Principle and the Laws of Reflection and Refraction, http://scipp.ucsc.edu/~haber/ph5B/fermat09.pdf
  2. 2.
    M. Born, E. Wolf, Principle of Optics, 7th edn. (Pergamon, Oxford, UK, 2007)Google Scholar
  3. 3.
    W. Singer, M. Totzek, H. Gross, Physical Image Formation (Wiley, 2005)Google Scholar
  4. 4.
  5. 5.
    M. Vollmer, K.-P. Mollmann, Infrared Thermal Imaging: Fundamentals, Research and Applications (Wiley-VCH Verlag GmbH & Co. KGaA, Germany, 2010)CrossRefGoogle Scholar
  6. 6.
    X. Luo, Principles of electromagnetic waves in metasurfaces. Sci. China Phys. Mech. Astron. 58, 594201 (2015)CrossRefGoogle Scholar
  7. 7.
    S.A. Maier, Plasmonis: Fundamentals and Applications (Springer, 2007)Google Scholar
  8. 8.
    X. Luo, D. Tsai, M. Gu, M. Hong, Subwavelength interference of light on structured surfaces. Adv. Opt. Photon. 10, 757–842 (2018)CrossRefGoogle Scholar
  9. 9.
    M. Pu, Y. Guo, X. Li, X. Ma, X. Luo, Revisitation of extraordinary Young’s interference: from catenary optical fields to spin-orbit interaction in metasurfaces. ACS Photonics 5, 3198–3204 (2018)CrossRefGoogle Scholar
  10. 10.
    J.B. Pendry, A.J. Holden, W.J. Stewart, I. Youngs, Extremely low frequency plasmons in metallic mesostructures. Phys. Rev. Lett. 76, 4773–4776 (1996)CrossRefGoogle Scholar
  11. 11.
    W. Rotman, Plasma simulation by artificial dielectrics and parallel-plate media. IRE Trans. Antennas Propag. 10, 82–95 (1962)CrossRefGoogle Scholar
  12. 12.
    J.B. Pendry, L. Martín-Moreno, F.J. Garcia-Vidal, Mimicking surface plasmons with structured surfaces. Science 305, 847–848 (2004)CrossRefGoogle Scholar
  13. 13.
    F.J. Garcia-Vidal, L. Martín-Moreno, J.B. Pendry, Surfaces with holes in them: new plasmonic metamaterials. J. Opt. A Pure Appl. Opt. 7, S97 (2005)CrossRefGoogle Scholar
  14. 14.
    S.A. Maier, S.R. Andrews, L. Martín-Moreno, F.J. García-Vidal, Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires. Phys. Rev. Lett. 97, 176805 (2006)CrossRefGoogle Scholar
  15. 15.
    X. Luo, Subwavelength optical engineering with metasurface waves. Adv. Opt. Mater. 6, 1701201 (2018)CrossRefGoogle Scholar
  16. 16.
    M. Pu, X. Ma, Y. Guo, X. Li, X. Luo, Theory of microscopic meta-surface waves based on catenary optical fields and dispersion. Opt. Express 26, 19555–19562 (2018)CrossRefGoogle Scholar
  17. 17.
    X. Luo, I. Teruya, Sub 100 nm lithography based on plasmon polariton resonance, in Digest of Papers (IEEE, 2003), pp. 138–139Google Scholar
  18. 18.
    L.B. Whitbourn, R.C. Compton, Equivalent-circuit formulas for metal grid reflectors at a dielectric boundary. Appl. Opt. 24, 217–220 (1985)CrossRefGoogle Scholar
  19. 19.
    Y. Huang, J. Luo, M. Pu, Y. Guo, Z. Zhao, X. Ma, X. Li, X. Luo, Catenary electromagnetics for ultrabroadband lightweight absorbers and large-scale flat antennas. Adv. Sci. 1801691 (2019)Google Scholar
  20. 20.
    J. Ducuing, N. Bloembergen, Observation of reflected light harmonics at the boundary of piezoelectric crystals. Phys. Rev. Lett. 10, 474–476 (1963)CrossRefGoogle Scholar
  21. 21.
    X. Luo, Subwavelength artificial structures: opening a new era for engineering optics. Adv. Mater. 31, 1804680 (2019)Google Scholar
  22. 22.
    X. Luo, Engineering optics 2.0: a revolution in optical materials, devices, and systems. ACS Photonics 5, 4724–4728 (2018)CrossRefGoogle Scholar
  23. 23.
    H.P. Stahl, Survey of cost models for space telescopes. Opt. Eng. 49, 053005 (2010)Google Scholar
  24. 24.
    R.A. Hyde, Eyeglass. 1. Very large aperture diffractive telescopes. Appl. Opt. 38, 4198–4212 (1999)CrossRefGoogle Scholar
  25. 25.
    P.D. Atcheson, C. Stewart, J. Domber, K. Whiteaker, J. Cole, P. Spuhler, A. Seltzer, J.A. Britten, S.N. Dixit, B. Farmer, L. Smith, MOIRE: initial demonstration of a transmissive diffractive membrane optic for large lightweight optical telescopes, in SPIE Astronomical Telescopes + Instrumentation (SPIE, 2012), p. 14Google Scholar
  26. 26.
    T. Xu, C. Wang, C. Du, X. Luo, Plasmonic beam deflector. Opt. Express 16, 4753–4759 (2008)CrossRefGoogle Scholar
  27. 27.
    X.G. Luo, T. Ishihara, Subwavelength photolithography based on surface-plasmon polariton resonance. Opt. Express 12, 3055–3065 (2004)CrossRefGoogle Scholar
  28. 28.
    L. Verslegers, P.B. Catrysse, Z. Yu, J.S. White, E.S. Barnard, M.L. Brongersma, S. Fan, Planar lenses based on nanoscale slit arrays in a metallic film. Nano Lett. 9, 235–238 (2008)CrossRefGoogle Scholar
  29. 29.
    M. Pu, X. Li, X. Ma, Y. Wang, Z. Zhao, C. Wang, C. Hu, P. Gao, C. Huang, H. Ren, X. Li, F. Qin, J. Yang, M. Gu, M. Hong, X. Luo, Catenary optics for achromatic generation of perfect optical angular momentum. Sci. Adv. 1, e1500396 (2015)CrossRefGoogle Scholar
  30. 30.
    X. Li, M. Pu, Y. Wang, X. Ma, Y. Li, H. Gao, Z. Zhao, P. Gao, C. Wang, X. Luo, Dynamic control of the extraordinary optical scattering in semicontinuous 2d metamaterials. Adv. Opt. Mater. 4, 659–663 (2016)CrossRefGoogle Scholar
  31. 31.
    X. Li, M. Pu, Z. Zhao, X. Ma, J. Jin, Y. Wang, P. Gao, X. Luo, Catenary nanostructures as compact Bessel beam generators. Sci. Rep. 6, 20524 (2016)CrossRefGoogle Scholar
  32. 32.
    N. Yu, P. Genevet, M.A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, Z. Gaburro, Light propagation with phase discontinuities: generalized laws of reflection and refraction. Science 334, 333–337 (2011)CrossRefGoogle Scholar
  33. 33.
    N. Yu, F. Capasso, Flat optics with designer metasurfaces. Nat. Mater. 13, 139–150 (2014)CrossRefGoogle Scholar
  34. 34.
    F. Aieta, P. Genevet, N. Yu, M.A. Kats, Z. Gaburro, F. Capasso, Out-of-plane reflection and refraction of light by anisotropic optical antenna metasurfaces with phase discontinuities. Nano Lett. 12, 1702–1706 (2012)CrossRefGoogle Scholar
  35. 35.
    M. Pu, C. Hu, C. Huang, C. Wang, Z. Zhao, Y. Wang, X. Luo, Investigation of Fano resonance in planar metamaterial with perturbed periodicity. Opt. Express 21, 992 (2013)CrossRefGoogle Scholar
  36. 36.
    H. Shi, X. Luo, C. Du, Young’s interference of double metallic nanoslit with different widths. Opt. Express 15, 11321–11327 (2007)CrossRefGoogle Scholar
  37. 37.
    M. Khorasaninejad, F. Capasso, Broadband multifunctional efficient meta-gratings based on dielectric waveguide phase shifters. Nano Lett. 15, 6709–6715 (2015)CrossRefGoogle Scholar
  38. 38.
    S. Larouche, Y.-J. Tsai, T. Tyler, N.M. Jokerst, D.R. Smith, Infrared metamaterial phase holograms. Nat. Mater. 11, 450–454 (2012)CrossRefGoogle Scholar
  39. 39.
    X. Li, X. Ma, X. Luo, Principles and applications of metasurfaces with phase modulation. Opto-Electron. Eng. 44, 255–275 (2017)Google Scholar
  40. 40.
    M.V. Berry, Quantal phase factors accompanying adiabatic changes. Proc. R. Soc. Lond. A 392, 45–57 (1984)CrossRefGoogle Scholar
  41. 41.
    A.G. Fox, An adjustable wave-guide phase changer. Proc. IRE 35, 1489–1498 (1947)CrossRefGoogle Scholar
  42. 42.
    W. Sichak, D.J. Levine, Microwave high-speed continuous phase shifter. Proc. IRE 43, 1661–1663 (1955)CrossRefGoogle Scholar
  43. 43.
    S. Pancharatnam, Generalized theory of interference, and its applications. Proc. Indian Acad. Sci. 44, 247–262 (1956)CrossRefGoogle Scholar
  44. 44.
    X. Zhang, Z. Tian, W. Yue, J. Gu, S. Zhang, J. Han, W. Zhang, Broadband terahertz wave deflection based on c-shape complex metamaterials with phase discontinuities. Adv. Mater. 25, 4567–4572 (2013)CrossRefGoogle Scholar
  45. 45.
  46. 46.
    D.W. Pohl, W. Denk, M. Lanz, Optical stethoscopy: image recording with resolution λ/20. Appl. Phys. Lett. 44, 651–653 (1984)CrossRefGoogle Scholar
  47. 47.
    E.A. Ash, G. Nicholls, Super-resolution aperture scanning microscope. Nature 237, 510 (1972)CrossRefGoogle Scholar
  48. 48.
    J.B. Pendry, Negative refraction makes a perfect lens. Phys. Rev. Lett. 85, 3966–3969 (2000)CrossRefGoogle Scholar
  49. 49.
    W. Wang, L. Lin, J. Ma, C. Wang, J. Cui, C. Du, X. Luo, Electromagnetic concentrators with reduced material parameters based on coordinate transformation. Opt. Express 16, 11431–11437 (2008)CrossRefGoogle Scholar
  50. 50.
    C. Wang, P. Gao, Z. Zhao, N. Yao, Y. Wang, L. Liu, K. Liu, X. Luo, Deep sub-wavelength imaging lithography by a reflective plasmonic slab. Opt. Express 21, 20683–20691 (2013)CrossRefGoogle Scholar
  51. 51.
    X. Luo, T. Ishihara, Surface plasmon resonant interference nanolithography technique. Appl. Phys. Lett. 84, 4780–4782 (2004)CrossRefGoogle Scholar
  52. 52.
    N. Fang, H. Lee, C. Sun, X. Zhang, Sub-diffraction-limited optical imaging with a silver superlens. Science 308, 534–537 (2005)CrossRefGoogle Scholar
  53. 53.
    P. Gao, N. Yao, C. Wang, Z. Zhao, Y. Luo, Y. Wang, G. Gao, K. Liu, C. Zhao, X. Luo, Enhancing aspect profile of half-pitch 32 nm and 22 nm lithography with plasmonic cavity lens. Appl. Phys. Lett. 106, 093110 (2015)CrossRefGoogle Scholar
  54. 54.
    X. Luo, Plasmonic metalens for nanofabrication. Natl. Sci. Rev. 5, 137–138 (2018)CrossRefGoogle Scholar
  55. 55.
    Z. Zhao, Y. Luo, W. Zhang, C. Wang, P. Gao, Y. Wang, M. Pu, N. Yao, C. Zhao, X. Luo, Going far beyond the near-field diffraction limit via plasmonic cavity lens with high spatial frequency spectrum off-axis illumination. Sci. Rep. 5, 15320 (2015)CrossRefGoogle Scholar
  56. 56.
    G.T. Di Francia, Super-gain antennas and optical resolving power. Il Nuovo Cimento 9, 426–438 (1952)CrossRefGoogle Scholar
  57. 57.
    E.T.F. Rogers, N.I. Zheludev, Optical super-oscillations: sub-wavelength light focusing and super-resolution imaging. J. Opt. 15, 094008 (2013)CrossRefGoogle Scholar
  58. 58.
    G. Lerosey, J. de Rosny, A. Tourin, M. Fink, Focusing beyond the diffraction limit with far-field time reversal. Science 315, 1120–1122 (2007)CrossRefGoogle Scholar
  59. 59.
    C. Wang, D. Tang, Y. Wang, Z. Zhao, J. Wang, M. Pu, Y. Zhang, W. Yan, P. Gao, X. Luo, Super-resolution optical telescopes with local light diffraction shrinkage. Sci. Rep. 5, 18485 (2015)CrossRefGoogle Scholar
  60. 60.
    M.V. Berry, S. Popescu, Evolution of quantum superoscillations and optical superresolution without evanescent waves. J. Phys. A Math. Gen. 39, 6965 (2006)CrossRefGoogle Scholar
  61. 61.
    F.M. Huang, N.I. Zheludev, Super-resolution without evanescent waves. Nano Lett. 9, 1249–1254 (2009)CrossRefGoogle Scholar
  62. 62.
    R.W. Wood, On a remarkable case of uneven distribution of light in a diffraction grating spectrum. Proc. Phys. Soc. London 18, 269 (1902)CrossRefGoogle Scholar
  63. 63.
    A. Ciattoni, B. Crosignani, P. Di Porto, Vectorial free-space optical propagation: a simple approach for generating all-order nonparaxial corrections. Opt. Commun. 177, 9–13 (2000)CrossRefGoogle Scholar
  64. 64.
    M. Pu, X. Ma, X. Li, Y. Guo, X. Luo, Merging plasmonics and metamaterials by two-dimensional subwavelength structures. J. Mater. Chem. C 5, 4361–4278 (2017)CrossRefGoogle Scholar
  65. 65.
    W. Woltersdorff, Über die optischen Konstanten dünner Metallschichten im langwelligen Ultrarot. Zeitschrift für Physik A Hadrons and Nuclei 91, 230–252 (1934)Google Scholar
  66. 66.
    E.F. Knott, J.F. Shaeffer, M.T. Tuley, Radar Cross Section, 2nd edn. (SciTech Publishing, USA, 2004)Google Scholar
  67. 67.
    W.W. Salisbury, Absorbent Body for Electromagnetic Waves (1952)Google Scholar
  68. 68.
    N.I. Landy, S. Sajuyigbe, J.J. Mock, D.R. Smith, W.J. Padilla, Perfect metamaterial absorber. Phys. Rev. Lett. 100, 207402 (2008)CrossRefGoogle Scholar
  69. 69.
    C. Hu, Z. Zhao, X. Chen, X. Luo, Realizing near-perfect absorption at visible frequencies. Opt. Express 17, 11039–11044 (2009)CrossRefGoogle Scholar
  70. 70.
    M. Pu, M. Wang, C. Hu, C. Huang, Z. Zhao, Y. Wang, X. Luo, Engineering heavily doped silicon for broadband absorber in the terahertz regime. Opt. Express 20, 25513–25519 (2012)CrossRefGoogle Scholar
  71. 71.
    M. Pu, C. Hu, M. Wang, C. Huang, Z. Zhao, C. Wang, Q. Feng, X. Luo, Design principles for infrared wide-angle perfect absorber based on plasmonic structure. Opt. Express 19, 17413–17420 (2011)CrossRefGoogle Scholar
  72. 72.
    M. Pu, Q. Feng, M. Wang, C. Hu, C. Huang, X. Ma, Z. Zhao, C. Wang, X. Luo, Ultrathin broadband nearly perfect absorber with symmetrical coherent illumination. Opt. Express 20, 2246–2254 (2012)CrossRefGoogle Scholar
  73. 73.
    W. Wan, Y. Chong, L. Ge, H. Noh, A.D. Stone, H. Cao, Time-reversed lasing and interferometric control of absorption. Science 331, 889–892 (2011)CrossRefGoogle Scholar
  74. 74.
    M. Pu, Q. Feng, C. Hu, X. Luo, Perfect absorption of light by coherently induced plasmon hybridization in ultrathin metamaterial film. Plasmonics 7, 733–738 (2012)CrossRefGoogle Scholar
  75. 75.
    S. Li, J. Luo, S. Anwar, S. Li, W. Lu, Z.H. Hang, Y. Lai, B. Hou, M. Shen, C. Wang, Broadband perfect absorption of ultrathin conductive films with coherent illumination: superabsorption of microwave radiation. Phys. Rev. B 91, 220301 (2015)CrossRefGoogle Scholar
  76. 76.
    S. Li, Q. Duan, S. Li, Q. Yin, W. Lu, L. Li, B. Gu, B. Hou, W. Wen, Perfect electromagnetic absorption at one-atom-thick scale. Appl. Phys. Lett. 107, 181112 (2015)CrossRefGoogle Scholar
  77. 77.
    C. Yan, M. Pu, J. Luo, Y. Huang, X. Li, X. Ma, X. Luo, Coherent perfect absorption of electromagnetic wave in subwavelength structures. Opt. Laser Technol. 101, 499–506 (2018)CrossRefGoogle Scholar
  78. 78.
    M. Hong, Metasurface wave in planar nano-photonics. Sci. Bull. 61, 112–113 (2016)CrossRefGoogle Scholar
  79. 79.
    K.N. Rozanov, Ultimate thickness to bandwidth ratio of radar absorbers. IEEE Trans. Antennas Propag. 48, 1230–1234 (2000)CrossRefGoogle Scholar
  80. 80.
    D. Wang, Q. Huang, C. Qiu, M. Hong, Selective excitation of resonances in gammadion metamaterials for terahertz wave manipulation. Sci. China Phys. Mech. Astron. 58, 08420 (2015)Google Scholar
  81. 81.
    X. Luo, M. Pu, X. Ma, X. Li, Taming the electromagnetic boundaries via metasurfaces: from theory and fabrication to functional devices. Int. J. Antenn. Propag. 2015, 204127 (2015)Google Scholar
  82. 82.
    Y. Guo, C.L. Cortes, S. Molesky, Z. Jacob, Broadband super-Planckian thermal emission from hyperbolic metamaterials. Appl. Phys. Lett. 101, 131106 (2012)CrossRefGoogle Scholar
  83. 83.
    I.M. Stanislav, R.S. Constantin, A.T. Sergei, Overcoming black body radiation limit in free space: metamaterial superemitter. New J. Phys. 18, 013034 (2016)CrossRefGoogle Scholar
  84. 84.
    L. Hu, A. Narayanaswamy, X. Chen, G. Chen, Near-field thermal radiation between two closely spaced glass plates exceeding Planck’s blackbody radiation law. Appl. Phys. Lett. 92, 133106 (2008)CrossRefGoogle Scholar
  85. 85.
    J.B. Pendry, Radiative exchange of heat between nanostructures. J. Phys. Condens. Matter 11, 6621 (1999)Google Scholar
  86. 86.
    H. Yijia, P. Mingbo, G. Ping, Z. Zeyu, L. Xiong, M. Xiaoliang, L. Xiangang, Ultra-broadband large-scale infrared perfect absorber with optical transparency. Appl. Phys. Express 10, 112601 (2017)CrossRefGoogle Scholar
  87. 87.
    A.P. Raman, M.A. Anoma, L. Zhu, E. Rephaeli, S. Fan, Passive radiative cooling below ambient air temperature under direct sunlight. Nature 515, 540 (2014)CrossRefGoogle Scholar
  88. 88.
    L. Zhu, A.P. Raman, S. Fan, Radiative cooling of solar absorbers using a visibly transparent photonic crystal thermal blackbody. PNAS 112, 12282–12287 (2015)CrossRefGoogle Scholar
  89. 89.
    Y. Zhai, Y. Ma, S.N. David, D. Zhao, R. Lou, G. Tan, R. Yang, X. Yin, Scalable-manufactured randomized glass-polymer hybrid metamaterial for daytime radiative cooling. Sci. 339, 1045–1047 (2017)Google Scholar
  90. 90.
    E.M. Purcell, Spontaneous emission probabilities at radio frequencies. Phys. Rev. Appl. 69, 681 (1946)Google Scholar
  91. 91.
    M. Pelton, Modified spontaneous emission in nanophotonic structures. Nat. Photon. 9, 427 (2015)CrossRefGoogle Scholar
  92. 92.
    N.I. Zheludev, What diffraction limit? Nat. Mater. 7, 420–422 (2008)CrossRefGoogle Scholar
  93. 93.
    J.-J. Greffet, R. Carminati, K. Joulain, J.-P. Mulet, S. Mainguy, Y. Chen, Coherent emission of light by thermal sources. Nature 416, 61 (2002)CrossRefGoogle Scholar
  94. 94.
    H.J. Lezec, A. Degiron, E. Devaux, R.A. Linke, L. Martin-Moreno, F.J. Garcia-Vidal, T.W. Ebbesen, Beaming light from a subwavelength aperture. Science 297, 820–822 (2002)CrossRefGoogle Scholar
  95. 95.
    H. Aouani, O. Mahboub, N. Bonod, E. Devaux, E. Popov, H. Rigneault, T.W. Ebbesen, J. Wenger, Bright unidirectional fluorescence emission of molecules in a nanoaperture with plasmonic corrugations. Nano Lett. 11, 637–644 (2011)CrossRefGoogle Scholar
  96. 96.
    H. Caglayan, I. Bulu, E. Ozbay, Beaming of electromagnetic waves emitted through a subwavelength annular aperture. J. Opt. Soc. Am. B 23, 419–422 (2006)CrossRefGoogle Scholar
  97. 97.
    R.F. Oulton, V.J. Sorger, T. Zentgraf, R.M. Ma, C. Gladden, L. Dai, G. Bartal, X. Zhang, Plasmon lasers at deep subwavelength scale. Nature 461, 629–632 (2009)CrossRefGoogle Scholar
  98. 98.
    N.I. Zheludev, S.L. Prosvirnin, N. Papasimakis, V.A. Fedotov, Lasing spaser. Nat. Photon. 2, 351–354 (2008)CrossRefGoogle Scholar
  99. 99.
    E. Plum, V.A. Fedotov, P. Kuo, D.P. Tsai, N.I. Zheludev, Towards the lasing spaser: controlling metamaterial optical response with semiconductor quantum dots. Opt. Express 17, 8548–8551 (2009)CrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.State Key Laboratory of Optical Technologies on Nano-Fabrication and Micro-Engineering, Institute of Optics and ElectronicsChinese Academy of SciencesChengduChina

Personalised recommendations